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2 years ago

Use the following image to answer the questions.

Mathematics

1 answer:

monitta2 years ago

8 0

(a.) The triangles presented in this problem are congruent. We can prove this using the AAA (angle-angle-angle) theorem of similarity. This states that if all three angles of a triangle are equivalent then the sides of the triangles are proportional. We know that all three angles of these triangles are the same since the image shows angle A = angle P, and angle B = angle Q, therefore, angle C = angle R.

(b.) Now that we know the triangles are similar and the sides are proportional, we can simply take a ratio of the sides to solve for x.

(3x+6)/24 = 28/32
3x+6 = (28/32)(24)
3x = 21 - 6
x = 15/3
x = 5

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Someone pls help me ASAP! Express the following as the sum of its partial fraction: 2x+4/x(x+2)(x-4)

den301095 [7]

The sum of the partial fraction is $\frac{2x + 4}{x(x + 2)(x -4)} = -\frac 12 + \frac{1}{2(x -4)}$

<h3>How to express as partial fractions?</h3>

The expression is given as:

$\frac{2x + 4}{x(x + 2)(x -4)}$

As a partial fraction, we have:

$\frac{2x + 4}{x(x + 2)(x -4)} = \frac Ax + \frac{B}{x + 2} + \frac{C}{x -4}$

Take the LCM

$\frac{2x + 4}{x(x + 2)(x -4)} = \frac {A(x + 2)(x -4) +Bx(x -4) + Cx(x + 2)}{x(x + 2)(x -4)}$

This gives

2x + 4 = A(x + 2)(x -4) +Bx(x -4) + Cx(x + 2)

Expand

$2x + 4 = A(x^2 - 2x - 8) + B(x^2 - 4x) + C(x^2 + 2x)$

Further expand

$2x + 4 = Ax^2 - 2Ax - 8A + Bx^2 - 4Bx + Cx^2 + 2Cx$

Collect like terms

$2x + 4 = Ax^2 + Bx^2 + Cx^2 - 2Ax - 4Bx + 2Cx - 8A$

By comparing the coefficients, we have:

A + B + C = 0

-2A - 4B + 2C = 2

-8A = 4

Divide both sides of -8A = 4 by -8

$A = -\frac 12$

Substitute $A = -\frac 12$ in the other equations

$-\frac 12 + B + C = 0$

$B + C = \frac 12$

$C = \frac 12 - B$

$-2*- \frac 12 - 4B + 2C = 2$

1 - 4B + 2C = 2

- 4B + 2C = 1

Substitute $C = \frac 12 - B$ in - 4B + 2C = 1

$- 4B + 2*\frac12 = 1$

- 4B + 1 = 1

Subtract 1 from both sides

-4B = 0

This gives

B = 0

Substitute B = 0 in $C = \frac 12 - B$

$C = \frac 12 - 0$

$C = \frac 12$

So, we have:

$A = -\frac 12$ , B = 0 and $C = \frac 12$

The equation $\frac{2x + 4}{x(x + 2)(x -4)} = \frac Ax + \frac{B}{x + 2} + \frac{C}{x -4}$ becomes

$\frac{2x + 4}{x(x + 2)(x -4)} = -\frac 12 + \frac{0}{x + 2} + \frac{1}{2(x -4)}$

Evaluate

$\frac{2x + 4}{x(x + 2)(x -4)} = -\frac 12 + \frac{1}{2(x -4)}$

Hence, the sum of the partial fraction is $\frac{2x + 4}{x(x + 2)(x -4)} = -\frac 12 + \frac{1}{2(x -4)}$

Read more about partial fraction at:

brainly.com/question/18958301

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8 0

1 year ago

Every 100 tons of the earth's crust contain about 28 tons of silicon. What is the ratio of the weight of silicon to the weight o

d1i1m1o1n [39]

<h3>Answer:</h3>

28/100 = 7/25
100/28 = 25/7

<h3>Explanation:</h3>

The wording "the ratio of A to B" means A/B.

Here, "the ratio of the weight of silicon to the weight of crust" means ...

... (28 tons)/(100 tons)

Canceling common factors (and common units), this is ...

... 28/100 = 7/25

___

Then "the ratio of the weight of crust to the weight of silicon" means ...

... (100 tons)/(28 tons) = 100/28 = 25/7

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3 years ago

Find the probability of its being a day of the week with a "T" in it remember to reduce your answer in simplest form is necessar

madreJ [45]

Monday <u>T</u>uesda<u>y</u> Wednesday <u>T</u>hursda<u>y</u> Friday Sa<u>t</u>urda<u>y</u> Sunday
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2 years ago

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maks197457 [2]

Answer:

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Step-by-step explanation:

68+70+a=180

138+a=180

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180-42=x

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