Two vectors v₁ and v₂ whose sum are (0, -1, -3), where v₁ is parallel to
(5, 0, -4) while v₂ is perpendicular to (5, 0, -4).
v1 = [40/13, -8/13 ]
v2 = [-1/13, -5/13]
Parallel vectors will be multiples of each other.
Perpendicular vectors will have a dot product of 0.
Let v₁ = [a, b] and v₂ = [c, d]
v₁ || [-5,1] means v₁ = N [-5,1] = [a, b]
So a = -5N and b = N
v₂ • [-5,1] = 0 (because they are perpendicular)
So [c, d] • [-5,1] = -5c + d = 0 or d = 5c
⇒ v₁ + v₂ = [a, b] + [c, d] = [3, -1]
So a + c = 3 and b + d = -1
Now,
Substitute -5N for
a. Substitute N for b.
and Substitute 5c for d.
This gives us a system of equations with two equations and 2 unknowns:
-5N + c = 3
N + 5c = -1
Multiply everything in the bottom equation by 5
-5N + c = 3
5N + 25c = -5
Now add vertically, eliminating the variable N and finding
26c = -2
or, c = -1/13
Now we work our way backwards.
-5N + c = -5N + (-1/13) = 3
-5N = 40/13
(-1/5) (-5N) = (40/13)(-1/5)
and
N = -8/13 and b = N so b = -8/13
d = 5c so d = -5/13
a = -5N, so a = 40/13
So the two vectors are:
v₁ = [40/13, -8/13 ]
v₂ = [-1/13, -5/13]
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A worker earning an hourly wage changes positions within a company. The new position comes with a 20% raise in hourly wage. The
worker also receives a $2 increase in hourly wage. Use composition of functions to write a function that represents the worker's new
hourly wage when the 20% raise is applied before the $2 raise.
f(x) =
This function gives the same result as the previous function we derived, but it expresses the calculation as a composition of the two separate functions that represent each raise separately.
What is function?A function is a set of instructions or statements that perform a specific task or computation and returns a value or result. In programming, a function is typically defined using a specific syntax and can be called or invoked by other parts of the program to carry out a particular operation.
Functions are used in programming to break down complex tasks into smaller, more manageable pieces of code, which can then be reused in multiple parts of the program. They can also help to improve the organization, readability, and maintainability of code.
by the question.
let the worker's original hourly wage be represented by the variable x. Then the function for the worker's new hourly wage when the 20% raise is applied before the $2 raise can be expressed as follows:
[tex]f(x) = (1.20x) + 2[/tex]
In this function, the expression (1.20x) represents the worker's hourly wage after the 20% raise is applied, and the additional $2 raise is added to this amount to determine the final hourly wage.
We can also express this function using function composition notation. Let g(x) represent the function that applies the 20% raise to the worker's hourly wage and let h(x) represent the function that adds the $2 raise to the resulting hourly wage. Then we have:
[tex]g(x) = 1.20x[/tex]
[tex]h(x) = x + 2[/tex]
Using function composition, we can write the function for the worker's new hourly wage as:
[tex]f(x) = h(g(x)) = h(1.20x) = 1.20x + 2[/tex]
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According to the money exchange rate of Nepal Rastra Bank, the purchasing and selling rates of 1 American dollar are NRS 119.70 and NRS 120.30 respectively, then. 1. How many American dollars can be exchanged with NRS 84,210?
2.how many nepali rupees can you exchange with $660? Find it.
To find out how many American dollars can be exchanged with NRS 84,210, we can use the selling rate of 1 American dollar, which is NRS 120.30.
Dividing NRS 84,210 by NRS 120.30 per dollar, we get:
$70 = (NRS 84,210 / NRS 120.30 per dollar)
Therefore, NRS 84,210 can be exchanged for $70.
To find out how many Nepali rupees can be exchanged with $660, we can use the purchasing rate of 1 American dollar, which is NRS 119.70.
Multiplying $660 by NRS 119.70 per dollar, we get:
NRS 79,002 = ($660 x NRS 119.70 per dollar)
Therefore, $660 can be exchanged for NRS 79,002.
true/false. the continuity correction must be used because the normal distribution assumes variables whereas the binomial distribution uses discrete variables
The statement " the continuity correction must be used because the normal distribution assumes variables whereas the binomial distribution uses discrete variables" is true because continuity correction is used to adjust for the discrepancy between continuous and discrete variables when approximating a discrete distribution
The continuity correction is used when approximating a discrete distribution, such as the binomial distribution, with a continuous distribution, such as the normal distribution. The normal distribution assumes continuous variables, while the binomial distribution uses discrete variables.
The continuity correction helps to account for the fact that the normal distribution is continuous, whereas the binomial distribution is not. It adjusts the boundaries of the intervals used in the approximation, to better reflect the underlying discrete nature of the data.
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What is the amount of interest to be paid if u got a reducing balance loan of $2700 and you will repay it over 5 years by quarterly installments of $1899.75 at interest rate 14% p.a. (compounded quarterly)
The total interest to be paid over the 5-year period is $403.22.
What is reducing balance loan?In a loan with a declining balance, interest is added to the outstanding balance at the start of each period, such as each month or each quarter. The outstanding balance, which decreases as the borrower makes repayments, is used to determine the interest rate. As a result, the borrower gradually pays less interest and more of each payment is used to lowering the main balance due. The lowering balance approach is frequently applied to mortgages, personal loans, and auto loans.
Given that, the quarterly installments are $1899.75.
For the entire year for a total of 5 years the total amount is:
Total amount = 4 * 5 * $1899.75 = $37995
For reducing balance loan the interest is calculated as:
For the first quarter, the interest to be paid is:
interest = (total amount - 0) * (0.14 / 4)
interest = (37995 - 0) * (0.14 / 4) = $94.50
Similarly for the remaining quarters we have:
Second quarter = $87.95
Third quarter: $81.05
Fourth quarter: $73.76
Fifth quarter: $65.96
The total interest to be paid over the 5-year period is:
$94.50 + $87.95 + $81.05 + $73.76 + $65.96 = $403.22
Hence, the total interest to be paid over the 5-year period is $403.22.
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Find the area of the regular polygon. The side of the polygon and apothem are given. Round your answer to the
, nearest tenth if needed.
14.5
10
The area of the regular polygon is 362.5 units².
How to find the area of a polygon?The polygon above is a pentagon because it has five sides. The polygon is a regular polygon because all its sides are equal to each other.
The side length and apothem of the pentagon is given. Therefore, the area of the regular pentagon can be found as follows:
area of the regular pentagon = 1 / 2 × perimeter × apothem
Therefore,
perimeter of the regular pentagon = 14.5 × 5 = 72.5 units
apothem = 10 units
Hence,
area of the regular pentagon = 1 / 2 × 72.5 × 10
area of the regular pentagon = 72.5 × 5
area of the regular pentagon = 362.5 units²
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Determine whether the function is linear. If it is, identify the rate of change. X -7, -5, -3, -1, 0 Y 11, 14, 17, 20, 23
Answer: Yes;
Step-by-step explanation: The function is linear in that the X values are increasing by 2 and the Y values are increasing by 3.
Answer:
Not linear
Step-by-step explanation:
X | -7 | -5 | -3 | -1 | 0
Y | 11 | 14 | 17 | 20 | 23
-5 - (-7) = +2
14 - 11 = +3
-3 - (-5) = +2
17 - 14 = +3
-1 - (-3) = +2
20 - 17 = +3
0 - (-1) = +1
23 - 20 = +3
There is a linear function graphed that would pass through the first 4 points, but not the last one;
You can discern this as there is a common pattern we can identify, everytime the x-value increases by 2 the y-value increases by 3, except with the last coordinates;
The rate of change, also known as the gradient, is the change in x divided by the change in y (Δx/Δy);
In the case of the first 4 points, the rate of change would be 3/2 or 1.5;
This simply means when x increases by 1, y increases by 1.5, IF the function is linear;
However, as mentioned the last point doesn't fit the pattern;
There, we can see the y-value increases by 3 when the x-value only increases by 1;
This means the point (0, 23) isnt on the graph of the function, the points (0, 21.5) and (1, 23), on the other hand, would be.
need help with this angle question, please help
A. 7.5
B. 8.7
C. 13.0
D. 26.0
Answer:
8.7 m
Option B
Step-by-step explanation:
The tree, the shadow and the line of sight from the tip of the shadow to the top of the tree form a right triangle
The angle formed is 30°
Using the relationship
[tex]\tan 30 = \dfrac{h}{15}[/tex]
we get
[tex]h = 15 \times \tan 30[/tex]
[tex]h = 15 \times \dfrac{1}{\sqrt{3}}[/tex]
[tex]h = 8.66 m[/tex]
Rounded up this would be 8.7 m which is option B
Prove the following using a direct proof:
The sum of the squares of 4 consecutive integers is an even integer
Answer: A positive whole number multiplied by any whole number will remain positive. In the case of the squares of 4, it will always end in a 6 which is a positive number.
Step-by-step explanation:
4^2= 16
16^2 = 256
256^2= 65,536
etc.
Find the value of Tan 15 without using a table or calcutator
Answer:
Step-by-step explanation:
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A baseball team plays in a stadium that holds 60000 spectators. With the ticket price at $9 the average attendance has been 23000. When the price dropped to $7, the average attendance rose to 30000. Assume that attendance is linearly related to ticket price. What ticket price would maximize revenue?
Answer:
Step-by-step explanation:
We can start by assuming that the relationship between the ticket price and attendance is linear, so we can write the equation for the line that connects the two data points we have:
Point 1: (9, 23000)
Point 2: (7, 30000)
The slope of the line can be calculated as:
slope = (y2 - y1) / (x2 - x1)
slope = (30000 - 23000) / (7 - 9)
slope = 3500
So the equation for the line is:
y - y1 = m(x - x1)
y - 23000 = 3500(x - 9)
y = 3500x - 28700
Now we can use this equation to find the attendance for any ticket price. To maximize revenue, we need to find the ticket price that generates the highest revenue. Revenue is simply the product of attendance and ticket price:
R = P*A
R = P(3500P - 28700)
R = 3500P^2 - 28700P
To find the ticket price that maximizes revenue, we need to take the derivative of the revenue equation and set it equal to zero:
dR/dP = 7000P - 28700 = 0
7000P = 28700
P = 4.10
So the ticket price that would maximize revenue is $4.10. However, we need to make sure that this price is within a reasonable range, so we should check that the attendance at this price is between 23,000 and 30,000:
A = 3500(4.10) - 28700
A = 5730
Since 23,000 < 5,730 < 30,000, we can conclude that the ticket price that would maximize revenue is $4.10.
what is true and what is not for this right triangle need help
Step-by-step explanation:
For RIGHT triangles, using S-O-H-C-A-H-T-O-A
A sinA= cosB yes 12/13 = 12/13
B. sinA=tanB no 12 /13 not equal to 5/12
C. sinB= tanA no 5/13 not equal to 12/5
D. sinB= cosB no 5/13 not equal to 12/13
A) sinA= cοsB statement is true. Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A.
What is a triangle?A triangle is a twο-dimensiοnal geοmetric shape that cοnsists οf three straight line segments, called sides, that cοnnect three nοn-cοllinear pοints, called vertices.
Based οn the given image, the fοllοwing statements are true:
1. The triangle is a right triangle, which means that οne οf the angles is a right angle (90 degrees).
2. The side οppοsite the right angle is called the hypοtenuse, which is the lοngest side οf the triangle. In this case, it is the side that is labeled "c".
3. The οther twο sides οf the triangle are called legs. In this case, they are labelled "a" and "b".
4. The Pythagοrean theοrem applies tο this triangle, which states that the sum οf the squares οf the lengths οf the legs is equal tο the square οf the length οf the hypοtenuse. In οther wοrds, [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].
Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A
A sinA= cοsB yes 12/13 = 12/13
B. sinA=tanB nο 12 /13 nοt equal tο 5/12
C. sinB= tanA nο 5/13 nοt equal tο 12/5
D. sinB= cοsB nο 5/13 nοt equal tο 12/13.
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Complete Question:
In Δ ABC , angle C is right Angle
Which Statement must be True?
A sinA= cosB
B. sinA=tanB
C. sinB= tanA
D. sinB= cosB
Help please! I have no idea!!!!
The values of the function from the graph are h(7) = 10, h(0) = 9, h(t) = 8, t = 5 and h(t) = 0, t = 4
How to determine the value of the functionGiven that the graph is the graph of height as a function of time
To calculate the values of h(t) from the graph of g(x), we need to follow these steps
Identify the value of t on the x-axis where you want to calculate the value of h(t)Locate that point on the graphWrite the values from the pointUsing the above, we have the following
h(7) = 10
h(0) = 9
h(t) = 8, t = 5
h(t) = 0, t = 4
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What is the slope of the line in the following graph?
Answer:
A. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
93. Electricity Usage The graph shows
the daily megawatts of electricity used
on a record-breaking summer day in
Sacramento, California.
(a) Is this the graph of a function?
(b) What is the domain?
(c) Estimate the number of megawatts
used at 8 A.M.
(d) At what time was the most electric-
ity used? the least electricity?
(e) Call this function f. What is f(12)?
Interpret this answer.
(f) During what time intervals is usage
increasing? decreasing?
The graph that shows the electricity usage on a record-breaking summer day is Sacramento, California is a function.
The domain is 24 hours of a day.
The number of megawatts used at 8 am is 1, 200 megawatts.
The time with the most electricity used was 4 pm to 6 pm and least used was 4 am.
f ( 12 ) would be 1, 900 megawatts.
Usage is increasing from 4 am to 5 pm and decreasing from 5 pm to 4 am.
What does the graph show ?The graph is a function because each point on the graph represents a distinct megawatt usage. The domain would be 24 hours of a day as this graph of electricity usage shows the usage per day.
The megawatts used at 8 am is:
= 1, 300 - ( 200 / 2 )
= 1, 200 megawatts
From 4 am to 5 pm, we see that electricity usage is increasing as people are getting ready for work and going to work, but from 5 pm to 4 am, electricity usage decreases.
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Julian Nestor is ready to purchase a new stroller. It is regularly priced at $127.99. The sale price is $88.54. What is the markdown?
Answer:
$39.45, about 31%
Step-by-step explanation:
You want to know the markdown represented by a sale price of $88.54 on a regular price of $127.99.
MarkdownThe dollar amount of the markdown is ...
88.54 -127.99 = -39.45
The price was marked down $39.45.
The percentage markdown from the original price is ...
-39.45/127.99 × 100% ≈ -30.823% ≈ -31%
The original price was marked down about 31% to get the sale price.
__
Additional comment
The negative price change means the price was marked down. If the change were positive, it would signify a markup.
Equation of the line in the graph is y=? X + ?
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{-6}{3 +3} \implies \cfrac{ -6 }{ 6 } \implies - 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-3)}) \implies y -2 = - 1 ( x +3) \\\\\\ y-2=-x-3\implies {\Large \begin{array}{llll} y=-x-1 \end{array}}[/tex]
Write each expression without the absolute value symbol |14-(x-6)|
To start, we need to recognize that absolute value is a way of expressing the magnitude of a number, regardless of its sign. Thus, to get rid of the absolute value, we need to consider the two cases in which the expression can have either a positive or a negative sign.
For the case of a positive sign, we can simply write the expression as: 14-(x-6)
For the case of a negative sign, we can multiply both sides of the equation by -1 to get: -14 + (x-6)
Overall, we can express the expression without the absolute value symbol as:
14-(x-6) or -14 + (x-6)
I will mark you brainiest!
Alternate interior angles are congruent.
A) False
B) True
Answer:
True.
Step-by-step explanation:
Alternate interior angles are congruent, meaning they have equal measure. When we have two parallel lines that are intersected by a transversal, and again my parallel lines are identified by using the same number of arrows, then two special angles are congruent and that is alternate interior angles.
Calculate the frequency in hertz of electromagnetic radiation that has a wavelength of 585.0 nm. (c = 3.00 X 10⁸ m/s)
The frequency in hertz of electromagnetic radiation which has a wavelength of 585nm is 5.13×10¹⁴ Hz.
The frequency(f) of electromagnetic radiation is related to its wavelength (λ) by the equation : f = c/λ;
Where, c = the speed of light in a vacuum, which is 3.00×10⁸ m/s.
So, to calculate the frequency of radiation with a wavelength of 585.0 nm, we need to convert the wavelength to meters:
⇒ 585.0 nm = 585.0×10⁻⁹ m;
Substituting the value in the above formula,
We get,
⇒ f = c/λ = 3.00×10⁸/(585.0×10⁻⁹)
⇒ 5.13×10¹⁴ Hz.
Therefore, the frequency of electromagnetic radiation is approximately 5.13 × 10¹⁴ Hz.
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Can someone please help with these 4
Answer:
Step-by-step explanation:
1) b (acute is less than 90)
2) a (obtuse: more than 90, less than 180)
3) c
4) c
Answer:
1. NOM, JOK, KOL
2. MOL, NOK, MOJ
3. NOJ, JOL
4. NOL, MOK
Give a reason for your answer to the following question. Assume that all variables represent integers.
If n = 4k + 3, does 8 divide n2 − 1?
Yes, 8 divides n^2 - 1 when n = 4k + 3.
We are given that n = 4k + 3, where k is an integer. We want to determine if 8 divides n^2 - 1, which means we want to know if there exists an integer m such that n^2 - 1 = 8m.
To start, we can rewrite n^2 - 1 as (n + 1)(n - 1). This is a common trick in number theory problems involving divisibility, and it can often help us factorize expressions in a useful way.
Substituting n = 4k + 3, we get:
(n + 1)(n - 1) = (4k + 3 + 1)(4k + 3 - 1) = (4k + 4)(4k + 2)
Now, we want to determine whether 8 divides this expression. In other words, we want to know if there exists an integer m such that:
(4k + 4)(4k + 2) = 8m
We can simplify the left-hand side of this equation by factoring out 4
4(k + 1)(2k + 1) = 8m
Now, we see that 8 divides the left-hand side of the equation, since it is equal to 4 times an even number. Moreover, (k + 1) and (2k + 1) are both integers, so we can conclude that 8 divides n^2 - 1 when n = 4k + 3.
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100 POINTS + BRAINLIEST PLS BE FAST!!
i) Find the mean, median, and mode of the frequency table as follows:
Mean = 6.6Median = 8Mode = 3.ii) The average that justifies the teacher's statement congratulating the class that 'over three quarters were above average' is the average mark of 10, which is 5.
What are the mean, median, and mode?The mean refers to the average or the quotient of the total values divided by the number of items.
The median is the middle value in the data, which occurs with marks 8 for the 13th and 14th students.
The mode is the value that occurs most frequently, which is 3 which occurs 6 times.
Frequency Table:
Mark Frequency Cumulative Frequency
3 6 18 (0 + 3 x 6)
4 3 30 (18 + 4 x 3)
5 1 35 (30 + 5 x 1)
6 2 47 (35 + 6 x 2)
7 0 47 (47 + 7 x 0)
8 5 87 (47 + 8 x 5)
9 5 132 (87 + 9 x 5)
10 4 172 (132 + 10 x 4)
Mean = 6.6 (172/26)
Median = 8
Mode = 3
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HELPPPPPP MEEEEE!!!!!!!
Question 1
What is the proper breakdown of 12x^2? (Make a prime factor tree for 12)
A. 12*x*x
B. 2*6*x*x
C. 2*2*3*x*x
D. 3*4*x
Question 2
What is the proper breakdown of 8x^3 - 12x^2 + 16x is the following:
2*2*2*x*x*x
2*2*3*x*x
2*2*2*2*x
What is the greasy common factor?
A. 2x
B. 4x
C. 4
D. 6
Question 3.
Rewrite 8x^3 -12x^2 + 16x, pulling the greatest common factor (gcf) out. (What is left?)
A. 4x(2x^2 - 3x + 4)
B. 4x (2x^2 + 3x + 4)
C. 4x (2^3 - 3x^2 + 4x)
D. 2x (4x^2 - 6x + 8)
Question 4.
What is the greatest common factor of 6x^2 + 16x + 10?
A. X
B. 2x
C. 6
D. 2
Question 5.
Factor: x^2 - 4x - 32
Remember what two numbers multiply to get -32 and add to get -4?
A. (X+8)(x-4)
B. (X+4)(x-8)
C. (X+8)(x+4)
D. (X+16)(x+2)
1. To break down 12x² into its prime factors,Start dividing 12 by 2, which gives you 6. Then, break 6 by 2, which gives 3. To write 12x² in terms of its prime factors, you simply need to add the x² term, giving you 2 * 2 * 3 * x * x or option C.
What is common factor?A common factor is a number or expression that divides two or more other numbers or expressions without leaving a remainder.
Since 3 is a prime number So the prime factorization of 12 is 2 * 2 * 3.
2. To find the greatest common factor of 8x³ - 12x² + 16x, you can start by factoring out any common factors that the terms share. In this case, all of the terms have a factor of 4x, so you can factor that out to get 4x(2x² - 3x + 4). Therefore, the greatest common factor is 4x or option B.
3. To rewrite 8x³ - 12x² + 16x, pulling out the greatest common factor, you can use the same method as in question 2. The greatest common factor of the terms is 4x, so you can factor that out to get 4x(2x² - 3x + 4) or option A.
4. To find the greatest common factor of 6x²+ 16x + 10, you can factor the expression using the quadratic formula or by factoring the expression as (3x + 5)(2x + 2). Since there is no other common factor between the terms, the greatest common factor is 1 or option A.
5. To factor x² - 4x - 32, you need to find two numbers that multiply to -32 and add to -4. These numbers are -8 and 4. Therefore, x² - 4x - 32 can be factored as (x - 8)(x + 4) or option C.
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algebraically determine the values of x that satisfy the system of equations below
The solutions to the system of equations are (x,y) = (0,1) and (5/2,3)
What is Algebraic Equations?
An algebraic equation is also known as a polynomial equation because both sides of the equal sign contain polynomials. An algebraic equation is built up of variables, coefficients, constants as well as algebraic operations such as addition, subtraction, multiplication, division, exponentiation, etc.
To solve the system of equations algebraically, we can set the two expressions for y equal to each other and solve for x:
[tex]-2x + 1 = -2x^2 + 3x + 1[/tex]
Simplifying, we get:
[tex]-2x^2 + 3x + 1 + 2x - 1 = 0[/tex]
[tex]-2x^2 + 5x = 0[/tex]
Factorizing x, we get:
x(-2x + 5) = 0
Therefore, the solutions for x are:
x = 0 or x = 5/2
To find the corresponding values of y, we can substitute these values of x into either of the original equations for y:
For x = 0:
y = -2(0) + 1 = 1
For x = 5/2:
[tex]y = -2(5/2)^2 + 3(5/2) + 1 = -13/2 + 15/2 + 1 = 3[/tex]
Therefore, the solutions to the system of equations are:
(x,y) = (0,1) and (5/2,3)
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PLEASEEE HELP!
Draw an angle that is 63 degrees.
Step-by-step explanation:
You probably have a graphing tool to do this:
Suppose some computations were done on a calculator.
The result displayed was 7.97E33 for one computation.
The result displayed was 7.6E-37 for another computation.
Write these numbers in scientific notation.
(a) 7.97E33 =
(b) 7.6E-37 =
Answer:
(a) 7.97E33 = 7.97 x 10^33
(b) 7.6E-37 = 7.6 x 10^-37
Step-by-step explanation:
In scientific notation, a number is written as the product of a decimal number between 1 and 10 and a power of 10. The decimal number is called the mantissa, and the power of 10 is called the exponent. The mantissa indicates the significant digits of the number, while the exponent tells us the size of the number relative to 1. In the given calculator computations, the numbers are already written in scientific notation, where "E" represents the exponent notation. We just need to convert them into the standard form of scientific notation by expanding the notation as a product of the mantissa and the power of 10.
Correct answer gets brainliest
Answer:
48 square feet
Step-by-step explanation:
Area of triangle = (1/2) · b · h
(1/2) · 3 · 4 = 6 square feet
There are 2 triangles, so we time 2
6 x 2 = 12 square feet
Area of rectangle = L × W
9 x 4 = 36 square feet
Now we take
12 + 36 = 48 square feet
34 M
The point (-1, 3) is the turning point of the graph with equation y = x² + ax + b₁
where a and b are integers.
Find the values of a and b.
In the equatiοn , the value οf a and b is 2 and 4.
What is equatiοn?A mathematical assertiοn that shοws the equality οf twο mathematical expressiοns is what an equatiοn in algebra is defined as. Fοr example, the equatiοn 3x + 5 = 14 is cοmpοsed οf the twο equatiοns 3x + 5 and 14, which are separated by the equal sign.
The equatiοn οf a parabοla in standard fοrm is
y = a(x - h)² + k
where (h, k) are the cοοrdinates οf the vertex and a is the cοefficient οf the x² term.
Here (h, k ) = (- 1, 3 ) and cοefficient οf x² term = 1 , then
=> y = (x - (- 1))² + 3 ,
=> y = (x + 1)² + 3
=> y = x² + 2x + 1 + 3
=> y = x² + 2x + 4
Nοw cοmpare tο y = x² + ax + b
Consequently, a = 2 and b = 4.
Thus, a and b have values of 2 and 4, respectively.
Tο learn more abοut equation refer the below link
https://brainly.com/question/29538993
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60. A triangle ABD, is reflected across the line y = x to
have the image A’ B’ D’ in the standard (x, y) coordinate
plane: thus A reflects to A'. The coordinates of point A
are (m, n). What are the coordinates of point A
F. (-m.n)
G. (m. -n)
H. (-m. -n)
J. (n, m)
K.Cannot be determined from the given information.
Answer:
Step-by-step explanation:
The line y = x is the line of symmetry in the reflection, which means that the x-coordinate and y-coordinate of each point get swapped. Therefore, the x-coordinate of A becomes its y-coordinate in its reflection A', and the y-coordinate of A becomes its x-coordinate in A'. Thus, the coordinates of A' are (n, m).
Therefore, the correct answer is J. (n, m).
find the value of the indicated ratio
Check the picture below.
[tex]\cot(\gamma )=\cfrac{\stackrel{adjacent}{24}}{\underset{opposite}{18}}\implies \cot(\gamma )= \cfrac{4}{3}[/tex]