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KATRIN_1 [288]
3 years ago
13

What is the length of AC?

Mathematics
1 answer:
natima [27]3 years ago
3 0

7/x = 84 / (156 -x)
84x = 7(156 -x)
84x = 1092 - 7x
91x = 1092
x = 12

AC = 156 - 12 = 144

answer
D. 144
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HELP ME ON THIS PLEASE!!!! SHOW WORK!!!!
Mumz [18]

Answer:

<h2>1. x = 4</h2><h2>2. x = 20</h2>

Step-by-step explanation:

1.

ΔABC and ΔAJK are similar (AA). Therefore the sides are in proportion:

\dfrac{AC}{AJ}=\dfrac{AB}{AK}

We have:

AC = 1 + 4 = 5

AJ = 1

AB = 1 + x

AK = 1

Substitute:

\dfrac{5}{1}=\dfrac{1+x}{1}

5=1+x           <em>subtract 1 from both sides</em>

4=x\to x=4

2.

ΔVUT and ΔVMN are similar (AA). Therefore the sides are in proportion:

\dfrac{VU}{VM}=\dfrac{VT}{VN}

We hve:

VU = x + 8

VM = x

VT = 49

VN = 49 - 14 = 35

Substitute:

\dfrac{x+8}{x}=\dfrac{49}{35}              <em>cross multiply</em>

35(x+8)=49x          <em>use the distributive property a(c + b) = ab + ac</em>

35x+280=49x              <em>subtract 35x from both sides</em>

280=14x         <em>divide both sides by 14</em>

20=x\to x=20

3 0
3 years ago
What is the solution to the equation 13.7y = 6.2y + 30?
il63 [147K]

Here, we are required to determine the solution to the equation: 13.7y = 6.2y + 30?

The solution to the equation is y = 7.5

The solution is thus,

  • 13.7y = 6.2y + 30
  • 13.7y - 6.2y = 30
  • 7.5y = 30

Therefore, y = 30/7.5 = 4

Therefore, y = 4 is the solution to the equation.

Read more:

brainly.com/question/12184348

8 0
2 years ago
Factor the expression using the GCF.<br><br> 18h+30k<br><br> The factored form is <br> .
Murljashka [212]

Answer:

6(3h+5k)

Step-by-step explanation:

18h+30k

Factors of 18:

1, 2, 3, 6, 9, 18

Factors of 30:

1, 2, 3, 5, 6, 10, 15, 30

GCF of 18 and 30: 6

18h+30k = 6(3h+5k)

Check your answer:

6(3h+5k)

6(3h) + 6(5k)

18h + 30k

Hope this helps!

7 0
2 years ago
Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the
maksim [4K]

Answer:

The line of symmetry is x = -3

Explanation:

Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:

y=ax^2+bx+c

The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:

x_v=-\frac{b}{2a}

In this problem, we have:

y=-x^2-6x-13

Then:

a = -1

b = -6

We write now:

x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3

Part 3:

For this part, we need to find the x-intercepts. This is, when y = 0:

-x^2-6x-13=0

To solve this, we can use the quadratic formula:

x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}

And solve:

x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}

Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.

Part 4:

To find the y intercept, we need to find the value of y when x = 0:

y=-0^2-6\cdot0-13=-13

The y-intercept is at (0, -13)

Part 5:

Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:

x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8

The two points are:

(1, -20)

(-1, -8)

Part 6:

Now, we can use 3 points to find the graph of the parabola.

We can locate (1, -20) and (-1, -8)

The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3

Then, y-coordinate of the vertex is:

y=-(-3)^2-6(-3)-13=-9+18-13=-4

The third point we can use is (-3, -4)

Now we can locate them in the cartesian plane:

And that's enough to get the full graph:

8 0
1 year ago
A private jet flies the same distance in 8 hours that a commercial jet flies in 7 hours. If the speed of the commercial jet was
mamaluj [8]

Solving a system of equations, we can see that:

  • Speed of the private jet: 168 mi/h
  • Speed of the commercial jet: 192mi/h

<h3>How to find the speeds of each jet?</h3>

Let's define the variables:

  • P = speed of the private jet.
  • C = speed of the commercial jet.

With the given information, we can write:

P*8h = D

C*7h = D

C = 2*P - 144mi/h

So we have a system of 3 equations, where D is the distance in the problem.

With the first and second equations we can write:

P*8h = D = C*7h

Isolating P, we get:

P = C*(7/8)

Now we can replace that in the last equation:

C = 2*P - 144mi/h

C = 2*C*(7/8) - 144mi/h

And now we can solve that for C.

C - 2*(7/8)*C = - 144mi/h

C*(1 - 14/8) = -144mi/h

C*(8/8 - 14/8) = - 144mi/h

C*(6/8) = 144mi/h

C = (8/6)*144mi/h = 192mi/h

Now that we know the speed of the commercial jet, we can find the speed of the private jet.

P = C*(7/8) = 192mi/h*(7/8) = 168 mi/h

If you want to learn more about systems of equations:

brainly.com/question/13729904

#SPJ1

6 0
2 years ago
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