A park has the shape of a trapezoid.
The shortest side of the park and its height have the same dimension.
Write numbers in the boxes to show the missing dimensions. What is the area of the park?
Hint: There are 3 parts in this question
Part 1 you need to find what is A
Part 2 you need to find what is B
Part 3 You need to calculate the area of all the figure ( find the area of the rectangle and two triangles then sum them all up)
Do not forget the unit!!
Answers
Answer:
[tex]the\: answer \: is \: {108 \: mi.}^{2} [/tex]
Step-by-step explanation:
Given hints:
a.) A park has the shape of a trapezoid.
b.) The shortest side of the park and its height have the same dimension.
In the given figure, the shortest side of the park is A. Since it is mentioned that the height and its shortest side have the same dimension, we can therefore say that the measure of A is 9 mi.
The longest side appears to be 6 miles longer that the shortest side:
[tex]b = a + 3 \: mi + 3 \: mi = a + 6 \: mi[/tex]
Therefore, B = A + 6 mi. = 9 mi. + 6 mi. = 15 mi.
Let's now determine the area of the park:
[tex]area = \frac{a + b}{2} h[/tex]
Where,
A = 9 mi.
B = 15 mi
H = 9 mi.
[tex]area = \frac{a + b}{2} h \\ \\ = \frac{9 \: mi. +15 \: mi. }{2} (9 \: mi.) \\ \\ = \frac{24 \: mi.}{2}(9 \: mi.) \\ \\ = (12 \: mi.)(9 \: mi. \\ \\ area = {108 \: mi.}^{2} [/tex]
The area of the park is 108 mi^2.
Related Questions
Find the x-intercept and y- intercept from the following linear equation: -7x+4y=56
Answers
Answer:
-52/7
Step-by-step explanation:
Dont care just do it or check it
lily beoug y a bag of gimmy bears and atw 1/3 if them the next day she
Answers
Answer:
whatttttttttttttttttt???????????????????
Step-by-step explanation:
The perimeter of an equilateral triangle is 12\/3 cm. Find the radius, apothem and area of the equilateral triangle.
Answers
Answer:
Radius - 4
Apothem - 2
Area - [tex]12\sqrt{3}[/tex] or 20.8
Step-by-step explanation:
Try to draw out my explanation so you know what this looks like.
~~~~
This is an equilateral triangle, so all sides are the same length. The perimeter can be divided by 3 to get each side length...
[tex]12\sqrt{3} \div3 = 4\sqrt{3}[/tex]
Now that we know the side lengths, we can get this started!
~~~~
Now, an equilateral triangle has angles that all equal 60 degrees. We can bisect this into TWO special case triangles of measures 90-60-30.
4 times the square root of 3 will be the hypotenuse, and the smallest leg is always half of that. The larger leg is represented as the small leg times the square root of 3.
[tex]Small=2\sqrt{3} \\Hypotenuse = 4\sqrt{3} \\Long =6[/tex]
By the way, the formula for the area can be either of the two:
[tex]A= \frac{1}{2} bh\\or\\A = \frac{1}{2} NAS[/tex]
we can easily find the area using the first formula.
[tex]A= \frac{1}{2} (4\sqrt{3} )(6)\\A=12\sqrt{3}[/tex]
The radius is the distance from the center to the corners & the apothem is the distance from the center to a side...
So we can divide the big triangle into a mini triangle at the bottom left/right
The height (small leg) of that triangle would be the apothem
The hypotenuse of that triangle would be the radius.
I did the math really quick because this is getting long. Anyhow, the small leg is 2 so is the apothem, and the hypotenus is 4, so is the radius
Happy April Fool's btw, lol.
A population of rabbits in a lab, p(x), can be modeled by the function p(x)=20(1.014)^x, where x represents the number of days since the population was first counted.
Answers
Answer:
(a) 20 represents the initial population and
1.014 represents 1 + % growth of rabbits each day
(b) Average Rate of change = 0.8
Step-by-step explanation:
P.S - The exact question is -
Given - A population of rabbits in a lab, p(x), can be modeled by
the function p(x)=20(1.014)^x, where x represents the number
of days since the population was first counted.
To find - (a) Explain what 20 and 1.014 represent in the context of
the problem.
(b) Determine, to the nearest tenth, the average rate of
change from day 50 to day 100.
Proof -
(a)
Given that the function p(x) is represented as
[tex]p(x) = 20(1.014)^{x}[/tex]
Here,
20 represents the initial population and
1.014 represents 1 + % growth of rabbits each day
(b)
Given,
[tex]p(x) = 20(1.014)^{x}[/tex]
When x = 50
[tex]p(50) = 20(1.014)^{50}[/tex] = 40.08000 ≈ 40.1
When x = 100
[tex]p(100) = 20(1.014)^{100}[/tex] = 80.32033 ≈ 80.3
Now,
Average Rate of change = [tex]\frac{p(100) - p(50)}{100 - 50}[/tex]
= [tex]\frac{80.3 - 40.1}{50}[/tex]
= [tex]\frac{40.2}{50}[/tex]
= 0.804 ≈ 0.8
⇒Average Rate of change = 0.8
What are the answers to these?
Answers
Answer:
XW in the first blank
Z in the second blank
18. Write a similarity statement relating the three triangles in the diagram.
Answers
Convert 639 into quinary system
Answers
Step-by-step explanation:
To convert decimal number 639 to quinary, follow these steps:
Divide 639 by 5 keeping notice of the quotient and the remainder.Continue dividing the quotient by 5 until you get a quotient of zero.Then just write out the remainders in the reverse order to get quinary equivalent of decimal number 639.Using the above steps, here is the work involved in the solution for converting 639 to quinary number:639 / 5 = 127 with remainder 4127 / 5 = 25 with remainder 225 / 5 = 5 with remainder 05 / 5 = 1 with remainder 01 / 5 = 0 with remainder 1Then just write down the remainders in the reverse order to get the answer, The decimal number 639 converted to quinary is therefore equal to :
10024
PLSS HELP! WILL GIVE BRAINLIEST!!
Answers
Answer:
the answer is c!
Step-by-step explanation:
:)
Help please !!!
Here are two equations. One defines function m and the other defines function p. m(x) = x(x + 6) p(n) = (x + 3) ^ n - 9
A. Are the equations equivalent? _________
B. What is the vertex of the graph of m? ____________
C. What are the x-intercepts of p? ____ and ____
D .function m is written In _____
F. Function p is written in _____
Answers
5. A robot that picks up tennis balls is on a straight path from (8,6) toward a ball at (-10,-5). The robot picks up a ball at (-10,-5) and then turns 90° right. What are the coordinates of appoint that the robot can move toward to pick up the last ball?
Answers
Answer:
Step-by-step explanation:
so this question is about perpendicular lines. keep in mind that a perpendicular line has a reciprocal slope of opposite sign, from the line it's perpendicular to . :) okay so what is that line the robot is on, let's first
find the slope , m
m = (y2 - y1) / ( x2 - x1)
P1 = (8,6) in the form ( x1,y1)
P2= (-10,-5) in the form (x2,y2)
then
m = (-5-6) / (-10-8)
m = -11 / -18
m = 11/ 18
and then lets use the point-slope formula with the slope we just found and one of the given points, let's pick P1
y-6 = 11/18(x-8)
y = 11/18x - 88/18 + 6
y = 11/18x -88/18 + 108/18
y = 11/18x + 20/18
now let's take the reciprocal of the slope and change the sign, then we have
y = - 18/11x +20/18 ( coordinates robot can move on )
on the graph I'm attaching the green line is the one where the robot first moves, then the purple one.. is the one it turns 90 ° on to .
please help with my geometry
Answers
14 = opposite
Use SOHCAHTOA
Give O and H, you can use sin
Sin^-1 = 14/25 = 34.0557
Round to hundreds
Solution: 34.06
the letters of the alphabet are written on pieces of paper and put into a hat. they are then pulled out and not replaced.
a) what is the chance of pulling out an A and then a Z in two consecutive turns?
b) starting again, what is the chance of pulling out two vowels in two consecutive turns?
Answers
Answer:
A: 3.84% chance.
B: 23.08% chance
The chance of pulling out an A and then a Z and two vowels in two consecutive turns will be 1 / 650 and 2 / 65, respectively.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The letters of the alphabet are written on pieces of paper and put into a hat. they are then pulled out and not replaced.
Then the total number of letters of the alphabet will be 26.
Then the chance of pulling out an A and then a Z in two consecutive turns will be given as,
P = (1 / 26) x (1 / 25)
P = 1/650
The chance of pulling out two vowels in two consecutive turns will be given as,
P = (5 / 26) x (4 / 25)
P = 20 / 650
P = 2 / 65
The chance of pulling out an A and then a Z and two vowels in two consecutive turns will be 1 / 650 and 2 / 65, respectively.
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ2
PLEASE HELP!!!!! AND HURRY TIMED!
Which method correctly solves the equation using the distributive property?
Negative 0.2 (x minus 4) = negative 1.7
Negative 0.2 (x minus 4) = negative 1.7.
Negative 0.2 x minus 4 = negative 1.7.
Negative 0.2 x = 2.3. x = negative 11.5.
Negative 0.2 (x minus 4) = negative 1.7.
x minus 4 = 0.34. x = 4.34.
Negative 0.2 (x minus 4) = negative 1.7.
Negative 0.2 x + 0.8 = negative 1.7.
Negative 0.2 x = negative 2.5. x = 12.5.
Negative 0.2 (x minus 4) = negative 1.7.
Negative 0.2 x minus 0.8 = negative 1.7.
Negative 0.2 x = negative 0.9. x = 4.5.
Answers
Answer:
Negative 0.2 (x minus 4) = negative 1.7.
Negative 0.2 x + 0.8 = negative 1.7.
Negative 0.2 x = negative 2.5. x = 12.5.
Step-by-step explanation:
i believe thats the correct anwser
Answer:
its c
Step-by-step explanation:
on egde
Please Help! Solve the equation for x.
1/3x-8= -12
A. x= -12
B. x= -6
C. x= 4
D x= 6
Answers
Answer:
A
Step-by-step explanation:
Given
[tex]\frac{1}{3}[/tex] x - 8 = - 12 ( multiply through by 3 to clear the fraction )
x - 24 = - 36 ( add 24 to both sides )
x = - 12 → A
how many tenths are equal to 3/5
Answers
Answer:
8
Step-by-step explanation:
3/5 ×2=8/10
..............
Please help me :C PLEASE I BEG
Answers
Answer:
$0.83
Step-by-step explanation:
Its teh only one that makes sense since the 2nd is under, 3rd is over, and 4th is for lazy people
Answer:
a
Step-by-step explanation:
giving brainliest to whoever explains best. don't answer if you don't speak english well. don't answer if you're 9 years old. don't answer if you don't understand the subject. don't answer anything other than QUESTION C. now stop wasting my points i beg
Answers
Answer:
Gillmans
Step-by-step explanation:
I feel like gillmans class did better cuz their class didnt have anyone get a score less than 60 but mr athens class had people who got below 50. Although athens class has people over 95 the most were 60-90 while gillmans was 70-90
Julio bought a fish tank shaped like a rectangular prism. The inside of the tank measures 24 inches in length, 10 inches in width, and 12 inches in height. The tank is filled with water to a height of 8 inches. How many more cubic inches of water are needed to fill the tank to the top? Use paper to show your work.
Answers
Answer:
[tex]Volume = 960in^3[/tex]
Step-by-step explanation:
Given
Empty Tank
[tex]Length = 24in; Width=10in; Height = 12in[/tex]
When filled with water, the height is:
[tex]Height = 8in[/tex]
Required
Determine how many more cubic inches needed
First, we calculate the difference between the height of the tank and the height of the water.
[tex]H = 12in - 8in[/tex]
[tex]H = 4in[/tex]
The volume of water to full the tank is then calculated as:
[tex]Volume = Length * Width * H[/tex]
[tex]Volume = 24in * 10in * 4in[/tex]
[tex]Volume = 960in^3[/tex]
Helpppppppp me please
Answers
9514 1404 393
Answer:
J = {4, -8, 7, 3}
Step-by-step explanation:
Sets F, G, H contain fractions, so are not limited to integers.
Set J simplifies to integers, so is the one you want.
7. These number share the same percentage
increase. Work out the missing value.
£20 and £25
£24 and £___
Answers
You find the difference and put this over the original price ie. 25-20=5. 5/20= 0.25 so the increase is 25%
24x 0.25= 6
6+24=£30
(Or 24x1.25=30)
18 is 14 percent of what?
Answers
Answer:
18 is 14% of 128.5714
Step-by-step explanation:
it's 77.78
Step-by-step explanation:
14: 18*100 =
(14*100): 18 =
1400: 18 = 77.78
Now we have: 14 is what percent of 18 = 77.78
Question: 14 is what percent of 18?
Percentage solution with steps:
Step 1: We make the assumption that 18 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$x.
Step 3: From step 1, it follows that $100\%=18$100%=18.
Step 4: In the same vein, $x\%=14$x%=14.
Step 5: This gives us a pair of simple equations:
$100\%=18(1)$100%=18(1).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
$\frac{100\%}{x\%}=\frac{18}{14}$100%x%=1814
Step 7: Taking the inverse (or reciprocal) of both sides yields
$\frac{x\%}{100\%}=\frac{14}{18}$x%100%=1418
$\Rightarrow x=77.78\%$⇒x=77.78%
Therefore, $14$14 is $77.78\%$77.78% of $18$18.
A loan of$8000 was repaid in 24 equal monthly installments of $400 . The rate of interest on the loan was
Answers
Answer:
1%
Step-by-step explanation:
24(400) = 9600 = total amt paid
9600 - 8000 = 1600 = amt of interest paid
I = PRT T = 2 yr
1600 = 8000(2)R
1600 = 16000R
1600/16000 = 1/10 = .01 = 1%
What are the coordinates of the focus of the parabola? (x+1)2=−8(y−2) (−1, 2) (1, −2) (−1, 0) (−1, 1)
Answers
Answer:
[tex](x,y) = (-1,0)[/tex]
Step-by-step explanation:
Given
[tex](x+1)^2 = -8(y-2)[/tex]
Required
The coordinates of the focus
First, write the expression in form of: [tex]y=a(x-h)^2+k[/tex]
[tex](x+1)^2 = -8(y-2)[/tex]
[tex](x+1)^2 = -8y + 16[/tex]
[tex]-8y + 16 = (x+1)^2[/tex]
Subtract 16 from both sides
[tex]-8y = (x+1)^2 - 16[/tex]
Divide through by -8
[tex]y = -\frac{1}{8}(x+1)^2 - \frac{16}{-8}[/tex]
[tex]y = -\frac{1}{8}(x+1)^2 +2[/tex]
In this case:
[tex]a = -\frac{1}{8}[/tex]
[tex]-h = 1[/tex] [tex]h = -1[/tex]
[tex]k = 2[/tex]
The focus of the parabola is:
[tex](x,y) = (h,k + \frac{1}{4a})[/tex]
This gives:
[tex](x,y) = (-1,2 + \frac{1}{4*-\frac{1}{8}})[/tex]
[tex](x,y) = (-1,2 + \frac{1}{-\frac{1}{2}})[/tex]
[tex](x,y) = (-1,2 -2)[/tex]
[tex](x,y) = (-1,0)[/tex]
HELP ASAP!!!!!!! PLEASEEEEE
Answers
Answer:
B
Step-by-step explanation:
This asks for data from multiple people, and it not just a yes or no question
Num supermercado vendem-se embalagens de bombons de 500 g. No gráfico de barras abaixo está o resultado da análise do número de bombons existentes em 20 embalagens.
A amplitude deste conjunto de dados é
8
e a amplitude interquartis é
Answers
Answer
Step-by-step explanation:
what is 6.2 ÷ 3.1 I NEED HELP PLEASE
Answers
Answer:
it's 2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
1,645/0.047
Please show your process
Answers
Answer: 35000
Step-by-step explanation:
Answer: 35
Step-by-step explanation:
329/200 / 0.047
329/200 / 47/1000
35
A vet borrows $12,000 for 4 years. The total interest paid was $960. What was the interest rate on the loan?
Answers
Answer:
2% per year.
Step-by-step explanation:
Solving our equation
r = 960 / ( 12000 × 4 ) = 0.02
r = 0.02
converting r decimal to a percentage
R = 0.02 * 100 = 2%/year
The interest rate required to
accumulate simple interest of $ 960.00
from a principal of $ 12,000.00
over 4 years is 2% per year.
please help me asap.
Answers
Answer:
21
Step-by-step explanation:
Yes I am here to help
pls hurry will give brainlyest or whatever !!!
Solve this equation:
1 - (x-4) = 2x + 2(x - 5)
a. 5
b. 3
c. 1
d. 4
Answers
Answer:
The answer is 3
Step-by-step explanation:
The answer is 3 because x= 15/5 = 3