3. The points (4, -1), (8, -3), and (12, -5) are
collinear. Write an equation in slope-intercept form.

f(0) means the function output when the input is x = 0. This is the same as saying the y value when x = 0.

f(x) = 3-2x

f(0) = 3-2(0)

f(0) = 3

The point (0,3) is on the graph. This is the y intercept which is where the graph crosses the y axis. The y intercept always occurs when x = 0.

So in other words, the special name for f(0) is the y intercept.

f(0) = 3 and the special name for f(0) is the y  - intercept of the function.

We have a function f(x) = 3 - 2x

We have to determine f(0) and investigate about the special name of f(0).

The Slope - intercept form of the equation of a straight line is as follows -

y = mx + c

where -

m - slope of line.

c - intercept of line on y - axis.

According to the question, we have -

f(x) = 3 - 2x

Now -

f(0) = 3 - 2 x 0 = 3

Now, re-write the function as follows -

f(x) = -2x + 3

Compare it with Slope - intercept form of the equation of a straight line, we get -

m = -2

c = 3

and

f(0) = 3 = c

Hence, f(0) = 3 and the special name for f(0) is the y  - intercept of the function.

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Answer:

Write 45 percent as 9 ´ 5 percent, and write 5 percent as . Then, find of 75: . Multiply 3.75 by 9 to get 33.75. So, 45 percent of 75 is 33.75

The value of 45 percent of 75 is 33.75 and this can be determined by using the unitary method and the given data.

Given :

Number  ---  75

The following steps can be used in order to determine the 45 percent of 75:

Step 1 - The unitary method can be used in order to determine the 45 percent of 75.

Step 2 - According to the given data, the given number is 75 which is 100%.

Step 3 - So, if 100% is 75 then the value of 45% is:

\(=\dfrac{45}{100}\times 75\)

Step 4 - Simplify the above expression.

= 33.75

Therefore, the correct option is A).

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Answer:

800÷2=400

Step-by-step explanation:

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Answer:

400

Step-by-step explanation:

Because 400+400=800

So 800/2 would be 400

The graph of y is vertically compressed by an factor of √8 which is the transformation of the function.

The important technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of the various algebraic equations which is a particular  kind of algebraic problem.

The base or parent function is y=√8x³+1.

Here the transformed function is y= x³+1.

Therefore the graph is vertically transformed by the factor of √8 .

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Answer:

(A∩B)' = A'∪B'

Step-by-step explanation:

U is the universal set

A and B are two subsets of U

let A' be the complement subset of A

and  B' be the complement subset of B

U = {-10,-9,…,-1,0,1,…,9,10}

A = {-1,0,1}

B = {1,2,…,9,10}

Then

A∩B = {1}

Then

the complement of A∩B :

(A∩B)' = {-10,-9,…,-1,0,2,…,9,10}

(notice the absence of 1)

On the other hand,

A' = {-10,…,-2}∪{2,…,10}

B' = {-10,…,0}

Then

A'∪B' = {-10,-9,…,-1,0}∪{2,…,10}

         =  {-10,-9,…,-1,0,2,…,9,10}

Conclusion:

(A∩B)' = A'∪B'

Answer:

55 i believe

28 + 27 = 55

Answer:

a = 7.4

Step-by-step explanation:

Since this is a right triangle, we will use the Pythagorean theorem:

c^2 = a^2 + b^2

28^2 = a^2 + 27^2

784 = a^2 + 729

55 = a^2

a = 7.4

The bird flies at an angle of 60° degrees from the water, and its height from the ground when it drops the fish is 86.6 yards.

The bird caught the fish at point, flew to which is 100 yds away, and dropped the fish at C, which is horizontally 50 yards from A.

Now,
let the angle be x,
cosx = 50 / 100
x = cos⁻¹(1/2)
x = 60°

height of the bird is given as,
sin60 = height / 100
√3 / 2 = height / 100
height = 50√3 = 86.6

Thus, the bird flies at an angle of 60 °degrees from the water, and its height from the ground when it drops the fish is 86.6 yards.

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(a) The marginal pmf of X: fX(1) = 9/32, fX(2) = 11/32

(b) The marginal pmf of Y: fY(1) = 7/64, fY(2) = 9/64, fY(3) = 11/64 fY(4) = 13/64

(c) P(X > Y) = 11/32

(d) P(Y = 2X) = 1/16

(e) P(X + Y = 3) = 1/8

(f) P(X ≤ 3 - Y) = 11/64

(g) X and Y are dependent.

(h) Mean of X (μX) = 41/32, Mean of Y (μY) = 205/64, Variance of X (σX²) = 113/1024 and Variance of Y (σY²) = 8199/8192

(a) To find fX(x), the marginal pmf of X, we sum the joint probabilities for each value of x:

fX(1) = f(1,1) + f(1,2) + f(1,3) + f(1,4) = 3 + 4 + 5 + 6 = 18

fX(2) = f(2,1) + f(2,2) + f(2,3) + f(2,4) = 4 + 5 + 6 + 7 = 22

Therefore, the marginal pmf of X is:

fX(1) = 18/64 = 9/32

fX(2) = 22/64 = 11/32

(b) To find fY(y), the marginal pmf of Y, we sum the joint probabilities for each value of y:

fY(1) = f(1,1) + f(2,1) = 3 + 4 = 7

fY(2) = f(1,2) + f(2,2) = 4 + 5 = 9

fY(3) = f(1,3) + f(2,3) = 5 + 6 = 11

fY(4) = f(1,4) + f(2,4) = 6 + 7 = 13

Therefore, the marginal pmf of Y is:

fY(1) = 7/64, fY(2) = 9/64, fY(3) = 11/64, fY(4) = 13/64

(c) P(X > Y) can be found by summing the joint probabilities where X is greater than Y:

P(X > Y) = f(2,1) + f(2,2) + f(2,3) + f(2,4) = 4 + 5 + 6 + 7 = 22/64 = 11/32

(d) P(Y = 2X) can be found by summing the joint probabilities where Y is twice the value of X:

P(Y = 2X) = f(1,2) = 4/64 = 1/16

(e) P(X + Y = 3) can be found by summing the joint probabilities where X + Y equals 3:

P(X + Y = 3) = f(1,2) + f(2,1) = 4 + 4 = 8/64 = 1/8

(f) P(X ≤ 3 - Y) can be found by summing the joint probabilities where X is less than or equal to 3 - Y:

P(X ≤ 3 - Y) = f(1,1) + f(1,2) + f(2,1) = 3 + 4 + 4 = 11/64

(g) To determine if X and Y are independent or dependent, we compare the joint pmf with the product of the marginal pmfs:

f(x,y) = 32x+y

fX(x) × fY(y) = (9/32) × (7/64) = 63/2048

Since f(x,y) is not equal to fX(x)× fY(y), X and Y are dependent.

(h) To find the means and variances of X and Y, we use the formulas:

Mean of X (μX) = ∑(x × fX(x))

Mean of Y (μY) = ∑(y×fY(y))

Variance of X (σX²) = ∑((x - μX)² * fX(x))

Variance of Y (σY²) = ∑((y - μY)² × fY(y))

Calculating the means:

μX = (1 × (9/32)) + (2 × (11/32)) = 41/32

μY = (1 × (7/64)) + (2× (9/64)) + (3 × (11/64)) + (4 × (13/64)) = 205/64

Calculating the variances:

σX²= ((1 - 41/32)² × (9/32)) + ((2 - 41/32)² × (11/32)) = 113/1024

σY² = ((1 - 205/64)²× (7/64)) + ((2 - 205/64)²× (9/64)) + ((3 - 205/64)² × (11/64)) + ((4 - 205/64)² × (13/64)) = 8199/8192

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Answer:

the answer is -18

Step-by-step explanation:

-6 × 3

= - (6 × 3)

= -18

______

Hope it helps ⚜

The material needed to make the tent assumes the shape of a triangular prism and the surface area of the material needed is 193.18 ft².

A triangular prism is indeed a three-sided prism made up of a triangle base, a translational copy, and triple faces connecting equivalent sides in geometry.

The properties of a triangular prism include:

Let's assume that the shape of the canvas tents is in form of a triangular prism, to determine the material needed to make the tent, we need to understand the surface area of a triangular prism.

However, let's assume that:

From the image attached below: the surface area of the triangular prism can be calculated by using the following  formula:

\(\mathbf{A = 2A_B +(a+b+c)h }\)

\(\mathbf{A_B = \sqrt{s(s-a)(s-b)(s-c)}}\)

\(\mathbf{s = \dfrac{a+b+c}{2}}\)

Combining the formulas together the surface area of the triangular prism can be computed as:
\(\mathbf{S.A = ah+bh+ch+\dfrac{1}{2} \sqrt{ -a^4+2(ab)^2+2(ac)^2-b^4 +2(bc)^2-c^4}}\)

\(\mathbf{S.A = (6\times9)+(6\times9)+(6\times9)+\dfrac{1}{2} \sqrt{ -6^4+2(6 \times 6)^2+2(6 \times 6)^2-6^4 +2(6 \times 6)^2-6^4}}\)

S.A = 193.18 ft²

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The area of a square is 14 times larger than the area of a triangle, so the length of a side of the square is 49 inches. The area of the triangle is 1/2  base  height, while the area of the square is 14 times larger.

Given, The area of a square is 14 times as large as the area of a triangle One side of the triangle is 7 inches long, and the altitude to that side is the same length as a side of the square. We need to find the length of a side of the square. Area of the triangle = 1/2 × base × height We know the base = 7 in and the height is equal to the side of the square. Let's say the side of the square is x. Area of the triangle = 1/2 × 7 in × x in = 7x/2 in²Area of the square = x²Given, the area of a square is 14 times as large as the area of a triangle.=> x² = 14(7x/2) in²=> x² = 49x in²=> x = 49 in Therefore, the length of a side of the square is 49 inches.

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Answer:

surface area of cone= πr²+πrl

151.58=3.14×4×4+3.14×4×l

151.58=50.24+12.56×l

151.58=62.8×l

62.8 62.8

l= 2.414

The slant height of the cone is approximately 8 inches when the surface area is about 151.58 in², and the radius of the base is 4 inches.

The formula for surface area of cone:

Surface Area = πr(r + l)

Given that the surface area is 151.58 in².

Radius (r) is 4 inches.

Substitute these values into the formula and solve for the slant height:

\(151.58 = 3.14 \times 4(4 + l)\)

\(151.58 = 12.56 \times (4 + l)\)

\(151.58=50.24+12.56l\)

Substitute 50.24 from both sides:

\(151.58-50.24 = 12.56l\)

\(101.34= 12.56l\)

Divide both sides by 12.56:

\(l=8.07\)

Slant height = 8 inches.

Hence, the slant height is 8 inches.

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Answer: The numbers are 5, 8, and 9

Step-by-step explanation:

x+y+z=22

y=x+3

z=2x-1

After you have those three equations, you can plug the y and z value into the first equation.

You get x+x+3+2x-1=22, so 4x+2=22

Therefore, 4x=20, so x=5

If x=8, then y=5+3, so y=8

Also, z=2(5)-1, so z=9

B, C, E and F are true statements.

A and D aren't.

Answer:

3 ➡ 12

5 ➡ 16

7 ➡ 20

9 ➡ 24

Step-by-step explanation:

Replace c, in b = 2c + 6, with each number in the c column to find that number's b counterpart.

For example: For the first one, you'd replace c with 3, so it would look like

b = 2(3) + 6, now just multiply 2 and 3 to get 6, and then add the other 6 to get 12. Keep doing this for the rest of the numbers.

I hope this helps ya out friend :)

The coordinate point of f(x + 1) will shift 1 unit to the left along the x-axis.

(x , y) ⇒ (x - 1, y).

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Let, y = f(x) = 3x.

Now, After the transformation f(x + 1) = g(x),

g(x) = 3(x + 1).

This is a horizontal transformation by 1 unit to the left.

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well, we know it's a regular polygon of 5 sides, namely a regular PENTAgon, and since we know one side's length, the perimeter is simply that much 5 times, namely

\(\begin{array}{ccllll} &2x^3-5x+3\\ &2x^3-5x+3\\ &2x^3-5x+3\\ &2x^3-5x+3\\ +&2x^3-5x+3\\\cline{1-2} &\underset{\textit{\LARGE Perimeter}}{10x^3-25x+15} \end{array}\)

Answer:

0

Step-by-step explanation:

Answer:

4/5=bc/8

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Edge 2021

Goodluck Everyone!

Answer:

D none of the above edge 2022

Step-by-step explanation:

Answer:

9 cm

Step-by-step explanation:

Total surface area of a cube =486 cm²

 We know that the surface area of the cube

=6l²

 Therefore,

6l ² =486

l² =81

l =9 cm

The required percentage of students who live on campus who do not have a part-time job is 24.5%.

Given that,
At a local college, only 30% of students live off campus. Of those who live off campus, 62% of those students get a part-time job. Of those who live on campus, 65% work part-time.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Number of students that life in the campus = 100% - 30% = 70%
Number of students that do not have job part-time and line in  campus,
= 70% - 65%×70%
= 70% - 0.65 × 70%

= 70% - 45.5%
= 24.5%

Thus, the required percentage of students who live on campus who do not have a part-time job is 24.5%.

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The amplitude of the graph of a sine function is 2.

Given is sinusoidal function, we need to find the amplitude of the function.

We know,

The amplitude of the graph of a sine function is the vertical distance from the top of a peak to the center line.

This is the same as the vertical distance from the top of a peak to the lowest point on the graph, divided by 2.

The vertical distance = 8

Amplitude = 8

Hence the amplitude of the graph of a sine function is 2.

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Answer:

Value of equation = 74

Step-by-step explanation:

Given:

-26x - y

And

x = -3

y = 4

Find:

Value of equation

Computation:

-26x - y

By putting value

-26(-3) - 4

78 - 4

74

Value of equation = 74

Answer:

- 6

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ - 1, 4 ] , then

f(b) = f(4) = 4³ - 6(4)² - 4 = 64 - 96 - 4 = - 36

f(a) = f(- 1) = (- 1)³ - 6(- 1)² - (- 1) = - 1 - 6 + 1 = - 6 , then

average rate of change = \(\frac{-36-(-6)}{4-(-1)}\) = \(\frac{-36+6}{4+1}\) = \(\frac{-30}{5}\) = - 6

Answer:

5.43 × 10⁶

Step-by-step explanation:

i hope this helps

Answer:

the length and width be 15 meters and 7 meters respectively

Step-by-step explanation:

The computation of the dimension of the field is given below;

Let us assume the fencing be p

Length be x

And, the width be x - 8

So,

P = 44

P = x - 8 + x - 8 + x + x

= 4x - 16

Now

4x - 16 = 44

4x = 44 + 16

4x = 60

x = 15

And, the width be 15 - 8 = 7

So, the length and width be 15 meters and 7 meters respectively

Answer:

2/7

Step-by-step explanation:

Assuming the table is

x         y

2          6

9           8

We have points ( 2,6) and (9,8)

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 8-6)/(9-2)

   = 2/7