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2 years ago

Rewrite each expression as a product of two or quotient of two powers

Mathematics

1 answer:

Paul [167]2 years ago

6 0

Answer:

The product is $5^{40}*3^{70}$

Step-by-step explanation:

To do this we must understand how the basic operations apply to powers. If the power has the same base and we multiply them, the base remains the same while we sum the powers, if we divide them the base remains the same and we subtract the powers, if we try to make a power of a power the two powers multiply. Applying this rule we have:

$(\frac{5^8*3^7}{5^4})^{10}\\(\frac{5^8}{5^4}*3^7)^{10}\\(5^4*3^7)^{10}\\5^{40}*3^{70}$

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Which function has a range of y < 3?

Setler79 [48]

Using a graphing tool

Let's graph each of the cases to determine the solution of the problem

case A) $y=3(2^{x})$

see the attached figure N $1$

The range is the interval--------> (0,∞)

$y> 0$

therefore

the function $y=3(2^{x})$ is not the solution

case B) $y=2(3^{x})$

see the attached figure N $2$

The range is the interval--------> (0,∞)

$y> 0$

therefore

the function $y=2(3^{x})$ is not the solution

case C) $y=-2^{x}+3$

see the attached figure N $3$

The range is the interval--------> (-∞,3)

$y< 3$

therefore

the function $y=-2^{x}+3$ is the solution

case D) $y=2^{x}-3$

see the attached figure N $4$

The range is the interval--------> (-3,∞)

$y>-3$

therefore

the function $y=2^{x}-3$ is not the solution

the answer is

$y=-2^{x}+3$

5 0

2 years ago

Read 2 more answers

Use complete sentences to describe the range of the sine function.

MA_775_DIABLO [31]

The Range of a function is the set of all values that that function can take.

Given the sine function f(x)=sinx,

This function is the function which calculates the sine of the values of x.

According to the definition of the sine of an angle x in the unit circle,

$-1 \leq sinx \leq 1$ ,

so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.

This means that the values that the sine function takes are any values between -1 and 1, inclusive.

This determines the Range of the sine function.

So the Range of the sine function is [-1, 1]

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2 years ago

Solve the equation 4x2 + 2 = 38 using square roots.

hammer [34]

Answer:

Step-by-step explanation:

Tiger Algebra gives you not only the answers, but also the complete step by step method for solving your equations 4x^2-2=38 so that you ... Step 2 : Step 3 :Pulling out like terms. 3.1 Pull out like factors : 4x2 - 40 = 4 • (x2 - 10) ... x2 = 10. When two things are equal, their square roots are equal.

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1 year ago

A highway had a landslide, where 3,000 cubic yards of material fell on the road, requiring 200 dump truck loads to clear. On ano

Orlov [11]

3,000 yd3 = 200 dtl
Chapter 1: Problem Solving 17 / 21

Rates Question
12 A highway had a landslide, where 3,000 cubic yards of material fell on the road, requiring 200 dump truck loads to clear. On another highway, a slide left 40,000 cubic yards on the road. How many dump truck loads would be needed to clear this slide?
3,000 yd3 = 200 dtl
40,000 yd3 × 200 dtl = 2,667 dtl
3, 000 yd3

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2 years ago

ΔABC is an isosceles triangle with AB = BC= 6 units. D and E are the midpoints or AB and BC, respectively. The length of AC is 8

nydimaria [60]

There are two triangles that exist in this problem. First is the given triangle ABC, witch AB = BC = 6 and AC = 8
Next is the smaller triangle formed by connecting points D and E; triangle EAD, with EA = AD = 3 and the length of DE is unknown.
Because these triangles are similar, a simple ratio may be set up in order to calculate DE.
DE / AC = EA / AB
DE = 3/6 * 8
DE = 4 units

7 0

1 year ago

Read 2 more answers

Rewrite each expression as a product of two or quotient of two powers ​

Rewrite each expression as a product of two or quotient of two powers