MATHEMATICS MIDDLE SCHOOL

2. If y varies inversely as x and
y = 3 when x = 5, find x when y = 2.5

Answers

Answer 1

Answer:

Step-by-step explanation:

From the law of variation,

y <> 1/x, where <> is the constant of proportionality. Therefore

y = k/x where k is a constant

3 = k/5 and k = 15

To find x when y = 2.5(5/2)

Go back to the second equation

y = k/x

5/2 = 15/x

When you cross multiply

5x = 30.

Divide through by 5,

x = 6.

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When George is 15 years old, His father is 45 years old. How old will his father be when George is half his age

Answers

George's father will be 80 years old when George is half his age.

Half his age is 50 so 35 + 15 is 50 so add that to his dads age

Answer: 80 years old

Numbers that are both larger than –2 and smaller than 3.

Answers

Answer:

vrhrienfv rjrir. rifbt eid r eid f risdfie rifoenr tidbe rkdoed gidiee f8e8ebrbt

Answer:

-1,0,1,2

Step-by-step explanation:

How many different ways can you write a fraction that has a numerator of 2 as a sum of fractions

Answers

Infinitely many ways!
Suppose you have the fraction 2/d.

Pick any pair of integers a and b where b ≠ 0.
Then 2b-ad is and integer, as is bd so that (2b - ad)/bd is a fraction.

Consider the fractions a/b and (2b - ad)/bd

Their sum is
a/b + (2b-ad)/bd = ad/bd + (2b-ad)/bd = 2b/bd = 2/d - as required.

Since a and b were chosen arbitrarily, there are infinitely many possible answers to the question.

An unknown number b is 10 more than an unknown number k. The number b is also k less than 8. The equations to find k and b are shown below:b = k + 10
b = −k + 8

Which is a correct step to find k and b?
Write the points where the graphs of the equations intersect the x-axis. Write the points where the graphs of the equations intersect the y-axis. Add the equations to eliminate k. Multiply the equations to eliminate b.

Answers

Answer:

Add the equations to eliminate k.

Step-by-step explanation:

When we add the equations we get

$2b =18$

$\boxed{b=9}$

next we put $b=9$ into $b=k+10$ and solve for k:

$9=k+10\n\n\boxed{k=-1}$

this way we have found k and b; therefore, adding the equations to eliminate k is a correct step for finding k and b.

Let us now look at other choices we were given.

Write the points where the graphs of the equations intersect the x axis.

These points may be the solutions to each equation, but they are not the solutions to the system of these two equations.

Write the points where the graphs of the equations intersect the y axis.

Same thing goes here: these points may be the solutions to each equation, but they are not the solutions to the system of these two equations.

Multiply the equations to eliminate b.

Multiplying the equations doesn't eliminate b, but rather it complicates the matter by producing a quadratic equation—we don't want to go down that road!

Why is Christopher Columbus important?

Answers

The explorer Christopher Columbus made four trips across the Atlantic Ocean from Spain: in 1492, 1493, 1498 and 1502. He was determined to find a direct water route west from Europe to Asia, but he never did. Instead, he accidentally stumbled upon the Americas..

So basically he was the first explorer to find America.

If f(x) = 2(x)^2 + 5 square root (x+2), complete the following statement (round your answer to the nearest hundredth): f(2) =