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siniylev [52]
3 years ago
12

Given right triangle DEF, what is the value of tan(F)?

Mathematics
2 answers:
Nataly [62]3 years ago
5 0

Answer: \frac{40}{9}

Step-by-step explanation:

We know that for any angle x in a triangle ,

\tan x=\frac{\text{side opposite to x}}{\text{side adjacent to x}}

Now, for the given triangle DEF, the value of tan(F) is given by :-

\tan F=\frac{\text{side opposite to F}}{\text{side adjacent to F}}\\\\\Rightarrow\ \tan F=\frac{40}{9}

Hence, the value of tan(F) = =\frac{40}{9}

IgorC [24]3 years ago
4 0

we know that

In the right triangle DEF

the tangent of the angle F is equal to

tan(F)=\frac{opposite\ side\ angle\ F}{adjacent\ side\ angle\ F}=\frac{DE}{EF}

substitute the values

tan(F)=\frac{40}{9}

therefore

<u>the answer is the option</u>

\frac{40}{9}

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Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36 Given ⇒ 3(x − 4) + 5x = 9x − 36 Step 1 ⇒ 3x − 12 +
7nadin3 [17]

In Step 6, the equation is ...

  -12 = x - 36

In step 7, the equation is ...

  -12 +36 = x -36 +36

Clearly, to get to step 7, 36 has been added to both sides of the equation.

Adding 36 to both sides of the equation is justified by ...

... C) Addition Property of Equality

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<em>More about the addition property of equality</em>

The addition property of equality says you can add the same value to both sides of an equation without changing the values of the variables that make the equation true. Here, x=24 makes the equation of step 6 true, and x=24 makes the equation of step 7 true.

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3 years ago
A classic car is now selling for $2500 less than three times its original price. If the selling price is now $14,000, what was t
Aneli [31]

Answer:

42000

Step-by-step explanation:

8 0
3 years ago
It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportat
Mrrafil [7]

Answer:

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is equal to 120 or not, the system of hypothesis would be:  

Null hypothesis:\mu = 120  

Alternative hypothesis:\mu \neq 120  

Part 2

Calculate the statistic

We can replace in formula (1) the info given like this:  

z=\frac{114-120}{\frac{22}{\sqrt{36}}}=-1.636    

P-value

Since is a two sided test the p value would be:  

p_v =2*P(z  

Step-by-step explanation:

Data given and notation  

\bar X=114 represent the sample mean  

\sigma=22 represent the population standard deviation

n=36 sample size  

\mu_o =120 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

Part 1

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is equal to 120 or not, the system of hypothesis would be:  

Null hypothesis:\mu = 120  

Alternative hypothesis:\mu \neq 120  

If we analyze the size for the sample is > 30 and we  know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Part 2

Calculate the statistic

We can replace in formula (1) the info given like this:  

z=\frac{114-120}{\frac{22}{\sqrt{36}}}=-1.636    

P-value

Since is a two sided test the p value would be:  

p_v =2*P(z  

8 0
3 years ago
Find the value of x<br> 12<br> 5<br> X
steposvetlana [31]

Answer:

x = 13

Step-by-step explanation:

Note that the side length x is opposite of the right angle, which means that it is the hypotenuse, which will usually be denoted as c.

Set the equation:

a² + b² = c²

let:

a = 5

b = 12

c = x

Plug in the corresponding numbers (& x) to the corresponding variables:

(5)² + (12)² = (x)²

Simplify. First, solve for the power, and then add:

x² = (5²) + (12²)

x² = (5 * 5) + (12 * 12)

x² = 25 + 144

x² =  169

Next, root both sides of the equation:

√x² = √169

x = √169 = √(13 * 13) = 13

x = 13

~

Note the rules, and it should be easier:

30-60-90° = 1 , √3 , 2

45-45-90° = 1 , 1 , √2

Any other measurements use the equation:  a² + b² = c²

5 0
2 years ago
Can someone please help me with this????<br> Thanks
natta225 [31]

Answer:

A (I believe)

Step-by-step explanation:

since the part with the triangle is 6 yards, and it looks about half of that whole side, I'm going to assume that that side is 12 yards, and since it's a square each side will be the same length. so multiply 12 and 12 to get 144.

Now divide that by four so you can get the area of a fourth of the square and find the area of the triangle. 144 ÷ 4 = 36

Now divide 36 by 2 to get the area of the little triangle. 36 ÷ 2 = 18

Now divide 18 by 6 to get x. 18 ÷ 6 = 3

In conclusion, the answer should be A.

Hope this helped!!! :3

8 0
2 years ago
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