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3 years ago

6

Quick can anyone help me please, only the ones who know what they are saying lol!!!!!!!!!!!!!!!! This is attempting #7 of trying

to get this question answered
Determine the value of x. ( no links as answers)

1 answer:

Alecsey [184]3 years ago

3 0

In a 30°-60°-90° triangle, the sides occur in a ratio of 1 to √3 to 2. In this case, <em>x</em> is half the length of the hypotenuse, so <em>x</em> = 4.

Or, using trig,

cos(30°) = <em>x</em>/8

<em>x</em> = 8 cos(30°) = 8 (1/2) = 4

You might be interested in

Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola

mote1985 [20]

ANSWER

This is an ellipse. The equation is:

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

$(a+b)^2=a^2+2ab+b^2$

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

$16x^2-32x=16(x^2-2x)$

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

$(x-1)^2=x^2-2x+1$

To maintain the equation, we have to subtract 1,

$16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16$

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

$16(x-1)^2-16+9y^2+72y+16=0$

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

$9y^2+72y=9(y^2+8y)$

Following the same reasoning as before, we have that the perfect binomial squared is,

$(y+4)^2=y^2+8y+16$

Remember to subtract the independent term to maintain the equation,

$9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144$

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

$16(x-1)^2-16+9(y+4)^2-144+16=0$

Add like terms,

$\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}$

Add 144 to both sides,

$\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}$

As we can see, this is the equation of an ellipse. Its standard form is,

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

$\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\ \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}$

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

$\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1$

Note that we can simplify a and b,

$\frac{12}{4}=3\text{ and }\frac{12}{3}=4$

Hence, the equation of the ellipse is,

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

3 0

1 year ago

Solve for r in terms of s, t, and u. <br> t=u-s+r

Verdich [7]

Answer:

r = t - u - s

Step-by-step explanation:

To solve for r in terms of s, t, and u, means to have r on one side and have t, u, and s.

t = u - s + r

t - u = s + r

t - u - s = r

6 0

3 years ago

The charge for electricity consumption E is partly constant and partly varies as the number N of units used. The charge for 82 u

balandron [24]

The charge per unit of electricity is #415

The formula for E in terms of N is E = 375 + 40N

<h3>What is variation?</h3>

Variation is a mathematical term that establishes the relationship between quantities and variables in an equation.

Analysis:

E = K + CN

where K and C are constants

When E = 3655, N = 82 and when E = 2055, N = 42

3655 = K + 82C ---------------1

2055 = K + 42C----------------2

subtract equation 2 from 1

40C = 1600

C = 40

substitute C in equation 1

3655 = K + 82(40)

3655 = K + 3280

K = 3655 - 3280 = 375

charge per unit is N = 1

E = 375 + 40(1) = #415

Formula for E in terms of N is E = 375 + 40N

In conclusion, the charge per unit of electricity is 415 and the equation connecting E and N is E = 375 + 40N

Learn more about Variation: brainly.com/question/6499629

SPJ1

3 0

2 years ago

The dataset Restaurant Tips contains data recorded from 157 restaurant bills at a bistro in New York over a two week period and

xz_007 [3.2K]

Answer: ($3.532, $4.166)

Step-by-step explanation:

Given : Significance level : $\alpha: 1-0.90=0.10$

Critical value : $z_{\alpha/2}=1.645$

Sample size : n= 157

Sample mean : $\overline{x}=\$\ 3.849$

Standard deviation : $\sigma= \$\ 2.421$

The confidence interval for population mean is given by :_

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$\text{i.e. }\$\ 3.849\pm (1.64)\dfrac{2.421}{\sqrt{157}}\\\\\approx\$\ 3.849\pm0.317\\\\=(\$\ 3.849-0.317,\$\ 3.849+0.317)=(\$\ 3.532,\$\ 4.166)$

Hence, the 0% confidence interval for the average tip given at this restaurant = ($3.532, $4.166)

5 0

2 years ago

1360 concert tickets were sold for a total of $13,328. If students paid $8 and non students paid $12, how many student tickets w

lyudmila [28]

748 student tickets were sold.

Step-by-step explanation:

Given,

Number of tickets sold = 1360

Revenue generated = $13328

Cost of each student ticket = $8

Cost of each non student ticket = $12

Let,

x be the number of student tickets sold

y be the number of non student tickets sold

According to given statement;

x+y=1360 Eqn 1

8x+12y=13328 Eqn 2

Multiplying Eqn 1 by 12

$12(x+y=1360)\\12x+12y=16320\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$(12x+12y)-(8x+12y)=16320-13328\\12x+12y-8x-12y=2992\\4x=2992\\$

Dividing both sides by 4

$\frac{4x}{4}=\frac{2992}{4}\\x=748$

748 student tickets were sold.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

5 0

3 years ago