Evaluate the expression 3.14(a2 + ab) when a = 3 and b = 4. (Input decimals only, such as 12.71, as the answer.) (4 points)

The height of the isosceles triangle is approximately 9.70 meters.

To find the height (y) of an isosceles triangle given its slant height and two angles, we can use trigonometry. Here are the steps to solve this problem:

Start by drawing a sketch of the isosceles triangle. Label the base as "b," the height as "y," and the slant height as "s."

Since the triangle is isosceles, the two base angles are congruent, meaning each angle measures 57 degrees. Label one of these angles as "θ."

We know that the slant height (s) is given as 11.5 m.

Apply the sine function to relate the slant height (s) to the angle (θ) and the height (y) of the triangle. The sine of an angle is defined as the ratio of the opposite side (y) to the hypotenuse (s). So, we have sin(θ) = y/s.

Substitute the given values into the equation: sin(57 degrees) = y/11.5.

Solve the equation for y by multiplying both sides by 11.5: y = 11.5 * sin(57 degrees).

Use a calculator to find the value of sin(57 degrees) and multiply it by 11.5 to obtain the height (y) of the triangle.

Performing the calculation, y = 11.5 * sin(57 degrees) ≈ 9.70 meters (rounded to two decimal places).

Therefore, the height of the isosceles triangle is approximately 9.70 meters.

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One of the transformations undergone by Triangle 1 is a rotation, which involves turning the triangle around a fixed point while preserving its shape and size.

A rotation is a transformation that turns an object around a fixed point, known as the center of rotation. In the given results, if the triangle appears in a different orientation but retains its shape and size, it indicates a rotation.

During a rotation, each point of the triangle is moved along a circular path around the center of rotation. The distance from the center of rotation remains constant, and the angle between any two corresponding points on the original and rotated triangles is preserved. The direction of rotation can be clockwise or counterclockwise, depending on the given results.

To describe a rotation, we need to specify the angle of rotation and the direction. For example, "Triangle 1 underwent a counterclockwise rotation of 90 degrees" would indicate that the triangle was rotated by 90 degrees in the counterclockwise direction.

The specific rotation can be described by stating the angle of rotation and the direction.

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The interval notation (-3, 4) represents the set of real numbers r that are greater than -3 and less than 4, excluding -3 and 4.

The set builder notation {r | -3 < r < 4} can be expressed in interval notation as (-3, 4).

In interval notation, the parentheses indicate that the endpoints, -3 and 4, are not included in the set.

The interval (-3, 4) represents all the real numbers r that are greater than -3 and less than 4, but not including -3 and 4.

It can also be visualized on a number line as an open interval between -3 and 4, where the endpoints are not filled in.

The interval (-3, 4) can be interpreted as a range of values for r. Any real number between -3 and 4, excluding the endpoints, would satisfy the given set builder notations.

For example, -2, 0, and 3 are all included in the interval (-3, 4), but -3 and 4 themselves are not part of the set.

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Answer:

Step-by-step explanation:

Answer:

math = 227.98

programming = 42.55

Step-by-step explanation:

Answer:

math = 227.98

programming = 42.55

Step-by-step explanation:

We have
3m + 4p = 854.14 -eq(1)

8m + 1p = 1866.39 -eq(2)

rq(2) x 4: 32m + 4p = 7465.56 -eq(3)

eq(3)-eq(1):

32m + 4p = 7465.56

- ( 3m + 4p = 854.14)

--------------------------------

29m = 6611.42

--------------------------------

⇒ m = 6611.42/29

m = 227.98

sub in eq(1)

3(227.98) + 4p = 854.14

4p = 854.14 - 683.94

4p = 170.2

p = 170.2/4

p = 42.55

Answer:

be more clear of what u mean edit the question so we can tell what u mean and answer correctly

Step-by-step explanation:

no explanation

The rates of change of the two functions that compare correctly is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.

To compare the rates of change of the two functions, we can calculate the slope of each function. The slope represents the rate of change of a linear function.

For Function A, the equation is y = 6x - 1. The coefficient of x, which is 6, represents the slope. The rate of change of Function A is 6.

For Function B, we are given three points: (13, 0), (4, 10), and (6, 15). We can calculate the slope using the formula: slope = (change in y) / (change in x). Taking the first two points, we have: slope = (10 - 0) / (4 - 13) = 10 / (-9) = -10/9.

Comparing the rates of change, we have:

A. The rate of change of function A is 6.

The rate of change of function B is -10/9.

The correct option is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.

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The length of line segment IG of the circle using the chord-chord power theorem is 6.

Chord-chord power theorem simply state that "If two chords of a circle intersect, then the product of the measures of the parts of one chord is equal or the same as the product of the measures of the parts of the other chord".

From the figure:

Line segment FG = 12

Line segment GH = 4

Line segment GJ = 8

Line segment IG = ?

Now, usig the chord-chord power theorem:

Line segment FG × Line segment GH = Line segment GJ × Line segment IG

Plug in the values:

12 × 4 = 8 × Line segment IG

48 = 8 × Line segment IG

Line segment IG = 48/8

Line segment IG = 6

Therefore, the line segment IG measures 6 units.

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Para representar gráficamente los vectores 2u, -3v y 1/4, necesitamos utilizar los vectores dados A(-1,3), B(-2,4), C(0,-2) y D(8,1).

Vector 2u:

El vector 2u se obtiene al multiplicar el vector u por 2. Si conocemos las coordenadas de u, podríamos multiplicar cada componente por 2. Sin embargo, no se proporciona información sobre las coordenadas de u, por lo que no podemos realizar este cálculo específico.

Vector -3v:

Similar al caso anterior, para obtener el vector -3v, debemos multiplicar el vector v por -3. Sin información sobre las coordenadas de v, no podemos realizar este cálculo específico.

Vector 1/4:

El vector 1/4 se obtiene al multiplicar cada componente de los vectores A, B, C y D por 1/4. Podemos calcular las nuevas coordenadas de estos vectores:A' = (-1/4, 3/4)

B' = (-1/2, 1)

C' = (0, -1/2)

D' = (2, 1/4)

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The cube root of 30 would be between 3 and 4, but closer to 3.

Cube root is the number that needs to be multiplied three times to get the original number.

The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:

Step 1: Start with the prime factorization of the given number.

Step 2: Then, divide the factors obtained into groups containing three same factors.

Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect cube and we cannot find the cube root of that number.

We have to find the cube root of 30.

Prime factorization of 30 = [tex]2\times3\times5[/tex].

Therefore the cube root of 30 = [tex]\sqrt[3]{ (2\times3\times5)}= \sqrt[3]{30}[/tex].

As [tex]\sqrt[3]{30}[/tex] cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.

So here we will use approximation method to find the cube root of 30 using Halley's approach:

Halley’s Cube Root Formula:

[tex]{\sqrt[3]{\text{a}} = \dfrac{\text{x}[(\text{x}^3 + 2\text{a})}{(2\text{x}^3 + \text{a})]}}[/tex]

The letter “a” stands in for the required cube root computation.

Take the cube root of the nearest perfect cube, “x” to obtain the estimated value.

Here we have a = 30

and we will substitute x = 3 because 3³ = 27 < 30 is the nearest perfect cube.

Substituting a and x in Halley's formula,

[tex]\sqrt[3]{30} = \dfrac{3[(3^3 + 2\times30)}{(2\times3^3 + 30)]}[/tex]

      [tex]= \dfrac{3[(27+60)}{(54+30)]}[/tex]

      [tex]= 3\huge \text(\dfrac{87}{84} \huge \text)[/tex]

      [tex]= 3\times1.0357[/tex]

[tex]\bold{\sqrt[3]{30} = 3.107}[/tex].

Hence, the cube root of 30 is 3.107.

Therefore, we can conclude that the cube root of 30 would be between 3 and 4, but closer to 3.

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Complete question:

Describe in words where cube root of 30 would be plotted on a number line.

A. Between 3 and 4, but closer to 3

B. Between 3 and 4, but closer to 4

C. Between 2 and 3, but closer to 2

D. Between 2 and 3, but closer to 3

The calculated value of x in the triangle is 15

From the question, we have the following parameters that can be used in our computation:

The triangles ABC and EDC

Since the triangles are similar, then we have

(3x - 5)/(5x - 5) = 32/56

This gives

32(5x - 5) = 56(3x - 5)

When solved for x, we have

x = 15

Hence, the value of x is 15

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Answer:

[tex] \sqrt{9} \sqrt{9} = 9[/tex]

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Given the equation f(x) = a · bx where a and b are constants. So, the answer to the given problem is g(x) = a · bx + h, and the explanation of the trigonometric function.

To find the equation of transformed function g in terms of function f is explained below: If f(x) = a · bx, then the transformed function g(x) can be represented by g(x) = a · bx + h, where h is the vertical shift (if h > 0, the graph shifts upward, and if h < 0, the graph shifts downward).

Now, we have to replace the value of 'a' to complete the equation of g(x). But, we don't have any value of 'a' provided in the question. Hence, we can't determine the equation of transformed function g in terms of function f for the given information.

Next, let's move to the trigonometric function. It is given that: R S 9 sin cos tan sin cos tan-¹ /ASin, Cos, Tan, Cosec, Sec, and Cot are six trigonometric functions. Let's see their definitions and their corresponding inverse functions:

1. Sine: It is defined as the ratio of the length of the side opposite the given angle to the length of the hypotenuse in a right-angled triangle. Its corresponding inverse function is sin⁻¹.

2. Cosine: It is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. Its corresponding inverse function is cos⁻¹.

3. Tangent: It is defined as the ratio of the length of the side opposite the given angle to the length of the adjacent side in a right-angled triangle. Its corresponding inverse function is tan⁻¹.

4. Cosecant: It is defined as the ratio of the length of the hypotenuse to the length of the side opposite the given angle in a right-angled triangle. Its corresponding inverse function is cosec⁻¹.

5. Secant: It is defined as the ratio of the length of the hypotenuse to the length of the adjacent side in a right-angled triangle. Its corresponding inverse function is sec⁻¹.

6. Cotangent: It is defined as the ratio of the length of the adjacent side to the length of the side opposite the given angle in a right-angled triangle. Its corresponding inverse function is cot⁻¹.

Hence, the answer to the given problem is g(x) = a · bx + h, and the explanation of the trigonometric function.

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The correct representation for the joint probability of two dependent events Y and Z is P(Y) * P(Z|Y). Option E

The joint probability of two dependent events Y and Z can be written as the probability of Y occurring multiplied by the conditional probability of Z given Y. This can be represented as P(Y) * P(Z|Y).

Here's the justification:

P(Y) represents the probability of event Y occurring independently.

P(Z|Y) represents the conditional probability of event Z occurring given that event Y has already occurred.

When Y and Z are dependent events, the occurrence of Y affects the probability of Z happening. Therefore, we need to consider the probability of Y occurring first (P(Y)) and then the probability of Z occurring given that Y has already occurred (P(Z|Y)).

Multiplying these two probabilities together gives us the joint probability of both Y and Z occurring simultaneously, which is denoted as P(Y and Z).

Hence, the correct representation for the joint probability of two dependent events Y and Z is P(Y) * P(Z|Y). Option E.

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Answer: substitute the given number for the variable in the expression and then simplify the expression using the order of operations

Step-by-step explanation:3a2 - 4b2 for a = -3/4 and b = 1/2

Answer:

f^(-1)(x) = ±√(x - 5).

Step-by-step explanation:

Replace f(x) with y: y = x^2 + 5.

Swap the x and y variables: x = y^2 + 5.

Solve the equation for y. To do this, we'll rearrange the equation:

x - 5 = y^2.

Take the square root of both sides (considering both positive and negative square roots):

±√(x - 5) = y.

Swap y and x again to express the inverse function:

f^(-1)(x) = ±√(x - 5).

Answer:

Step-by-step explanation:

0

Answer:

0

Step-by-step explanation:

25 ÷ 5+7-(4 x 3)

25 ÷ 5+7-(4 x 3)

5+7-(4 x 3)

5+7-(4 x 3)

5+7-12

12-12

0

I wrote in bold the steps you need to follow using PEMDAS (Parentheses, Exponents, Multiplication and Divison left to right, and Addition and Subtraction left to right).

The calculated vertex of the function y = 2(x + 4)(x - 2) is (-1, -18)

From the question, we have the following parameters that can be used in our computation:

y = 2(x + 4)(x - 2)

Expand the equation

So, we have

y = 2x² + 4x - 16

Differentiate the function and set to 0

So, we have

4x + 4 = 0

So, we have

4x = -4

Evaluate

x = -1

Next, we have

y = 2(-1 + 4)(-1 - 2)

Evaluate

y = -18

This means that the vertex is (-1, -18)

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a. Mean = 3

Standard deviation = 2

b. The z-scores for each score in the sample are: 1, -1.5, 0.5, 1, -1, -0.5, 0.5.

a. To compute the mean and standard deviation for the sample, we follow these steps:

Calculate the mean (average)

Mean = (sum of all scores) / (number of scores)

Mean = (5 + 0 + 4 + 5 + 1 + 2 + 4) / 7

Mean = 21 / 7

Mean = 3

The mean of the sample is 3.

Calculate the standard deviation

The formula for standard deviation for a sample is given by:

Standard deviation = sqrt((sum of squared differences from the mean) / (number of scores - 1))

First, calculate the squared differences from the mean for each score:

(5 - 3)^2 = 4

(0 - 3)^2 = 9

(4 - 3)^2 = 1

(5 - 3)^2 = 4

(1 - 3)^2 = 4

(2 - 3)^2 = 1

(4 - 3)^2 = 1

Next, sum up these squared differences:

4 + 9 + 1 + 4 + 4 + 1 + 1 = 24

Now, divide this sum by (number of scores - 1):

24 / (7 - 1) = 24 / 6 = 4

Finally, take the square root of this result:

Standard deviation = sqrt(4) = 2

The standard deviation of the sample is 2.

b. To find the z-score for each score in the sample, we use the formula:

z = (X - Mean) / Standard deviation

For each score, we substitute the values into the formula:

X = 5, z = (5 - 3) / 2 = 2 / 2 = 1

X = 0, z = (0 - 3) / 2 = -3 / 2 = -1.5

X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5

X = 5, z = (5 - 3) / 2 = 2 / 2 = 1

X = 1, z = (1 - 3) / 2 = -2 / 2 = -1

X = 2, z = (2 - 3) / 2 = -1 / 2 = -0.5

X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5

The z-scores for each score in the sample are:

z = 1, z = -1.5, z = 0.5, z = 1, z = -1, z = -0.5, z = 0.5

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The correct answer is option (a): Var(X) = E(X^2) - (E(X))^2.

The variance of a random variable X is defined as the average of the squared differences between each value of X and its expected value (E(X)). Mathematically, it can be expressed as Var(X) = E((X - E(X))^2).

Expanding the squared term, we have Var(X) = E(X^2 - 2XE(X) + (E(X))^2). Distributing and rearranging, we get Var(X) = E(X^2) - 2E(X)E(X) + (E(X))^2. Simplifying, we obtain Var(X) = E(X^2) - (E(X))^2.

Answer:

Below, rises, more, 2, 5

Step-by-step explanation:

Its an positive exponential growth function which means it increases sharply to the right it also is above the x-axis.

The graph is 2 times the graph of 5^x so its steeper or rises more

Plug in 0 to get 1*2=2

Plug in 1 to get 5*1=5

Answer:

a. 16

c. 120°

e. 60°

Step-by-step explanation:

Properties of Parallelogram:

For Question:

a.

DC= AB=16 Opposite side is congruent.

c.

m ∡DCB = m ∡DAB=120° Opposite angles are congruent.

e.

m ∡ABC= ​?

m ∡ABC+ m∡DAB =180° Consecutive angles are supplementary.

Substituting value

m ∡ABC + 120°=180°

m ∡ABC =180°-120°=60°

m ∡ABC=60°

Answer:

a)  DC = 16

c)  m∠DCB = 120°

e)  m∠ABC = 60°

Step-by-step explanation:

The opposite sides of a parallelogram are equal in length. Therefore, DC is the same length as AB.

As AB = 16, then DC = 16.

[tex]\hrulefill[/tex]

The opposite angles of a parallelogram are equal in measure. Therefore, m∠DCB is equal to m∠DAB.

As m∠DAB = 120°, then m∠DCB = 120°.

[tex]\hrulefill[/tex]

Adjacent angles of a parallelogram sum to 180°. Therefore:

⇒ m∠ABC + m∠DAB = 180°

⇒ m∠ABC + 120° = 180°

⇒ m∠ABC + 120° - 120° = 180° - 120°

⇒ m∠ABC = 60°

Answer:

Step-by-step explanation:

Let the centre be C.

Since TR is a straight line,  

∠SCT + ∠SCR = 180

∠SCT = 180 - 53

∠SCT = 127

The angle of a semicircle is 180°. Minor arcs are arcs less than a semicircle i.e. less than 180° and major arcs are arcs greator than a semicircle i.e. greater than 180°.

a) arc(SPT) has measure of 90 + 65 + 25 + 53 = 233° > 180° and hence a major arc

Also 1° = π/180 radians

233° = 233 * π/180 = 1.29π radians

b) arc(ST) has measure of 127° < 180° and hence a minor arc

127° = 127 * π/180 = 0.71π radians

c) arc(RST) has a measure of  53 + 127 = 180° which is a semicircle

180° = 180* π/180 = π radians

d) arc(SP) has a measure of 53 + 25 + 65 = 143° < 180° and hence a minor arc

143° = 143* π/180 = 0.79π radians

e) arc(QST) has a measure of 25 + 53 + 127 = 205° > 180° and hence a major arc

205° = 205 * π/180 = 1.14π radians

f) arc(TQ) has a measure of 90 + 65 = 155° < 180° and hence a minor arc

155° = 155 * π/180 = 0.86π radians

Answer:

[tex]\text{a.} \quad \text{Major arc}:\;\;\overset{\frown}{SPT}=233^{\circ}[/tex]

[tex]\text{b.} \quad \text{Minor arc}:\;\;\overset{\frown}{ST}=127^{\circ}[/tex]

[tex]\text{c.} \quad \text{Semicircle}:\;\;\overset{\frown}{RST}=180^{\circ}[/tex]

[tex]\text{d.} \quad \text{Minor arc}:\;\;\overset{\frown}{SP}=143^{\circ}[/tex]

[tex]\text{e.} \quad \text{Major arc}:\;\;\overset{\frown}{QST}=205^{\circ}[/tex]

[tex]\text{F.} \quad \text{Minor arc}:\;\;\overset{\frown}{TQ}=155^{\circ}[/tex]

Step-by-step explanation:

A major arc is an arc in a circle that measures more than 180°.

It is named with three letters: two endpoints and a third point on the arc.

A minor arc is an arc in a circle that measures less than 180°.

It is named with two letters: its two endpoints.

A semicircle is a special case of an arc that measures exactly 180°.  

The endpoints of the semicircle are located on the diameter, and the semicircle divides the circle into two equal parts.

The measure of an arc of a circle is equal to the measure of its corresponding central angle.

[tex]\hrulefill[/tex]

a)  Arc SPT is a major arc since it is named with three letters.

It begins at point S, passes through point P, and ends at point T.

    [tex]\begin{aligned}\overset{\frown}{SPT}&=\overset{\frown}{SR}+\overset{\frown}{RQ}+\overset{\frown}{QP}+\overset{\frown}{PT}\\&=53^{\circ}+25^{\circ}+65^{\circ}+90^{\circ}\\&=233^{\circ}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

b)  Arc ST is a minor arc since it is named with two letters.

It is measured in a counterclockwise direction from point S to point T.

    [tex]\begin{aligned}\overset{\frown}{ST}&=360^{\circ}-\overset{\frown}{SPT}\\&=360^{\circ}-233^{\circ}\\&=127^{\circ}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

c)  Arc RST is a semicircle.

Arc RST is a semicircle since its endpoints are located on the diameter of the circle, RT.

    [tex]\overset{\frown}{RST}=180^{\circ}[/tex]

[tex]\hrulefill[/tex]

d)  Arc SP is a minor arc since it is named with two letters.

It is measured in a clockwise direction from point S to point P.

(If it was measured in a counterclockwise direction, it would be a major arc, as it would be more than 180°, and therefore would be named using three letters).

    [tex]\begin{aligned}\overset{\frown}{SP}&=\overset{\frown}{SR}+\overset{\frown}{RQ}+\overset{\frown}{QP}\\&=53^{\circ}+25^{\circ}+65^{\circ}\\&=143^{\circ}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

e)  Arc QST is a major arc since it is named with three letters.

It begins at point Q, passes through point S, and ends at point T.

    [tex]\begin{aligned}\overset{\frown}{QST}&=\overset{\frown}{QR}+\overset{\frown}{RS}+\overset{\frown}{ST}\\&=25^{\circ}+53^{\circ}+127^{\circ}\\&=205^{\circ}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

f)  Arc TQ is a minor arc since it is named with two letters.

It is measured in a counterclockwise direction from point T to point Q.

(If it was measured in a clockwise direction, it would be a major arc, as it would be more than 180°, and therefore would be named using three letters).

    [tex]\begin{aligned}\overset{\frown}{TQ}&=\overset{\frown}{TP}+\overset{\frown}{PQ}\\&=90^{\circ}+65^{\circ}\\&=155^{\circ}\end{aligned}[/tex]

Consider functions fand g below g(x)=-x^2+2x+4 is option D.As x approaches infinity, the value of f(x) decreases and the value of g(x) increases.

The limit of a function, as x approaches infinity, is defined as a certain value if the function approaches the same value as x approaches infinity from both sides. The behavior of a function, as x approaches infinity, is determined by the function's rate of increase or decrease and the value of the function at x = 0.

The value of f(x) and g(x) will both increase as x approaches infinity in situation C. This implies that the functions are continuously increasing without bound, i.e., the function's value at any given point will always be greater than the previous point. Consider the example of f(x) = x² and g(x) = 2x. As x approaches infinity, f(x) and g(x) will both continue to increase indefinitely.

This is because x² and 2x are both monotonically increasing functions.As x approaches infinity, the value of f(x) decreases and the value of g(x) increases in situation D. As the value of f(x) approaches infinity, it will eventually reach a point where its rate of increase slows and the function will start to decrease.

On the other hand, g(x) will continue to increase because its rate of increase is faster than f(x) and does not slow down as x approaches infinity. Consider the example of f(x) = 1/x and g(x) = x². As x approaches infinity, f(x) decreases towards zero while g(x) continues to increase without bound.The correct answer is d.

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I can't really see the graph clearly but I think that the x-intercepts should be (-16/7, 0) and (32/7, 0).

Answer:

x-intercepts:  -2, 4

Step-by-step explanation:

The given graph shows a parabola that opens downwards.

The y-intercept is the point at which the curve crosses the y-axis, so when x = 0. From inspection of the given graph, we can see that the parabola crosses the y-axis when y = 8. Therefore, the y-intercept is (0, 8).

The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0. From inspection of the given graph, we can see that the parabola crosses the x-axis when x = -2 and x = 4. Therefore, the x-intercepts are (-2, 0) and (4, 0).

Answer: y = 12.6

Step-by-step explanation:

Since x = 2 and y = 6.3 * x, y = 6.3 * 2.

6.3 * 2 is equal to 12.6, so y is 12.6.

Answer:

y = 12.6

Step-by-step explanation:

y = 6.3x                     x = 2

Solve for y.

y = 6.3(2)

y = 12.6

So, the answer is 12.6