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2 years ago

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

Mathematics

1 answer:

Aleksandr [31]2 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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3 years ago

Read 2 more answers

The equation h = 0.019s

TEA [102]

Answer:

s = 28.09 m/s

Step-by-step explanation:

Given that,

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We need to find the wind speed if the largest waves are 15 feet high.

Put h = 15 feet in the above equation as follows :

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3 years ago

Please help me ! Reduced to lowest terms

Mandarinka [93]

Answer:

Step-by-step explanation:

7) 2ab + 4ac = 2*a*b + 2 *2 *a*c

= 2a(b + 2c)

$\dfrac{2ab^{2}c}{2ab+4ac}=\dfrac{2*a* b^{2}*c}{2a(b+2c)}\\\\\\\text{2a in the denominator and numerator get cancelled}\\\\ = \dfrac{b^{2}c}{b+2c}$

8) ac - a²c² = c( a - a²c)

bc - abc = c(b - ab)

$\dfrac{ac - a^{2}c^{2}}{bc-abc^{2}}=\dfrac{c(a-a^{2}c)}{c(b-ab)}\\\\$

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9) b²+ 4b - 5 = b² + 5b - 1b - 5

= b(b + 5) - 1(b + 5)

= (b +5)(b - 1)

b² + 8b + 15 = b² + 5b + 3b + 15

= b(b + 5) + 3(b + 5)

= (b + 5 )(b + 3)

$\dfrac{b^{2}+4b-5}{b^{2}+8b+15}=\dfrac{(b+5)(b-1)}{(b+5)(b+3)}\\\\\\$

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8 0

2 years ago

Find f¹(x) for the function f(x) = -4. 2 f¹(x) = [?]x + [ ]

g100num [7]

Answer:

${f}^{ - 1}(x) = 2x + 8$

Step-by-step explanation:

$f(x) = \frac{x}{2} - 4 \\ \\ y = \frac{x}{2} - 4 \\ \\ y = \frac{x - 8}{2} \\ \\ x = 2y + 8 \\ \\ {f}^{ - 1} (x) = 2x + 8$

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2 years ago

NEED HELP FAST!!

Dafna11 [192]

Answer:

see below

Step-by-step explanation:

dilation with a scale factor of 1/3 means the distances to the center shrink by 1/3

so for center (4,-2)

distance of (7,4) is 3 n 6 to center

1/3 of distance = 1 n 2

so (7,4) become (4+1, -2+2) = (5, 0) after the dilation

similarly u can find the other 2 pts

distance of (-2,4) is -6 n 6 to center

1/3 of distance = -2 n 2

so (-2,4) become (4-2, -2+2) = (2, 0) after the dilation

distance of (1, 10) is -3 n 12 to center

1/3 of distance = -1 n 4

so (1,10) become (4-1, -2+4) = (3, 2) after the dilation

plot the new triangle using the 3 pts

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2 years ago