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3 years ago

the area of a square can be quadrupled by increasing the side length and width by 4 inches. what is the side length?

Mathematics

2 answers:

vodomira [7]3 years ago

7 0

The number could be anything because whatever it is it can be quadrupled

Elenna [48]3 years ago

5 0

Let the original side of the square be x inches.When sides are increased by 4 inches the sides are x+4 inches.

Area of square with side x inches= $x^{2}.$

Area of square with sides x+ inches= $(x+4)^{2}.$

According to question:The area of a square can be quadrupled by increasing the side length and width by 4 inches.\

Or $4x^{2}=(x+4)^{2}$

Expanding we have:

$4x^{2}=x^{2}+8x+16.$

Or, $3x^{2}-8x-16=0.$

Factoring,

(3x+4)(x-4)=0

3x+4=0 or x=4

x= $-\frac{4}{3}.$ Or x=4.

Sides can not be negative so x=4.

The sides of the square will be 4 inches.

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Find the volume of the following. Please round your answer to the nearest tenth. Please do not put units. Hint: You need to use

Sophie [7]

Answer:

Step-by-step explanation:

<u>The Volume of a Square Pyramid</u>

Given a square-based pyramid of base side a and height h, the volume can be calculated with the formula:

$\displaystyle V=\frac{1}{3}a^2h$

We are given a square pyramid with a base side a=14 ft but we're missing the height. It can be calculated by using the right triangle shown in the image attached below, whose hypotenuse is 25 ft and one leg is 7 ft

We use Pythagora's theorem:

$25^2=h^2+7^2$

Solving for h:

$h^2=25^2-7^2=625-49=576$

$h=\sqrt{576}=24$

The height is h=24 ft. Now the volume is calculated:

$\displaystyle V=\frac{1}{3}*14^2*24$

V = 1,568

3 0

2 years ago

Which table shows y as a function of x

ANTONII [103]

The answer should be C :) in order for there to be a function, first rule is the x number cannot repeat

3 0

2 years ago

In a sample of 1000 cases, the mean of a certain test is 14 and the standard deviation is 2.5. Assume the distribution to be nor

Maslowich

Answer:

The top 20% of the students will score at least 2.1 points above the mean.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The mean of a certain test is 14 and the standard deviation is 2.5.

This means that $\mu = 14, \sigma = 2.5$