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TEA [102]
3 years ago
12

Which of the following describes the graph of y=\sqrt[3]{8x-64}-5 compared to the parent cube root function?

Mathematics
2 answers:
Anit [1.1K]3 years ago
8 0

Answer:

Stretched by a factor of 2 and translated 8 units right and 5 units down

Step-by-step explanation:

Given  

y =\sqrt[3]{8x-64}-5

Taking greatest common factor.

y =\sqrt[3]{8 \times (x-8)}-5

Separating the cube root over the multipliers

y =\sqrt[3]{8} \times \sqrt[3]{x-8}-5

y = 2 \times \sqrt[3]{x-8}-5

The parent cube root function is

y =\sqrt[3]{x}

Stretched by a factor of 2 is equal to

y =2 \times \sqrt[3]{x}

Then, translated 8 units right is equal to

y =2 \times \sqrt[3]{x - 8}

Finally, translated 5 units down is equal to

y =2 \times \sqrt[3]{x - 8} - 5  

andriy [413]3 years ago
5 0
Answer: stretched by a factor of 2 and translated 8 units right and 5 units down

Explanation:

These is the set of choices that accompany with this question:


<span>a) stretched by a factor of 2 and translated 64 units right and 5 units down
b) stretched by a factor of 8 and translated 8 units right and 5 units down
c) stretched by a factor of 2 and translated 8 units right and 5 units down
d) stretched by a factor of 8 and translated 64 units right and 5 units down


Solution:

</span>Let's work a little the given function to compare it with the parent function.

1) The given function is y = ∛[8x - 64] - 5

2) Extract common factor 8 of the expression inside the square brackets:

y = ∛[ 8( x - 8) ] - 5

3) Extract 8 from the root:

y = 2∛(x - 8) - 5

4) The parent function is ∛x. Call the parent function g(x) => g(x) = ∛x

5) Compare: y is 2 * g(x - 8) - 5

6) Analyze the meaning of that:

g(x - 8) means that the graph of the function is translated 8 units to the right

scaling by 2 means that the graph is stretch vertically (by a scale factor of 2)

- 5 means that the entire graph is shifted 5 units downward.

So, the description of the graph y = ∛(8x - 64) - 5 compared to the parent cube root function is: stretched by a factor of 2 and translated 8 units right and 5 units down


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Convert the angle \theta=260^\circθ=260
mel-nik [20]

Question:

Convert the angle θ=260° to radians.

Express your answer exactly.

θ = ___ radians

Answer:

260° = 13π/9 or 4.54 rad

Step-by-step explanation:

Given

θ=260°

Required

Convert from degree to radians

To convert an angle in degrees to radians, we simply follow the steps below.

1° = 1 * π/180 rad

Replace the 1° with x

So,

x° = x * π/180 rad.

Now, we assume that x = 260

This means that we substitute 260 for x. This gives

260° = 260 * π/180

260° = 260π/180

Divide numerator and denominator by 20

260° = 13π/9

We can leave the answer in this form or solve further.

Take π as 22/7. This gives

260° = 13/9 * 22/7

260° = 286/63

260° = 4.5396825397

260° = 4.54 rad (Approximated)

3 0
3 years ago
PLEASE HELP ME
olga_2 [115]

The measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°

Explanation:

Given that the quadrilateral ABCD is inscribed in a circle.

The given angles are ∠A = (2x + 3), ∠C  = (2x + 1) and ∠D = (x - 10)

We need to determine the measures of the angles A, C and D

<u>The value of x:</u>

We know that, the opposite angles of a cyclic quadrilateral add up to 180°

Thus, we have,

\angle A+\angle C=180^{\circ}

Substituting the values, we have,

2x+3+2x+1=180

             4x+4=180

                   4x=176

                     x=44

Thus, the value of x is 44.

<u>Measure of ∠A:</u>

Substituting x=44 in ∠A = (2x + 3)°, we get,

\angle A=(2(44)+3)^{\circ}

     =(88+3)^{\circ}

\angle A=91^{\circ}

Thus, the measure of angle A is 91°.

<u>Measure of ∠C :</u>

Substituting x=44 in ∠C = (2x + 1)°, we get,

\angle C=(2(44)+1)^{\circ}

     =(88+1)^{\circ}

\angle C=89^{\circ}

Thus, the measure of angle C is 89°.

<u>Measure of ∠D :</u>

Substituting x=44 in ∠D = (x - 10)°, we get,

\angle D=(44-10)^{\circ}

\angle D=34^{\circ}

Thus, the measure of angle D is 34°.

Hence, the measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°

7 0
3 years ago
How much fabric is required to cover x buttons in the shape of a circle whose radius is 3x ?
Leviafan [203]

Radius of 1 button = r = 3x

Fabric required to cover 1 button = Area of the circle

= \pi r^{2}

= \pi (3x)^{2}

= 9\pi x^{2}

Total number of buttons = x

Fabric required to cover 1 button = 9\pi x^{2}  

Fabric required to cover x buttons = x(9\pi x^{2} )

=9\pi x^{3}

Hence, fabric required to cover x buttons =9\pi x^{3}  sq. units


3 0
3 years ago
PLZ HELP 1 part out of 50 is milk fat.which type of milk has more milk fat per cup?
Darya [45]
Is it a multiple choice question?
3 0
3 years ago
What symbol makes the comparison true
olga_2 [115]
Depend on the comparison. if u want to see greater or less then use = < > or the difrent subtract . add if finding the total.
3 0
2 years ago
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