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4 years ago

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Triangle X Y Z is shown. The length of X Z is 16, the length of Y Z is 12, and the length of Y X is 17. Law of cosines: a2 = b2

+ c2 – 2bccos(A) What is the measure of AngleY to the nearest whole degree? 58° 64° 68° 73°

2 answers:

ehidna [41]4 years ago

8 0

Answer:

64

Step-by-step explanation:

11Alexandr11 [23.1K]4 years ago

5 0

Answer:

Therefore A = $cos^{-1}$ (0.4338) = 64.29°

Step-by-step explanation:

i) Law of cosines: $a^{2}$ = $b^{2}$ + $c^{2}$ – 2bccos(A)

ii) XZ = a = 16 , YZ = b = 12, XY = 17, ∠Y = ∠A

iii) $16^{2}$ = $12^{2}$ + $17^{2}$ - (2 $\times$ 12 $\times$ 17 $\times$ cos(A))

⇒ 256 = 144 + 289 - 408cos(A)

⇒ 256 - 144 - 289 = -408cos(A)

⇒ -177 = -408cos(A)

⇒ cos A = $\frac{-177}{-408}$ = 0.4338

Therefore A = $cos^{-1}$ (0.4338) = 64.29°

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What would y=x^2 +x+ 2 be in vertex form

balu736 [363]

Answer:

$y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

Step-by-step explanation:

$y = {x}^{2} + x + 2$

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

$y = a(x - h)^{2} + k$

The following equation above is the vertex form of Quadratic Function.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Formula</u>

$h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a}$

We substitute the value of these terms from the standard form.

$y = a {x}^{2} + bx + c$

$h = - \frac{1}{2(1)} \\ h = - \frac{ 1}{2}$

Our h is - 1/2

$k = \frac{4(1)(2) - ( {1})^{2} }{4(1)} \\ k = \frac{8 - 1}{4} \\ k = \frac{7}{4}$

Our k is 7/4.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Calculus</u>

We can use differential or derivative to find the vertex as well.

$f(x) = a {x}^{n}$

Therefore our derivative of f(x) —

$f'(x) = n \times a {x}^{n - 1}$

From the standard form of the given equation.

$y = {x}^{2} + x + 2$

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

$f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times {x}^{1 - 1} ) + 0$

Any constants that are differentiated will automatically become 0.

$f'(x) = 2 {x}+ 1$

Then we substitute f'(x) = 0

$0 =2x + 1 \\ 2x + 1 = 0 \\ 2x = - 1 \\x = - \frac{1}{2}$

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

$y = {x}^{2} + x + 2$

$y = ( - \frac{1}{2} )^{2} + ( - \frac{1}{2} ) + 2 \\ y = \frac{1}{4} - \frac{1}{2} + 2 \\ y = \frac{1}{4} - \frac{2}{4} + \frac{8}{4} \\ y = \frac{7}{4}$

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

$y = a {(x - h)}^{2} + k \\ y = (x - ( - \frac{1}{2} ))^{2} + \frac{7}{4} \\ y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

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3 years ago

VashaNatasha [74]

Answer:

-7.11°F

Step-by-step explanation:

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4 0

3 years ago

What is the sum of all the angles that are labeled?

Tasya [4]

Based on the information provided, the sum of all the labeled angles is 235° (option b).

<h3>How to calculate the sum of all labeled angles?</h3>

To calculate the sum of all the labeled angles we must add the different values of each labeled angle as shown below:

80° + 92° + 40° + 23° = 235°

According to the above, it can be inferred that the correct option is B because the result of the sum of the values coincides with this sum.

Learn more about degrees in: brainly.com/question/1217620

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2 years ago

Confused on my math work.

MrRissso [65]

Answer:

The right answer is the last option, 12,12.

Step-by-step explanation:

$GI^2=FI*IH\\ GI^2 = 7*21\\ GI = \sqrt{147}$

$\sqrt{147} = 12,124... = 12,12$

7 0

3 years ago

An electronics company has four stores, all about the same size, within the city. The graph shows last month’s sales figures for

Burka [1]

Answer:

Answer: 1/10 of the store's total sales last month were in appliances (lower right corner)

Step-by-step explanation:

Explanation:

Let's go through the four possible answers

In the upper left corner it says "Total mobile phone sales is likely 27,000" which is a paraphrase of what is given. The chart gives 9000 as the phone sales for that one particular store. If all stores are identical in performance, then we have 4*9000 = 36000 in total mobile phone sales. Of course, it's impossible to know for sure how the other stores did. So we can eliminate this as one of the answers.

In the upper right corner, it says "13% of the stores sales was in car electronics" (also paraphrased). We have 13 thousand in car electronics out of 17+13+6+9+15 = 60 thousand total. Divide the two values: 13/60 = 0.2167 = 21.67% approximately. So we can eliminate this as an answer.

In the lower left corner, it says "the total sales is likely greater than $300,000" but we don't know for sure because again we don't have the other charts for the three other stores. Assuming the four stores perform the same, then we'd have 4*60 = 240 thousand as the total and not 300 thousand. It's safe to say we can eliminate this as an answer.

In the lower right corner, it says "1/10 of the stores sales were appliances". This statement is true. Why? Because 6 thousand is the sales figure for appliances out of 60 thousand total. Divide the values: 6/60 = 1/10. So this is why the lower right corner is the answer.

4 0

3 years ago