<h3>Solution</h3>
arc DE = 36/360 × (2 × π × 10)
⟹ 1/10 × 20π
⟹ 2π
⟹ 2 × 3.14
⟹ 6.28 ≈ 6.3 cm (third option)
You answer is: she will make $363
Given:
The figure of two triangle XYZ and UWV.
To find:
The theorem that is used to verify
.
Solution:
In triangle XYZ,
(Angle sum property)
![70^\circ+90^\circ+m\angle Z=180^\circ](https://tex.z-dn.net/?f=70%5E%5Ccirc%2B90%5E%5Ccirc%2Bm%5Cangle%20Z%3D180%5E%5Ccirc)
![160^\circ+m\angle Z=180^\circ](https://tex.z-dn.net/?f=160%5E%5Ccirc%2Bm%5Cangle%20Z%3D180%5E%5Ccirc)
![m\angle Z=180^\circ-160^\circ](https://tex.z-dn.net/?f=m%5Cangle%20Z%3D180%5E%5Ccirc-160%5E%5Ccirc)
![m\angle Z=20^\circ](https://tex.z-dn.net/?f=m%5Cangle%20Z%3D20%5E%5Ccirc)
In triangle XYZ and triangle UWV,
(Right angles)
(Equal measures)
Two angles of one triangle are congruent to corresponding angles of another triangle. So, the triangles are similar by AA property of similarity.
(AA similarity theorem)
Therefore, the correct option is B.
Answer:
CO or C0
Step-by-step explanation:
Answer:
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient.
Step-by-step explanation:
Solving the equation of statement (1) with the quadratic formula:
![x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x_%7B1%2C2%7D%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
![x^2+40x+391=0\\x_{1,2}=\frac{-40\pm\sqrt{40^2-4(1)(391)}}{2(1)}\\x_{1,2}=\frac{-40\pm\sqrt{1600-1564}}{2}\\x_{1,2}=\frac{-40\pm\sqrt{36}}{2}\\x_{1}=\frac{-40+6}{2}=\frac{-34}{2}=-17\\x_{1}=\frac{-40-6}{2}=\frac{-46}{2}=-23\\](https://tex.z-dn.net/?f=x%5E2%2B40x%2B391%3D0%5C%5Cx_%7B1%2C2%7D%3D%5Cfrac%7B-40%5Cpm%5Csqrt%7B40%5E2-4%281%29%28391%29%7D%7D%7B2%281%29%7D%5C%5Cx_%7B1%2C2%7D%3D%5Cfrac%7B-40%5Cpm%5Csqrt%7B1600-1564%7D%7D%7B2%7D%5C%5Cx_%7B1%2C2%7D%3D%5Cfrac%7B-40%5Cpm%5Csqrt%7B36%7D%7D%7B2%7D%5C%5Cx_%7B1%7D%3D%5Cfrac%7B-40%2B6%7D%7B2%7D%3D%5Cfrac%7B-34%7D%7B2%7D%3D-17%5C%5Cx_%7B1%7D%3D%5Cfrac%7B-40-6%7D%7B2%7D%3D%5Cfrac%7B-46%7D%7B2%7D%3D-23%5C%5C)
In this equation, one of the values of x is bigger than -20 but the other is smaller, this statement doesn't give enough information to answer the question.
Solving the quadratic equation of the statement (2):
![x^2=529\\x_{1,2}=\pm\sqrt{529} \\x_1=\sqrt{529}=23\\x_2=-\sqrt{529}=-23](https://tex.z-dn.net/?f=x%5E2%3D529%5C%5Cx_%7B1%2C2%7D%3D%5Cpm%5Csqrt%7B529%7D%20%5C%5Cx_1%3D%5Csqrt%7B529%7D%3D23%5C%5Cx_2%3D-%5Csqrt%7B529%7D%3D-23)
Again, one of the values of x is bigger than -20 and the other is smaller than -20. But if the information of this statement is considered along with the other x must be equal to -23, that is the value that appears as an answer in both equations, and with this information is possible to answer the question.