MATHEMATICS HIGH SCHOOL

A square and a rectangle have the same area. The length of the rectangle is twelve more than twice times the side of the square. The width of the rectangle is eight less than the side of the square. Let x be the length of the side of the square. Using the information above, what is the value of x?

Answers

Answer 1

Answer:

Answer:

$x = 12$

Step-by-step explanation:

Given

Shapes: Square and Rectangle

Square:

$Length = x$

Rectangle:

$Length = 12 + 2x$

$Width = x- 8$

Required

Find x

First, we calculate the area of the square.

$Area = x * x$

$Area = x^2$

Next, we calculate the area of the rectangle

$Area = (12 + 2x) * (x - 8)$

$Area = 12x -96 + 2x^2 - 16x$

$Area = 2x^2 - 16x + 12x -96$

$Area = 2x^2 -4x -96$

Since both areas are equal, we have:

$x^2 = 2x^2 -4x -96$

Equate to 0

$2x^2 -x^2 -4x -96= 0$

$x^2 -4x -96= 0$

Expand:

$x^2 - 12x + 8x -96 = 0$

$x(x - 12) + 8(x - 12) = 0$

$(x + 8)(x - 12) = 0$

$x + 8 = 0$ or $x - 12 = 0$

$x = -8$ or $x = 12$

But x can't be negative.

Hence:

$x = 12$

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it is called the POLE hope i am the brainliest i need it to gt the next rank

Answer:

In polar coordinates, the origin is called the pole.

Paulo uses an instrument called a densitometer to check that he has the correct ink colour.For this print job the acceptable range for the reading on the densitometer is 1.8 ± 10%.

What is the acceptable range for the densitometer reading?

exactly 1.8

from 0 to 3.6

from 1.0 to 2.6

from 1.62 to 1.98

from 1.8 to 1.98

Answers

If it is said that the range of the answer should be +/- 10% of the particular value, we have to find out the percentage of that particular value. Therefore 10% of 1.8 is,

1.8 * 10/100 = 0.18

If we add this value to the original value,
1.8+0.18 = 1.98

If we subtract this value from the original value,
1.8-0.18 = 1.62

therefore the range will be,
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John has a large number of pennies, dimes, and quarters. How many ways can he make $1.00out of his coins? Note that order doesn’t matter.

Answers

Answer:

28 ways

Step-by-step explanation:

28 ways

Select all that apply.Which of the following expressions could you use to estimate 47% of 89?

1/2 · 90
0.5 · 90
0.47 · 89
90/2

Answers

Given:
47% of 89

Exact solution is : 0.47 * 89 = 41.83

Estimates: you round the number to the nearest tens.
47% can be 50% ; 89 can be 90

0.50 * 90 = 45

50% is the same as 1/2
1/2 * 90 = 45

90/2 is also applicable to estimate for the above figure. 90/2 = 45

Answer:

The first and second one

Step-by-step explanation:

a student has an average of 76 on the first 5 quizzes, what average is needed on the next 5 quizzes to pull his quiz average up to an 80?

Answers

The student has an average of 76 on his first 5 quizzes. Remember that average is also known as mean. Mean is calculated by adding the values in a data set and dividing it by the amount of numbers you added.

In this case,the mean is 76. That means five numbers were added and divided by 5 and the quotient was 76.

$(x+x+x+x+x)/(5)=76$

You can find the dividend by cross multiplying.

$(x+x+x+x+x)/(5)=76 \rightarrow x+x+x+x+x=76 *5 \rightarrow 380$

The total points he got on his first 5 quizzes was 380.

If he wants to boost his average grade up to an 8 after taking another 5 quizzes, you need to multiply his average goal by the amount of quizzes, which is 10(5+5=10).

$80 * 10=800$

His total points after taking all his quizzes(that is, if he reached his goal) should be 800. Because he already took 5 quizzes and got a total score of 380, you're going to subtract 380 from 800 and divide it by the remaining quizzes left, which is 5.

First subtract 380 from 800:

$800-380=420$

That means his next 5 quizzes need to sum up to a total of 420 points. Since you're trying to find the average of his next 5 quizzes in order to average up to an 80, you need to divide 420 by 5(number of remaining quizzes).

Divide:

$420 / 5=84$

Your answer is 84(84%).

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Answers

Answer:

Model A and 64%

Step-by-step explanation:

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