The basis for the eigenspace corresponding to lambda=5,1,4 are None,[tex]\left[\begin{array}{c}-1 \\\frac{1}{2} \\0\end{array}\right][/tex] and [tex]$\left[\begin{array}{l}2 \\ 1 \\ 1\end{array}\right]$[/tex]
[tex]$$A=\left[\begin{array}{ccc}5 & -12 & 10 \\0 & 7 & -3 \\0 & 6 & -2\end{array}\right]$$[/tex]
Eigenspace corresponding to lambda=5,1,4
The eigenspace E_lambda corresponding to the eigenvalue lambda is the null space of the matrix a [tex]\mathrm{A}-(\lambda) \mathrm{I}"[/tex]
for lambda=5
[tex]$$\mathrm{E}_5=\mathrm{N}(\mathrm{A}-5 \mathrm{I})$$[/tex]
Reducing the matrix A-5I by elementary row operations
[tex]$$\begin{aligned}A-5 I & =\left[\begin{array}{ccc}5-5 & -12 & 10 \\0 & 7-5 & -3 \\0 & 6 & -2-5\end{array}\right] \\& =\left[\begin{array}{ccc}0 & -12 & 10 \\0 & 2 & -3 \\0 & 6 & -7\end{array}\right] \\& \sim\left[\begin{array}{ccc}0 & -12 & 10 \\0 & 1 & -\frac{3}{2} \\0 & 6 & -7\end{array}\right] R_2 \rightarrow \frac{R_2}{2} \\& \sim\left[\begin{array}{ccc}1 & 0 & -8 \\0 & 1 & -\frac{3}{2} \\0 & 6 & -7\end{array}\right] R_1 \rightarrow R_1+2 R_2\end{aligned}$$[/tex]
[tex]\sim\left[\begin{array}{ccc}1 & 0 & -8 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 2\end{array}\right] R_3 \rightarrow R_3-6 R_2$$\\\sim\left[\begin{array}{ccc}1 & 0 & -8 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 1\end{array}\right] R_3 \rightarrow \frac{\mathrm{R}_3}{2}$$\\\sim\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 1\end{array}\right] \mathrm{R}_1 \rightarrow \mathrm{R}_1+8 \mathrm{R}_3$[/tex]
[tex]$\sim\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] R_2 \rightarrow R_2+\frac{2 R_3}{2}$[/tex]
The solutions x of A-5I=0 satisfy x_1=x_2=x_3=0 that is, the null space solves the matrix
[tex]$$\left[\begin{array}{lll}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]$$[/tex]
Hence The null space is [tex]\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] E_5[/tex] has no basis
[tex]$$\begin{aligned}& \text { case: } 2 \\& \text { for } \lambda=1 \\& \mathrm{E}_5=\mathrm{N}(\mathrm{A}-(1) \mathrm{I})\end{aligned}$$[/tex]
we reduce the matrix A-I by elementary row operations as follows.
[tex]$$\begin{aligned}A-1 & =\left[\begin{array}{ccc}5-1 & -12 & 10 \\0 & 7-1 & -3 \\0 & 6 & -2-1\end{array}\right] \\& =\left[\begin{array}{ccc}1 & -3 & \frac{5}{2} \\0 & 6 & -3 \\0 & 6 & -3\end{array}\right] R_1 \rightarrow \frac{R_1}{4} \\& \sim\left[\begin{array}{ccc}1 & -3 & \frac{5}{2} \\0 & 1 & -\frac{1}{2} \\0 & 6 & -3\end{array}\right] R_2 \rightarrow \frac{R_2}{6}\end{aligned}[/tex]
[tex]$$$\sim\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 6 & -3\end{array}\right] R_1 \rightarrow R_1+3 R_2$\\$\sim\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 0 & 0\end{array}\right] R_3 \rightarrow R_3-6 R_2$[/tex]
Thus, the solutions x of (A-I) X=0 satisfy
[tex]$\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 0 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$[/tex]
x_3=t
[tex]$\Rightarrow \mathrm{x}_1=-\mathrm{t}, \mathrm{x}_2=\frac{\mathrm{t}}{2}$[/tex]
[tex]$\vec{x}=\left[\begin{array}{c}-t \\ \frac{t}{2} \\ t\end{array}\right]=\left[\begin{array}{c}-1 \\ \frac{1}{2} \\ 1\end{array}\right] t$[/tex]
The Basis for the nullspace A-I will be: [tex]$\left.\left(\begin{array}{c}-1 \\ \frac{1}{2} \\ 1\end{array}\right]\right)$[/tex]
case:3
lambda=4
[tex]$$\mathrm{E}_5=\mathrm{N}(\mathrm{A}-(4) \mathrm{I})$$[/tex]
we reduce the matrix A-4I by elementary row operations as follows.
[tex]$\begin{aligned} A-4 \mid & =\left[\begin{array}{ccc}5-4 & -12 & 10 \\ 0 & 7-4 & -3 \\ 0 & 6 & -2-4\end{array}\right] \\ & =\left[\begin{array}{ccc}1 & -12 & 10 \\ 0 & 3 & -3 \\ 0 & 6 & -6\end{array}\right] \\ & \sim\left[\begin{array}{ccc}1 & -12 & 10 \\ 0 & 1 & -1 \\ 0 & 6 & -6\end{array}\right] R_2 \rightarrow \frac{R_2}{3}\end{aligned}$[/tex]
[tex]$\begin{aligned} & \sim\left[\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & -1 \\ 0 & 6 & -6\end{array}\right] \mathrm{R}_1 \rightarrow \mathrm{R}_1+12 \mathrm{R}_2 \\ & \sim\left[\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & -1 \\ 0 & 0 & 0\end{array}\right] \mathrm{R}_3 \rightarrow \mathrm{R}_3-6 \mathrm{R}_2\end{aligned}$[/tex]
Thus, the solutions x of (A-4IX)=0 satisfy
[tex]$$\left[\begin{array}{ccc}1 & 0 & -2 \\0 & 1 & -1 \\0 & 0 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]$$[/tex]
x_3=t
[tex]$\Rightarrow \mathrm{x}_1=2 \mathrm{t}, \mathrm{x}_2=\mathrm{t}$[/tex]
[tex]$$\vec{x}=\left[\begin{array}{c}2 t \\t \\t\end{array}\right]=\left[\begin{array}{l}2 \\1 \\1\end{array}\right] t$$[/tex]
The Basis for the nullspace A-4 I will be [tex]\left(\left[\begin{array}{l}2 \\ 1 \\ 1\end{array}\right]\right)[/tex]
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Write the ratio of the first measurement to the second measurement. Compare in inches.
Answer:
when the ratio of the first measurment is already there, get the pot, put it in place and chec the correct ratio, the slope should help the gaurdian. so in that case, the answer is 75inch
b) Sita had.50 sweets. She ate 10 sweets and gave 8 sweets to her brother. If she divided the rest of them among her 8 friends equally, how many sweets would each friend get?
Answer:
4 sweets each
Step-by-step explanation:
50 sweets to begin with and eats 10 , so 50 - 10 = 40 left
she then gives 8 to her brother , leaving 40 - 8 = 32 sweets
she then shares 32 equally among her 8 friends , so
32 ÷ 8 = 4
that is each friend got 4 sweets
a salesman goes to Murano and buys three dozen vases paying €16.25 each. During transport if they break me 9. How much did each remaining vase sell for if he earned €360
The vase sells for € 34.41, and he made €360 during a break on the ninth transfer.
what is unitary method ?
The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)
given
A salesperson purchases three dozen vases (12 * 3 = 36),
at a cost of 36 * €16.25 (or $585),
with seventeen remaining.
The cost of selling each remaining vase is € 585 / 17
= € 34.41.
The vase sells for € 34.41, and he made €360 during a break on the ninth transfer.
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PLEASE HELP!
The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails. The manager found that 0.3 pounds of nails in the sample were defective. They were either bent, the heads were damaged, or they had been clipped too short during manufacture. How many pounds of defective nails should the manager expect the 350-pound delivery to contain? Round your answer to the nearest tenth of a pound.
There are 23.33 pounds of defective nails should the manager expect the 350-pound delivery to contain.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails.
And, The manager found that 0.3 pounds of nails in the sample were defective.
Since, The manager found that 0.3 pounds of nails in the sample were defective.
Hence, Amount of pounds of defective nails should the manager expect the 350-pound delivery to contain is,
⇒ 350 × 0.3 / 4.5
⇒ 23.33 pounds
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Is halting problem is solvable or unsolvable?
Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.
Define algorithm.An algorithm is a process for carrying out a computation or resolving a challenge. Algorithms work as a detailed set of guidelines that lead hardware- or software-based routines through a series of predetermined actions step by step. Algorithms are frequently used in all areas of IT.
Here,
The halting problem, which claims that no program can be created that can anticipate whether or not any other program will halt after a finite number of steps, is an intractable algorithmic challenge.
The inability to solve the stopping problem directly affects software development.
Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.
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Please give me a step by step explanation
Answer:
[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]
Step-by-step explanation:
The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].
[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]
We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].
Now add these equations together to get our equation.
[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]
Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].
=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]
The annual gym subscription for a single member is Rs.1000, while an annual family membership is Rs.1500. The gym is considering increasing all membership fees by the same amount. If this is done then a single membership would cost 5/7 of a family membership. Determine the amount of the proposed increase.
The amount of the proposed increase is, Rs 1071.4
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The annual gym subscription for a single member is Rs.1000,
And, An annual family membership is Rs.1500.
Here, A single membership increased cost 5/7 of a family membership.
Hence, The increased cost = 5/7 of 1500
= 1071.4 Rupees
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200 T-hirt have been bought for a Fun Run at a cot of £400 plu VAT at
17. 5%. The cot of entry for the run i £5 per peron. What i the minimum number of entrie needed in order to cover the total cot of the T-hirt?
The minimum number of entries needed in order to cover the total cost of the T-shirts is 94.
What is linear inequality?
A linear inequality is an inequality that can be written in the form of
ax + b > c or ax + b < c or ax + b = c
Where x and y are variables and a,b,c are constants.
The cost of the T-shirts plus VAT is £400 + (17.5/100) * £400 = £400 + £70 = £470
In order to cover the total cost of the T-shirts, you need to find out how much money you will make from the entry fees.
Let's call the number of entries N. The total revenue from the entry fees is N * £5 = £5N
So, in order to cover the cost of the T-shirts, the revenue from the entry fees must be greater than or equal to the cost of the T-shirts plus VAT:
£5N ≥ £470
To find the minimum number of entries needed, you can divide both sides of the inequality by 5:
N ≥ £470 / £5
N ≥ 94
Hence, the minimum number of entries needed in order to cover the total cost of the T-shirts is 94.
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The minimum number of entries needed in order to cover the total cost of the T-shirts is 94.
What is linear inequality?
A linear inequality is an inequality that can be written in the form of
ax + b > c or ax + b < c or ax + b = c
Where x and y are variables and a,b, and c are constants.
The cost of the T-shirts plus VAT is £400 + (17.5/100) * £400 = £400 + £70 = £470
In order to cover the total cost of the T-shirts, you need to find out how much money you will make from the entry fees.
Let's call the number of entries N. The total revenue from the entry fees is N * £5 = £5N
So, in order to cover the cost of the T-shirts, the revenue from the entry fees must be greater than or equal to the cost of the T-shirts plus VAT:
£5N ≥ £470
To find the minimum number of entries needed, you can divide both sides of the inequality by 5:
N ≥ £470 / £5
N ≥ 94
Hence, the minimum number of entries needed in order to cover the total cost of the T-shirts is 94.
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What is the domain of √?
The domain of √ (square root) is all non-negative real numbers.
The domain of a function represents the set of all input values that can be used in the function without resulting in an undefined or meaningless output.
The square root function, represented by √, is only defined for non-negative real numbers. This is because the square root of any negative number is not a real number, it becomes an imaginary number.
This is because in order for the square root to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. Therefore, any real number greater than or equal to zero can be used as the input for the square root function, making its domain all non-negative real numbers.
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Williamston Daily is a new daily newspaper. When they first started printing three years ago they had 5900 home delivery subscribers. The number of subscribers increases by 66 every month. Write an equation that expresses the number of subscribers B in terms of n, the number of months the paper has been printed.a.B
this is a question of set of equations and solution is as follows,
Williamston Daily newspaper started printing newspaper.
Three years ago they had 5900 subscribers.
every month there is an increase of 66 new subscribers.
n is the number of months the paper has been printed.
so, the linear model will be
B= early subscriber + number of month × increments
B= 5900 + n × 66
B= 66 n + 5900
Example - subscribers after 3 months,
n = 3
= 66 x 3 +5900
= 198 + 5900
= 6000
set of equations
A system of equations is a set or collection of equations that you deal with all together at once. Linear equations are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
Linear equations
Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.
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Kylie ran 7/10 of a mile and walked 2/5 of a mile. How much farther did Kylie run than walk?
Write your answer as a fraction or as a whole or mixed number.
The farther distance run by Kylie is 3 /10 miles.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Kylie ran 7/10 of a mile and walked 2/5 of a mile. The distance will be calculated as,
Distance = ( 7/10 ) - ( 2 / 5)
Distance = ( 7 - 4 ) / 10
Distance = 3 / 10 miles
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I WILL MARK BRAINLYEST AND 40 POINTS
Describe a meal that you could put together that provides 4 servings of both a main course and a side dish. Explain how you know that it will not exceed the weight limit of the box
The total number of servings of chicken the food bank can provide is 70 servings.
What is per unit?Per-unit is a technique of expressing a quantity's value in terms of a base or reference quantity. Each system variable or quantity in a per-unit system is normalized in relation to its own base value.
Two chickens make up the main course of a plate of food, according to the table's content. Each chicken served by the food bank weighs 12.6 ounces. 110.9 pounds of chicken are available at the food bank (1,774.4 ounces of chicken)
Thus,
The mass of chicken per serving = 2 × 12.6 = 25.2 oz/serving
The total number of servings of chicken the food bank can provide = (The quantity of chicken the food bank has)/(The mass of chicken per serving)
∴ The total number of servings of chicken the food bank can provide = (1,774.4 oz)/(25.2 oz/serving) ≈ 70.413
Given that the servings are in whole numbers, we have;
therefore, To the nearest whole number, the food bank can offer a maximum of 70 servings of chicken.
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253 x 804 =
Solve by using standard algorithms
Answer:
203412
Step-by-step explanation:
253
*804
___
16
40
32
20
12
______
203412
This is a Vedic Math trick you can use to multiply fast, called the criss-cross method.
Factor the quadratic expression
4a²+27a+18
The factors of given quadratic expression are (4a+3) and (a+6).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The given quadratic expression is 4a²+27a+18.
By splitting middle term method, we get
4a²+3a+24a+18
= a(4a+3)+6(4a+3)
= (4a+3)(a+6)
Therefore, the factors of given quadratic expression are (4a+3) and (a+6).
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Nellie had $48.She spent 1/4 of it on a calculator. She also bought a book for $14.How much money did she spend all together?
Answer:
26$
Step-by-step explanation:
¼×48=12
so 12 was spent on calculator
12+14= 26
Arlene buys a phone case and charging cord for 15% off. The original cost of the phone case is $18. Her total discount is $4. 20.
Write and solve an equation to find the original price of the charging cord, x
The equation to find the original price of the charging chord is 0.15x + 0.15y = 4.20 and the original price of the charging cord is $10.
Let the price of the phone case is x.
And the price of the charging cord is y.
Discounted price for phone case: 15% of x = 0.15x
Discounted price for charging cord = 0.15y
Now, according to the question, the total discount is $4. 20
⇒0.15x + 0.15y = 4.20
⇒0.15 * 18 + 0.15y = 4.20
⇒2.7 + 0.15y = 4.20
⇒0.15y = 4.2 - 2.7
⇒y = 1.5/0.15
⇒y = $10
Therefore the equation to find the original price of the cord is 0.15x + 0.15y = 4.20 and the original price of the charging cord is $10.
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3/5 times 1/4 simplest form
Answer:
3/20
Step-by-step explanation:
To do this multiply the numerators (the top numbers) together first.
3 * 1 = 3
This is the numerator (the top number) of the answer fraction.
Next we take the bottom numbers:
5 * 4 = 20
We have 3/20 as our fraction. We know 3 is a prime number and can only be divided by 1 or 3. 20 cannot be divided by 1 or 3 so this fraction cannot be simplified any more.
How to do elimination with 3 equations?
Elimination is a method of solving a system of equations using addition or subtraction to eliminate one of the variables.
Here we will use the elimination method to solve a system of three equations with three variables.
Let's say we have three equations with three variables x, y and z.
Equation 1: ax + by + cz = d
Equation 2: ex + fy + gz = h
Equation 3: ix + jy + kz = l
We will start by multiplying the first equation by a number that will make the coefficients of y in the two equations the same.
Let's say we choose to multiply the first equation by -f, so that we get:
-fax -fby -fcz = -fd
Now we add the two equations to eliminate y:
ax + by + cz + (-fax -fby -fcz) = d -fd
ax -fax + by -fby + cz -fcz = d -fd
(a -f)x + (b -f)y + (c -f)z = d -fd
Now we can multiply the second equation by a number that will make the coefficients of z in the two equations the same. Let's say we choose to multiply the second equation by -k, so that we get:
-kex -kfy -kgz = -kh
Now we add the two equations to eliminate z:
(a -f)x + (b -f)y + (c -f)z + (-kex -kfy -kgz) = d -fd -kh
(a -f)x + (b -f)y + (c -f)z -kex -kfy -kgz = d -fd -kh
(a -f -k)x + (b -f -k)y = d -fd -kh
We can now solve this equation for x:
x = (d -fd -kh - (b -f -k)y) / (a -f -k)
Now we can substitute this expression for x in any of the original equations and solve for y:
Let's choose to substitute in the first equation:
ax + by + cz = d
(d -fd -kh - (b -f -k)y) / (a -f -k) + by + cz = d
y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)
Now we can substitute this expression for y in any of the original equations and solve for z:
Let's choose to substitute in the second equation:
ex + fy + gz = h
e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + gz = h
gz = h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))
z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g
Now we have
x = (d -fd -kh - (b -f -k)y) / (a -f -k)
y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)
z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g
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I need help on these questions. They confuse me.
The graphic solution for each system of equations is given as follows:
20. (5/3, 28/3).
21. (0.205, 3.846).
22. (-1/2, -5/2).
23. (-4.615, 7.462).
How to solve a system of equations graphically?The graphic solution of a system of equations is given by the point of intersection of all the equation that compose the system.
For this problem, the systems are composed by functions of the first degree, hence they are linear functions.
For each system, the graph is traced, and then the point of intersection is identified on the graph given at the end of the answer.
Each system is traced on a different color, as follows:
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5)48 I need help I suck at math
On solving the question resultant answer from the given data we have algebraic expression 5/48 could be 0.10
what is an algebraic expression ?Algebraic expression can be defined as the combination of constants , variables and operators. Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.
So, the given expression , 5/48
5/48 = 0.10
The resultant answer from the given expression 5/48 could be 0.10
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The correct question is -
Solve the equation.
p= −6p=48
Please help I suck at math
Q 23
Regina writes the expression y + 9
Which expression is equivalent to the one Regina writes?
A) (9. 3 • 4) + y
B 9+ y (3 = 4)
© (y + 9)(3 = 4)
None of these
The expression written by Regina is y + 9, which means adding nine to some number y. None of the given expressions are equivalent to this expression.
The expression written by Regina is y + 9, which means adding nine to some number y. None of the given expressions are equivalent to this expression. In order for two expressions to be equivalent, they must have the same value when the same values are plugged into them. For example, if y is equal to 5, then y + 9 would be equal to
14, while (9. 3 • 4) + y
would be equal to
27, (9+ y (3 = 4))
would be equal to 17, and
(y + 9)(3 = 4)
would be equal to 21. As these values are not equal, the given expressions are not equivalent to the one written by Regina.
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The nth term of a sequence is 3n squared -1. The nth term of a different sequence is 30 - n squared. Find the only number that is in both of these sequences
The number that belongs to both sequences is 26.
The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number."
By changing the term number's value, we can create a series that uses the nth term (n).
To find the 10th term we would follow the formula for the sequence but substitute 10 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.
We have two sequences, let's call one as A and the other as B.
The n-th term of sequence A is written as:
aₙ = 3*n^2 - 1
the nth term of sequence B is written as:
bₙ = 30 - n^2
We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)
Then we want to find:
aₙ = bₓ
where n and x are integer numbers.
Then we will heave:
3*n^2 - 1 = 30 - x^2
To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.
Let's isolate n.
3*n^2 = 30 - x^2 + 1
3*n^2 = 31 - x^2
n^2 = (31 - x^2)/3
n = √( (31 - x^2)/3)
Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.
Then let's start with x = 1.
n(1) = √( (31 - 1^2)/3) = √(30/3) = √10
We know that √10 is not an integer.
now with x = 2,
n(2) = √( (31 - 2^2)/3) = √( (31 - 4)/3) = √(27/3) = √9 = 3
then if x = 2, we have n = 3.
Both of them are integers, then we get:
a₂ = 3*(3)^2 - 1 = 27 - 1 = 26
b₃ = 30 - 2^2 = 30 - 4 = 26
Therefore, The number that belongs to both sequences is 26.
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An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A
The equation of the magnitude of the force applied at the back of otter is F is (P+P0)A F is ( P + P 0 ) A .
What does the term magnitude of the force mean?The amount that encapsulates the force's power is known as its magnitude. Consider the following scenario: the force is 10 N in the east. The direction is indicated by "towards east," while the force is indicated by "10." Magnitude may be thought of as simply the "value" or "amount" of any physical quantity.
The surface area of the otter's back is A = 0.55 m2.
The fluid pressure at the depth of the otter is P = 11500 Pa.
Thus, the equation of the magnitude of the force applied at the back of otter is F=(P+P0)A F = ( P + P 0 ) A .
The complete question is
An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A = 0.55 m2. The fluid pressure at the depth of the otter is P = 11500 Pa.
Write an equation for the magnitude of the force F on the back of the otter in terms of the pressure P and the atmospheric pressure P0.
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Write an inequality with the solution x > or equal to 4. The inequality should have the variable on both sides, a fractional coefficient of the variable on the left side, and a fraction anywhere on the right side.
The inequality equation ( x ≥ 4 ) is given as ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
x ≥ 4 be equation (1)
On simplifying the equation , we get
Divide by 4 on both sides of the equation , we get
( x / 4 ) ≥ 1
Adding x on both sides of the equation , we get
x + ( x/4 ) ≥ 1 + x
Now , adding ( 1/4 ) on both sides of the equation , we get
x + ( 1/4 ) + ( x/4 ) ≥ 1 + x + ( 1/4 )
On simplifying the equation , we get
( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
Therefore , the value of A is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
Hence , the inequality equation is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
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Solve |x| + 7 < 4.
{x | x < -11 or x > -3}
Ø
{x | -3 < x < 3}
The solution of equation is ∅.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols.
Given equation |x| + 7 < 4
subtract 7 from both sides
|x| + 7 - 7 < 4 - 7
|x| < -3
but |x| ≥ 0, for all real values,
so solution is ∅.
Hence the solution of equation is ∅.
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Simplify the following: (3 + 10i) - (-9 - 4i)
*PLEASE INCLUDE EXPLANATION
Answer:
12+14i
Step-by-step explanation:
For -(-9-4i), you need to clean up the parentheses so you would distribute. -1 times -9 and -1 times -4i.
You will get 9+4i
Now you have 3+10i+9+4i. You will now add like terms. 10i+4i= 14i. 9+3= 12.
12+14i
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One angle of a triangle meaure 140°. The other two angle are in a ratio of 3:5. What are the meaure of thoe two angle
One angle of a triangle measure 140°. The other two angles are in a ratio of 3:5.The smaller angle would measure 84°, and the larger angle would measure 56°. This can be found through the use of basic trigonometry.
A triangle is a three-sided polygon with three angles that add up to 180°. Since one of the angles is already known, the remaining two angles can be calculated by subtracting 140° from 180°, which equals 40°. This 40° can then be divided by the ratio 3:5, which is 8° and 32°.
If 8° is the smaller angle, then 32° must be the larger angle. To convert 8° and 32° to the final answer of 84° and 56°, 8° must be multiplied by 10 and 32° must be multiplied by 5. This gives a total of 84° and 56° for the other two angles.
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One angle of a triangle measures 140°. The other two angles are in a ratio of 3:5. What are the measures of that two angles?
A grocery store has increased its prices over time. The price per pound of apples in 2016 was $0.45. Today, the price per pound of apples is $0.85.
What is the equation of the line that would represent the price increase per pound of apples over time?
Answer:
C = 0.06x + 0.45
Step-by-step explanation:
Today is 2023
So, from 2016 to 2023, it has been 7 years.
0.85 - 0.45 = $0.40
So, $0.40 is the increase in 7 years
0.40 / 7 = $0.06
So, $0.06 is the change per year
Let C represent the total cost and x represent the number of years and we have
C= 0.06x + 0.45
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497
The probability is 0.4444.
What is probability?Probability is a measure of the likelihood of a particular outcome occurring in a given situation. It is the chance that something will happen or is true. Probability is expressed as a number between 0 (impossible) and 1 (certain). Probability is a mathematical way of predicting what will happen in the future based on a given set of data. It is used to analyze the likelihood of various outcomes in a range of scenarios, such as gambling, finance, insurance, and weather forecasting.
The probability of a randomly selected tester from the group of college-bound seniors having a score between 1497 and 1507 can be calculated using the standard normal distribution. First, we need to convert the scores to standard scores, or z-scores. Subtract the mean from the scores and divide by the standard deviation to get z-scores.
For XXX = 1497, z = (1497 - 1497) / 322 = 0.
For XXX = 1507, z = (1507 - 1497) / 322 = 0.31.
Using a standard normal table, we can calculate the area under the normal curve between 0 and 0.31. The probability of randomly selecting a tester with a score between 1497 and 1507 is 0.4444. The probability is therefore P(1497 ≤ XXX ≤ 1507) = 0.4444.
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Complete questions as follows-
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497 ≤ XXX ≤ 1507).
Carlos bought 515 Euros for his holiday to Germany. He spent £ 412 to obtain these Euros. How many Euros would Carlos have obtained if he spent £500 ?
Carlos needs a total of 400 Euros for buying 500 Euros.
The total amount available with Carlos for his holiday to Germany = 515 Euros
Amount spent to obtain these 515 Euros = £ 412
As it is clear that for buying 515 Euros he spent 412 Euros.
So, we will first find the Euros spent on buying 1 Euro.
For that, we will use Unitary Method:
So, the total Euros spent for buying 1 Euro will be = (412/515) = 0.8
So, for finding the total Euros spent for obtaining 500 Euros we will simply multiply the total Euros needed by the Euro spent for buying 1 Euro.
Thar will be equal to (0.8 * 500) = 400 Euros.
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