All of the angles of Triangle ABC measure 60 o. AB = 3x – 4, BC = 4x – 12 and CA = 5x – 20.

Solve for x and find the length of AB.

Answers

Answer 1

Answer:

The length of AB is 20 units

Step-by-step explanation:

The equilateral triangle is the triangle that has 3 equal sides and 3 equal angles, the measure of each angle is 60°

∵ All of the angles of triangle ABC measure 60 °

→ By using the fact above

∴ Triangle ABC is an equilateral triangle

→ That means its 3 sides are equal

AB = BC = CA

∵ AB = 3x - 4

∵ BC = 4x - 12

∵ CA = 5x - 20

→ Equate 2 of them to find x

∵ BC = CA

5x - 20 = 4x - 12

→ Subtract 4x from both sides

∵ 5x - 4x - 20 = 4x - 4x - 12

∴ x - 20 = -12

→ Add 20 to both sides

∴ x - 20 + 20 = -12 + 20

x = 8

→ To find AB substitute the value of x in its expression

∵ AB = 3x - 4

∴ AB = 3(8) - 4

∴ AB = 24 - 4

AB = 20

The length of AB is 20 units


Related Questions

In 2011, a U.S. Census report determined that 71% of college students work. A researcher thinks this percentage has changed since then. A survey of 110 college students reported that 91 of them work. Is there evidence to support the reasearcher's claim at the 1% significance level? A normal probability plot indicates that the population is normally distributed.

Answers

Answer:

Note: The full question is attached as picture below

a) Hо : p = 0.71

Ha : p ≠ 0.71

p = x / n

p = 91/110

p = 0.83.

1 - Pо = 1 - 0.71 = 0.29.

b) Test statistic = z

= p - Pо / [√Pо * (1 - Pо ) / n]

= 0.83 - 0.71 / [√(0.71 * 0.29) / 110]

= 0.12 / 0.043265

= 2.77360453

Test statistic = 2.77

c) P-value

P(z > 2.77) = 2 * [1 - P(z < 2.77)] = 2 * 0.0028

P-value = 0.0056

∝ = 0.01

P-value < ∝

Reject the null hypothesis.  There is sufficient evidence to support the researchers claim at the 1% significance level.

Which graph shape represents the polar curve r = 1 + 4sin(θ)?
a cardioid
a rose curve
a limaçon with an inner loop
a limaçon without an inner loop

Answers

Answer:

A cardioid

Step-by-step explanation:

A cardioid is a curve in the shape of a heart traced by a point on the circumference of a circle as it rolls around a fixed circle of the same radius.

The equation of vertical cardioid is [tex]r=a[/tex] ± [tex]a\sin \theta[/tex]

Given the polar curve is [tex]r=[/tex] [tex]1+[/tex] 4 [tex]\sin \theta[/tex]

This is an equation of vertical cardioid.

So, it represents a cardioid.

Answer:

C - a limaçon with an inner loop

Step-by-step explanation:

If you have a graphing calculator, use it to plug in the equation.

Based on what you have learned, you will recognize the graph is C

ASAP please & thank you

Answers

The answer is d.line segments that have the same length

I will give 26 points for this!!!!

1) GST is 5% and the subtotal is $818.75 what is the Grand total?
2) PST is 8% and the subtotal is $818.75 what is the Grand total?

Answers

Answer:

37.5%

Step-by-step explanation:

Answer:

37.5%

Step-by-step explanation:

Michelle bought 2 teddy bears and 3 flower vases for $27 in a shopping mall. Shannon bought 3 teddy bears and 2 flower vases for $30.5 from the same mall. what is the cost of the flower vase?

Answers

Answer:

$4

Step-by-step explanation:

let t represent teddy bear and v represent vase, then

2t + 3v = 27 → (1)

3t + 2v = 30.5 → (2)

Multiplying (1) by 3 and (2) by - 2 , then adding will eliminate t, that is

6t + 9v = 81 → (3)

- 6t - 4v = - 61 → (4)

Add (3) and (4) term by term to eliminate t, that is

5v = 20 ( divide both sides by 5 )

v = 4

The cost of the flower vase is $4

Answer:

It is going to be $4.00

Step-by-step explanation:

Hope this helped have an amazing day!

Please help ASAP thank you

Answers

Answer:

Scalene, Acute

Step-by-step explanation:

scalene because the sides are of different length, and acute because it's less than 90°

A certain brand of tea costs $7.99 for 16.2 ounces.

What is the unit rate?

Enter your answer, rounded to the nearest cent, in the box.

$
per ounce

Answers

Answer:

49 cents per ounce

Step-by-step explanation:

49 cents per once,because if you divide $7.99/16.2 once’s you’ll get .49 cents :)



Convert €85.10 to pounds.
Give your answer rounded to 2 DP.

Answers

Answer:

77.10-pound sterling

Step-by-step explanation:

Has not been rounded

A store is instructed by corporate headquarters to put a markup of 67​% on all items. An item costing ​$6 is displayed by the store manager at a selling price of ​$4. As an​ employee, you notice that this selling price is incorrect. Find the correct selling price. What was the​ manager's likely​ error?

Answers

Answer:

The correct selling price = $10.02

The manager's likely​ error = $6.02

Step-by-step explanation:

Markup of 67​% on all items

An item cost $6

The correct selling price = $6 + 67% of $6

= $6 + 0.67 × $6

= $6 + $4.02

= $10.02

The correct selling price = $10.02

The store manager's selling price is ​$4.

The manager's likely​ error = The correct spelling price - the manager's selling price

= $10.02 - $4

= $6.02

The manager's likely​ error = $6.02

0.18 divided by 0.33

Answers

Answer:

I am pretty sure it is 0.54

Answer:

The answer is 0.54. I have included a screenshot that shows the work and how to get 0.54. I hope this helps!

And by the way yes, I do know this is a 1-year-old question but I would like points and I have the answer.

:D

- Your friendly (late) responder

HELP PLEASE!!!!! I need help

Answers

Answer:

5 hours and 8 minutes is what I got, but i'm not really sure so only put that answer if someone else got that to. (The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest.

- •Trix•

( Yes I know my - •Trix• thingy is not my user but its what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)

In 2010, there were approximately 6 million girls living in Orange City. In 2011, the population was down to 4 million girls. How many girls lived in Orange City in 2011 in comparison to 2010? Write your answer in scientific notation.

Answers

Answer:2010 +2011+2010=6021

6+4 =11

Step-by-step explanation:add then you divide

What is 3/7 divided by 15?

Answers

Answer: Your answer is 1/35 or 35

Step-by-step explanation:

The sum of two numbers is 240. If one of them
is y find the other number.​

Answers

Answer:

120?

Step-by-step explanation:

Let's solve the problem step by step: Let's assume the other number is x. According to the problem, the sum of the two numbers is 240. so we can write the equation as: [tex]x + y = 240[/tex]

To find the value of x, we need to substitute the value of y into the equation. Since y is given, we can substitute it. [tex]x + y = 240 x + y = 240 x + y + (-y) = 240 + (-y) x = 240 - y[/tex] Now, we have an equation expressing x in terms of y. To determine the value of x, we need to know the value of y.

Without that information, we cannot calculate the value of x specifically. However, based on the information given, we can conclude that the value of x will be equal to 240 subtracted by the value of y.

To know more about equation visit:

https://brainly.com/question/33622350

#SPJ2

1)such A coffee maker costs $ 563 more than a blender. The total cost of two such coffee makers and 5 such blenders is $6915.How much does 1 coffee maker cost?

Answers

Answer:

$1390

Step-by-step explanation:

Given that :

Let :

Cost of blender = x

Cost of coffee maker = x +563

2(x + 563) + 5x = 6915

2x + 1126 + 5x = 6915

7x = 5789

x = 827

Cost of coffee maker = (827 + 563) = 1390

HELP MEH PLEASE TwT I WILL GIVE BRAINLIEST TO FIRST PERSON WITH
RIGHT ANSWER

Answers

Answer:

a

Step-by-step explanation:

because its parallel while d is perpendicular and b and c are diagonal

And a survey of 500 households 23% say that they have a dog as a pet the standard deviation is 2% determine an interval that if I need to contain the 95% of all households who has a dog as a pet

Answers

Answer:

(114.123, 115.877)

Step-by-step explanation:

Given that :

Sample size (n) = 500

Mean = 23% of 500 = 115

Standard deviation (s) = 2% of 500 = 10

α = 95%

Zcritical at 95% = 1.96

Confidence interval = Mean ± Error

Error = Zcritical * standard deviation /sqrt (n)

Error = 1.96 * 10/sqrt(500)

Error = 0.8765386

Lower boundary : 115 - 0.8765386 = 114.1234614

Upper boundary : 115 + 0.8765386 = 115.8765386

(114.123, 115.877)

Which is NOT an example of kinetic energy

Question 8 options:

a skateboard rolling down a hill.


an arrow after it has hit the target and is at rest.


a skydiver as they decrease speed after opening their parachute.


an elevator moving up to the 3rd floor,

Answers

Answer: an arrow after it has hit the target and is at rest.

Step-by-step explanation:

Kinetic energy has to do with energy which a body possesses by virtue of being in motion. The arrow is not in motion anymore

What is the measure of the angle?​

Answers

The angle is a 90 degree angle.

Answer:

80degrees

Step-by-step explanation:

please help meeeeeeeeeee

Answers

A straight line is 180 degrees so the two angles together must equal 180. 180-54=126

The coordinates of which point are (-3, 6)?
Ty
A
6
5
4
13
1
123457
Х
2
3
B
5
6
O point A
O point B
O point
point D

Answers

Answer:

point d based on my stuck knowledge

Answer:

i cant tell what your asking but i guess point a...

Step-by-step explanation:

The table and graph both represent the same relationship. Which
equation also represents that relationship?




PLEASE someone HELP

Answers

Answer:

y=x^2

Step-by-step  explanation:

what is the equation for the line that passes through the point (3,7) and has a slope of 2?

Answers

Answer:

y=3/7x+2

Step-by-step explanation:

can i have brainliest?

Help me plzzzz!!!!!

Answers

Store A is cheaper than B
The way to solve is pretty simple for B.
You have to divide the cost by the number of tubes.
So in this case:
9/3=3
15/5=3
21/7=3
See the pattern?
So the cost per lip gloss is $3.
Now for Store A:
Just divide 5.50/2
The answer is 2.75
Compare both numbers


2.75<3.00
So, store A is cheaper.

What is the first step in solving the equation 1 + 3/5x = 3?
What is the second step in solving the equation?

Answers

Answer:

subtract 1 from both sides

cube both sides

Step-by-step explanation:

nhfbgdvzfsdfexgrdtbfvdcfewzsxrdfcgvhjyvtfhcdgrxesrgdfcgvh

Which of the following expressions are equivalent to c/d?

Choose all answers that apply:

Answers

Answer:

Both A and B are correct because a negative divided by a negative makes a positive.

Hence, the expression which are equivalent to [tex]\frac{c}{d}[/tex] is both (A) and (B).

What are the expressions?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Here both the options (A) and (B) are correct because negative got cancel and it would be like the given expression.

Hence, the expression which are equivalent to [tex]\frac{c}{d}[/tex] is both (A) and (B).

To know more about the expression

https://brainly.com/question/24242989

#SPJ2

will give brainliest

Answers

Answer:

d

Step-by-step explanation:

What is the What is the Linear Equation for

13/2 x12 ? The y intercept is 4

Answers

Answer:

6.5x*16= y

Step-by-step explanation:

6.5x*12+4 =y

6.5x*16= y

i believe this is correct...

What is the value of x?

Answers

Answer:

5

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c² plug in the info you have

a²+12²=13² (c is always the side opposite from the right angle)

Solve for a

a²+144=169

   -144  -144

a²=25   take the square root of both sides

√a²=√25

a=5

24 is what precent of 30 ?

Answers

Answer:

80%

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

This can be written algebraically as 24 = x of 30, where we have to find what percent of 30 is equal to 24. Of is the same as multiplication: 24 = x · 30  Then, solve for x. The answer is x = 0.8 and 0.8 as a percent is 80%.

Hope this helped! :)

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