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3 years ago

the hypotenuse of a right triangle has a length of 13cm the longer of the two legs is 7cm longer than the shorter leg

Mathematics

1 answer:

Margarita [4]3 years ago

6 0

Let's say the shorter side is x.

So, the longer side would be ( 7 + x )

Now we have to use the Pythagorean Theorem to find the value of x.

a² + b² = c²

( 7 + x )² + x² = 13

7² + x² + x² = 13²

49 + 2x² = 169

2x² = 169 - 49

2x² = 120

x² = 60

x = √60

So the longer side is ( 7 + √60 ) and the shorter side is √60

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An item is regularly priced at $70. Keiko bought it on sale for 80% off the regular price. How much did Keiko pay? $

pantera1 [17]

Answer:

$14

Step-by-step explanation:

80% of $70 is $14, saving him $56

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2 years ago

Read 2 more answers

I need graph help plz

Likurg_2 [28]

Answer:

Step-by-step explanation:

Part A

x-intercepts of the graph → x = 0, 6

Maximum value of the graph → f(x) = 120

Part B

Increasing in the interval → 0 ≤ x ≤ 3

Decreasing in the interval → 3 < x ≤ 6

As the price of goods increase in the interval [0, 3], profit increases.

But in the price interval of (3, 6] profit of the company decreases.

Part C

Average rate of change of a function 'f' in the interval of x = a and x = b is given by,

Average rate of change = $\frac{f(b)-f(a)}{b-a}$

Therefore, average rate of change of the function in the interval x = 1 and x = 3 will be,

Average rate of change = $\frac{f(3)-f(1)}{3-1}$

= $\frac{120-60}{3-1}$

= 30

6 0

2 years ago

Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

liubo4ka [24]

Answer:

12 inches

Step-by-step explanation:

Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

is twice the width. The volume of the box is 3,456 in? What is the height of the box?

Volume of a Rectangular pyramid = Length × Width × Height

From the above question

Height = Width = x

Length = 2 × Width

Length = 2x

Volume = 3,456 cubic inches

Hence,

3,456 = 2x × x × x

3456 = 2x³

x³ = 3456/2

x³ = 1728

Cube root both sides

Cube root(x³) = cube root (1728 cubic Inches)

x = 12 inches

Therefore, the height is 12 inches

3 0

3 years ago

I need help fast i don’t understand please give detailed explanation

alex41 [277]

Answer:

<4 = 63°

Step-by-step explanation:

32° + 31° = < 4 ( exterior angle of a triangle is equal to the sum of two opposite interior angles)

<4 = 63°

Hope it will help :)

5 0

3 years ago

Suppose a marketing company wants to determine the current proportion of customers who click on ads on their smartphones. It was

andrezito [222]

Answer:

The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 100, p = 0.42$

92% confidence level

So $\alpha = 0.08$ , z is the value of Z that has a pvalue of $1 - \frac{0.08}{2} = 0.96$ , so $Z = 1.75$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.3336$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.5064$

The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).

4 0

3 years ago