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2 years ago

Which expressions are equivalent to 7^{-2}\cdot 7^67

Mathematics

2 answers:

AleksandrR [38]2 years ago

3 0

Answer:

${7}^{ - 2} \cdot \: {7}^{6} = {7}^{ 4}$

Step-by-step explanation:

The given expresion is;

${7}^{ - 2} \cdot {7}^{6}$

We apply the product rule of indices;

${a}^{m} \cdot \: {a}^{n} = {a}^{m + n}$

We apply this property to our expression to get:

${7}^{ - 2} \cdot \: {7}^{6} = {7}^{ - 2 + 6}$

Simplify the exponent on the right;

${7}^{ - 2} \cdot \: {7}^{6} = {7}^{ 4}$

We can't see the options, but I hope this helps!

MrRa [10]2 years ago

3 0

Answer:

7^2/7^-2 and (7^2)^2

Step-by-step explanation:

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solmaris [256]

799 represents the initial value of the painting

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Step-by-step explanation:

The form of the exponential function is $f(x)=a(b)^{x}$ , where

a is the initial value ⇒ (at x = 0)
b is the growth/decay factor ⇒ (rate of change)
If b > 1, then the function is growth ⇒ (increasing)
If 0 < b < 1, then the function is decay ⇒ (decreasing)

The value of a rare painting has increased each year since it was

found at a garage sale

The value of the painting is modeled by the function $f(x)=799(1.03)^{x}$

We need to know what 799 represents and what the painting will

be worth after 5 years

∵ $f(x)=799(1.03)^{x}$

∵ The form of the function is $f(x)=a(b)^{x}$

- By comparing the two forms

∴ a = 799 and b = 1.03

∵ a is the initial value at x = 0

∴ 799 represents the initial value of the painting

∵ x represents the number of years

∴ x = 5

- Substitute the value of x in the function by 5

∵ $f(5)=799(1.03)^{5}$

∴ f(x) = 926.26

∴ The painting will be worth $926 after 5 years to the nearest dollar

799 represents the initial value of the painting

The painting will be worth $926 after 5 years to the nearest dollar

Learn more:

You can learn more about the functions in brainly.com/question/10382470

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2 years ago

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Break even point is where all the expense is already covered by the revenue. In this case, the expense would be the stand ($75,000) and the lemon+sugar+water ( $1.25 per glass). The revenue comes from lemonade($30/glass). Then the equation would be:

$30 * glass of lemonade= $75,000 + $1.25 * glass of lemonade
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2 years ago

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TEA [102]

Answer:

They purchased 14 adult tickets and 4 kids tickets.

Step-by-step explanation:

14 x 5 = 70

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2 years ago

The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm.

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2 years ago

You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing th

finlep [7]

The <u>correct answer</u> is:

9.2 ft.

Explanation:

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$d=\frac{|Am+Bn+C|}{\sqrt{A^2+B^2}}$

We first need to write our equation in the form Ax+By+C=0.
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First we will add 6/7x to each side:
y+6/7x=(-6/7x)+7+(6/7x)
y+6/7x=7

Now we will subtract 7 from each side:
y+6/7x-7=7-7
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It will be easier to work with this equation if we do not have fractions. We can accomplish this by multiplying everything by the denominator of the fraction, 7:
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Now we rearrange the terms to the x term is in front:
6x+7y-49=0

This is in the form Ax+By+C=0, where A=6, B=7 and C=-49.

Substituting these into our formula above along with our coordinates from our point (m,n)=(6, 14) we have:
$d=\frac{|Am+Bn+C|}{\sqrt{A^2+B^2}}
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\\d=\frac{|6(6)+7(14)-49|}{\sqrt{6^2+7^2}}
\\
\\d=\frac{|36+98-49|}{\sqrt{36+49}}
\\
\\d=\frac{|85|}{\sqrt{85}}=\frac{85}{\sqrt{85}}=9.2
$

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2 years ago