Answer in fraction form: x = 55/4
Answer in decimal form: x = 13.75
Both forms are equivalent, but they say it in a slightly different way.
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Work Shown:
AC/QY = CD/YW
(x+5)/15 = 5/4
4(x+5) = 15*5
4x+20 = 75
4x = 75-20
4x = 55
x = 55/4
x = 13.75
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Explanations:
- The first step is possible because the polygons are similar. Similar figures have their corresponding sides be in the same proportion or ratio. Note how side AC has the double red angle (at point A) and a single red angle (point C). The side QY has the same idea in the same order. This is why AC corresponds to QY. The ratio AC/QY is the same as CD/YW.
- In the second step, I plugged in the expressions that the diagram shows. This is the substitution property.
- On step 3, I cross multiplied. The general format is A/B = C/D cross multiplies to A*D = B*C.
Answer:
![a=10.92 units](https://tex.z-dn.net/?f=a%3D10.92%20units)
![b=14.51 units](https://tex.z-dn.net/?f=b%3D14.51%20units)
Step-by-step explanation:
We are given that c=6 units
![\angle A=43^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20A%3D43%5E%7B%5Ccirc%7D)
![\angle B=115^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20B%3D115%5E%7B%5Ccirc%7D)
We have to find the side length a and b.
We know that sum of angles of a triangle =180 degrees
![\angle A+\angle B+\angle C=180](https://tex.z-dn.net/?f=%5Cangle%20A%2B%5Cangle%20B%2B%5Cangle%20C%3D180)
Substitute the values then we get
![43+115+\angle C=180](https://tex.z-dn.net/?f=43%2B115%2B%5Cangle%20C%3D180)
![158+\angle C=180](https://tex.z-dn.net/?f=158%2B%5Cangle%20C%3D180)
![\angle C=180-158=22^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20C%3D180-158%3D22%5E%7B%5Ccirc%7D)
sine law: ![\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%20A%7D%3D%5Cfrac%7Bb%7D%7Bsin%20B%7D%3D%5Cfrac%7Bc%7D%7Bsin%20C%7D)
![\frac{a}{sin 43^{\circ}}=\frac{6}{sin 22^{\circ}}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%2043%5E%7B%5Ccirc%7D%7D%3D%5Cfrac%7B6%7D%7Bsin%2022%5E%7B%5Ccirc%7D%7D)
![a=\frac{6}{sin 22^{\circ}}\times sin 43^{\circ}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B6%7D%7Bsin%2022%5E%7B%5Ccirc%7D%7D%5Ctimes%20sin%2043%5E%7B%5Ccirc%7D)
![a=10.92 units](https://tex.z-dn.net/?f=a%3D10.92%20units)
![\frac{b}{sin 115^{\circ}}=\frac{6}{sin 22^{\circ}}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Bsin%20115%5E%7B%5Ccirc%7D%7D%3D%5Cfrac%7B6%7D%7Bsin%2022%5E%7B%5Ccirc%7D%7D)
![b=\frac{6}{sin 22^{\circ}}\times sin 115^{\circ}=14.51](https://tex.z-dn.net/?f=%20b%3D%5Cfrac%7B6%7D%7Bsin%2022%5E%7B%5Ccirc%7D%7D%5Ctimes%20sin%20115%5E%7B%5Ccirc%7D%3D14.51)
![b=14.51 units](https://tex.z-dn.net/?f=b%3D14.51%20units)
Answer:
72
Step-by-step explanation:
9/11 = ?/88
<em>multiply each side by 8 (because 88 divided by 11 is 8)</em>
72/88 = ?/88
<em>multiply each side by 88</em>
72 = ?
Answer:
the answer is A. Elijah is correct.
Answer:
The answer to your question is letter D
Step-by-step explanation:
Formula
m∠E = ![\frac{1}{2} ( DGF - DF)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%28%20DGF%20-%20DF%29)
Data
m∠E = 48°
DGF = 228°
DF = x°
Substitution
48° = ![\frac{1}{2} ( 228° - x°)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%28%20228%C2%B0%20-%20x%C2%B0%29)
Solution
2(48) = 228 - x°
96 = 228 - x°
96 - 228 = - x°
- 132 = - x°
x° = 132°