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
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.
Answer:
A, B, D
Step-by-step explanation:
Related Questions
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:
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)
HELP WILL MARK YOU BRAINLIEST NO GUESSES PLZ!!!!!!!!!!!!
Answers
Answer:72
Step-by-step explanation:
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:
I dont have a question anymmore lol k thanks
Answers
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
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:
Write an equation parallel to 2x+5y=15 that passes through the point (-10,1).
Answers
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
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
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.
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.
Is 0.88 a terminating decimal
Answers
hope this helped you
Answer:
no
Step-by-step explanation:
its a equation not a decimal making it false.
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:
1. What is 10% of 75?
Answers
Answer:
7.5
Step-by-step explanation:
i hope this helps!!
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!
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.
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
What is 54 ÷ 2/3 ?
Answers
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
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:
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)
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
what is the value of x in 5x−3(x−11)=7(2x−5)+2
Answers
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]
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.
2hr+20min+60sec are equal to _____ minutes
Answers
It is correct
Anyone know the right answer?
Answers
Answer:
41 and 24
Step-by-step explanation:
(-2,7)(0,-3) write the equation that goes through the points
Answers
-10/-2
Slope is
5
Answer
Y=5x-3
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*
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:
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.