1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Radda [10]
3 years ago
12

Triangle ABC is shown below. What is the length of line segment AC?

Mathematics
1 answer:
Rzqust [24]3 years ago
3 0

Answer:

The length of the line segment AC is equal to 14

Step-by-step explanation:

The triangle above is an isosceles triangle, In an Isosceles triangle the two angles; B and C are the same, hence the two sides; AB and AC are also the same.

AB=2x    and AC= 3x - 7

AB = AC

which implies;

2x = 3x - 7

subtract 3x from both-side of the equation

2x - 3x = 3x -3x -7

-x = -7

Multiply through by -1

x = 7

But we were ask to find the the length of the line segment AC

AC = 3x - 7

substituting x = 7 into the above equation will yield;

AC = 3(7) - 7 = 21 - 7 =14

Therefore the length of the line segment AC is equal to 14

You might be interested in
The gear is one of the oldest mechanical devices. It has been used since ancient times for its ability to increase or decrease r
eduard

The large gear attached to the pedals connected to the smaller gear

attached to the wheel allows the bicycle to travel further per rotation.

Correct responses:

Part A: Approximately 10.47 inches

Part B: 300°The d

Part C: Approximately 125.66 inches

Part D: The distance traveled increases by approximately 62.83 inches

<h3 /><h3>Methods used to calculate the above values</h3>

Given:

The radius of the large central gear, <em>r</em> = 4 inches

Radius of the small gear = 2 inches

Part A:

The distance travelled by the larger gear when the angle of rotation is 150° is given as follows;

\displaystyle Distance \ travelled \ by \ larger \ gear = \mathbf{\frac{150^{\circ}}{360^{\circ}} \times 2 \times \pi \times  4 \, inches} = \frac{10}{3} \cdot \pi \ inches

  • \displaystyle Distance \ traveled \ by \ the \ outer \ edge = \frac{10}{3} \cdot \pi \ inches  \approx \underline{ 10.47 \ inches}

Part B:

When the small gear travels the same linear distance as the large gear in part A, we have;

\displaystyle Degree \ of \ rotation = \frac{\frac{10}{3} \cdot \pi }{2 \times \pi \times  2 } \times 360^{\circ}= 300^{\circ}

  • The degree of rotation of the small gear = <u>300°</u>

Part C:

The distance travelled, <em>C</em>, by a single rotation of the large gear is given as follows;

C = 2 × π × 4 inches = 8·π inches

The degree of rotation of the smaller gear following one rotation of the large gear is therefore;

Degree  \ of \ rotation = \displaystyle \frac{8\cdot \pi \ inches}{4 \cdot \pi \ inches } \times 360^{\circ} = \mathbf{ 720^{\circ}}

720° = 2 × 360°

1 complete rotation is equivalent to 360°.

Therefore'

720° is equivalent to two complete rotation.

Therefore, the smaller gear and the wheel rotates twice for each rotation of the large gear

The distance the bicycle travels = 2 × The circumference of the wheel

Therefore;

Distance traveled by the bicycle = 2 × 2 × π × 10 inches = 40·π inches

  • Distance traveled by the bicycle = 40·π inches ≈ <u>125.66 inches</u>

Part D:

If the radius of the small gear is 1.5 inches and the radius of the large gear is 4.5 inches, we have;

Number of rotation of the small gear for each rotation of the large gear = 3 rotations

Therefore, number of rotation of the wheel = 3

Distance the bicycle travels = 3 × 2 × π × 10 inches = 60·π inches

The difference in distance traveled = 60·π inches - 40·π inches = 20·π inches

  • The distance traveled by the bicycle increases by 20·π inches ≈ <u>62.83 inches</u>

Learn more about gear transmission here:

brainly.com/question/14646065

brainly.com/question/3926797

8 0
2 years ago
Solve.
ZanzabumX [31]

Answer:

ok the answer is C

Step-by-step explanation:

1.75*4=7

.75*2=1.5

7+1.5=8.50

8 0
3 years ago
Read 2 more answers
8.<br> y<br> 5<br> х<br> -5<br> Ut<br> --5<br> slope =<br> Please help me
Burka [1]
Go choose the one you think
4 0
2 years ago
Evaluate each expression for g = -7 and h = 3 and match it to its value.
Molodets [167]

The given expressions are solved and matched

<h3><u>Solution:</u></h3>

To match the given expressions we need to solve the expressions with the given values of g and h and find their value.

Given that g = -7 and h = 3

\begin{array}{l}{\text { 1) } g+h=-7+3=-4} \\\\ {\text { 2) } g-h=-7-3=-10} \\\\ {\text { 3) } h-g=3+7=10} \\\\ {\text { 4) } g h=-7 \times 3=-21} \\\\ {\text { 5) } g+h^{2}=-7+3^{2}=-7+9=2} \\\\ {\text { 6) } g^{2}-h=(-7)^{2}-3=49-3=46}\end{array}

3 0
3 years ago
You are given a bag with 8 green marbles, 6 blue marbles, 14 yellow marbles, and 12 red marbles. Find the theoretical probabilit
AysviL [449]
A) 8/40 = 1/5
b) 12/40 or 6/20
c) 26/40 or 13/20
6 0
3 years ago
Other questions:
  • Halp plz i dont know the answwer
    10·2 answers
  • Solve for s. y=sx+g.
    15·2 answers
  • The solution set x ≤ 2 or x ≥ 4 is consistent with an equation of the form
    7·2 answers
  • Please help don't know how to do
    8·1 answer
  • HELP!!! ITS TIMED!!!! Please explain the answer!!
    14·1 answer
  • Can somone please help me
    8·1 answer
  • plz help!!!!!Mia creates a box plot using 28, 34, 40, 24, 44, 49, and 32 as the data. Which of the following box plots shows the
    8·1 answer
  • Pleaseee helpppp Please!!!
    11·2 answers
  • Graph the equation. y = − 5/4 ( x − 1 ) ( x + 3 )
    15·1 answer
  • Choose whether the expression is a result of multiplying
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!