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anastassius [24]
3 years ago
10

Find the missing side of the triangle

Mathematics
1 answer:
Gnom [1K]3 years ago
6 0
Use the Pythagorean theorem.
x^2 + 5^2 = 13^2
x^2 + 25 = 169
x^2 = 144
x = 12
You might be interested in
Y=-x^2+2x+10<br> y=x+2<br><br> Substitution <br> Please show your work<br> Need ASAP
erik [133]

Answer:

The solutions of the system of equations are the points

(\frac{1-\sqrt{33}} {2},\frac{5-\sqrt{33}} {2})  

(\frac{1+\sqrt{33}} {2},\frac{5+\sqrt{33}} {2})  

Step-by-step explanation:

we have

y=-x^{2} +2x+10 ----> equation A

y=x+2 ----> equation B

Solve the system by substitution

substitute equation B in equation A

x+2=-x^{2} +2x+10

solve for x

-x^{2} +2x+10-x-2=0

-x^{2} +x+8=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-x^{2} +x+8=0

so

a=-1\\b=1\\c=8

substitute in the formula

x=\frac{-1\pm\sqrt{1^{2}-4(-1)(8)}} {2(-1)}

x=\frac{-1\pm\sqrt{33}} {-2}

x=\frac{-1+\sqrt{33}} {-2}  -----> x=\frac{1-\sqrt{33}} {2}  

x=\frac{-1-\sqrt{33}} {-2}  -----> x=\frac{1+\sqrt{33}} {2}  

<em>Find the values of y</em>

For x=\frac{1-\sqrt{33}} {2}  

y=x+2

y=\frac{1-\sqrt{33}} {2}+2  ---->y=\frac{5-\sqrt{33}} {2}  

For x=\frac{1+\sqrt{33}} {2}  

y=x+2

y=\frac{1+\sqrt{33}} {2}+2  ---->y=\frac{5+\sqrt{33}} {2}  

therefore

The solutions of the system of equations are the points

(\frac{1-\sqrt{33}} {2},\frac{5-\sqrt{33}} {2})  

(\frac{1+\sqrt{33}} {2},\frac{5+\sqrt{33}} {2})  

5 0
2 years ago
The amount of money the banker or broker makes in commission on your loan is called the_____. Down payment, interest, yield spre
vovangra [49]

<u><em>Answer:</em></u>

<u><em>I believe the answer is Yield Spread</em></u>

<u><em>Step-by-step explanation:</em></u>

<u><em> So Basically what a down payment is, it is an initial up-front partial payment for the purchase of expensive items such as a car or a house. It is usually paid in cash or equivalent at the time of finalizing the transaction. A loan of some sort is then required to finance the remainder of the payment. You usually pay 10-20% of its value.</em></u>

<u><em>Interest is when you don't pay your bills on time and what ever company you owe money to will add a certain percentage on top of what you own. So if you owe 10 dollars and didn't pay it depending on its interest rate it would be 10.70 for 7% interest rate. So the banker or broker would make that on there commission.</em></u>

<u><em>Yield Spread is a really interesting the yield spread or credit spread is the difference between the quoted rates of return on two different investments, usually of different credit qualities but similar maturities. It is often an indication of the risk premium for one investment product over another. The phrase is a compound of yield and spread.</em></u>

8 0
3 years ago
Please help asap pleaseeeew
wel

Answer:

6.

Step-by-step explanation:

1) OA=d/2=20/2=10;

2) AB=AC/2=16/2=8;

3) \ OB=\sqrt{OA^2-AB^2} =6.

3 0
1 year ago
Find the formula for an exponential function that passes through the two points given.
goldenfox [79]

Answer:

y = 7(3^x)

Step-by-step explanation:

Given

(x_1,y_1) = (0,7)

(x_2,y_2) = (4,567)

Required

Determine the formula

An exponential function is of the form:

y = ab^x

For point (x_1,y_1) = (0,7)

7 = ab^0

7 = a*1

7 = a

a = 7

For point (x_2,y_2) = (4,567)

567 = ab^4

Substitute 7 for a

567 = 7*b^4

Divide both sides by 7

81 = b^4

Take 4th root of both sides

\sqrt[4]{81} =\sqrt[4]{b^4}

\sqrt[4]{81} =b

b = \sqrt[4]{81}

b = 3

Substitute 7 for a and 3 for b in y = ab^x

y = 7 * 3^x

y = 7(3^x)

3 0
3 years ago
A sample of 40 observations is selected from one population with a population standard deviation of 5. The sample mean is 102. A
marin [14]

1) This is a Two tailed Test.

2) Decision rule is; If the p-value is greater than 4% fail to reject H₀.

3) P-value = 0.00968764 and so we reject H₀

<h3>How to state the decision rule in hypothesis testing?</h3>

We are given the hypothesis as;

Null Hypothesis; H₀: m₁ = m₂

Alternative Hypothesis; H₁: m₁ ≠ m₂

1) Since the alternative hypothesis has "not equal to sign", then it is a two tailed test.

2) Since we are told to use significance level as 0.04, then we can say that the decision rule is;

If the p-value is greater than 4% fail to reject H₀.

3) Using a 2-Sample Z-Test online TI calculator gives the test statistic as;

z = 2.5868

4) From z-score calculator, p-value equals 0.00968764. This is less than 0.04 and as such the decision regarding H₀ is to reject H₀.

5) P-value = 0.00968764

Read more about decision rule in Hypothesis Testing at; brainly.com/question/17192140

#SPJ1

3 0
2 years ago
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