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3 years ago

How do I solve this?

Mathematics

1 answer:

Tanya [424]3 years ago

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A square with an area of A2 is enlarged to a square with an area of 25A2. How was the side of the smaller square changed?

Mamont248 [21]

Answer:

second option : the side length was multiplied by 5.

Step-by-step explanation:

a = side length of the original square

A² = a×a

(a+5)×(a+5) = a² + 10a + 25

and that should be equal to a²×25

a² + 10a + 25 = 25a² ?

10a + 25 = 24a²

no, that is not true for all a

a×5 × a×5 = a²×25 = 25A²

this is the correct solution, as it is true for all a.

5 0

3 years ago

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How do you simplify this expression?

alisha [4.7K]

Solve the terms in parentheses first. We'll start on the denominator.

The denominator has an exponent for a fraction that also includes exponents. To multiply exponents within parentheses that are raised to a power, use this rule:

$(x^a)^b = x^{a \cdot b}$

Simplify the denominator:

$(\frac{3^4}{7^3} )^2 = \frac{3^8}{7^6}$

Solve the fractions in the numerator:

$(\frac{3}{5})^5 = \frac{3^5}{5^5}$

$(\frac{9}{7})^2} = \frac{9^2}{7^2}$

The problem should now read:

$\frac{\frac{3^5}{5^5} \cdot \frac{9^2}{7^2}}{\frac{3^8}{7^6}}$

There is a denominator in a denominator. We can bring that to the numerator of the overall fraction:

$\frac{\frac{3^5}{5^5} \cdot \frac{9^2}{7^2}}{\frac{3^8}{7^6}} = \frac{\frac{3^5}{5^5} \cdot \frac{9^2}{7^2} \cdot {7^6}}{3^8}}$

Using a calculator, simplify the numerator:

$\frac{3^5}{5^5} \cdot \frac{9^2}{7^2} \cdot {7^6} = \frac{19683}{7}$

The fraction should now read:

$\frac{\frac{19683}{7}}{3^8}$

There is a denominator in the numerator. This can be brought down to the overall denominator:

$\frac{\frac{19683}{7}}{3^8} = \frac{19683}{3^8 \cdot 7}$

Factor 19683:

$19683 = 3 \cdot3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 = 3^9$

$\frac{19683}{3^8 \cdot 7} = \frac{3^9}{3^8 \cdot 7}$

Simplify the exponents:

$\frac{3^9}{3^8} = 3$

The following fraction will be your answer:

$\boxed{\frac{3}{7}}$

8 0

3 years ago

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Suppose the theater decides to have a third popcorn size, the super box. They want the super box to have a length of 6.5 inches,

nignag [31]

Answer:

(if their are no measurements for the smaller boxes) the biggest should cost the most

Step-by-step explanation:

it should hold the most popcorn and their for cost the moast

4 0

4 years ago

Brandon's car used 15 gallons to travel 435 miles. At what rate does the car use gas,

strojnjashka [21]

Answer:

29 miles per gallon

Step-by-step explanation:

Take the miles and divide by the gallons

435/15

29 miles per gallon

8 0

3 years ago

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Question 1 (1 point)

taurus [48]

Answer:

question no 1:slope=5

Step-by-step explanation:

let(x=5andy=8)(a=7andb=18)

now

slope=(b-y)/(a-x)=(18-8)/(7-5)=5

5 0

3 years ago

Read 2 more answers