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3 years ago

How do I solve this?

Mathematics

1 answer:

Korolek [52]3 years ago

6 0

(x−8)2=(x+−8)(x+−8)=(x)(x)+(x)(−8)+(−8)(x)+(−8)(−8)=x2−8x−8x+64=x2−16x+64

(x−8)2=x2−82Step 1: Simplify both sides of the equation.x2−16x+64=x2−64Step 2: Subtract x^2 from both sides.x2−16x+64−x2=x2−64−x2−16x+64=−64Step 3: Subtract 64 from both sides.−16x+64−64=−64−64−16x=−128Step 4: Divide both sides by -16.−16x−16=−128−16x=8

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It must be given as $\frac{2}{5}$ divided by $\frac{3}{4}$ .

Step-by-step explanation:

Given:

After $\frac{3}{4}$ of an hour of rain the rain gauge is $\frac{2}{5}$ filed.

To find the fraction of the rain that will be filled in the gauge if it continues to rain at the same rate for 15 more minutes.

Solution:

15 minutes in hours will be = $15\ min \times \frac{1\ hour}{60\ min}$ = $\frac{1}{4}$ of an hour.

Given that it has rained for $\frac{3}{4}$ of an hour, and it continues to rain for $\frac{1}{4}$ of an hour more.

Thus, total time of rain will be = $\frac{3}{4}+\frac{1}{4}=\frac{4}{4}=1\ hour$

Using unitary method to find the fraction of rain filled in the gauge after 1 hour of rain.

If in $\frac{3}{4}$ of an hour of rain the rain gauge is $\frac{2}{5}$ filed.

Thus, in 1 hour of rain the gauge will be filled by = $\frac{2}{5}\div \frac{3}{4}$

To divide fractions, we take reciprocal of the divisor and replace division by multiplication.

⇒ $\frac{2}{5}\times\frac{4}{3}$

⇒ $\frac{8}{15}$

Thus, the fraction of the rain filled in the gauge will be = $\frac{8}{15}$

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