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klemol [59]
4 years ago
7

Select the correct answer from each drop-down menu. In the figure, line segment AB is parallel to line segment CD. The measure o

f angle C is degrees, and the measure of angles D is degrees.

Mathematics
1 answer:
victus00 [196]4 years ago
3 0
<h3>Answer:</h3>

∠C = 40°

∠D = 75°

<h3>Step-by-step explanation:</h3>

AB ║ CD, so AD and BC are transversals. The angle pairs (A, D) and (B, C) are "alternate interior angles", hence congruent.

∠C = ∠B = 40°

∠D = ∠A = 75°

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What is the answer to the system of equations problem<br> 3x=2y+10<br> 9y=3x-7
Gemiola [76]
Solving:

\left \{ {{3x = 2y + 10} \atop {9y = 3x-7}} \right.
<span>Organize by putting the unknowns left and right the numbers without letter, changing the signal when changing sides.
</span>\left \{ {{3x-2y=10\:(I)} \atop {-3x+9y=-7\:(II)}} \right.
<span>Eliminate opposites (+ 3x and -3x)
</span>\left \{ {{\diagup\!\!\!\!3x-2y=10} \atop {-\diagup\!\!\!\!3x+9y=-7}} \right.
\left \{ {{-2y=10} \atop {9y=-7}} \right.
----------------------------
7y = 3
\boxed{y =  \frac{3}{7} }

<span>Now substitute the found value "y" in the first equation:
</span>3x-2y=10\:(I)
3x-2* \frac{3}{7} =10
3x- \frac{6}{7} = 10
\frac{21x}{\diagup\!\!\!\!7} - \frac{6}{\diagup\!\!\!\!7} = \frac{70}{\diagup\!\!\!\!7}
21x - 6 = 70
21x = 70 + 6
21x = 76
\boxed{x =  \frac{76}{21} }

Answer:
(x,y) = ( \frac{76}{21} ,  \frac{3}{7} )\end{array}}\qquad\quad\checkmark


<span>
Taking the truth proof
</span>
3x - 2y = 10\:(I)
3* \frac{76}{21} - 2* \frac{3}{7} = 10
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\frac{1596-126}{147} = 10
\frac{1470}{147} = 10
10 = 10\:(TRUE)






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