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3 years ago

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The hypotenuse of a right triangle is 95 inches long. One leg is 4 inch(es) longer than the other. Find the lengths of the legs

of the triangle. Round your answers to the nearest tenth of an inch.

2 answers:

diamong [38]3 years ago

6 0

Answer:

65.1 and 69.1

Step-by-step explanation:

a^2+b^2=c^2

c=95

b=a+4

Solve for a^2+(a+4)^2=95^2

a=65.1

b=a+4=69.1

arsen [322]3 years ago

5 0

Answer:

65.1 and 69.1

Step-by-step explanation:

c² = a² + b²

c= 95

a - one leg

b= (a + 4) - second leg

95² = a² + (a + 4)²

9025 = a² + a² + 2*4a + 16

2a² + 8a - 9009 = 0

$a= \frac{-b +/-\sqrt{b^2 - 4ac} }{2a} \\\\a = \frac{-8 +/-\sqrt{8^2 - 4*2*9009} }{2*2} \\\\a=65.1 \ and \ a=- 69.1$

A leg length can be only positive. a = 65.1

b = 65.1 + 4 = 69.1

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Which of the binomials below is a factor of this

Illusion [34]

Answer:

A

Step-by-step explanation:

Given

x² - 13x + 30

Consider the factors of the constant term (+ 30) which sum to give the coefficient of the x- term (- 13)

The factors are - 3 and - 10, since

- 3 × - 10 = + 30 and - 3 - 10 = - 13 , thus

x² - 13x + 30 = (x - 3)(x - 10) ← in factored form

Thus (x - 3) is a factor of the polynomial → A

7 0

3 years ago

Read 2 more answers

What is the value of 4*(-1+2-3+4-3+6-7+....+100) Show your work. [Pls help I am really drowning in work. 50 points + brainliest

KengaRu [80]

Answer:

200

Step-by-step explanation:

We have:

$4(-1+2-3+4-5+6-7...+100)$

We can rearrange the numbers to obtain:

$4((-1-3-5-7-...-99)+(2+4+6...+100))$

From the left, we can factor out a negative. So:

$4(-(1+3+5+7+...+99)+(2+4+6...+100))$

In other words, we want to find the sum of all the odd numbers from 1 to 99.

And the sum of all the even numbers from 2 to 100.

Let's do each one individually:

Odd Terms:

We have:

$(1+3+5+7+...+99)$

We can use the arithmetic series formula, where:

$S=\frac{k}{2}(a+x_k)$

Where k is the number of terms, a is the first term, and x_k is the last term.

Since it's all the odd numbers between 1 and 99, there are 50 terms.

Our first term is 1 and our last term is 99. So, the sum of all the odd terms are:

$S=\frac{50}{2}(1+99})$

Divide the fraction. Add within the parentheses:

$S=25(100)$

Multiply:

$S=2500$

So, the sum of all the odd terms is 2500.

Even Terms:

We have:

$(2+4+6+...+100)$

Again, we can use the above formula.

Our first term is 2, last term is 100. And since it's from 2-100, we have 50 even terms. So:

$S=\frac{50}{2}(2+100)$

Divide and add:

$S=25(102)$

Multiply:

$S=2550$

We originally had:

$4(-(1+3+5+7+...+99)+(2+4+6...+100))$

Substitute them for their respective sums:

$4(-(2500)+2550)$

Multiply:

$4(-2500+2550)$

Add:

$=4(50)$

Multiply:

$=200$

So, the sum of our sequence is 200.

And we're done!

Note: I just found a <em>way</em> easier way to do this. We have:

$4\cdot(-1+2-3+4-5+6-7+...+100)$

Let's group every two terms together. So:

$=4((-1+2)+(-3+4)+(-5+6)...+(-99+100))$

We can see that they each sum to 1:

$=4((1)+(1)+(1)+...+(1))$

Since there are 100 terms, we will have 50 pairs, so 50 times 1. So:

$=4(50)$

Multiply:

$=200$

Pick which one you want to use! I will suggest this one though...

Edit: Typo

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3 years ago

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Jet001 [13]

Answer:

The answer is

<h2>44 ft</h2>

Step-by-step explanation:

The figure above is a rectangle

To find the perimeter of a rectangle we use the formula

Perimeter of a rectangle = 2l + 2w

where

l is the length of the rectangle

w is the width of the rectangle

From the question

length = 14 ft

width = 8ft

Substituting the values into the above formula we have

Perimeter = 2(14) + 2(8)

= 28 + 16

We have the final answer as

<h3>Perimeter = 44 ft</h3>

Hope this helps you

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3 years ago

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Marta_Voda [28]

Answer:

The number of pink pens can be 19 .

Step-by-step explanation:

Total Number of pens = 20

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Probability of choosing a pink pen = $\frac{\text{Number of pink pens}}{\text{Total Number of pens}}$

Probability of choosing a pink pen = $\frac{x}{20}$

ATQ

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So, the number of pink pens can be 19 .

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3 years ago

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Rainbow [258]

Answer:

The critical value that should be used in constructing the confidence interval is T = 1.316.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 26 - 1 = 25

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.8}{2} = 0.9$ . So we have T = 1.316

The critical value that should be used in constructing the confidence interval is T = 1.316.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.316\frac{0.23}{\sqrt{26}} = 0.059$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.059 = 2.741 pounds

The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.059 = 2.859 pounds.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

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3 years ago