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Inessa05 [86]
2 years ago
8

Use an algebraic approach to solve the problem.

Mathematics
1 answer:
qaws [65]2 years ago
6 0

Answer:

Her first exam score was a 78, her second exam score was a 89, and his third exam score was a 94.

Step-by-step explanation:

Use the formula for the mean: sum of elements / number of elements

Let x represent her first exam score.

Her second exam score can be represented by x + 11, since it was 11 points better than her first.

Her third exam score can be represented by (x + 11) + 5, since it was 5 points better than her second.

Plug in all of these expressions into the mean formula. Plug in 87 as the mean, and plug in 3 as the number of elements (since there are 3 scores):

mean = sum of elements / number of elements

87 =  ( (x) + (x + 11) + (x + 11) + 5 ) / 3

Add like terms and solve for x:

87 = (3x + 27) / 3

261 = 3x + 27

234 = 3x

78 = x

So, her first score was a 78.

Find her second score by adding 11 to this:

78 + 11 = 89

Find her third score by adding 5 to the second score:

89 + 5 = 94

Her first exam score was a 78, her second exam score was a 89, and his third exam score was a 94.

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What must the radius of C be for PR to be tangent to it at Q?
Setler79 [48]

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D. 8

Step-by-step explanation:

Draw segment CQ which will be perpendicular to tangent PR.

So, triangle CQR will be right angled triangle right angle at Q.

Let radius of the circle be r.

Therefore,

CQ = CS = r

By Pythagoras Theorem:

{(r + 9)}^{2}  =  {r}^{2}  +  {15}^{2}  \\  \\  {r}^{2}  + 18r + 81 =  {r}^{2}  + 225 \\  \\ 18r = 225 - 81 \\  \\ 18r = 144 \\  \\ r =  \frac{144}{18}  \\  \\ r = 8

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Use mental math to find the equations that are true. Select all that apply. A. 400 ÷ 80 = 50 B. 4 , 000 ÷ 80 = 5 C. 400 ÷ 8 = 50
NeX [460]

As per the mental math calculation, the correct division equations are

C. 400 ÷ 8 = 50

D. 40,000  ÷ 800 = 50

E. 40,000 ÷ 80 = 50

Mental math calculation:

Mental math calculation means a group of skills that allow people to do math “in their head” without using pencil and paper or a calculator.

We can done any type of calculation like addition, subtraction, division etc. based on this method.

Given,

Here we have the following equations,

A. 400 ÷ 80 = 50

B. 4 , 000 ÷ 80 = 5

C. 400 ÷ 8 = 50

D. 40 , 000 ÷ 800 = 50

E. 40 , 000 ÷ 80 = 500

And we need to find the equations that are true by using the mental math calculation.

While we looking into the given expressions,

A. 400 ÷ 80 = 50

This one is false because when we cancel zero, and divide it we get 5 alone.

Then the next one is,

B. 4,000 ÷ 80 = 5

This one is false because when we cancel zero, and divide it we get 50 alone.

Third one is

C. 400 ÷ 8 = 50

This one is true because when we cancel zero, and divide it we get 50 as result.

Next is,

D. 40,000 ÷ 800 = 50

This one is true because when we cancel zero, and divide it we get 50 as result.

Final one,

D. 40,000 ÷ 80 = 500

This one is true because when we cancel zero, and divide it we get 500 as result.

Therefore, options C, D and E are true.

To know more about Mental math here.

brainly.com/question/680614

#SPJ1

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