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3 years ago

Given that ABC~LMN What is the length of AC?

Mathematics

1 answer:

sleet_krkn [62]3 years ago

6 0

Answer:

B. 12

Step-by-step explanation:

✔️Find the value of x

The side lengths of two similar triangles are always proportional.

Given that ∆ABC ~ ∆LMN, therefore:

$\frac{AB}{LM} = \frac{AC}{LN}$

AB = 5

LM = 10

AC = x + 5

LN = 3x + 3

Plug in the values

$\frac{5}{10} = \frac{x + 5}{3x + 3}$

Cross multiply

$5(3x + 3) = 10(x + 5)$

$15x + 15 = 10x + 50$ (distributive property)

Collect like terms

$15x - 10x = -15 + 50$

$5x = 35$

Divide both sides by 5

x = 7

✔️Find AC

AC = x + 5

Plug in the value of x

AC = 7 + 5

AC = 12

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← How many solutions does this linear system have y = x+2 6x - 4y = -10

defon

Answer:

This linear system has one solution.

Step-by-step explanation:

First equation: y = x + 2

Second equation: 6x - 4y = -10

Let's change the second equation in slope-intercept form y = mx + b.

Slope-intercept form

y = mx + b

m ... slope

b ... y-intercept

$6x - 4y = -10$

$6x + 10 = 4y$

$\frac{6}{4}x + \frac{10}{4} = y$

$\frac{3}{2}x + \frac{5}{2} = y$

If two lines have the same slope but different y-intercept, they are parallel - system has no solutions.

If two lines have the same slope and the same y-intercept, they are the same line and are intersecting in infinite many points - system has infinite many solutions.

If two lines have different slopes then they intersect in one point - system has one solution.

We see that lines have different slopes. First line has slope 1 and the other line has slope $\frac{3}{2}$ . So the system has one solution.

You can also check this by solving the system.

Substitute y in second equation with y from first.

6x - 4y = -10

6x - 4(x + 2) = -10

Solve for x.

6x - 4x - 8 = -10

2x = -2

x = -1

y = x + 2

y = -1 + 2

y = 1

The lines intersect in point (-1, 1). <-- one solution

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1 year ago

An object weighs 1 pound on earth weighs about 1/15 pounds on Pluto. If a man weighs 240 pounds on earth how many pounds would h

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Answer:

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Dan's business loses $9 each day. Which equation would be used to show how much money Dan's business has lost in a week? A. -9 ×

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The definition of quadratic function is given by:

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So the problem asks for two conditions:

1. Write the quadratic function in factored form. 
2. The vertex has an x-coordinate of 3.

Then the equation (1) must be written as follows:

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$\frac{m+n}{2}=3$

So we are free to choose the value of one root, say:

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Finally, the answer is:

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