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solmaris [256]
3 years ago
7

Segment DF bisects angle EDG. Enter the value of x. The diagram is not to scale.​

Mathematics
1 answer:
maksim [4K]3 years ago
7 0

Answer:

\displaystyle 6 = x

Step-by-step explanation:

Since DF is a SEGMENT BISECTOR, you set 15x and 8x + 42 equal to each other:

8x + 42 = 15x

- 8x - 8x

___________

\displaystyle \frac{42}{7} = \frac{7x}{7} \\ \\ 6 = x

I am joyous to assist you anytime.

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Solve the triangle. Round your answers to the nearest tenth. A. m∠A=43, m∠B=55, a=16 B. m∠A=48, m∠B=50, a=23 C. m∠A=48, m∠B=50,
alexgriva [62]

Answer:

D. m∠A=43, m∠B=55, a=20

Step-by-step explanation:

Given:

∆ABC,

m<C = 82°

AB = c = 29

AC = b = 24

Required:

m<A, m<C, and a (BC)

SOLUTION:

Find m<B using the law of sines:

\frac{sin(B)}{b} = \frac{sin(C)}{c}

\frac{sin(B)}{24} = \frac{sin(82)}{29}

sin(B)*29 = sin(82)*24

\frac{sin(B)*29}{29} = \frac{sin(82)*24}{29}

sin(B) = \frac{sin(82)*24}{29}

sin(B) = 0.8195

B = sin^{-1}(0.8195)

B = 55.0

m<B = 55°

Find m<A:

m<A = 180 - (82 + 55) => sum of angles in a triangle.

= 180 - 137

m<A = 43°

Find a using the law of sines:

\frac{a}{sin(A)} = \frac{b}{sin(B)}

\frac{a}{sin(43)43} = \frac{24}{sin(55)}

Cross multiply

a*sin(55) = 25*sin(43)

a = \frac{25*sin(43)}{sin(53)}

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Caleb has an assignment to draw a contour map. What type of landform is he most likely drawing?
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  • If the contour lines are drawn close, then steeper the figure is. And more distant the lines are drawn, then less steep the figure is.
  • Here, the lines seem to be likely circle in shape. The distance of the outermost contour line is 20 ft. The <u>next inner lines will have reduced values of 20 ft.</u>
  • Therefore, <u>the elevation gets reduced from higher to lower points</u> which provides a diagram of a hill. Since there is no continuous high and low elevations, this cannot be a valley (a range of mountains).
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