An equilateral triangle has a side length of 1.4x + 2 inches. A regular hexagon has a side length of 0.5x + 2 inches. The perimeters are equal. What is the side length of the triangle? What is the side length of the hexagon? Show your work.
Answer:
9 inches; 4.5 inches.
Step-by-step explanation:
Given the following data;
Length of sides of the equilateral triangle = 1.4x + 2 inches.
Length of sides of the hexagon = 0.5x + 2 inches.
We know that the perimeter of a hexagon is given by the formula;
P = 6 * length of sides
Substituting into the equation, we have;
P = 6*(0.5x + 2)
P = 3x + 12
Perimeter of an equilateral triangle is given by the formula;
P = 3 * length of sides
Substituting into the equation, we have;
P = 3(1.4x + 2)
P = 4.2x + 6
Since perimeter of hexagon = perimeter of equilateral triangle. Therefore;
3x + 12 = 4.2x + 6
Rearranging the equation, we have;
12 - 6 = 4.2x - 3x
6 = 1.2x
x = 6/1.2
x = 5
I. To find the length of each sides of the equilateral triangle;
Length of a side = 1.4x + 2
Substituting the value of "x" into the equation, we have;
Length of sides = 1.4*(5) + 2
Length of sides = 7 + 2
Length of sides = 9 inches.
II. To find the length of each sides of the hexagon;
Length of sides = 0.5x + 2
Substituting the value of "x" into the equation, we have;
Length of sides = 0.5*(5) + 2
Length of sides = 2.5 + 2
Length of sides = 4.5 inches.
The side length of the equilateral triangle 9 inches.
The side length of the hexagon 4.5 inches.
The side length of the equilateral triangle = 1.4x + 2
So, the perimeter = 3(1.4x + 2) = 4.2x + 6.
The side length of the hexagon = 0.5x + 2
So, the perimeter = 6(0.5x + 2) = 3x + 12.
Given tha the perimeters are equal.
So,
[tex]4.2x+6=3x+12\\4.2x-3x=12-6\\1.2x=6\\x=5[/tex]
Hence,
The side length of the equilateral triangle = 1.4x + 2 = 1.4(5) + 2 = 9
The side length of the hexagon = 0.5x + 2 = 0.5(5) + 2 = 4.5
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HELP NOW!!!! thx :DDDD
Answer:
the second one
Step-by-step explanation:
Answer:
Answer A
Step-by-step explanation:
3 parts ginger ale to 2 parts raspberry juice
HELP!!! Is this the expanded form of a number? 40*1000+7*10. If yes, What is it?
Answer:
40070
Step-by-step explanation:
What is the value of 2cos2(105⁰) − 1?
Step-by-step explanation:
-1 - root3
The value of the given expression 2cos2(105⁰) − 1 is,
⇒ - 1 - √3
What is trigonometric functions?A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively used in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many others.
We have to find the value of;
⇒ 2cos2(105⁰) − 1
Now, We can Plug 105° = θ
So, the expression becomes,
⇒ 2cos2θ - 1
Using the formula;
cos2θ = 1 - 2sin^2θ
We get;
⇒ 2cos2θ - 1 = 2(1-2sin^2θ) - 1
= 2 - 4sin^2θ - 1
⇒ 2cos2θ - 1 = 1 - 4sin^2θ
Now, Again plug θ = 105°
⇒ 2cos2(105°) - 1 = 1 - 4sin¹⁰⁵
⇒ 2cos2(105°) - 1 = -1 - √3
Hence, The value of the given expression is,
⇒ (-1 - √3)
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2x + 2y = 4 -x+ 2y = 4
Answer:
x = 0, y = 2
Step-by-step explanation:
We can use substitution method to substitute 2y into 2x + 2y = 4.
-x + 2y = 4
2y = 4 + x --- Equation 1
2x + 2y = 4 --- Equation 2
Substitute Equation 1 into Equation 2:
2x + 2y = 4
2x + 4 + x = 4
3x + 4 = 4
Isolate 3x.
3x = 4-4
= 0
Find x.
x = 0 ÷ 3
x = 0
Substitute x = 0 into Equation 1:
2y = 4 + x
2y = 4 + 0
= 4
Find y.
y = 4 ÷ 2
y = 2
Assuming all model requirements for conducting the appropriate procedure have been​ satisfied, is the mean IQ of the students in the​ professor's statistics class higher than that of the general​ population, 100? Explain what statistical procedure should be used for this research objective.
Answer:
Step-by-step explanation:
The right statistical procedure is by applying a hypothesis test that uses a single mean. Here, if we are to talk about comparison, it should be between the mean IQ of the students in the class and the national average IQ. The class is not for a comparison between two population means because it is viewed as the sample of the population. That is to say, the required task is to determine if the sample mean is greater than the population mean. We can conclude that this obeys a hypothesis test rather than a confidence interval.
Jason drove 110 miles in 2 3/4hours. What was Jason’s speed in miles per hour?
Answer: His MPH is 40
Step-by-step explanation: 100/2.75 = 40. Converting the fraction to decimal form makes this problem much easier.
PLEASE HELP WILL GIVE 50 POINTS
Write an equation for a line perpendicular to f(x)=5x−1 and passing through the point (5,20).
Answer:
f(x)=-5x+1
Step-by-step explanation:
I hope this answer works for you!. but I am not completely confident in it.
What is- If x = 5 find the value of (x + 3)2
A survey asked 200 students to name their favorite fruit. The table shows the results of the survey. How many more students chose peaches compared to oranges as their favorite fruit? Explain your thinking.
Answer:
Without seeing the table I can't answer the question
Step-by-step explanation:
But if you take the number of Peaches and subtrqact the number of oranges will have your answer.
Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 3
What is the value of x? PLEASE ANSWER ASAP!!
Answer:
...........................................................
Step-by-step explanation:
what can graphs involving constant rate be used for
Please Help
I Keep asking if someone can help me with this and no one actually helped me, please help!
This is the Second day that I have been asking about this!
9514 1404 393
Answer:
m∠ABC = 81°
m∠FEC = 90°
Step-by-step explanation:
The median BE of isosceles triangle ABC is also an altitude and the angle bisector of ∠ABC. This means ...
m∠ABC = 2×m∠ABE = 2(40°30')
m∠ABC = 81°
It also means that all of the angles at the intersection of BF and AC are right angles, so ...
m∠FEC = 90°
Raspberries are hannas favorite fruit. She can only buy one pins for 2.55$ how many pounds of raspberries can Hannah but for $12? Find 12 /2.55 round to nearest hundredth
Answer:
She can buy 36
Step-by-step explanation:
Solve these following equations
A.3÷25.50=
B. 8÷1.624=
C.7 ÷21.56=
D.5 ÷1.005
Which number line shows the correct placement of 20%, 1/3
and 2/3?
Answer:
the answer is option A why because its basiclly telling us that 1/3 and 2/3 are close to each other and they need to find the percent on how to get to the whole number in this case is 1
Step-by-step explanation:
Answer A you welcome
an old movie theater
Answer: ummmmmm bow tie cinamas
Step-by-step explanation: yw:))
true or false 7b + 14bc = 5
Answer: False
Step-by-step explanation:
Hey there! 7b + 14b = 5 would equal 21b + 5 after you add 7b + 14b.
21b = 5 is false because it doesn't match with 5.
If the answer was true then it would be 5 = 5.
~I hope I helped :)~
Is chewing gum independent of having a cavity filled recently?
A.
B.
C.
D.
Answer:
did you figure out the answer I'm sorry they don't have a comment section on ur photo
Answer:
P(Gum) ≠ P(Gum/Cavity)
Step-by-step explanation:
Answer on Edge
Need answer ASAP ROCKY!!
The triangle with vertices at L (-2,5), E ( 1,4), and D(2,-2) is 4 units left, 3 units up, and then reflected over the line y=4 to form the image L'E'D. Which vertex of the image is the greatest distance from the origin?
Answer:
L'(6,8)
Step-by-step explanation:
If i had to take a guess what i would is subtract 4 from each x number and add 3 to each y number and then reflect over the line y=4 so then that would give me each distance. And by the looks it seems L'(6,8) is the farthest from he origin (0,0)
Which volleyball court is longer
a. gym volleyball court
b. Olympic volleyball court
c. beach volleyball court
d. concrete volleyball court
The beach volleyball court, which accomodates teams of two players to each side, is slightly larger that its traditional counterpart, measuring 16 meters (52 feet, six inches) long and eight meters (26 feet, three inches) wide.
Carpet costs $7.84 per yard. What is the cost of 21.5 yards?
Answer:
$168.56
Step-by-step explanation:
Answer:168.56
Step-by-step explanation:
A rectangular building with a square base is being designed to minimize heat loss. The building designers state that the volume of the building must be exactly 4000 m^3. Write an equation for y, the height of the building, in terms of x, the length and width of the base.
Answer:
y = 4000/x²
Step-by-step explanation:
The volume of the building is expressed as;
V = x²y where;
x is the length and width of the base.
y is the height of the building
Given
Volume V = 4000m³
Substitute the given volume into the equation as shown;
4000 = x²y
Make y the subject of the formula by dividing both sides by x²
4000/x² = x²y/x²
4000/x² = y
Rearrange
y = 4000/x²
Hence equation for y, the height of the building, in terms of x, the length and width of the base is expressed as y = 4000/x²
What’s quadratic equation
Answer:
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation that can be rearranged in standard form as ax^2+bx+c-0 where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a .0, then the equation is linear, not quadratic, as there is no ax^2 term. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.
Step-by-step explanation:
Good Question I just had a class about it 10 minutes ago such a coincidence! :)
Answer:
ax^2+bx+c=0
Explanation:
This is the typical style of a quadratic equation to be in. The only varieties there would be within the pronumerals used.
Liang has a goal of walking at least 18 miles. She walks at a rate of 4 miles per hour. Which inequality can liang use to find h, the number of hours she should walk in order to meet or exceed her goal
Answer:
t ≤ 4.5
Step-by-step explanation:
We are told that the goal is to walk at least 18 miles
She walks at a rate of 4 miles per hour, speed is 4mph
Required
the inequality for the time taken to walk the distance and the said speed
Step two:
we know that
speed= distance/time
time=distance/speed
substitute
time= 18/4
time= 4.5 hours
Time≤ 4.5 hours
2/3x24 = 16
Write a situation for this equation and draw a picture that goes with it
Answer:
16
Step-by-step explanation:
2/3×24=16
2/1×8=16
FInd the value of x if L, M belongs to line KM
Answer:
k
Step-by-step explanation:
k=k
Mac uses 3.5 liters of water with 4
lemons to make lemonade. How many
lemons are needed if Mac uses 7 liters of
water to make lemonade?
Answer:
if I'm correct, it should be 6.125. I'm sorry if I'm wrong,
Step-by-step explanation:
take 3.5 and divide it by 4, which gives you the amount for 1 lemon. times that by 7, and you get 6.125
Answer:
8 lemons
Step-by-step explanation:
7- 3.5= 3.5
Therefore we multiple 3.5 by 2.
We always do the same on the other side.
4 times 2 equals 8
7 liters of water: 8 lemons
F(x)=43
f(x)=-6×+7
Not sure how to get the answer wondering if someone can break it down for me please
Step-by-step explanation:
Since f(x) is 43 you would replace it for the f(x) in the bottom equation like this 43=-6×+7 then you would multiply the left side so now it would be 43=-42 and this a no solution.
The diameter of a cookie is 2 inches. If \piπ = 3.14, what is the area of the cookie, rounded to the nearest tenth?
Answer:
6.28 or 7
Step-by-step explanation:
you have to time pie x inches
pie x inches
3.14 x 2
=6.28 rounded up 7