Answers
====================================================
Explanation:
The hexagon is broken up into 6 congruent or identical equilateral triangles. If we find the area of one triangle, then we multiply by 6 to get the area of the hexagon.
Going in reverse, we divide the hexagon's area by 6 to get the area of one equilateral triangle
We're told the hexagon has an area of [tex]18\sqrt{3}[/tex] square inches. Divide this by 6 and you should get the result [tex]3\sqrt{3}[/tex]. So each of the six equilateral triangles has area of [tex]3\sqrt{3}[/tex] square inches.
-------------------------------------
Each triangle has a base of [tex]2(\sqrt{3})^{x/12}[/tex] and a height of [tex](\sqrt{3})^{x/6}[/tex]
The x/12 and x/6 are exponents.
Let [tex]b = 2(\sqrt{3})^{x/12}[/tex] and [tex]h = (\sqrt{3})^{x/6}[/tex] be the base and height respectively.
Also, let [tex]A = 3\sqrt{3}[/tex] be the area of the triangle
We can then solve for x like so:
[tex]A = 0.5*b*h\\\\3\sqrt{3} = 0.5*2(\sqrt{3})^{x/12}*(\sqrt{3})^{x/6}\\\\3*3^{1/2} = (\sqrt{3})^{x/12+x/6}\\\\3^1*3^{1/2} = (\sqrt{3})^{x/12+2x/12}\\\\3^{1+1/2} = (\sqrt{3})^{3x/12}\\\\3^{3/2} = (3^{1/2})^{x/4}\\\\3^{3/2} = 3^{(1/2)*(x/4)}\\\\3^{3/2} = 3^{x/8}\\\\[/tex]
Since the bases are equal to 3, this means the exponents must be equal as well (for both sides overall to be equal)
3/2 = x/8
3*8 = 2*x ... cross multiply
24 = 2x
2x = 24
x = 24/2
x = 12
Related Questions
Can somebody plz help answer these questions (only if u know how to do this) thanks a lot! :)
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DDD
Answers
Answer:
12. 3:12
Step-by-step explanation:
that is 12
What is the value of x in the system of equations shown below?
5x + 4y = 1
y = 1 - x
Answers
Answer:
x=-3
Step-by-step explanation:
Answer:
x = -3
Step-by-step explanation:
Plug in
5x + 4(1 - x) = 1
(y gets replaced by 1 - x)
Multiply
5x + 4 - 4x = 1
(multiply 4 by whats in the parenthesis)
Combine Constants
5x - 4x = -3
(constant = numbers without a variable)
(separate constants from variables = numbers with letters)
Combine Variables
1x = -3
(then you got your answer and you can take the "1" off the x)
If a woman making $25 an hour gets a
10% raise, how much will she now
make in an 8-hour workday?
Answers
Step-by-step explanation:
She gets $220 in an 8 hour work day.
CASLAN UR HERE 56+6x567890-9
Answers
Answer: 35, 209, 171
Step-by-step explanation: hope i helped
Answer:
56+6x567890-9 = 3407387
7x+7+2z+9= please help me
Answers
Answer:
7x+2z+16
Step-by-step explanation:
find like terms
7 9
add them
7+9=16
7x+2z+16
Which transformation was performed on PQRS to form P'QʻR'S'? (1 point)
1) A dilation factor of 2
2) A dilation factor of 4
3) A dilation factor of 1/2
4) A dilation factor of 1/4
Answers
Given:
A transformation was performed on PQRS to form P'QʻR'S'.
To find:
The transformation.
Solution:
The given graph shows two similar polygons. It means, dilation was performed.
From the given graph it is clear that,
[tex]PS=2[/tex] units
[tex]P'S'=1[/tex] units
Now,
[tex]\text{Scale factor}=\dfrac{P'S'}{PS}[/tex]
[tex]\text{Scale factor}=\dfrac{1}{2}[/tex]
A dilation factor of [tex]\dfrac{1}{2}[/tex] was performed on PQRS to form P'QʻR'S'.
Therefore, the correct option is (3).
Write an equation in paint-slope form of the line that passes through the point (3, 5) and has a slope of m = - 1
Answers
9514 1404 393
Answer:
y -5 = -(x -3)
Step-by-step explanation:
The point-slope form of the equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
For m=-1 and (h, k) = (3, 5), the equation of the line is ...
y -5 = -(x -3)
Answer:
y-5=-1(x-3)
Step-by-step explanation:
Point slope form: y-y1=m(x-x1)
Simplify this surd expression
√12 x √8
Please complete the following by 5pm today, thx, and I will mark as brainliest answer
Answers
[tex] \sqrt{12} \times \sqrt{8} [/tex]
means
[tex] \sqrt{12 \times 8} [/tex]
then it will be
[tex] \sqrt{96} [/tex]
96 is not perfect square so
[tex] \sqrt{16 \times 6} [/tex]
and then
[tex] \sqrt{16} \times \sqrt{6} [/tex]
finally
[tex]4 \sqrt{6} [/tex]
is the answer
if it's helpful ❤❤❤
THANK YOU
Nicholas got a 2% raise. His previous salary was $12,000. What will be his next salary?
Answers
Answer: 240
Step-by-step explanation:
1. 12,000×.04=240
2. 12,000+240= 12,240
Answer:
$12,240
Step-by-step explanation:
$12,000 = 100%
$12,000 / 100 = $120
$120 = 1%
$120x 2 = %240.
$240 = 2%
$12,000+ 240 = $12,240
Need help with Geometry proof please!!!
Answers
Step-by-step explanation:
QR is parallel to TU | Given
S is the midpoint of QT | Given
QS = ST | Definition of midpoint
<QSR = <TSU | definition of vertical angles
<QRS = <STU | Definition of Alternate Interior Angles
QSR = TSU | ASA
Pretty sure that's right :D
Also, wherever it says "=", I mean congruency symbol
HELP Determine which lines, if any, must be parallel. Check all that apply. HELP WITH THE ENTIRE QUESTION
Answers
Jordan has 300 pieces of candy. He gives Adrian ¼ pieces, 10% was given to Darien and he gave his little brother 25 pieces. Explain in writing (typing) how to find the number of pieces each person received then explain in writing (typing) how to find the number of pieces Jordan has left. (Remember to write 5 or more complete sentences)
Answers
Answer:
300-225=74 pieces
Step-by-step explanation:
1/4 of 300= 75
10% of 300 = 30
lil bro has 25
total of 75+30+25=225
Please help please please help ASAP ASAP please
Answers
Answer: 37°
Step-by-step explanation:
Please help before i fail my assignment, i need to find the point slope form of all five of these graphs
Answers
Answer:
1. 4/2
2. 2/4
3. 4/-4
4. 0/2
5.3/4
i am so sorry if i am wrong
Work out the area of this circle
Answers
Answer:
area = 25.136
Step-by-step explanation:
to find the area of a circle, you use the formula v=pi times the radius squared
14. Mrs. Buchanan is planning marching routines for the school band. The band has 36 members. Band members can march in any number of rows as long as each row has the same number of members. The marching path, however, limits members to 6 per row.
Answers
Question:
Make a list of the different arrangements that Mrs. Buchanan could use.
Answer:
[tex](x,y) = \{(1,36),(2,18),(3,12),(4,9),(6,6)\}[/tex]
Step-by-step explanation:
Given
[tex]Members = 36[/tex]
[tex]Rows\ Limit = 6[/tex]
Represent the rows with x and the column, y.
This means that:
[tex]x * y = 36[/tex]
Make y the subject:
[tex]y = \frac{36}{x}[/tex]
The list is then generated as follows:
When x = 6.
[tex]y = \frac{36}{6} = 6[/tex]
[tex](x,y) = (6,6)[/tex]
When x = 5
[tex]y = \frac{36}{5} = 7.2[/tex]
This result can not be use because the result of the number of columns must be an integer
When x = 4
[tex]y = \frac{36}{4} = 9[/tex]
[tex](x,y) = (4,9)[/tex]
When x = 3
[tex]y = \frac{36}{3} = 12[/tex]
[tex](x,y) = (3,12)[/tex]
When x = 2
[tex]y = \frac{36}{2} = 18[/tex]
[tex](x,y) = (2,18)[/tex]
When x = 1
[tex]y = \frac{36}{1} = 36[/tex]
[tex](x,y) =(1,36)[/tex]
So, the possible list is:
[tex](x,y) = \{(1,36),(2,18),(3,12),(4,9),(6,6)\}[/tex]
what is the algebraic expression for milo earns $13 per hour at his new job
Answers
Answer:
The expression would be 13x = y
Step-by-step explanation:
x= number of hours
y= how much money he has after x hours.
Someone help me find the answer to this problem. 15a - 20 + 10a =
Answers
Answer:
5a +20
Step-by-step explanation:
add or subtract the same variables
Answer:
25a-20
Step-by-step explanation:
Since there is no value after the equal sign, all you can do is combine like terms
It takes 40 minutes for Sarah to get ready for school. If it is 7:55 A.M. when Sarah leaves, what time does Sarah get up?
Answers
Answer:
It was 7:15 a.m.
Step-by-step explanation:
Answer:
7:15
Step-by-step explanation:
I went and looked at my hand clock lol. I pointed at 7:55 and subtracted 40 and got to 7:15
HELP please what is this question? 6358 was rounded to the nearest one. What is the lower bound?
Answers
Answer:
8
because there are no decimal places so the answer is rounded to 8 as you cant change it
Step-by-step explanation:
is 6 divided (-3) the same as -6 divided 3?
Answers
Answer:
Yes
Step-by-step explanation:
Positive divided by negative is negative.
Negative divided by positive is negative.
Remember that negative * negative is a positive and positive * negative is a negative.
⚠️HELP PLZZZ ⚠️‼️help plz I’ve been on this question for an while now and I don’t understand
Answers
Answer:
3:6
Step-by-step explanation:
8:24 and 24:72 reduce down to 1:3. 3:6 is 1:2.
Arthur's dinner bill totaled $13.72, before sales tax and tip.
• Sales tax at the restaurant is 5.8%.
• After sales tax, he left a 15% tip.
What was Arthur's total bill, including sales tax and tip?
Answers
Answer:
16.69
Step-by-step explanation:
if its wrong than report this awnser for incorrect but I am 95 percent sure its correct
Answer:
16.70 total bill including tax and tip
Step-by-step explanation:
13.72 x .058 (5.8%) =.80 sales tax
13.72+.80=14.52 price with sales tax
14.52 x .15=2.18 tip
14.52 + 2.18 = 16.70 total price including tip
An eight grader has 18 coins in her pocket. The coins are all dimes and quarters. Their total value is 2.85. Find how much of each coin is in her pocket.
Answers
Answer:
1 dimes and 9 quarters
Step-by-step explanation:
9 quarters = 2.75
1 dime = 10c
all together equals 2.85
PLS HELP ME I HAVE ONLY 10 MINS
Answers
Identify the side lengths that form a right triangle.
a. 12, 13, 16
b. 15, 20, 21
c. 9, 40, 42
d. 10, 24, 26
Identify the side lengths that form a right triangle.
a. 3, 4, 8
b. 30, 40, 45
c. 5, 12, 13
d. 6, 12, 13
3. do the side lengths of 8, 10, and 13 form a right triangle?
4. Determine if ▼ABC is a right triangle if AB=36, AC=48 and BC=60
Answers
Answer:
1. a. no.
b. no.
c. no.
d. yes.
2. a. no.
b. no.
c. yes.
d. no.
3. no it does not.
Step-by-step explanation:
im not sure about number 4 but i hope the others helped!
Can y’all plz help me for brainliest
Answers
Answer:
Step-by-step explanation:
Answer:
x = 2
Step-by-step explanation:
f (x) = x2 + 4
What is the value of x when f (x) = 42
A. -2
В. 0
C 12
D. 20
Answers
Answer:
f(x)=X^2+4
f(x)=42
42=X^2+4
X^2+4=42
X^2=42-4
X^2=38
X=sqrt(38)=6.16
[tex] \sqrt{?} [/tex]
What is -20x - (-2x) – 6
Answers
I need a lot of help omgggg
Answers
Answer: A. A' (0, 6), B' (0, 4), C' (-3, 3)
Step-by-step explanation:
A (3, 0), B (3, -2), C (0, -3)
A translation by vector <-3, 6>
Add the x-coordinate of each points to -3 and add the y-coordinates to 6
A (3, 0) -> 3 + -3 = 0 0 + 6 = 6 A' (0, 6)
B (3, -2) -> 3 + -3 = 0 -2 + 6 = 4 B' (0, 4)
C (0, -3) -> 0 + -3 = -3 -3 + 6 = 3 C' (-3, 3)
A' (0, 6), B' (0, 4), C' (-3, 3)
Hope this helped!