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2 years ago

10 points. Please help me with numbers 9-13. Numbers 9-13 is the picture.

Mathematics

1 answer:

melomori [17]2 years ago

8 0

Answer:

x = 18

y = 15

Step-by-step explanation:

Remark

Step One

The main step is to realize that if the lower left hand angle is 90 degrees, then the upper left hand angle is also 90. That is because the interior angles of parallel lines are supplementary. If one of the angle is 90 degrees, so is the other.

Conclusion from the Remark

5x = 90

x = 90/5

x = 18 degrees

Step Two

Find y

y is just a bit harder to find . The safest way is to add all four interior angles together. For any trap*zoid (you cannot spell this word properly. The editor has a fit), the interior angles add up to 360 degrees.

So just add the 4 angles together and equate to 360

5(y + 11) + 4y - 10 + 90 + 90 = 360 Combine like terms

5(y + 11) + 4y - 10 + 180 = 360 Combine again

5(y + 11) + 4y + 170 = 360 Subtract 170 from both sides

5(y + 11) + 4y = 360 - 170 Combine like terms

5(y + 11) + 4y = 190 Remove the brackets

5y + 55 + y4 = 190 Combine like terms

9y + 55 = 190 Subtract 55 from both sides.

9y = 190 - 55

9y = 135 Divide by 9

y = 135 / 9

y = 15

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Step-by-step explanation:

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D. 3x + 5(x - 1)

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17.) A, B, D

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4 0

1 year ago

General solutions of sin(x-90)+cos(x+270)=-1 {both 90 and 270 are in degrees}

mixer [17]

Answer:

$\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

Step-by-step explanation:

Given:

$\sin (x-90^{\circ})+\cos(x+270^{\circ})=-1$

First, note that

$\sin (x-90^{\circ})=-\cos x\\ \\\cos(x+270^{\circ})=\sin x$

So, the equation is

$-\cos x+\sin x= -1$

Multiply this equation by $\frac{\sqrt{2}}{2}:$

$-\dfrac{\sqrt{2}}{2}\cos x+\dfrac{\sqrt{2}}{2}\sin x= -\dfrac{\sqrt{2}}{2}\\ \\\dfrac{\sqrt{2}}{2}\cos x-\dfrac{\sqrt{2}}{2}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos 45^{\circ}\cos x-\sin 45^{\circ}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos (x+45^{\circ})=\dfrac{\sqrt{2}}{2}$

The general solution is

$x+45^{\circ}=\pm \arccos \left(\dfrac{\sqrt{2}}{2}\right)+2\pi k,\ \ k\in Z\\ \\x+\dfrac{\pi }{4}=\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{4}\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

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2 years ago

Two times a number increased by 7.

Akimi4 [234]

Answer:

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7 0

2 years ago

Read 2 more answers

What additional information do you need to prove ∆ABC ≅ ∆DEF by the SAS Postulate?

Anton [14]

Answer: BC = EF (third choice)

The acronym SAS stands for "side angle side". Specifically it refers to using two pairs of sides, and one pair of angles between the sides, to prove the triangles congruent.

We are given that AC = FD as one pair of congruent sides (shown by the similar tickmarks). Also, we are given the angles C and F are congruent as well. We need another pair of sides to be congruent. We can't use AB and DE because those sides are not adjacent to the congruent angles mentioned. So the only thing possible is BC = EF

Check out the attached image below.

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2 years ago

A 21- pound turkey was cooked for a small banquet. The caterer figures they will discard 6 pounds of bone and that each person w

salantis [7]

Answer:

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Step-by-step explanation:

(21 - 6) / 0.6

21 pound turkey, take away 6

Divide up the remaining number (15) by 0.6 which equals 25

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