An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b. Which statements about finding the area of the equilateral triangle are true? Select three options

Answers

Answer 1

The image of the triangle is missing, so i have attached it.

Also, the options are;

A) The apothem can be found using the Pythagorean theorem.

B) The apothem can be found using the tangent ratio.

C) The perimeter of the equilateral triangle is 15 cm.

D) The length of the apothem is approximately 2.5 cm.

E) The area of the equilateral triangle is approximately 65 cm².

Answer:

Options A, B & D are true

Step-by-step explanation:

A) We are told that the triangle is an equilateral triangle.

Thus, the 3 sides equal 8.7 cm.

Now from the image, b is half of one of the sides.

Thus, b = 8.7/2 = 4.35 cm

Now, we want to find the apothem "a".

Using Pythagoras theorem, we have;

a² + 4.35² = 5²

a² = 25 - 18.9225

a² = 6.0775

a = √6.0775

a ≈ 2.5 cm.

Thus, option A is true as pythagoras theorem was able to calculate the apothem "a"

B) since the main triangle is equilateral, it means each angle is 60°.

Now,the radius line from one corner point to the centre will divide the 60° angle into 2 equal parts.

Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°

Now,from tangent ratios, we know that;

Opposite/Adjacent = tan θ

In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm

Thus;

a/4.35 = tan 30

a = 4.35 tan 30

a ≈ 2.5 cm.

Thus, option B is correct as Tangent ratio can be used to find the apothem

C) The perimeter of equilateral triangle = 3x

Where x is length of one side.

One side is 8.7 cm

Thus, perimeter = 3 × 8.7 = 26.1 cm

Thus option C is not correct.

D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.

Thus, option D is true.

E) Area of triangle is;

A = ½ × base × height

Base = 8.7 cm

To get height, we will use trigonometric ratio. Thus;

h/8.7 = sin 60°

h = 8.7 sin 60°

Thus;

A = ½ × 8.7 × 8.7 sin 60°

A = 32.77 cm²

Thus is not equal to 65 cm². Thus, option E is not correct.

An Equilateral Triangle With Side Lengths Of 8.7 Centimeters Is Shown. An Apothem Has A Length Of A And
Answer 2

Answer:

A, B, D

Step-by-step explanation:


Related Questions

The equation yˆ=20646·0.86x estimates the value of a brand of car x years after it was purchased new. Milo purchased this brand of car when it was new. To the nearest dollar, what will be the approximate value of Milo's car 11 years after he purchased it?

Answers

Answer:

$195311

Step-by-step explanation:

Given the expression yˆ=20646*0.86x

Given that the number years 11

And x represent the number of years

Substituting x=11 in the expression for the cost we have

yˆ=20646*0.86(11)

yˆ=20646*9.46

yˆ=20646*9.46

yˆ=195311.16

From the analysis he purchased the car fro $195311

Answer:

K12 answer added in attachment below. :)

Step-by-step explanation:

What percent of 462 is 851?

Answers

Answer:

It is 54.29%.

Answer:

54.29

Step-by-step explanation:

Percentage Calculator: 462 is what percent of 851? = 54.29.

DO NOT AWNSER IF YOU DON'T KNOW
WILL GIVE BRAINLIEST, LIKE, COMMENT, AND 10 POINTS
Could you please help me with this question and explain thoroughly?

Answers

Answer:

Please don't hold me to this. I think I'm right, but I'm rusty.

Step-by-step explanation:

Constant of proportionality is how much the graph grows for each increasing x value. Slope.

Also remember, rise over run.

Slope: 2nd y- 1st y

           2nd x-1st x

y=mx+b

A) 4.95-3.75      =            1.2                 =            about $0.09 per ounce (x=0.9)

    24-10                          14

For every 14 oz, the cost goes up $1.2.

B) 360-150        =            210               =                  15 calories per ounce (x=15)

     24-10                          14

For every 14 oz, there are 210 calories in the drink.

Write an equation parallel to 2x+5y=15 that passes through the point (-10,1).

Answers

2x + 5y = 15
5y = -2x + 15
y = -(2/5)x + 3

y = mx + b
1 = -(2/5)(-10) + b
1 = 4 + b
-3 = b
So the equation of the line would be:
y = -(2/5)x - 3

What is the value of the expression: 144 100​

Answers

Answer:

14,400

Step-by-step explanation:

I'm assuming this is multiplication so it would be 14,400

Point AAA is at {(1, 5)}(1,5)left parenthesis, 1, comma, 5, right parenthesis and point CCC is at {(-5,-7)}(−5,−7)left parenthesis, minus, 5, comma, minus, 7, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that ACACA, C is 666 times as long as ABABA, B.

Answers

Answer:

(0, 3)

Step-by-step explanation:

If a point O(x, y) divides a line XY in the ratio n:m with [tex]X\ at\ (x_1,y_1)\ Y\ at\ (x_2,y_2)[/tex], the coordinates of O is:

[tex]x=\frac{n}{n+m} (x_2-x_1)+x_1\\\\y=\frac{n}{n+m} (y_2-y_1)+y_1[/tex]

AC is 6 times AB, this means that point B, divides line AC in the ratio 1:5. Given A at (1,5) and C at (-5, -7)

Let us assume B to be at (x, y), hence:

[tex]x=\frac{1}{1+5}(-5-1)+ 1=\frac{1}{6}(-6)+1 =0\\\\y=\frac{1}{1+5}(-7-5)+5=\frac{1}{6} (-12)+5=3[/tex]

Therefore the location of B is (0, 3)

Answer:

(0, 3)

Step-by-step explanation:

HELP WILL MARK YOU BRAINLIEST NO GUESSES PLZ!!!!!!!!!!!!

Answers

Answer:72

Step-by-step explanation:

Which expression is equivalent to Start root80 ?
O ^4start root2end root•√5
0 start root2^4•start root5
0 start root2end root•start root2end root•start root5end root
0 start root2^2end root•start root2^2end root•start root5^2end root

Answers

Answer:

I believe your answer is C

Hope this helps!

Answer:

It's B

Step-by-step explanation:

If α, β are the zeroes of the polynomials f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1) =

Answers

Answer:

f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)

Step-by-step f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)explanation:

f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(xf(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1) + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(xf(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1) + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)

PLEASE HELP IM
GOING TO FAIL IF NOBODY ANSWERS THIS

Answers

Answer:

1) 180

2) 67

3) angle 4 and angle 1 are alternate interior angles

4) congruent

5) 59 degrees

6) alternate interior angles

7) congruent

8) 54 degrees

9) 180 degrees

10) 180 degrees

Step-by-step explanation:

I dont have a question anymmore lol k thanks

Answers

Have a great day ;) I hope this was helpful.

The number of concurrent users of a social networking site has increased dramatically since . By ​, this social networking site could connect concurrently 70 million users online. The function ​P(t)​(​)​, where t is the number of years after ​, models this increase in millions of users. Estimate the number of users of this site that could be online concurrently in ​, in ​, and in . Round to the nearest million users.

Answers

Complete question:

The number of concurrent users of a social networking site has increased dramatically since 2005. By 2014, this social networking site could connect concurrently 70 million users online. The function P(t) = 2.459(1.475)^t, where t is the numbe of years after 2005, models this increase in millions of users. Estimate the number of users of this site that could be onlin concurrently in 2006, in 2010, and in 2013. Round to the nearest million users

Answer:

Kindly check explanation

Step-by-step explanation:

Given the function :

The function P(t) = 2.459(1.475)^t, where t is the numbe of years after 2005

Estimate the number of users of this site that could be online concurrently in:

2006:

t = (2006 - 2005) = 1

P(t) = 2.459(1.475)^t

P(1) = 2.459(1.475)^1

P = 2.459(1.475)

= 3.627025 = 4 million users (nearest million)

2010 :

t = (2010 - 2005) = 5

P(t) = 2.459(1.475)^t

P(5) = 2.459(1.475)^5

P = 2.459(6.981682607421875)

= 17.1679575 = 17 million users (nearest million)

2013:

t = (2013 - 2005) = 8

P(t) = 2.459(1.475)^t

P(8) = 2.459(1.475)^8

P = 2.459(22.404546753)

= 55.09278 = 55 million users (nearest million)

1. What is 10% of 75?

Answers

Answer:

7.5

Step-by-step explanation:

i hope this helps!!

Given f(x)=70+11x, find f(x)=158

Answers

Answer:

x=8

Step-by-step explanation:

I am assuming you need to find which x value fits this.

So set the two equations equal to each other

158=70+11x, subtract 70 from both sides

88=11x, now, divide by 11 to get x by itself,

8=x, to find these answers, use a calculator or any other method you want.

2hr+20min+60sec are equal to _____ minutes​

Answers

Answer:81 minutes (2h =120 min +20+1)

It is correct


Does this represent a function?

Answers

Answer:

Yes

Step-by-step explanation:

Use the Vertical Line Test

Vertical Line Test: If a vertical line intersects a graph more than once, then the graph is not a function.

So if you draw a vertical line through that graph, it is only intersected once. Therefore, it is a function.

(-2,7)(0,-3) write the equation that goes through the points

Answers

-3-7/0-2
-10/-2
Slope is
5
Answer
Y=5x-3

I'll give brainliest to correct answer please please please please help me I need these answers really fast I've already filled out a few blanks on the ss (they're probably incorrect) but I need you to check my answers and fill out the rest, please

Fill in each blank with a reason that justifies the statement.​ Given: XY = 36.

Statements Reasons
XZ + ZY = XY a. _____
3(n - 2) + 3n = 36 b. _____
3n - 6 + 3n = 36 c. _____
6n - 6 = 36 d. _____
6n = 42 e. _____
n = 7 f. _____

Answers

Answer:

[tex]6n - 6 = 36 \: d. - - - addition \:property \: of \: equality \\

6n = 42 \: e. - - - division \: property \: of \: equality \: \\ [/tex]

what is the value of x in 5x−3(x−11)=7(2x−5)+2

Answers

The value of x is 5.5. I got this answer by first distributing -3 amongst (x-11), and distributing 7 amongst (2x-5). Next I combined like terms and subtracted 3x from 5x, and added -35 and 2. Next I subtracted 33 from both sides. Next I subtracted 14x from both sides. And finally I divided both sides by -12 to get the final answer of 5.5.

Choose two statements that are true fo of this expression. 5x^3- 6x^2 - 25/y + 18

Answers

Answer:

5x^3- 6x^2 - 25/y + 18 / y

Step-by-step explanation:

It would be that expression over y.

Sorry if its wrong I'm still learning too:)

Answer:

The answers are

*There are four terms.

*The term -25/y is a ratio.

Step-by-step explanation:

Anyone know the right answer?

Answers

Answer:

41 and 24

Step-by-step explanation:

Plz helllllpppppp meeeeee

Answers

Answer: x = 25 mi

Step-by-step explanation:

Sides QO and TR are corresponding.

Sides QP and TS are corresponding.

Sides OP and RS are corresponding.

Create the proportion to solve for x:

5/x = 6/30

Cross multiply:

6x = 150

Divide both sides by 6:

x = 25 mi

Hope this helps!

25mi. I’m pretty sure I hope I helped

if a=3 and b=5, what is the value of a^2 + b^2?

Answers

Answer:

31

Step-by-step explanation:

6+25=

Answer:

34

Step-by-step explanation:

3^2 = 9

5^2 = 25

25 + 9 = 34

Angie is going to varnish the floor. Continued on other side of the page She needs 1 litre of varnish for 5 m2 of floor. There are 2.5 litres of varnish in each tin of varnish. Angie has 3 tins of varnish. Does she have enough varnish for all the floor? You must show all your working

Answers

Answer:

No, she doesn't have enough varnish for all the floors.

Step-by-step explanation:

Area of the floor, A= 10x6-5x2=50 [tex]m^2[/tex]

Since 5 m^2 required 1 liter of varnish.

So, the amount of varnish required for 1 [tex]m^2[/tex] = 1/5= 0.2 liters.

The amount of varnish required for 50 [tex]m^2[/tex] = 0.2X50=10 liters.

Now, as 1 tin has 2.5 liters of varnish.

So, the total amount of varnish available = 3x2.5=7.5 liters, which is less than the total requirement.

Hence, she doesn't have enough varnish for all the floors.

Is 0.88 a terminating decimal

Answers

yes
hope this helped you

Answer:

no

Step-by-step explanation:

its a equation not a decimal making it false.

Which values of x and y would make the following expression represent a real number? (4+5i)(x+ yi)
Ox=4,y= 5
Ox=-4, y = 0
Ox=4, y=-5
Ox=0, y= 5​

Answers

Answer:

C

Step-by-step explanation:

We have the expression [tex](4+5i)(x+yi)[/tex] and we want to find the values of [tex]x[/tex] and [tex]y[/tex] such that the expression will evaluate to a real number.

So, let's first expand the expression. Distribute:

[tex]=4(x+yi)+5i(x+yi)[/tex]

Distribute:

[tex]=4x+4yi+5xi+5yi^2[/tex]

Simplify:

[tex]=(4x-5y)+(4yi+5xi)[/tex]

So, we want to make the second part within the real numbers.

Notice that we only have two ways of doing this: 1) Either both [tex]x[/tex] and [tex]y[/tex] are imaginary numbers themselves canceling out the [tex]i[/tex], or 2), the entire expression equals 0.

Since our answer choices consists of only real numbers, this means that the imaginary part must be equal to 0. So:

[tex]4yi+5xi=0[/tex]

We can divide everything by [tex]i[/tex]:

[tex]4y+5x=0[/tex]

Now, we can use our answer choices.

Running down the list, we can see that the choice that works is C. If we substitute the values of C into the equation, we get:

[tex]4(-5)+5(4)=0\\\Rightarrow -20+20=0\stackrel{\checkmark}{=}0[/tex]

Therefore, our answer is C.

Answer:

c

Step-by-step explanation:

Please HELP!!! I will give 23 points!! Answer the following questions. Please answer correctly!!! Thanks!

Answers

1. c

2. c

3. a

4. a

5. d

HELP ME ASAP BRO THIS IS DUED BY TONIGHT, LITERALLY ANYONE OUT THERE
Show Work Pleaseeee

What is the m< BAD? ( If you are confused look at the picture provided)

Answers

Answer:

The measurement of angle BAD would be 120°.

How To Do It:

You set the expressions equal to each other & solve for x. Then you plug x into each expression & add them.

Set Expressions Equal To Each Other To Find The Value Of X:

(13x-31)=(x+53)----------add 31 to each side

13x=(x+84)----------subtract x from both sides

12x=84----------divide both sides by 12

x=7

Plug-In The Value Of X To Each Expression & Add:

(13(7)-31)+((7)+53)----------distribute the 7 to each coefficient

(91-31)+(7+53)----------add/subtract numbers inside the parentheses

(60)+(60)----------add the final products together

120----------*Final Answer*

What is 54 ÷ 2/3 ? ​

Answers

The answer to your question is 81.

Answer: 79 1/2

 Convert any mixed numbers to fractions.

    Then your initial equation becomes:

       53/1 ÷ 2/3

Applying the fractions formula for division,

multiply 53/1 by 2/3

      = 159/2

Simplifying 159/2, the answer is

79 1/2

What is the place value of 7 in 7,000.2

Answers

Answer: The thousands place

Step-by-step explanation: the two is the tenths place, all the 0 are one, tens, and hundreds place

Other Questions
What did rivers contribute to the development of early civilizations?a.fertile land, irrigation, and transportationb.fertile land, bathing area, and livestock supplyc.irrigation, trade, and defense against invadersd.none of the above which fraction is greater 4/6 or 2/10 or is it equal Which correctly solves the equation ab+c=d solve for b. What conclusions can you makeabout who might have been at thescene of Anna's death? Explain. Hello, I need help on this :)Enter a number/answerWhat is the measurement of b? can you guys help me and can you tell me by number Whats this called please help Emily Wilson was the top scorer in a women's professional basketball league for the 2006 regular season, with a total of 854 points. The number of two-point field goals that Emily made was 73 less than double the number of three-point field goals she made. The number of free throws (each worth one point) she made was 34 less than the number of two-point field goals she made. Find how many free throws, two-point field goals, and three-point field goals Emily Wilson made during the 2006 regular season. made Please help ASAP its due today This is philosophy: We are studying about Locke's TheoryYou and I have been kidnapped by a mad scientist. He tells us that, tomorrow morning hes going to transfer all of your mental contentall your beliefs, memories, personality, everythinginto my brain. And then hes gonna move all of your mental content into your brain. Presumably, this is how he earned the title of mad scientist. But he also tells us that, after the procedure is completeand your mental content is in this body, and my mental content is in yourshell give one of the bodies a million dollar, and the other body will be tortured. And hes decided to let you pick which body gets the tortured. And hes decided to let you pick which body gets the torture and which one gets the cash. What do you decide? Your answer should give you a clue where you think your identity lies. Who can translate the following poem from English to German?I give you light, you give me purpose,I fathom your delighted soul,You are the only thing that keeps me awake,In which is a feeling I can't let go. Describe and explain what you wouldobserve when the chlorine gas supplyis turned off. The Greek philosopher Empedocles proposed the idea thatALL matter was made of_____elements. Whom does Dante find in the ninth circle of Hell? Why are thy there?. Please cite the Divine Comedy to support your answers. What is anology? What is microscope? Find the value of x so that line m is parallel to line l. When pouring food coloring into warm water and cold water, we can see that themolecules in warm water move faster and spread the food coloring more quickly.(Conduction Lab Experiment)truefalse Elena finds that the area of a house on a scale drawing is 25 square inches. The actual area of the house is 2,025 square feet. What is the scale of the drawing? Which statement best expresses a basic scientific assumption? Summarize the light dependent reaction, first stage of photosynthesis