All categories

2 years ago

B is the midpoint of AC. What is the length of AB? AB is 9x+7 and BC is -3x+20

Mathematics

1 answer:

ahrayia [7]2 years ago

8 0

<h3>Answer:</h3>

$AB = \frac{67}{4}\\$

<h3>Step-by-step explanation:</h3>

If $B$ is the midpoint of $\overline{AC}$ then $AB$ is just half of $AC$ and also, $BC$ is just half of $AC$ . This means that $AB$ must be equal to $BC$ . Essentially, $9x +7 = -3x +20$ and we can solve for the of $x$ from that equation.

$9x +7 = -3x +20 \\ 9x +7 +3x = -3x +20 +3x \\ 12x +7 = 20 \\ 12x +7 -7 = 20 -7 \\ 12x = 13 \\ \frac{12x}{12} = \frac{13}{12} \\ x = \frac{13}{12}$

Now we can solve for $AB$

$AB = 9(\frac{13}{12}) +7 \\ AB = 3(\frac{13}{4}) +7 \\ AB = \frac{39}{4} +7 \\ AB = \frac{39}{4} +\frac{28}{4} \\ AB = \frac{67}{4}$

You might be interested in

In Triangle XYZ, measure of angle X = 49° , XY = 18°, and

marissa [1.9K]

Answer:

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

Step-by-step explanation:

There are mistakes in the statement, correct form is now described:

<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>

The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:

$YZ^{2} = XZ^{2} + XY^{2} -2\cdot XY\cdot XZ \cdot \cos X$ (1)

If we know that $X = 49^{\circ}$ , $XY = 18$ and $YZ = 14$ , then we have the following second order polynomial:

$14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}$

$XZ^{2}-23.618\cdot XZ +128 = 0$ (2)

By the Quadratic Formula we have the following result:

$XZ \approx 15.193\,\lor\,XZ \approx 8.424$

There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:

$XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y$

$\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}$

$Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)$

1) $XZ \approx 15.193$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 54.987^{\circ}$

2) $XZ \approx 8.424$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 27.008^{\circ}$

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

6 0

2 years ago

-233.2 - 25.8<br> Please help.

Anon25 [30]

Answer:

-259

Step-by-step explanation:

brainliest

3 0

1 year ago

Read 2 more answers

What is the area, in square feet, of the trapezoid below?

slavikrds [6]

Answer:

68.75

Step-by-step explanation:

Measure the length of the parallel sides and add them together. Then multiply this number by the height of the area. Then multiply by ½ or divide by two to find the square footage of the trapezoid.

13.6 + 5.9= 19.5

19.5 + 8 = 27.5

27.5 x 5 = 137.5

137.5 x 1/2 = 68.75

3 0

2 years ago

What is the answer to this multiple choice question?

evablogger [386]

Answer:

All expressions are correct

Step-by-step explanation:

9z+7z = 16 z

We need to find an expression ( or expressions ) that are equal to 16z

6z+3z+ 7z = 16z Correct

z+8z+7z = 16z Correct

z*16 = 16z Correct

21z+ -5z = 16z Correct

6 0

2 years ago

A sports broadcaster predicts a basketball team will score 88 point me in the next game. If the team actually scored 98 points w

gavmur [86]

Answer:

The percentage error in the prediction = 10.20%

Step-by-step explanation:

A sports broadcaster predicts a basketball team will score 88 point me in the next game.

If the team has actually scored 98 points we have to find the percentage error in the broadcaster's prediction.

The deviation of the prediction from the actual value = 98 - 88 = 10.

The formula for finding error percentage = $\frac{deviation from actual value}{prediction}$

= $\frac{10}{98} \times 100$

= 10.20 %

The percentage error = 10.20%

5 0

2 years ago