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3 years ago

How to solve this pythagoras theorem

Mathematics

1 answer:

My name is Ann [436]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

The hypotenuse is the longest side thus is (4x + 1)

The legs are 2x and (4x - 1)

Using Pythagoras' theorem, then

(4x + 1)² = (2x)² + (4x - 1)² ← expanding factors

16x² + 8x + 1 = 4x² + 16x² - 8x + 1 , that is

16x² + 8x + 1 = 20x² - 8x + 1 ( subtract 20x² - 8x + 1 from both sides )

- 4x² + 16x = 0 ( multiply through by - 1 )

4x² - 16x = 0 ← factor out 4x from each term

4x(x - 4) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

x - 4 = 0 ⇒ x = 4

Now x > 0, thus x = 4

2x = 2(4) = 8

4x - 1 = 4(4) - 1 = 16 - 1 = 15

4x + 1 = 4(4) + 1 = 16 + 1 = 17

Thus

perimeter = 8 + 15 + 17 = 40 cm

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when you sign up for video games are you get 400 points you earn 50 more points for each hour that you play how many hours do yo

aleksandr82 [10.1K]

This is a linear equation
y=mx+b
y=50x+400 (when x equals the number of hours played)

1000=50x+400
*first, isolate the variable (x)
-50x=-1000+400
*divide by -50 to get x by itself
x=20+8

The answer is x=28

4 0

3 years ago

Read 2 more answers

Solve:<br> -2/3 a - 6 = 12 <br> what is a

Hitman42 [59]

Answer:

a = - 27

Step-by-step explanation:

- $\frac{2}{3}$ a - 6 = 12 ( add 6 to both sides )

- $\frac{2}{3}$ a = 18 ( multiply both sides by 3 to clear the fraction )

- 2a = 54 ( divide both sides by - 2 )

a = - 27

8 0

2 years ago

May you guys help :)

goblinko [34]

Answer:

its the last one (d)

Step-by-step explanation:

5 0

3 years ago

The freshmen competed with the sophomores to see who could raise the most money by recycling. The appropriate design for testing

brilliants [131]

Answer:

Independent-samples t-test.

Step-by-step explanation:

We are looking for the appropriate design for testing the significance of the difference between the means.

Now, there is a parametric test known as the Independent Samples t Test and what this test does is that it compares the mean of two independent groups in order to find out whether there is statistical evidence that the related population mean is significantly different.

Thus, the test to be used here is Independent-samples t-test.

8 0

3 years ago

Which expression can be simplified to find the slope of the trend line in the scatterplot?

Maslowich

Answer:

1. $\frac{24-79}{12-2}$

Step-by-step explanation:

We have been given a graph of a scatter-plot and we are asked to find the correct expression than can be solved to find the slope of the trend line in the scatter-plot.

Since we know that slope of a line can be found by dividing the difference of the y-coordinates of 2 points on a line by difference of the x-coordinates of these same points.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

We can see that (2,79) and (12,24) are two given points of our trend line. So let us substitute x and y-coordinates of our given points in slope formula to find the our desired expression.

$x_1=2$

$x_2=12$

$y_1=79$

$y_2=24$

$\text{Slope}=\frac{24-79}{12-2}$

Therefore, the expression $\text{Slope}=\frac{24-79}{12-2}$ can be solved to find the slope of the trend line in the scatter-plot and 1st option is the correct choice.

7 0

3 years ago

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