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3 years ago

Using the diagram, calculate the values of the unknown variables: a, b, and c.

Mathematics

1 answer:

Lady_Fox [76]3 years ago

3 0

Answer:

a = 82

b = 130

c = 118

Step-by-step explanation:

A quadrilateral is inscribed in a circle. So, it is a cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

Therefore,

a° + 98° = 180°

a° = 180° - 98°

a° = 82°

a = 82

By inscribed angle theorem:

a° = 1/2(b° + 34°)

82° * 2 = b° + 34°

164° - 34° = b°

b° = 130°

b = 130

Again by inscribed angle theorem:

76° = 1/2(c° + 34°)

76° *2 = c° + 34°

152° - 34° = c°

c° = 118°

c = 118

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3 years ago

5 pounds of apples cost $12. How many pounds of apples can you buy for $1.

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3 years ago

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A collection of nickels and dimes is worth $9.45. If the number of dimes is doubled, the value is

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Answer:

The number of nickels is 45 and the number of dimes is 72.

Step-by-step explanation:

Let

x ----> number of nickels

y ----> number of dimes

Remember that

$1\ nickel=\$0.05$

$1\ dime=\$0.10$

$0.05x+0.10y=9.45$ ------> equation A

$0.05x+0.10(2y)=16.65$

$0.05x+0.20y=16.65$ ------> equation B

<em>Solve the system by substitution</em>

we have

$0.05x+0.10y=9.45$ ------> equation A

$0.05x+0.20y=16.65$ ------> equation B

Multiply both equations by 100 both sides

$5x+10y=945$ ----> $5x=945-10y$ --> equation C

$5x+20y=1,665$ ----> equation D

substitute equation C in equation D

$(945-10y)+20y=1,665$

solve for y

$945+10y=1,665$

$10y=1,665-945$

$10y=720$

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Find the value of x

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<em>Alternative Method</em>

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

the solution is the point (45,72)

therefore

The number of nickels is 45 and the number of dimes is 72.

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3 years ago

In the question, "35 is what percent of 40?" what is the 35?

schepotkina [342]

Answer:

35 is the 'is' and 40 is the 'of'

Step-by-step explanation:

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35/40 = x/100

cross-multiply to get:

40x = 3500

x = 3500/40

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