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3 years ago

Find the value of two numbers if their sum is 23 and their difference is 5

Mathematics

1 answer:

yKpoI14uk [10]3 years ago

6 0

Let the two numbers be represented by x and y respectively.

Then x + y = 23, and x - y = 5.

Solve this system of linear equations for x and y. Start by rearranging them vertically:

x + y = 23

x - y = 5

--------------- Combining the two equations eliminates y:

2x = 28.

Then x = 14. If x = 14, then 14 + y = 23, and y = 9..

The solution is (14, 9); that is, x = 14 and y = 9.

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Find the average rate of change of the function below over the interval (-4,-1).

babymother [125]

Answer:

-2

Step-by-step explanation:

$\frac{f(b)-f(a)}{b-a}\\ \\=\frac{f(-1)-f(-4)}{-1-(-4)}\\ \\=\frac{-4-2}{-1+4}\\ \\=\frac{-6}{3}\\ \\=-2$

Therefore, the average rate of change over the interval [-4,-1] is -2.

5 0

2 years ago

The dimensions for a rectangular prism are x + 2 for the length, x + 3 for the width, and x for the height. What is the volume o

Jlenok [28]

V = lwh

V = (x + 2)(x + 3)(x)

V = (x)(x^2 + 3x + 2x + 6)

V = (x^3 + 3x^2 + 2x^2 + 6x)

V = x^3 + 5x^2 + 6x

All you do is foil the dimensions together and then combine like terms. Hope this helps!

7 0

3 years ago

Is my answer choice correct??

kolezko [41]

Yes that would be right

6 0

3 years ago

Are this two triangles similar?

Alex73 [517]

<h3>Answer: </h3><h3>Yes, the triangles are similar</h3><h3>AC = 6</h3>

======================================================

Explanation:

Focus on triangle ABC. Let's find the missing angle

A+B+C = 180

113+B+22 = 180

B+135 = 180

B = 180-135

B = 45

Between the triangles, have two pairs of angles that are congruent

A = D = 113

B = E = 45

Which is enough to prove the triangles are similar through the angle angle (AA) similarity theorem. This must mean that C = F = 22

Since we have A pair with D, and B pair with E, this means that $\triangle ABC \sim \triangle DE F$

The order of the letters is important so we know how the angles pair up. The first letters pair up together, the second letters pair up, and so on.

Consequently, this means sides BC and EF pair up and AC and DF pair up

We can then say...

BC/EF = AC/DF

18/12 = x/4

18*4 = 12*x

72 = 12x

12x = 72

x = 72/12

x = 6

AC = 6

5 0

3 years ago

Write an equation for each figure side

Rashid [163]

Do you have a photo of the picture?

6 0

3 years ago