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3 years ago

Which solution finds the value of x in the triangle below?

Mathematics

2 answers:

LuckyWell [14K]3 years ago

7 0

Answer:

Step-by-step explanation:

Since this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees.

We can see that this is a 30-60-90 degree triangle.

The rules of 30-60-90 degree triangles are that the side opposite the 90 degree angle, or the hypotenuse can be measured with the variable $2a$ . The side opposite the 30 degree angle can be measured with $a$ , and the side opposite the 60 degree angle will be measured with $a\sqrt{3}$ .

We can see that 8 represents $2a$ because it is the hypotenuse. Since the side marked $x$ is separated by the hypotenuse by an angle of 60 degrees, we note that side marked $x$ is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked $a$ , and since we already know that 8 is equal to $2a$ , we realize that the side marked x is equal to $a$ , or 4.

forsale [732]3 years ago

5 0

I didn't get it can you post a picture with it too?

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The "cold start ignition time" of an automobile engine is being investigated by a gasoline manufacturer. The following times, in

Nezavi [6.7K]

Answer:

1. Sample Mean = 2.50

2. Sample Variance = 1.35

3. Standard Deviation = 1.16

Step-by-step explanation:

Note: As this question is not complete, similar can be found on internet where following are asked to calculate and here I will calculate these as well.

1. Sample Mean.

2. Sample Variance.

3. Sample Standard Deviation.

So, for sample mean to calculate from the given data points. We need to apply to following formula to calculate sample mean.

Sample Mean = (X1 + X2 + .... + XN) divided by Total number of data points.

Sample Mean = (0.17 + 1.94 + 2.62 + 2.35 + 3.05 + 3.15 + 2.53 + 4.81 + 1.92) divided by (9).

Sample Mean = 2.50

Likewise, from the answer of sample mean we can calculate sample variance by following steps.

Solution:

1. Subtract the obtained mean from each of the data point given.

(0.17 - 2.50) = -2.33

(1.94 - 2.50) = -0.56

(2.62 - 2.50) = 0.12

(2.35 - 2.50) = -0.15

(3.05 - 2.50) = 0.55

(3.15 - 2.50) = 0.65

(2.53 - 2.50) = 0.03

(4.81 - 2.50) = 2.31

(1.92 - 2.50) = -0.58

2. Square each of the differences obtained in step 1.

$-2.33^{2}$ = 5.43

$-0.56^{2}$ = 0.31

$0.12^{2}$ = 0.01

$-0.15^{2}$ = 0.02

$0.55^{2}$ = 0.30

$0.65^{2}$ = 0.42

$0.03^{2}$ = 0.01

$2.31^{2}$ = 5.34

$-0.58^{2}$ = 0.34

3. Sum all of these squares.

(5.43 + 0.31 + 0.01 + 0.02 + 0.30 + 0.42 + 0.01 + 5.34 + 0.34) = 12.18

4. Divide 12.18 by (n-1), where n = 9.

Sample Variance = 12.18/9 = 1.35

Now, by using sample variance, we can calculate standard deviation with easy simple steps.

So, in order to find standard deviation, we just need to take the square root of sample variance that we have already calculated above.

Standard Deviation =  $\sqrt{1.35}$  = 1.16 

Good Luck!

6 0

3 years ago

What is the answer to (-5)(-44)1/5

slavikrds [6]

Answer:

Step-by-step explanation:

((−5)(−44))(1)

(220)(1)

220

=44

4 0

3 years ago

Please answer and explain how you go the answer

AfilCa [17]

Answer:

38°

Step-by-step explanation:

It's simple think of it like this: A right angle is exactly 90 degrees. Subtract the 90° and the 52° and you'll get your answer of 38° which is x°.

Hope this helped you out :)

6 0

3 years ago

Read 2 more answers

Write the product using exponents. 6.4.6.4.6.4.6.4.b.b.b

maks197457 [2]

Step-by-step explanation:

I count four 6s, four 4s and three b.

so, we have

6⁴×4⁴×b³ or (using the same symbols as above)

6⁴.4⁴.b³

4 0

3 years ago

Consider the graph of the quadratic function y = 3x2 – 3x – 6. What are the solutions of the quadratic equation 0 = 3x2 − 3x − 6

son4ous [18]

Y = 3x^2 - 3x - 6 {the x^2 (x squared) makes it a quadratic formula, and I'm assuming this is what you meant...}

This is derived from:
y = ax^2 + bx + c

So, by using the 'sum and product' rule:

a × c = 3 × (-6) = -18

b = -3

Now, we find the 'sum' and the 'product' of these two numbers, where b is the 'sum' and a × c is the 'product':

The two numbers are: -6 and 3

Proof:

-6 × 3 = -18 {product}

-6 + 3 = -3 {sum}

Now, since a > 1, we divide a from the results

-6/a = -6/3 = -2

3/a = 3/3 = 1

We then implement these numbers into our equation:

(x - 2) × (x + 1) = 0 {derived from 3x^2 - 3x - 6 = 0}

To find x, we make x the subject of 0:

x - 2 = 0

OR

x + 1 = 0

Therefore:

x = 2

OR

x = -1

So the x-intercepts of the quadratic formula (or solutions to equation 3x^2 - 3x -6 = 0, to put it into your words) are 2 and -1.

We can check this by substituting the values for x:

Let's start with x = 2:

y = 3(2)^2 - 3(2) - 6
= 3(4) - 6 - 6
= 12 - 6 - 6
= 0 {so when x = 2, y = 0, which is correct}

For when x = -1:

y = 3(-1)^2 - 3(-1) - 6
= 3(1) + 3 - 6
= 3 + 3 - 6
= 0 {so when x = -1, y = 0, which is correct}

7 0

3 years ago

Read 2 more answers