Answer:
SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.
Graph the first equation.
Graph the second equation on the same rectangular coordinate system.
Determine whether the lines intersect, are parallel, or are the same line.
Identify the solution to the system. ...
Check the solution in both equations.
Step-by-step explanation:
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
The length of a rectangle is twice its width. The perimeter is 30. Find it’s dimensions.
Answer:
Length = 10 Width = 5Step-by-step explanation:
Let's assume that,
→ Length = 2x
→ Width = x
→ Perimeter = 30
Perimeter of rectangle formula,
→ P = 2(L + W)
Now the value of x will be,
→ P = 2(L + W)
→ 2(2x + x) = 30
→ 2 × 3x = 30
→ 6x = 30
→ x = 30/6
→ [ x = 5 ]
Then required dimensions are,
→ Length = 2x = 2 × 5 = 10
→ Width = x = 5
Hence, these are the dimensions.
Length = 10
width = 5
Given-
Perimeter =30
l=2b........................................................ i
so
P =2(l+b)
here
30 = 2(2b +b)... ... .............. as l=2b from i
30 = 2*3b
30 = 6b
b= 5
which implies l= 2*5 --->10............................................ from i
so
Length = 10
width = 5
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In 2000 a company increased its workforce by 60%. In 2001 it decreased its workforce by 60%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the beginning of 2000?
A) It is 36% lower.
B) It is 6% lower.
C) It is unchanged.
D) It is 36% higher.
I know that the answer is A, but I'm having trouble figuring out the steps. Can anyone help me?
Therefore, the solution of given problem of percentage indicates that from the beginning of 2000 and the end of 2001, there was no net change in the workforce.
A percentage is defined.A% is a number that expresses a quantity as a percentage of 100; it can also be expressed as a decimal or a fraction. Placing 100 in the denominator and the percentage value in the numerator will allow you to convert a percentage to a fraction.
Here,
Before any changes,
let w represent the size of the workforce. There are:
50 percent growth is equivalent to increasing by 1.5, therefore w(2000) = w(1999) * 1.5
A 50% drop is equal to dividing by 1.5, therefore w(2001) = w(2000)/1.5
Reverse the first equation to create the second equation.
w(2001) = w(1999) * 1.5/1.5
Remove the 1.5 from the top and bottom so that w(2001) = w (1999)
Therefore, this indicates that from the beginning of 2000 and the end of 2001, there was no net change in the workforce.
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What information will be useful to know to answer the main question? How can you get it? How will you use that information
Answer:
Step-by-step explanation:
Can u give more detail as to what the question is asking pease
Refer to the diagram shown.
I need help with this please help me
Answer: Angle-Side-Angle Theorem
Step-by-step explanation:
The two triangles are shown to have congruent angles. By the Reflexive Property of Congruence, Side PM is shared and congruent between the two.
Because the angles are on either side (left and right) of the shared side, the triangles are congruent by the Angle-Side-Angle Theorem.
12a-3b squared, when a=9, b=4
Answer:
60
Step-by-step explanation:
12a - 3b²
12(9) - 3(4)²
108 - 3(16)
108 - 48
60
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{12a - 3b^2}\\\mathsf{= 12(9) - 3(4)^2}\\\mathsf{= 12(9) - 3(4\times4)}\\\mathsf{= 12(9) - 3(16)}\\\mathsf{108 - 3(16)}\\\mathsf{= 108 - 48}\\\mathsf{= 60}\\\\\huge\text{Therefore, your answer should be: }\\\huge\boxed{\mathsf{60}}\huge\chdckmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
S+S+S+S AND 4S I don't know it could someone help me who knows it is it equivalent or not equivalent
Yes, the expressions S+S+S+S AND 4S as required in the task content are equivalent expressions.
Are the given expressions equivalent expressions?It follows from the task content that the expressions given S+S+S+S AND 4S are to be compared and determine if they are equivalent or not.
Since the given expressions are; S + S + S + S and 4S.
S + S + S + S can be written by factorisation as;
S ( 1 + 1 + 1 + 1 ) = S (4)
= 4S.
On this note, it can be inferred that the two expressions given are equivalent expressions.
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Is (7, 9) a solution of y > 2x − 5?
HELP
Answer:
no
Step-by-step explanation:
y > 2x - 5
9 > 2(7) - 5
9 > 14 - 5
9 > 9. not a solution
9=9
to solve 2/5 x = 14, you multiply both sides of the equation by 5/2. your friend divides both sides of the equation by 2/5. who is right? explain.
Answer:
both are right
Step-by-step explanation:
2/5x = 14
multiply both sides by 5/2:
(5/2)(2/5)x = 14(5/2)
x = 70/2 = 35
However, dividing by 2/5 is the same as multiplying by 5/2, so you are BOTH right. Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
If there are estimated to be 10 ^ 11 galaxies in the known universe and 10 ^ 11 stars in each galaxy, how many stars are estimated to be in the universe?
Answer: We can use the information given to find the number of stars in the universe by multiplying the number of galaxies by the number of stars per galaxy:
number of stars = (10 ^ 11 galaxies) x (10 ^ 11 stars per galaxy)
This is a simple arithmetic problem and we can find the solution by multiplying the numbers 10^11 and 10^11
10^11 * 10^11 = (10101010101010101010)(101010101010101010*10) = 10^(11+11) = 10^22
So, there are estimated to be 10 ^ 22 stars in the known universe.
Step-by-step explanation:
(5b + 16)
(b + 32)°
What is the value of b ?
b =
Answer:
b = -8
Step-by-step explanation:
To determine the value of b, we can use the factoring method. We can factor the expression
(5b + 16)(b + 32) as (b + 8)(5b + 16).
Setting each factor to 0, we get b + 8 = 0 and 5b + 16 = 0.
Solving for b in the first equation, we get b = -8.
Substituting this value into the second equation, we get 5(-8) + 16 = 0, which simplifies to -40 + 16 = 0.
This equation is true only when the value of b is -8. Therefore, the value of b is -8.
2. What are the domain and range for the exponential parent function,
where b is a positive real number not equal to 1 and a > 0?
On solving the provided question, we can say that - the value of the given polynomials domain will be ( - infinity, 0)
what is domain?The range of values a function may accept is referred to as its domain. These numbers represent the x-values of a function like f. (x). The range of values that a function may operate on is referred to as its domain. The value that the function returns following the insertion of the x value is this set. A function containing the independent variable x and the dependent variable y is said to be y = f(x). A value of x is said to be in the domain of a function f if it can be used to successfully create a single value y utilizing the value of x for that purpose.
domain will be ( - infinity, 0)
range = (-infinity, +infinity)
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the total cost for 5 adult tickets and 18 student tickets at a local theater is $98. The total cost was 98. The total cost for 4 adult tickets and 22 student tickets at the theater is $105. What’s the cost for one adult ticket and one student ticket? PLEASEE BRO
The cost of one adult ticket is 3.6 and cost of one student ticket is 4.3
Tickets for a school talent show cost $2 for students and $3 for adults. If Chris spends at least $11 but no more than 14 on x student tickets and 1 adult ticket, what is one possible value of x?Either 4 or is the appropriate response.
Chris spends a total of 2 x + 3 dollars on x student tickets and a total of x adult tickets because each student ticket costs $ 2 and each adult ticket costs $ 3.
Because Chris spends at least $ 11 but no more than $ 14 on the tickets, the entire inequality 2 x + 3 1 can be written.
x = 4 and x = 5.5 are obtained by subtracting 3 from each side of both inequalities and then dividing each side of both inequalities by 2.
A number higher than or equal to 4 and less than or equal to 5.5 must both be integers in order for x to have a value.
Therefore, either x = 4 or x = 5.
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Tamara uses 8.5 of blue paint and white paint to paint her bedroom walls. Three fourths of this amount is blue paint, and the rest is white paint . How many pints of white paint did she used to paint her bedroom walls
The amount of white paint used by Tamara to paint the bedroom walls is 2.125.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Total amount of paint = 8.5
Three fourths of this amount is blue paint.
Amount of blue paint = (3/4) × 8.5 = 6.375
Rest is white paint.
Amount of white paint = Total paint - Amount of blue paint
= 8.5 - 6.375
= 2.125
Hence the amount of white paint used to paint bedroom walls is 2.125.
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for values of x f(x) = 2x-3 and g(x)= x^2+1 find gf(x)
Answer:
g(f(x)) = 4x² - 12x + 10
Step-by-step explanation:
to find g(f(x)) substitute x = f(x) ino g(x)
g(f(x))
= g(2x - 3)
= (2x - 3)² + 1 ← expand parenthesis using FOIL
= 4x² - 6x - 6x + 9 + 1
= 4x² - 12x + 10
What Is the slope for these two points (3,-2) and (5,6)?
Answer:
4
Step-by-step explanation:
m = Δy/Δx = (6-(-2))/(5-3) =8/2 = 4
Write an expression to represent: 2 times the difference of x and 3
Answer:
2(x-3)
Step-by-step explanation: 2 is being multiplied by the difference (subtraction) of x-3.
-POINTS-
(4IZ0 Don’t even try.)
Answer:
Step-by-step explanation:
axf
A measurement of 50.8 centimeters is equivalent to how many inches? A. 25 B. 12 C.20 D. 10
Answer: C. 20
Step-by-step explanation:
1 inch is equal to 2.54 cm.
So we have to divide the amount of centimeters given by how many centimeters are in an inch to find how many inches.
50.8 ÷ 2.54 = 20
Hope this helps!!! :)
Find the LCM of the first five primes
Answer:
The first 5 prime numbers are 2, 3, 5, 7 and 11. Their LCM is 2310
The altitude of the hypotenuse of a right triangle divides the hypotenuse into two segments. If the ratio of lengths of the segments is 1:9 and the length of the altitude is 6 meters, find the lengths of the two segments?
Answer:
2 m18 mStep-by-step explanation:
You want the lengths of the segments of the hypotenuse of a right triangle when an altitude of 6 m divides the hypotenuse into parts with the ratio 1:9.
Geometric meanThe altitude to the hypotenuse of a right triangle is the geometric mean of the parts it divides the hypotenuse into. If the shorter part is x, then the longer part is 9x, and their geometric mean is ...
6 = √(x(9x)) = 3√x² = 3x
x = 2 . . . . . . . divide by 3
The length of the shorter segment is 2 m; the longer one, 18 m.
pls help due tomorrow
On solving the provided question, we can say that - by doing the equation, we have -12 +18 = p + 7 => 6 = p + 7 => p = -1
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here,
-12 +18 = p + 7
6 = p + 7
p = -1
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(7) = -1 B. g(-4) = -11 C. g(0) = 2 D. g(-13) = 20
Answer: B
Step-by-step explanation:
write a mutiplcation exprresion that shows ten to the third
Answer:
10x10x10 or 10*3......
After 9 years in an account with a 3.9% annual interest rate compounded continuously, an investment is worth a total of $17,757.16. What is the value of the principal investment? Around the answer to the nearest penny.
The value of the principal investment would be = $12,500.75
What is a principal investment?A principal investment is defined as the capital amount of money that is being deposited into an account with the purpose of receiving interest for a particular period of time.
The years of investment (t) = 9 years
The annual interest rate (r) = 3.9% = 3.9/100= 0.039
The total worth of the investment (A) = $17,757.16
Then, solve the equation for P
P = A / ert
P = 17,757.16 / e(0.039*9)
P = $12,500.75
Therefore, the principal amount that is needed which can be compounded continuously to get the total amount given = $12,500.75
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There are t counters in a box.
Write an expression for the total number of counters.
Answer: 4t
Step-by-step explanation:
You just do t times the amount of boxes you have, which is 4. So you have 4 times t, but in algebra, we don't write the multiplication sign. So the expression would be written as 4t. Yw!
Also please tell me if I was unhelpful/incorrect, thanks!
I just need help appreciate it and have a great day
On solving the provided question, we can say that - by doing the fraction we have 3/12 = 1/4
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
balloons is 12
blew up is 1/3
friend blew up is 5
1/3*12 = 4
4+5 = 9
3/12 = 1/4
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A machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long. What is the total length needed in inches?
The total length needed in inches will be 490.5 inches.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long The total length needed in inches will be:
= (3 ft 4 7/8 inch × 12)
Note that 1 feet = 12 inches
= (12 × 3) + (4 7/8) × 12
= (36 + 4.875) × 12
= 490.5 inches
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solve for inequality for graph y + 4 > 1/2 {x + 2}
Answer:
y > X/2 - 3
I think that's the answer.
Show your work please help
The error in the work lies in line 3 where the square root is calculated inaccurately.
What is square root of a number?The opposite of squaring an integer is finding its square root. The square root of a number can be found by looking for a number that, when squared, yields the original value.
The error is in line 3, line 4 and line 5.
The error in line 3 is inaccurate calculation of the value of square root of 4.
The error in line 4 is a mathematical calculation error.
The error in line 5 is a mathematical calculation error.
The correct answer in Line 3 is:
[tex]6 * 2 *\sqrt{5} -3\sqrt{5}[/tex]
The correct answer in Line 4 is:
[tex]12\sqrt{5} - 3\sqrt{5}[/tex]
The correct answer in Line 5 is:
[tex]9\sqrt{5}[/tex]
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Rose decided to buy a photocopy machine that is projected to yield cash savings of RM2,000 per year over a 20 years period. Using a 15% discount rate, calculate the present value of the savings.
(Assume that the cash savings occur at the end of the year)
Answer:
RM832.29
Step-by-step explanation:
Calculate PV Savings
To calculate the present value of the savings, we can use the formula:
PV = cash savings / (1 + r)^t
Where PV is the present value, r is the discount rate, and t is the number of years.
Plugging in the values given in the problem, we get:
PV = RM2,000 / (1 + 0.15)^20
= RM2,000 / 1.15^20
= RM832.29
So the present value of the savings is RM832.29.
Answer: RM25,919.89.
Step-by-step explanation:
The present value of the cash savings is the sum of the present value of each year's cash savings.
To calculate this, the formula for the present value of a single cash flow is used:
Present Value = Future Value / (1 + r)^n
Where r is the discount rate, and n is the number of years.
So, for the first year's cash savings, the present value would be:
PV = 2000 / (1 + 0.15)^1 = 1739.13
For the second year's cash savings, the present value would be:
PV = 2000 / (1 + 0.15)^2 = 1510.71
This can be repeated for the remaining 18 years, and the sum of all the present values is the total present value of the cash savings over 20 years:
Total PV = 1739.13 + 1510.71 + .... + 437.66 = RM25,919.89
Therefore, the present value of the cash savings over 20 years with a 15% discount rate is RM25,919.89.