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
Describe the transformation
A) translation 2 units down
B) reflection across y=-1
C) reflection across the x-axis
D) across the y-axis
Answers
Answer:
C.
Step-by-step explanation:
if a2+b2+c2=ab+bc+ca find a+b/b
Answers
Answer:
Step-by-step explanation:
a² + b² + c² = ab + bc + ca
On multiplying both sides by “2”, it becomes
2 ( a² + b² + c² ) = 2 ( ab + bc + ca)
2a² + 2b² + 2c² = 2ab + 2bc + 2ca
a² + a² + b² + b² + c² + c² – 2ab – 2bc – 2ca = 0
a² + b² – 2ab + b² + c² – 2bc + c² + a² – 2ca = 0
(a² + b² – 2ab) + (b² + c² – 2bc) + (c² + a² – 2ca) = 0
(a – b)² + (b – c)² + (c – a)² = 0
=> Since the sum of square is zero then each term should be zero
⇒ (a –b)² = 0, (b – c)² = 0, (c – a)² = 0
⇒ (a –b) = 0, (b – c) = 0, (c – a) = 0
⇒ a = b, b = c, c = a
∴ a = b = c.
hence
a+b/b
a+a/a= (since a=b)
2a/a=
a....
A jewelry artist is selling necklaces at an art fair. It costs $135 to rent a booth at the fair. The cost of materials for each necklace is $4.50. The artist is selling the necklaces at $12 each. The inequality LaTeX: 12n > 135 + 4.50n12n>135+4.50n12n>135+4.50n represents the situation in which the artist makes a profit.
Answers
Answer:
The artist makes profits when n>8.18
that is when the number of necklaces exeeds 8.18
Step-by-step explanation:
Given
let the number of necklaces be n
booth rent= $135
The cost of materials for the necklaces = $4.5n
the selling price for all the necklaces =$12n
total expenses= booth rent+cost of material = $135+4.5n
profit = selling price -total expenses
12n > 135 + 4.50n
solving for n we have
12n=135 + 4.50n
12n+4.5n=135
16.5n=135
n=135/16.5
n=8.18
The artist makes profits when n>8.18
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Answers
Answer:
44670
Step-by-step explanation:
5.67*1000+3.9*10000
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Answers
Answer:
(x,y)→(x+7,y)
Step-by-step explanation:
Cuz the point isn't moving up or down so the y is the same and x+7 cuz the point moved 7 units to the right so its position changed in the x-axis.
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Answer:
Given a=35 and ∠β=42°,
b = 31.51414
c = 47.09715
∠α = 48° = 0.83776 rad = 4/15π
h = 23.41957
area = 551.49748
perimeter = 113.61129
inradius = 9.7085
circumradius = 23.54857
Step-by-step explanation:
Arya deposit $8000 in a 5 year cd at 2% interest compounded daily. What is aryas new balance at the time of maturity
Answers
Answer:
Step-by-step explanation:
Use the given functions to set up and simplify
2%.8000=a⋅(5yearcd)= 5ea2yrcd2%=0.02
Answer:
100
Step-by-step explanation:
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Answer:
The 2nd one is no symmetry the 1st one is (reflection) last one rotational only
Step-by-step explanation:
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Answer:
1) x=2
2) n=0
3) x=-7
4) a=0
5) m=-1
6) p=1
7) p=-6
8) r=3
9) x=-4
10) x=0
IF YOU ANSWER CORRECTLY I WILL GIVE YOU BRAINLIEST. Can someone give me the answers to this: CLOSURE REVIEW CL A-98 thru CL 108
Todays the last day of the quarter and I really need to turn it in but I cant focus.
Answers
Answer:
nfw
Step-by-sntep explanation:
fwjfba
Carlos sold 6 cellphones every hour during the day, but in the morning he already ha $1,250 in the register. What is the expression that represents the total amount of money that he should have in the register in a given hour?
A: $1250
B: 6x
C: 6x + 1250
D: 1250x + 6
Answers
Answer: 6x+1250
Step-by-step explanation:
Amount already in the register = $1250
Number of phones sold every hour = 6
Price of the phone = x
The expression that represents the total amount of money that he should have in the register in a given hour will be:
= $1250 + $6x.
Therefore, option C that is 6x + 1250 is the correct answer.
Original
Point
Reflection Over
The y-axis
(1,4)
Answers
Step-by-step explanation:
reflection over the y-axis the values of x will change so it's going to be -1,4
In a rectangle KLMN, the diagonals KM and LN intersect at O. (i) If KO = 4y + 6 and ON = 3y + 11, find the lengths of its diagonals. (ii) If ∠NKM = 32°, find ∠KON and ∠KMN. GUYS, IT'S VERY URGENT. I HAVE TO SUBMIT TOMORRIW. PLS ANS. PLS DON'T GIVE WRONG ANSWERS
Answers
Answer:
Step-by-step explanation:
In a rectangle KLMN, if the diagonals KM and LN intersect at O, then KO = ON
GIVEN
KO = 4y+6
ON = 3y+11
Equate
4y+6 = 3y+11
Collect like terms
4y-3y = 11-6
y = 5
KO = 4(5)+6
KO = 20+6
KO = 26
Note that KO = OM = LO = ON = 26
Hence ON = 26
For diagonal KM,
KO+OM = KM
KM = 26+26
KM = 52
LN = LO+ON
LN = 26+26
LN = 52
From.the digram, ∆KON is isosceles triangle hence <KON = KNO =32°
<KON = 180-(32+32)
<KON = 180-64
<KON = 116°
<ONM = 90-32
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<ONM = <OMN = 58°
Hence <KMN = 58°
THANKS FOR EVERYBODY HELPING ME I WILL GIVE FREE ROBUX
Answers
Answer:
6 times
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
add me on discord fun54658#0871
Can someone please Help me. ( picture included)
Answers
Answer:
The height of the flagpole is 20 feet.
banana cheese salad with cheese on top
Answers
Step-by-step explanation:
question is notcorrect
Answer:
[tex]x<-5[/tex]
Step-by-step explanation:
[tex]4-x<9[/tex]
Subtract 4 to both sides
[tex]x<-5[/tex]
Hope this helps and pls do mark me brainliest if you can:)
Solve for x plz show all the work. x/3=6
Answers
Answer: x=18
Step-by-step explanation:
X/3=6
We want to get x alone so we multiply both sides by 3
X=18
Fatima invests a total of $29,000 in two accounts. The first account earned a rate of return of 11%. However, the second account suffered a 7% loss in the same period. At the end of one year, the total of money gained was $1,570.00. How much was invested into each account?
Answers
Step-by-step explanation:
given data:
gained = $1,570
amount invested = $29,000
0.11x – 0.07( $29,000 – x ) = 1540
0.11x – ( 2030 – 0.07x ) = 1540
0.11x + 0.07 = 1540 +2030
0.18x = 3570
divide both sides by 0.18
x = 19833.33 ( amount invested at 11%.
$29,000 – 19833.33
= $9166.7 ( amount invested at 7%)
Olivia started her banking account with $100 and is increasing the account $20 per month. Which function is correct?
f(x) = 100 + |20x|
f(x) = 20x + 100
f(x) = 100x; f(x) = 20x; f(x) = x
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Answers
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Answers
2. 5, π+ 2, 17/3,
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5. √13, 3.7, π + 1
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f(3) = 3x + 2
f(3) = 8
x=
Answers
Answer:
f(3) =3(2)+2
Step-by-step explanation:
Therefore, x = 2
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Answers
The slope of the line is x = 2
The y intercept is (0,16)
Aubrey's dinner cost $85 She tips the waitstaff 30% for excellent service
Answers
Answer:
The total amount she paid would be $105.50.
Answer:
25.5 is the tip -- 110.50 is the total bill.
Step-by-step explanation:
You would calculate .30 (move the decimal over twice to switch from a percentage to a decimale) multiplied with 85 and this gives you 25.5.
85 * .3 = 25.5
Depending on the rest of the question, I added the tip to the amount of the dinner cost to obtain the total bill. You will need to see what the rest of the question is in order to verify which answer you are looking for.
Your answer should be a polynomial in standard form. ( d^2 +3) (d^2 +2d +1)
Answers
Answer:d^4+2d^3+4d^2+6d+3
Step-by-step explanation:
ANSWER ASAP PLEASE I WILL GIVE BRAINLIEST TO FIRST ANSWER!!!!
Which one would you choose? Explain your reasoning.
1. A 5-pound jug of honey for $15.35
2. Three 1.5-pound jars of honey for $13.05
Answers
Answer:
Three 1.5-pound jars of honey for $13.05
Step-by-step explanation:
15.35/5 = 3.07
3x1.5=4.5
13.05/4.5 = 2.90
convert 56.6 into radical form
Answers
-3x+3y=3 and -5x+y=13
Answers
Answer:
y = x + 3
y = 5x + 13
Which of the following is a possible value for X
Answers
Answer:
E)3
Step-by-step explanation:
4/3-1=2
3+1/2=2
First, You cross multiply.
(x - 1)(x + 1) = 8
x^2 - 1 = 8
Now subtract 8 from both sides.
x^2 - 9 = 0
x^2 - 9 is a difference between 2 squares.
(x + 3)(x - 3) = 0
For an equation with only multiplying to be equal to 0, one of its factors must be 0.
So either x + 3 = 0 or x - 3 = 0.
So x could be -3 or 3.
The answer is (E).
Hope this helps!
Mt. Young bought some hamburgers for his cookout. The price was $32,17, but, le found that hamburger parties were on special for $22.692. What was hubs DOcent Bio
A $3.20
B. 29.68%
OC45%
D. $87.25
Answers
A is too little
C is too much off
D is way too much
So B is your answer
kala needs to make a total of 80 deliveries this week. So far she has completed 28 of them. What percentage of her total deliveries has kala completed?
Answers
Answer:
35 %
Step-by-step explanation:
50 % of 80 is 40 so 28% of 80 is 35%
if you just divide 80 by 28 you will get 35.