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3 years ago

Hazel works at The Last Page Booksellers. Her total earnings were $24,000 last year. Hazel

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

4 0

Answer:

Step-by-step explanation:

157x24 = ...

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Natalie walked 3/5 miles in 1/2 hour . How fast did she walk, in miles per hour?

ella [17]

Answer:

6/5

Step-by-step explanation:

you multiply by 2

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3 years ago

2 ^ x - 12/2 ^ x is equal to -4

Anastaziya [24]

Answer:

-3071/16

Step-by-step explanation:

Hope this helps, if you wrote it wrong or need help understanding please let me know!

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3 years ago

What is the nth term rule of the quadratic sequence below?<br> 8,14,22,32 ,44, 58, 74...

DanielleElmas [232]

Answer:

y=n^2+3n+4

Step-by-step explanation:

Sequence,S: 8,14,22,32 ,44, 58, 74...

First differences of S: 6,8,10,12,14,16,...

Second differences of S: 2,2,2,2,2,2,....

It is indeed a quadratic since the 1st differences that are the same are the second differences.

So the 1st term is 8. If the 0th term was listes it would be 4 since 8-4=4 and 6-4=2.

This means our quadratic it is in the form

y=an^2+bn+c where c=4.

So we have y=an^2+bn+4.

Now we can find a and b using two points from our sequence to form a system of equations to solve.

(1,8) gives us 8=a(1)^2+b(1)+4

Simplifying gives 8=a+b+4

Subtracting 4 on both sides gives: 4=a+b

(2,14) gives us 14=a(2)^2+b(2)+4

Simplifying gives 14=4a+2b+4

Subtracting 4 on both sides gives 10=4a+2b

So we have the following system to solve:

4=a+b

10=4a+2b

I'm going to solve using elimination/linear combination style.

Dividing second equation by 2 gives the system as:

4=a+b

5=2a+b

Subtract the 2nd equation from the first gives:

-1=-1a

This implies a=1 since -1=-1(1) is true.

If a+b=4 and a=1, then b=3. Because 3+1=4.

So the equation is y=1n^2+3n+4 or y=n^2+3n+4.

8 0

3 years ago

Solve the compound inequality 8 < 3 - 5x < 18

otez555 [7]

Answer:

−1 > x > −3

Step-by-step explanation:

Let's solve your inequality step-by-step.

8<3−5x<18

6 0

3 years ago

A lab technician made a 14 cm diameter hole through the middle of a cylinder that has a diameter of 20 cm and a height of 28 cm.

Step2247 [10]

Answer:

The volume of the finished cylinder is $4486.2 m^3$

Step-by-step explanation:

To find the volume of the finished cylinder, we have to first find the volume of the hole (with 14 cm diameter and a height of 28 cm) and subtract it from the volume of the original cylinder (with diameter of 20 cm and a height of 28 cm).

Note: The hole is also cylindrical in shape.

The volume of a cylinder is given as:

$V = \pi r^2h$

where r = radius, h = height

VOLUME OF THE HOLE

The diameter of the hole is 14 cm, hence, its radius is 7 cm (14 / 2 = 7)

Its volume is:

$V = \pi *7^2 * 28\\V = 4310.3 m^3$

VOLUME OF THE ORIGINAL CYLINDER

The diameter of the cylinder is 20 cm, hence, its radius is 10 cm (20 / 2 = 10)

Its volume is:

$V = \pi *10^2 * 28\\V = 8796.5 m^3$

Hence, the volume of the finished cylinder will be:

$8796.5 - 4310.3 = 4486.2 m^3$

The volume of the finished cylinder is $4486.2 m^3$

8 0

3 years ago