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3 years ago

Solve the system of linear equations by elimination. 3x+2y=3 3x−2y=−9

Mathematics

1 answer:

kondaur [170]3 years ago

6 0

Answer:

x=-1, y=3

Step-by-step explanation:

3x+2y=3

3x-2y=-9

since we have -2y and 2y we can just add the equations

6x=-6

x+0y=-1

x=-1

to solve x using elimination multiply the top equation by -1

-3x-2y= -3

3x-2y=-9

and add

0x-4y=-12

-4y=-12

y=3

and substitute x and y to double; check

3(-1)+2(3)=3

-3+6=3

3=3

checks out so these are correct

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What is 80 in its simplest form as a fraction?

Ann [662]

I believe the correct given problem is:

“What is 80% in its simplest form as a fraction?”

Take note that you missed to place the percent sign which is very important.

Now to solve this, 80% when converted to decimal form is 0.80 which means that you have 80 parts per 100 parts. Therefore the fraction form of this would be 80 / 100.

fraction = 80 / 100

However this fraction is not yet the answer because we can still simplify this further. First step in simplifying is to divide both the numerator and denominator by 10 so that we are left with:

8 / 10

Next step is to divide by 2:

4 / 5

Now we can see that we can no longer divide this (numbers should be whole number). Therefore the simplest form as a fraction is 4/5

Answer:

4/5

6 0

3 years ago

You and Mr. Fowles have decided to race each other at the Boston Marathon (26 miles long). Mr. Fowles runs at a steady 4.2 miles

Maslowich

Answer:

The answer is below

Step-by-step explanation:

Speed is the time rate of change of velocity, it is the ratio of distance to time.

Mr. Fowles runs at a steady 4.2 miles per hour. The time taken to cover 26 miles is:

speed = distance / time

time = distance / speed = 26 / 4.2 = 6.19 hour

I run at 3 miles per hour. I was given 3 mile lead, so the remaining distance is 23 miles (26 - 3). The time needed to complete the 23 miles is:

time = distance / speed = 23 / 3 = 7.67 hour

a) Let d be the distance Mr Fowles catches me. Hence:

time = (d + 3)/4.2; also time = d/3

(d + 3)/4.2 = d/3

3d + 9 = 4.2d

1.2d = 9

d = 7.5 miles

He would catch me at 10.5 (7.5 + 3) miles from the starting point.

b) Mr. fowles finishes after 6.19 hour. At that time, the distance is have covered is:

distance = 6.19 * 3 mi/hr = 18.57 mile

Distance behind = 23 mile - 18.57 = 4.43 mile

c) time longer = 7.67 hour - 6.19 hour = 1.48 hour

4 0

2 years ago

A toy manufacturer wants to know how many new toys children buy each year. A sample of 601 children was taken to study their pur

Lilit [14]

Answer:

The confidence interval is 6.6<μ<6.8.

Step-by-step explanation:

We have:

Number of observations = 601

Mean = 6.7

Standard deviation σ = 1.5

The z-score for a 95% confidence interval is 1.96.

The limits of the confidence interval can be calculated as

$X \pm z*\frac{\sigma}{\sqrt{n}}\\\\LL=X-z*\frac{\sigma}{\sqrt{n}}=6.7-1.96*\frac{1.5}{\sqrt{601} } =6.7-0.1199=6.6\\\\UL=X+z*\frac{\sigma}{\sqrt{n}}=6.7+1.96*\frac{1.5}{\sqrt{601} } =6.7+0.1199=6.8$