All categories

3 years ago

Find the value of x. Round to the nearest tenth a. 12.9b. 8.5c. 12.4d. 8.1

Mathematics

2 answers:

UkoKoshka [18]3 years ago

7 0

Use cosine:
cos36= x/10
8.09

aksik [14]3 years ago

4 0

Answer: The required value of x is 8.1 units.

Step-by-step explanation: We are given to find the value of x from the figure.

From the figure, we notice that

it is a right-angled triangle with the length of the hypotenuse 10 units and one of the acute angle is of measure 36°.

Now, for the angle with measure 36°, the length of the base is x units and the length of the hypotenuse is 10 units.

Therefore, from the laws of trigonometry, we have

$\cos 36^\circ=\dfrac{base}{hypotenuse}\\\\\\\Rightarrow \cos 36^\circ=\dfrac{x}{10}\\\\\\\Rightarrow x=10\times \cos 36^\circ\\\\\Rightarrow x=10\times 0.8090\\\\\Rightarrow x=8.09\\\\\Rightarrow x=8.1.$

Thus, the required value of x is 8.1 units.

You might be interested in

Need pre-cal help. Will mark best answer brainliest

OlgaM077 [116]

so, let's keep in mind that

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}$

so let's make a quick table of those solutions, say A, B, C solutions with x,y,z liters of acid, with an acidity of 0.25, 0.40 and 0.60 respectively.

$\bf \begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{liters of }}{amount}\\ \cline{2-4}&\\ A&x&0.25&0.25x\\ B&y&0.40&0.4y\\ C&z&0.60&0.6z\\ \cline{2-4}&\\ mixture&78&0.45&35.1 \end{array} \\\\\\ \begin{cases} x+y+z=78\\ 0.25x+0.4y+0.6z=35.1 \end{cases}$

we know she's using "z" liters and those are 3 times as much as "y" liters, so z = 3y.

$\bf \begin{cases} x+y+3y=78\\ x+4y=78\\[-0.5em] \hrulefill\\ 0.25x+0.4y+0.6(3y)=35.1\\ 0.25x+0.4y=1.8y=35.1\\ 0.25x+2.2y=35.1 \end{cases}\implies \begin{cases} x+4y=78\\\\ 0.25x+2.2y=35.1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x+4y=78\implies \boxed{x}=78-4y \\\\\\ \stackrel{\textit{using substitution on the 2nd equation}}{0.25\left( \boxed{78-4y} \right)+2.2y=35.1}\implies 19.5-y+2.2y=35.1$

$\bf 1.2y=15.6\implies y=\cfrac{15.6}{1.2}\implies \blacktriangleright y=13 \blacktriangleleft \\\\\\ x=78-4y\implies x=78-4(13)\implies \blacktriangleright x=26 \blacktriangleleft \\\\\\ z=3y\implies z=3(13)\implies \blacktriangleright z=39 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{25\%}{26}\qquad \stackrel{40\%}{13}\qquad \stackrel{60\%}{39}~\hfill$

5 0

2 years ago

Solve for x please help ! (show work)

Alina [70]

Answer:

x = -5

Step-by-step explanation:

-(5x-2) = 27

Distribute the minus sign

-5x +2 = 27

Subtract 2 from each side

-5x +2-2 = 27-2

-5x = 25

Divide by -5

-5x/-5 = 25/-5

x = -5

5 0

3 years ago

Read 2 more answers

Decimals that have the same value are

shepuryov [24]

<span>Decimals that have the same value are equivalent decimals. Equivalent decimals are decimal numbers that have the same value (the same amount). In other words equivalent decimal numbers have the same value but different number of decimals. For example:
0.5 and 0.50 are equivalent decimals.
0.5 and 0.500
0.05 and 0.0500

</span>

4 0

3 years ago

Please help. Could you explan your answer also? thanks

natulia [17]

Answer: Choice B) -4

The lower quartile, also known as Q1 or the first quartile, is the left edge of the box. In this case, that is at -4. We can drop a vertical line from the left edge of the box until we hit -4 on the number line.

Side Note: 25% of the data values are below Q1, while 75% of the data values are above Q1

4 0

3 years ago

You wish to find a 95% confidence interval for the mean number of times men change channels with a remote control during a comme

gogolik [260]

For margin of error to be a maximum of 3:
3 = z*(SD / sqrt(n)), where z is the z-score, SD is the standard deviation and n is the sample size.
z = 1.96 for a 95% confidence interval, and we are given SD = 15.
3 = 1.96*15/sqrt(n)
sqrt(n) = 9.8
n = 96.04 ~ 96 commercials.

4 0

3 years ago