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2 years ago

Analyze the graph of the cube root function shown

Mathematics

1 answer:

Greeley [361]2 years ago

7 0

The values of a, h, and k in the general equation is h=1, k=4 and a=2

<h3>What is parent function?</h3>

The function which can be transformed into different ways is the parent function.

On a coordinate plane, a cubic function approaches the x-axis in quadrant 2, crosses the y-axis at (0, 2), has an inflection point at (1, 4), and the goes through (2, 6).

The given function is

y =a³ √(x -h) + k

Put the coordinate (0,2) in the equation, we get

2 = a³ √(0 -h) + k..................(1)

Plug (1, 4), we have

4 = a³ √(1 -h) + k..................(2)

Plug (2, 6), we have

6 = a³ √(2 -h) + k..................(3)

On solving these three equations, we have

h=1

k=4

a=2

Thus, value of h is 1, k is 4 and a is 2.

Learn more about parent function

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Write an equation in standard form passing through the points (-2, 0) and (-3, -1). I know the answer to the question, but I do

g100num [7]

Answer:

$y - x = 2$

Step-by-step explanation:

Given

Points (-2,0) and (-3,-1)

Required

Equation of Line

The first step is to determine the slope of the line; using the following formula

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$Where\ (x_1,y_1) = (-2,0)\ and\ (x_2,y_2) = (-3,-1)$

$m = \frac{y_2 - y_1}{x_2 - x_1}$ becomes

$m = \frac{-1 -0}{-3 - (-2)}$

$m = \frac{-1}{-3 +2}$

$m = \frac{-1}{-1}$

$m = 1$

The next is to determine the equation of the line using any of the points

The formula is as thus;

$m = \frac{y - y_1}{x - x_1}\ or\ m = \frac{y - y_2}{x - x_2}$

Using $m = \frac{y - y_1}{x - x_1}$

$Where\ (x_1,y_1) = (-2,0)\ and\ m =1$

$1 = \frac{y-0}{x - (-2)}$

$1 = \frac{y-0}{x +2}$

$1 = \frac{y}{x +2}$

Multiply both sides by x + 2

$(x+2)*1 = \frac{y}{x +2} * (x+2)$

$(x+2)*1 = y$

$x+2 = y$

$y = x + 2$

Subtract x from both sides

$y - x = x - x +2$

$y - x = 2$

Hence, the equation of the line in standard form is $y - x = 2$

4 0

3 years ago

The mall is located 2.4 kilometers north of jays house. The caffe shop is located 0.7 kilometers east of the mall. What is the d

Iteru [2.4K]

The distance<u> between </u>Jays hair and the caffe shop is 2.5 km.

Since the mall is located 2.4 kilometers<u> north</u> of jays house and the caffe shop is located 0.7 kilometers <u>east </u>of the mall, both directions are perpendicular. So, the distance between Jays hair and the caffe shop forms the hypotenuse side of this right angled triangle.

So, using Pythagoras' theorem, we find the hypotenuse side of this triangle, L.

Pythagoras' theorem states that the sum of squares of the sides of a right angled triangle equal the square of the hypotenuse side.

So, L = √[(2.4 km)² + (0.7 km)²]

L = √[(5.76 km² + 0.49 km²]

L = √(6.25 km²)

L = 2.5 km

So, the distance<u> between </u>Jays hair and the caffe shop is 2.5 km.

Learn more about Pythagoras' theorem here:

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4 0

2 years ago

eric and his crew have 50 trees to plant in 8 hours today they planted 40 trees. if they work at the same rate tomorrow how long

Inessa05 [86]

1.6 hours for the rest of the 10 trees

6 0

3 years ago

Read 2 more answers

Which equation has a constant of proportionality equal to

seraphim [82]

There are many equations that has a constant of

proportionality, might want to make it more specific.

5 0

3 years ago

What is the solution to the inequality 2n+5| > 1?

hodyreva [135]

Answer:

n < - 3 or n > - 2

Step-by-step explanation:

Inequalities of the type | x | > a , have solutions of the form

x < - a or x > a

Then

2n + 5 < - 1 or 2n + 5 > 1

Solve both inequalities

2n + 5 < - 1 ( subtract 5 from both sides )

2n < - 6 ( divide both sides by 2 )

n < - 3

2n + 5 > 1 ( subtract 5 from both sides )

2n > - 4 ( divide both sides by 2 )

n > - 2

Solution is n < - 3 or n > - 2

3 0

3 years ago