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3 years ago

Three friends got the prize money worth $231,000

Mathematics

2 answers:

Semmy [17]3 years ago

6 0

Answer: y = $11,000

z = 4($11,000) = $44,000

x = 4($44,000) = $176,000

Step-by-step explanation:

Degger [83]3 years ago

5 0

There are three unknowns in this problem. First, let's assign variables for these unknowns.

Let
x be the amount received by the first friend
y be the amount received by the second friend
z be the amount received by the third friend

Next, we formulate equations for the relationships

x = 4z
z = 4y
x + y + z = $231,000

Solving simultaneously,

4(4y) + y + 4y = $231,000
21y = $231,000
y = $11,000
z = 4($11,000) = $44,000
x = 4($44,000) = $176,000

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13 POINTS- please help me

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Answer:

See explanation

Step-by-step explanation:

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$6x+20=x+100\\ \\6x-x=100-20\\ \\5x=80\\ \\x=16$

Then

$(6x+20)^{\circ}=(6\cdot 16+20)^{\circ}=116^{\circ}\\ \\(x+100)^{\circ}=(16+100)^{\circ}=116^{\circ}$

17. Two parallel lines are cut by transversal. Angles with measures $(2x+12)^{\circ}$ and $(3x-22)^{\circ}$ are alternate interior angles. By alternate interior angles, the measures of alternate interior angles are the same:

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Then

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18. Two parallel lines are cut by transversal. Angles with measures $(6x-7)^{\circ}$ and $(5x+10)^{\circ}$ are alternate exterior angles. By alternate interior angles, the measures of alternate exterior angles are the same:

$6x-7=5x+10\\ \\6x-5x=10+7\\ \\x=17$

Then

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19. The diagram shows two complementary angles with measures $2x^{\circ}$ and $56^{\circ}$ . The measures of complementary angles add up to $90^{\circ},$ then

$2x+56=90\\ \\2x=90-56\\ \\2x=34\\ \\x=17$

Hence,

$2x^{\circ}=2\cdot 17^{\circ}=34^{\circ}$

Check:

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20. Angles $\angle 1$ and $\angle 2$ are vertical angles. By vertical angles theorem, vertical angles are congruent, so

$m\angle 1=m\angle 2\\ \\5x+7=3x+15\\ \\5x-3x=15-7\\ \\2x=8\\ \\x=4$

Hence,

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Therefore,

$m\angle 5=(3x-40)^{\circ}=(3\cdot 34-40)^{\circ}=62^{\circ}\\ \\m\angle 8=(7x-120)^{\circ}=(7\cdot 34-120)^{\circ}=118^{\circ}\\ \\62^{\circ}+118^{\circ}=180^{\circ}$

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3 years ago

Three friends got the prize money worth ​$231,000

Three friends got the prize money worth $231,000