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2 years ago

Please try to give me the answers

Mathematics

1 answer:

gladu [14]2 years ago

5 0

Answer:

a = 1, b = 2, c = 3

Step-by-step explanation:

$a + \frac{1}{b + \frac{1}{c} } = \frac{10}{7} \\ \\ a + \frac{1}{b + \frac{1}{c} } = 1 + \frac{3}{7} \\ \\ a + \frac{1}{b + \frac{1}{c} } = 1 + \frac{1}{\frac{7}{3} } \\ \\ a + \frac{1}{b + \frac{1}{c} } = 1 + \frac{1}{2 + \frac{1}{3} } \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ a = 1 \\ \\ b = 2 \\ \\ c = 3$

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3 years ago

The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Wri

emmainna [20.7K]

Answer:

a. i. x + y = 180 (1) and x - 4y = 5 (2)

ii. The two acute angles are 35° each and the two obtuse angles are 145° each.

Step-by-step explanation:

a. The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.

i. Write a system of equations to find the measures of all the angles.

Let x be the obtuse angles and y be the acute angles.

Since we have two obtuse angles at the top of the isosceles trapezoid and two acute angles at the bottom of the isosceles trapezoid, and also, since the sum of angles in a quadrilateral is 360, we have

2x + 2y = 360

x + y = 180 (1)

Its is also given that the measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles.

So, x = 4y + 5 (2)

x - 4y = 5 (2)

So, our system of equations are

x + y = 180 (1) and x - 4y = 5 (2)

ii. Solve a system of equations to find the measures of all the angles.

Since

x + y = 180 (1) and x - 4y = 5 (2)

Subtracting (2) from (1), we have

x + y = 180 (1)

x - 4y = 5 (2)

5y = 175

dividing both sides by 5, we have

y = 175/5

y = 35°

From (1), x = 180° - y = 180° - 35° = 145°

So, the two acute angles are 35° each and the two obtuse angles are 145° each.

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3 years ago

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2 years ago

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3 years ago

I DONT KNOW THESE! HELP!

kkurt [141]

Answer:

20. x = 5, y = -2

21. x = 11, y = 12

22. x = 22, y = 11

23. x = 11, y = 10

Step-by-step explanation:

20. Opposite sides in the parallelogram are congruent, so

$2y+18=3x-1\\ \\6x-3=17-5y$

Solve this system of two equations:

$\left\{\begin{array}{l}2y-3x=-19\\ \\6x+5y=20\end{array}\right.$

Multiply the first equation by 2 and add two equations:

$2(2y-3x)+6x+5y=2\cdot (-19)+20\\ \\4y-6x+6x+5y=-38+20\\ \\9y=-18\\ \\y=-2$

Substitute it into the first equation:

$2\cdot (-2)-3x=-19\\ \\-3x=-19+4\\ \\-3x=-15\\ \\x=5$

21. Opposite angles in the parallelogram are congruent, so

$11x+5=10y+6$

Consecutive angles are supplementary, so

$6x-y+11x+5=180^{\circ}$

Solve this system of two equations:

$\left\{\begin{array}{l}11x-10y=1\\ \\17x-y=175\end{array}\right.$

From the second equation

$y=17x-175$

Substitute it into the first equation:

$11x-10(17x-175)=1\\ \\11x-170x+1750=1\\ \\-159x=-1749\\ \\x=11\\ \\y=17\cdot 11-175=187-175=12$

22. Opposite angles in the parallelogram are congruent, so

$2x-5=3y-12$

Consecutive angles are supplementary, so

$2x-5+7y+x=180^{\circ}$

Solve this system of two equations:

$\left\{\begin{array}{l}2x-3y=-7\\ \\3x+7y=185\end{array}\right.$

From the first equation

$x=-3.5+1.5y$

Substitute it into the second equation:

$3(-3.5+1.5y)+7y=185\\ \\-10.5+4.5y+7y=185\\ \\-105+45y+70y=1,850\\ \\115y=1,850+105\\ \\115y=1,955\\ \\y=17\\ \\x=-3.5+1.5\cdot 17=22$

23. Opposite sides in the parallelogram are congruent, so

$2x+9=4y-9\\ \\3x-5=2y+8$

Solve this system of two equations:

$\left\{\begin{array}{l}2x-4y=-18\\ \\3x-2y=13\end{array}\right.$

Multiply the second equation by 2 and subtract it from the first equation:

$2x-4y-2(3x-2y)=-18-2\cdot 13\\ \\2x-4y-6x+4y=-18-26\\ \\-4x=-44\\ \\x=11$

Substitute it into the first equation:

$2\cdot 11-4y=-18\\ \\-4y=-18-22\\ \\-4y=-40\\ \\y=10$

3 0

3 years ago