PLEASE HELP?!
Both trapezoids are similar. The area of the larger trapezoid is 61 ft2. Which is the best approximation for the area of the smaller trapezoid?
39 ft2
34 ft2
49 ft2
44 ft2
Answers
The best approximation for the area of the smaller trapezoid is 39 [tex]ft^2[/tex].
Since the trapezoids are similar, the ratio of their corresponding side lengths is constant. We know the base of the larger trapezoid is 30 ft and the smaller one is 24 ft. Therefore, the ratio of their bases is:
ratio of bases = [tex]\frac{30 ft}{24 ft}[/tex] = [tex]\frac{5}{4}[/tex]
The area of a trapezoid is given by:
Area = [tex]\frac{1}{2}[/tex] * base * height
For similar shapes, the ratio of their areas is proportional to the square of the ratio of their corresponding side lengths. In this case, the ratio of areas will be:
Ratio of areas = [tex](Ratio \ {of \ { bases)^2[/tex] = [tex]({\frac{5}{4} })^2[/tex] = [tex]\frac{25}{16}[/tex]
We know the area of the larger trapezoid is 61 [tex]ft^2[/tex]. Applying the ratio of areas:
Area of smaller trapezoid = (61 [tex]ft^2[/tex]) * [tex]\frac{16}{25}[/tex]
Area of smaller trapezoid ≈ 38.91 [tex]ft^2[/tex] ≈ 39[tex]ft^2[/tex]
Related Questions
Determine the solution of the system. Show your work.
Y = 5x – 9
Y = 2x + 6
Answers
5x-9=2x+6
3x-9=6
3x=15
x=5
Then plug in x into any of the equations
y=2(5)+6
y=10+6
y=16
Final answer: (5,16)
The solution is (x, y) = (5, 16). My "work" is to make use of a graphing calculator.
_____
You can subtract the second equation from the first. This gives
... 0 = 3x -15
Then, divide by 3 and add 5.
... 0 = x - 5
... 5 = x
Substitute this value into either equation to find y.
... y = 2x +6
... y = 2·5 +6
... y = 16
The strategy to subtract the second equation from the first is based on the observation that both equations give expressions for y, and the x-coefficient in the first equation is the larger of the two x-coefficients. Thus, the subtraction we chose will eliminate y and give an x-term with a positive coefficient.
Five times a number is equal to the number increased by 12
Answers
5 times of it is 5x
it's equal to the number increased by 12 or 12+x
remember, you can do anything to an equation as long as you do it to both sides
5x=12+x
minus x from both sides
4x=12
divie both sides by 4
x=3
the number is 3
The required expression is [tex]5n = n+ 12[/tex] and the unknown number is [tex]3[/tex]
Let the unknown number be "n"
Five times the number is expressed as 5nThe number increased by 12 is expressed as n + 12Equating both expressions will give:
[tex]5n = n + 12[/tex]
Solve for n:
[tex]5n - n = 12\\4n = 12\\n = 12/4\\n = 3[/tex]
Hence the required expression is [tex]5n = n+ 12[/tex] and the unknown number is [tex]3[/tex]
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Can u solve 6x-21=5x+17+x
Answers
6x - 21 = 6x + 17
6x - 6x = 21 + 17
0 = 38, untrue
cannot be solved
hope this helps
Look at the diagram. If RS= 8y + 4, ST = 4y + 8, and RT = 36, find the value of y.
Answers
RS + ST = RT
8y + 4 + 4y + 8 = 36
12y + 12 = 36
12y = 24
y = 2
answer
y = 2 (first choice)
Answer:
(A) y=2
Step-by-step explanation:
It is given that [tex]RS=8y+4[/tex], [tex]ST=4y+8[/tex]and [tex]RT = 36,[/tex] then
According to the figure given, we have
[tex]RT=RS+ST[/tex]
[tex]36=8y+4+4y+8[/tex]
[tex]36=12y+12[/tex]
[tex]24=12y[/tex]
[tex]y=\frac{24}{12}[/tex]
[tex]y=2[/tex]
Thus, the value of y will be 2.
Hence, option A is correct.
What is the area of a circle with radius 14 units, to the nearest hundredth?
Answers
14×2=28
28×pi=88
40% of a 12,000 acre forest is being logged how many acres will be logged
Answers
12000 - 4800 = 7200
7200 acres are being logged
hope this helps
0.40 (12,000) = 4,800
answer
4,800 acre is 40% of a 12,000 acre
1. Find the perimeter and area of a rectangle with a length of 3.2 m and a width of 1.5 m.
A) p=4.7 m; A=2.25 m^2
B) p=4.7 m; A=4.8^2
C) p=9.4 m; A=2.4 m^2
D) p=9.4 m; A= 4.8^2
2. Find the area of a triangle with a base of 27 feet and a height of 14 feet.
A) 41 ft^2
B) 82 ft^2
C) 189 ft^2
D) 378 ft^2
Answers
Evaluate these questions
3a+2a=
c+d there is a line under this one
ad
Answers
1)
For this question we can combine the terms together as they are like:
[tex]3a+2a[/tex]
Combine like terms.
[tex]=5a[/tex]
Hope this helps.
-Benjamin
Gretchen and Ezia received equal scores on a test made up of multiple choice questions and an essay. Gretchen got 18 multiple choice questions correct and received 19 points for her essay. Ezia got 15 multiple choice questions correct and received 31 points for her essay.
How many points was each multiple choice question worth?
Enter your answer in the box.
Answers
NOT Guaranteed this is the Answer. Best of luck to you.
If a measurement follows a normal (bell-shaped) frequency curve, then percent of the population will have a z-score below .36.
Answers
From the normal distribution tables, when z < 0.36, obtain
P(z < 0.36) = 0.6406 ≈ 64 percent
Answer: 64% (nearest integer)
Staci has seven more cats then Taylor. Write an expression that illustrates how many cats Staci has. Use x to represent the number of cats Taylor has./4899345/032a37eb?utm_source=registration
Answers
Staci has seven more than this so:
x + 7 = number of cats Staci has
luke scored 21 goals in 7 soccer games. if he scores goals at the same rate, how many goals will he score in 23 games
Answers
Sorry if it didnt help.
Answer:
69
Step-by-step explanation:
My bad if it's wrong
A segment with endpoint M Left parenthesis 5 comma 9 right parenthesis and N Left parenthesis 4 comma 3 right parenthesis is rotated 270°. What are the coordinates of M prime and N prime?
The correct answer is : M prime (9,-5) and N prime (3,-4)
Answers
If we draw a line that connects the center of rotation to one of the points, say point N, and take this line as the 0° position, then we need three 'turn' of 90° to get to 270°.
Coordinate of N' (-3, 4)
Coordinate of M' (-9, 5)
Algebra problem below!
The sum of two consecutive even integers is -50
What are the numbers?
Answers
The formula is:
x + (x + 2) = -50
Solving:
2x + 2 = -50
2x = -52
x = -26
Finding the second number:
-26 + 2 = -24
-24,-26
Hope this helps!
Write a story that matches the expression
42x - 5
Answers
Answer: Hello there!
The equation is: 42x - 5
That can be phrased as "the difference between 42 times a number x and 5"
And we want to write a story that matches this.
an example can be:
Suppose that Jon craft musical instruments and he sells them in the beach, then you could write:
"The revenue in a day for Jon is equal to $42 for each instrument that he sells, less a 5 dollar fee that he needs to pay every day"
where the number of instruments would be x.
Parallelogram JKLM is shown on the coordinate plane below:
If parallelogram JKLM is rotated 270° clockwise around the origin, what are the coordinates of the endpoints of the side congruent to side JM in the image parallelogram?
Answers
Answer-
The coordinates of the endpoints of the side congruent to side JM will be,
(-2, -6) and (1, -5).
Solution-
When rotating a point 270° clockwise or 90° counter-clockwise around the origin, we apply the rule (x, y) → (-y, x).
The co-ordinates of the original parallelogram are,
J = (-6, 2)
M = (-5, -1)
L = (-3, 3)
K = (-4, 6)
After the rotation, the new co-ordinates will be,
J = (-2, -6)
M = (1, -5)
L = (-3, -3)
K = (-6, 4)
∴ The coordinates of the endpoints of the side congruent to side JM will be,
(-2, -6) and (1, -5).
One month, Ruby worked 8 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together they worked 112 hours. Find the number of hours each person worked.
Answers
S=4R
R+I+S=112
R+R-8+4R=112
6R=120
R=20
So therefore, Ruby worked 20 hours, Svetlana worked 80 hours, and Isaac worked 12 hours.
Find a point on the y-axis that is equidistant from the points (4, −4) and (1, 1).
Answers
a point on the y-axis is : P( 0, y)
PA = PB or PA² = PB².... A(4 , -4) B(1,1)
(4-0)²+(-4-y)² = (1-0)² + (1-y)²
16 +y² +8y +16 = 1 + 1 -2y +y²
10y = -30
y = -3
What is the answer for this problem
Answers
9 + 3 x 13 =
9 + 39 = 48
3x13=39
39+9=48
Suppose that (y) varies with (x). Write an equation for the inverse variation.
y=4 when x=7
A: y= x/28
B: y=3x
C: x= y/3
D: y= 28/x
Answers
y = k/x, where k is the constant
if x = 7 and y = 4
4=k/7
k = 4*7 = 28
y = 28/x
answer is D
In November 2010, ING Direct was offering 2.4% interest on its Orange Savings Account, with interest reinvested quarterly.† Find the associated exponential model for the value of a $3,000 deposit after t years
Answers
i = (1 + r/m)^m - 1
where m is the number of quarters in a year (m = 4)
i = (1 + 0.024/4)⁴ -1
i = 0.024217
The model would then be:
Future Worth = $3,000(1 + 0.024217)^t, where t is the number of years
Mikel creates the table below to help her determine 40% of 70
Answers
To Find: 40 % of 70
Solution:
x % of y means = [tex]\frac{x \times y}{100}[/tex]
40 % of 70= [tex]\frac{40 \times 70}{100}=\frac{2800}{100}=28[/tex]
This is the way Mikel can determine 40 % of 70.
Points a, b, c, and d are collinear. in how many ways can the line be named using only these points
Answers
Which would hold more water a teaspoon or a milliliter?
Answers
From reliable source, the number of millimeters in a teaspoon is 5. Five millimeters is obviously more than 1 millimeter. Hence, the answer is that a teaspoon will be able to hold more volume of water.
Jeff wants to make an a in his math course this semester. To do so, he must have an average of 90 or above. If his test scores this semester or 88, 92 and 96 what is the score that he would need to make on his final test to attain an average on exactly 90
Answers
(276 + x) / 4 = 90
276 + x = 90 * 4
276 + x = 360
x = 360 - 276
x = 84 <=== he would need an 84
Point M is the midpoint of segment JK. Find JK when JM=6x-7 and MK=2x+3.
Answers
so
6x-7=2x+3
minus 2x both sides
4x-7=3
add 7 both sides
4x=10
divide both sides by 4
[tex]x=\frac{10}{4}[/tex]
[tex]x=\frac{5}{2}[/tex]
sub back
JM=6x-7
[tex]JM=6(\frac{5}{2})-7[/tex]
[tex]JM=\frac{30}{2}-7[/tex]
[tex]JM=15-7[/tex]
JM=8
JM=MK=8
JM+MK=8+8=16=JK
[tex]x=\frac{5}{2}[/tex] and JM=8=MK and JK=16
The value of JK will be 16.
It is given that M is the midpoint of segment JK.
We have to find out the value of JK.
What will be the value of x , if 4x + 12 = 8x + 4 ?
The value of x will be 2.
As M is the midpoint of JK.
JK = MK + JM
So,
MK = JM
2x + 3 = 6x - 7
4x = 10
x =2.5
So ,
MK = 2x + 3 = 8
JM = 6x - 7 = 8
Hence ,
JK = MK + JM = 8 + 8
JK = 16
Thus , value of JK will be 16.
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Find the angle measure of the hands of a clock at the given time. 5:00
Answers
[tex] \frac{5}{12}*360=5*30=150^o [/tex]
Answer is 150°
The angle measured by the hands of a clock at the given time at 5:00 will be 150°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
We know that the hour hand will be on 5 and the minute hand will be on 12 at 5:00 o'clock.
Then the angle measured by the hands of a clock at the given time at 5:00 will be
⇒ (360° / 12) x 5
⇒ 30° x 5
⇒ 150°
The angle measured by the hands of a clock at the given time at 5:00 will be 150°.
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The distributive property is used to help simplify math experssions. True False
Answers
hope it helped
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
TRUE
This is because when you distribute 1 thing between 2 (or more) things, it (in a way) simplifies the problem...
For Example:
solve for x
f(x) = 5*(x - 4)
The only way to solve a question like this would be to distribute the 5 to the x and to the 4...
So...
The answer is: TRUE
Solve x(−2) 2 =4(−2)
Answers
x(−2) 2 =4(−2) = -2
Explanation:To solve this equation, we first need to understand the order of operations in mathematical equations. The acronym PEMDAS is often used to remember the order: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
In this equation, we have parentheses and exponents. According to PEMDAS, we need to solve the parentheses first before moving on to the exponent. So, let's start by simplifying the parentheses on the left side of the equation.
x(-2)^2 = 4(-2)
= x(4) = -8
= 4x = -8
= x = -2
In the first step, we distributed the exponent of 2 to the -2 within the parentheses, resulting in (-2)^2 = (-2)(-2) = 4. This simplifies the left side of the equation to x(4) = 4x.
In the second step, we substituted the value of -2 on the left side of the equation, resulting in 4(-2) = 4x. This simplifies to -8 = 4x.
To isolate x, we divide both sides by 4, resulting in x = -2. This gives us our final answer.
In conclusion, when solving equations with multiple operations, it is important to remember the order of operations and follow it step by step. In this equation, we simplified the parentheses first, then solved for x by isolating it on one side of the equation. By following these steps, we were able to find the value of x, which is -2.
what do you add 15/4 to make 4