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3 years ago

Can you help me with 4 and 5 and 7 please please

Mathematics

1 answer:

Aleksandr [31]3 years ago

6 0

Answer:

4. Nelson: 14; Alison: 36

5. May: 12; April: 18

7. Student: 7; Instructor: 27 -- caveat emptor

Step-by-step explanation:

4. Quick answer: The time between Alison being 2 times her son's age (age ratio = 4:2) and 3 times her son's age is 11 years. That means each "ratio unit" stands for 11 years. 3 years ago, when Alison was 3 times her son's age, he was 11 and she was 33. Now, he is 14 and she is 36.

Check

In 8 years, he will be 22 and she will be 44, twice his age.

If you want to write a system of equations, you can use A for Alison's age and N for Nelson's age.

A+8 = 2(N+8) . . . . relation of ages in 8 years

A -3 = 3(N -3) . . . . relation of ages 3 years ago

We can equate expressions for A:

2(N +8) -8 = A = 3(N -3) +3

2N +8 = 3N -6

14 = N

A = 2(14 +8) -8 = 36

Alison is 36; Nelson is 14.

____

5. Quick answer: The sum of ages 6 years from now will be 36. Then April will be twice May's present age. That is, May's present age is 1/3 0f 36 = 12. April is 30 -12 = 18. Now, April is 18 and May is 12.

Check

10 years from now, April will be 28. That is 4 years more than 2·12 = 24.

Once again, you can write a system of equations:

A + M = 30

A +10 = 2M +4

Again, equating expressions for A, we have ...

30 -M = A = (2M +4) -10

36 = 3M . . . . . simplify, add M+6

12 = M

A = 30 -12 = 18

April is 18; May is 12.

_____

7. Makes no sense. The first sentence says the age difference is 20 years. The second sentence says the age difference is 5 years. It can't be both. Something is missing somewhere.

If we assume the word "twice" is missing, then the system of equations for Instructor and Student can be ...

I = S + 20

I + 8 = 2(S +8) +5

Substituting for I, we have ...

S +20 +8 = 2S +16 +5

7 = S . . . . . . subtract S+21

I = 7+20 = 27

The instructor is 27, the student is 7.

Check

In 8 years, the instructor will be 35 and the student will be 15. At 35, the instructor will be 5 years more than twice the student's age.

We have essentially written our own problem statement here. Your problem statement, and your answer, may vary.

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Answer:

No, the cone will not hold all of the ice cream.

Step-by-step explanation:

Given:

" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a height of 6 inches.

If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches would let it melt.

Now, to explain mathematically will the cone hold all of the ice cream.

Taking the value of π = 3.14.

So, to get the volume of waffle cone we put formula:

Height (h) = 6 inches.

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Thus radius (r) = Diameter ÷ 2 = $\frac{\frac{21}{8}}{2} =\frac{21}{16} \ inches.$

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$Volume=3.14\times \frac{21}{16} \times \frac{21}{16} \times \frac{6}{3}$

$Volume=3.14\times 1.31\times 1.31\times 2$

$Volume=10.78\ inches^3.$

The volume of waffle cone = 10.78 inches³.

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Diameter = $2\frac{7}{8} =\frac{23}{8} \ inches.$

Thus radius (r) = Diameter ÷ 2 $=\frac{\frac{23}{8}}{2} =\frac{23}{16} \ inches.$

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The volume of one scoop of ice cream = 12.47 inches³.

So, as the volume of scoop of ice cream is more than the volume of cone.

Thus, if placing one scoop of ice cream in the cone and let it melt, the cone will not hold all of the ice cream.

Therefore, no the cone will not hold all of the ice cream.

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Answer:

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Step-by-step explanation:

4x^2+12x=7

We need to subtract 7 to get it in the proper form

4x^2+12x-7=7-7

4x^2+12x-7=0

The discriminant is b^2 -4ac

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(12)^2 - 4(4)(-7)

144 +112

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If b^2 -4ac = 0 we have one real root

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Answer:

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Step-by-step explanation:

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