S.I= PRT /100
where,
P = price $500
R = rate 10%
T = time =8months
= $500*10*8/100
= $40,000/100
S.I = $400
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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a television that usually sells for $499 is on sale for 10% off. what is the discount of the television?
Answer:
The discount is $49.90 the final price is $449.10
Step-by-step explanation:
I need some help on this
Answer:
b, k = -4
Step-by-step explanation:
3/2 = k + 11/2
=> 3/2 - 11/2 = k
=> -8/2 = k
=> k = -4
Answer:
the answer to this problem is -4
Marta used a coupon to save $3.50 on a book she bought. when marta bought the book,she gave the Clark a $20.00 bill,and the coupon.the sales gave Marta $9.01 in change.
Answer: OMG MY HERO ACADEMIA I LOVE YOUR PROFILE PICTURE!!!!!!!!!
Step-by-step explanation: Thanks for the points!!!! :)
What is the slope of the line that passes through the given points?
(-12,-4) and (11,-10)
Answer:
Y2-y1
X2-×1 = m
-12-(-10)
11-5 = -2/3
m= -2/3
Step-by-step explanation:
This scatter plot shows the height of a card tower and time in minutes used to build it. Based on the information in the scatter plot, what is the best prediction for the height of a card tower at 10 minutes?
A 3 inches
B 5 inches
C 7 inches
D 8 inches
The required measure of the height of the card tower at time 10 minutes is 5 inches. option B is correct.
Given that,
This scatters plot shows the height of a card tower and time in minutes used to build it. Based on the information in the scatter plot,
A scatter plot is a collection of points plotted on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the extent, if any, of correlation between the values of observed quantities or phenomena (called variables).
Here,
From the graph, the measure of the height of the card tower at time 10 minutes is to be more than 5, Following the greatest integer function the measure of the card tower is given as 5 inches.
Thus, the required measure of the height of the card tower at time 10 minutes is 5 inches. option B is correct.
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help
graph
i understand it but will it be to the right or left
Answer:I believe left
Step-by-step explanation:
What is the hardest subject in Middle School?
Answer:
in my middle school it was history
Step-by-step explanation:
70% of the 30 sandcastles at Donatello Beach have moats. how many more moats are there
Answer:
21 moats
Step-by-step explanation:
.70 x 30 = 21
It’s not b!!!! Help me please
Answer:
D maybe? im not sure
Step-by-step explanation:
help me.............
Answer:
is there a right angle?
Step-by-step explanation:
2u = u + 43
u = 43?
please help solve this.
Simplify 18 - 6x + 5x - 11
Answer:
7-x
Step-by-step explanation:
18-11=7
-6x+5x=-x
therefore, the answer is 7-x
The solution of the expression is,
⇒ - x + 7
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 18 - 6x + 5x - 11
Now, We can solve the expression as;
⇒ 18 - 6x + 5x - 11
Rearrange as;
⇒ - 6x + 5x + 18 - 11
Combine like term as;
⇒ - x + 7
Thus, The solution of the expression is,
⇒ - x + 7
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Help plz ^-^ will give brainliest!
Answer:
E
Step-by-step explanation:
I took the test too!
There are 15 members of the show choir. In how many different ways can you arrange any 8 members in the front row? Show work. I will give brainliest!
Answer:
259,459,200 ways.
Step-by-step explanation:
That is the number of permutations of 8 from 15.
= 15! / 15-8!
= 15! / 7!
= 15*14*13*12*11*10*9*8
= 259459200
Solve for x. (Simplify)
Answer:
x = 8.75
Step-by-step explanation:
the ratio of [tex]\frac{4}{7}[/tex] : [tex]\frac{5}{x}[/tex]
x = 8.75
Solve each equation. Check your solution.
3(n - 7) = -30
Doug hits a baseball straight towards a 15 ft high fence that is 400 ft from home plate. The ball is hit 2.5ft above the ground and leaves the bat at an angle of 30∘ with the horizontal. Find the minimum initial velocity needed for the ball to clear the fence.
Answer:
[tex]125.4\ \text{m/s}[/tex]
Step-by-step explanation:
u = Initial velocity of baseball
[tex]\theta[/tex] = Angle of hit = [tex]30^{\circ}[/tex]
x = Displacement in x direction = 400 ft
y = Displacement in y direction = 15 ft
[tex]y_0[/tex] = Height of hit = 2.5 ft
[tex]a_y[/tex] = g = Acceleration due to gravity = [tex]32.2\ \text{ft/s}^2[/tex]
t = Time taken
Displacement in x direction
[tex]x=u_xt\\\Rightarrow x=u\cos\theta t\\\Rightarrow t=\dfrac{x}{u\cos\theta}\\\Rightarrow t=\dfrac{400}{u\cos30^{\circ}}\\\Rightarrow t=\dfrac{400}{u\dfrac{\sqrt{3}}{2}}\\\Rightarrow t=\dfrac{800}{u\sqrt{3}}[/tex]
Displacement in y direction
[tex]y=y_0+u_yt+\dfrac{1}{2}a_yt^2\\\Rightarrow y=y_0+u\sin\theta t+\dfrac{1}{2}a_yt^2\\\Rightarrow 15=2.5+u\sin30^{\circ}(\dfrac{800}{u\sqrt{3}})+\dfrac{1}{2}\times -32.2\times (\dfrac{800}{u\sqrt{3}})^2\\\Rightarrow \dfrac{400}{\sqrt{3}}-\dfrac{10304000}{3u^2}-12.5=0\\\Rightarrow 218.44=\dfrac{10304000}{3u^2}\\\Rightarrow u=\sqrt{\dfrac{10304000}{3\times218.44}}\\\Rightarrow u=125.4\ \text{m/s}[/tex]
The minimum initial velocity needed for the ball to clear the fence is [tex]125.4\ \text{m/s}[/tex]
Your restaurant bill is $42.16. You want to leave a 20% tip. What is your best
estimate of a 20% tip?
Your answer
Answer:
$8.40
Step-by-step explanation:
Since this is an estimate, you need to do it in your head. The way I did it was I divided 40 by 5 since 20% is one fifth of 100%, then I divided 2 by 5 and added them together which equaled 8.40.
Answer:
About $8
Step-by-step explanation:
Move decimal point one place to the left (making $4.20), then double that answer (making $8.40). You said estimate so I rounded down to $8 but a more precise answer would be $8.40.
Hope this helps :).
Which of the following numbers
does NOT have the same value as
one quarter?
Yuki works at a garden store. She is stacking 40-pound bags of soil. Write an equation that gives the total weight, w, of the soil in pounds when yuki stacks b bags.
The answer is w=40b Answer:
Step-by-step explanation:
Answer:200
Step-by-step explanation:
w=40b
=40(5)
=200
8.A wedding venue holds no more than 485 guests. If 319 people have said they are attending, how many more people does the venue have room for?
Answer:
They have room for 166 more people.
Step-by-step explanation:
485 - 319 = 166
Answer:
166 people.
Step-by-step explanation:
If there is room for 485 and 319 people are coming, just subtract. 485-319=166.
Solve the inequality
Answer:
x<2
Step-by-step explanation:
5x+10>14x-8
18>9x
2>x
What is proportional reasoning and how does it help you solve percent equations?
Answer:
We can't set up a proportion to solve for x in a percent equation. For example, 34/100=5/x
Step-by-step explanation:
How to simplify 1/3a+2/5a
Answer:
The simplified answer is 11a/15
Step-by-step explanation:
what are the missing angles?
A group of students organized a car wash to raise money for a local charity. The students charged $5.00 for each car they washed. In 3 hours, they washed 12 cars. At that rate, how much money could they earn from washing cars for eight hours?A grocery store sells a bag of 5 lemons for $2.00. What is the unit cost of each lemon in the bag?
Answer:
$160 0.4/lemon
Step-by-step explanation:
5 per car wash
12 cars in 3 hours
4 cars per hour times 8= 32 cars in 8 hours
32 times 5= 160
5 lemons for 2.00
Unit cost= 0.4 per lemon
What value(s) of b will cause 3x2 + bx + 3 = 0 to have one real solution? Select all that apply.
b = –6
B.b = –9
C.b = 6
D.b = 9
Answer: -6 and 6
Step-by-step explanation:
Possible factors that could produce 3x² + 6x +3 are (x + 1)(3x + 3)
the solution for values of x: x+1=0, x= -1 3x+3=0, 3x= -3 . x= -1 . Same.
Possible factors that could produce 3x² - 6x +3 are (x - 1)(3x - 3)
the solution for values of x: x-1=0, x= 1 3x-3=0, 3x= 3 . x= 1 . Same.
From the attached graph of the possible equations, you can see that 9 and -9 won't produce ONE real solution. They each have "zeros" at two points on the x-axis. That is two solutions that would make x = 0.
The equations with -6 and +6 each touch the x-axis at only one point each.
What should the following equation be multiplied by in order to eliminate the fractions? x/3+x/6=11/9
Answer:
Multiply by 18
Step-by-step explanation:
Given
[tex]\frac{x}{3} + \frac{x}{6} = \frac{11}{9}[/tex]
Required
Eliminate the fraction
To eliminate the fraction, we first determine the LCM of the denominators (3, 6 and 9)
This is show below:
List out the multiplies of 3, 6 and 9
[tex]3 = 3,6,9,12,15,18,21,24,27,30...[/tex]
[tex]6 = 6,12,18,24,30...[/tex]
[tex]9 = 9,18,27...[/tex]
The least common multiple is 18.
Hence, when both sides of the equation is multiplied by 18, the fraction is eliminated;
See proof
[tex]18 * (\frac{x}{3} + \frac{x}{6}) = \frac{11}{9} * 18[/tex]
[tex]\frac{18x}{3} + \frac{18x}{6} = \frac{11*18}{9}[/tex]
[tex]6x + 3x = 11 * 2[/tex]
[tex]6x + 3x = 22[/tex]
The fraction is eliminated
Give an example of a sequence whose first term is positive, whose second and third terms are negative, and the rest are positive.
If you are asking for just an arbitraty sequence, here it goes:
[tex]a_n=\{3,-5,-8,1,1,1,1,\dots\}[/tex]