Find the perimeter and the area of the figure. A right-angled trapezoid has a shorter base of 7 centimeters, longer base of 9.5 centimeters, and height of 6 centimeters. The trapezoid is divided into a rectangle and a right triangle. The height of the triangle is aligned with the width of the rectangle and it has a hypotenuse of 6.5 centimeters.
Answers
The given dimensions of 9.5, 6, 7, and 6.5 cm gives the following
perimeter and area of the trapezium.
Perimeter: 29 cmArea: 49.5 cm²How can the area and perimeter of the trapezium be found?The perimeter of a trapezoid is given as follows;
Perimeter = The sum of the lengths of the sides
Which gives;
Perimeter = 6 + 7 + 6.5 + 9.5 = 29
The perimeter of the trapezoid = 29 cm
Perimeter: 29 cmThe area of the trapezoid is given as follows;
[tex]Area = \mathbf{ \dfrac{Sum \ of \ the \ parallel \ sides }{2} \times Height}[/tex]
Which gives;
[tex]Area = \dfrac{7 + 9.5 }{2} \times 6 = 49.5[/tex]
The area of the trapezoid = 49.5 cm²
Area: 49.5 cm²Learn more about the area and perimeter of geometric shapes here:
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Related Questions
The tables in the pottery class sit 8 students each. If there are 35 students in the class, how many tables are needed?
Group of answer choices
5
4
280
4.375
Answers
Answer:
35 students
And 8 tables
So you jsut divide
35/8 = 4.375
So you have 4.375 tables but you can’t have .375 of a table so
You really need 5 tables to seat all the students.
If the width of a rectangle plot is “x” and the length of the plot is 100-x/2, what is the maximum area of the plot?
Answers
Answer:Let x = length of the plot (in meters).
Then the two lengths use up 2x meters of the fencing,
. . . leaving 100 - 2x meters for the two widths.
This means each width is (100 - 2x)/2 = 50 - x meters.
The area of a rectangle is: Length x Width
. . . so we have: . A .= .x(50 - x)
We have a <u>parabola</u>: . A .= .- x<sup>2</sup> + 50x</sup>
We know that this parabola opens down (don't we?)
. . . so its vertex must be the highest point.
We're expected to know that the vertex is at: . x = -b/2a
For this problem, a = -1, b = 50, so we have: . x = -50/(2(-1) = 25
We have maximum A when x = 25.
This leaves 50 - x = 25 for the width.
Therefore, for maximum area, make the plot a 25-by-25 square.
Step-by-step explanation:
Answer:
1250 units squared
Step-by-step explanation:
if you're allowed to use a calculator;
On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2). How do the areas of the parallelograms compare? The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2. The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2. The area of parallelogram 1 is equal to the area of parallelogram 2. The area of parallelogram 1 is 2 square units less than the area of parallelogram 2.
Answers
Answer:
A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
Step-by-step explanation:
I just took the test
Diego paid $47 for 3 tickets to a concert. Andre paid $141 for 9 tickets to a concert.
Did they pay at the same rate? Explain your reasoning.
Answers
Answer:
Yes, they paid the same price per each ticket.
Step-by-step explanation:
You will have to find each of their individual prices per ticket. For Diego it would be 47/3 or $15.67 per ticket. For Andre it would be 141/9 or $15.67 per ticket. This means that they paid the same price per ticket so they are paying at the same rate for their tickets.
In rectangle ABCD, the diagonals intersect each other at point 0 and mABD=30°.
Find BC if AC = 16 in.
Answers
Answer:
Step-by-step explanation:
The length of the diagonal BC is equal to 18.47in
Data;
m∠ABD = 30°
BC = ?
AC = 16 in
Length BC
Since the length of AC = 16in and angle m∠ABD = 30°, let us consider that the edges form a right angle triangle.
We can use trigonometric ratio to find the length BC since it is the length of the diagonal.
Since we have the value of opposite and angle, we can find the hypothenuse using sine angle.
The length of the diagonal BC is equal to 18.47in
The area of a bedroom door is 24 square feet. The perimeter is 22 feet. What are the dimensions of the door?
Answers
Answer:
8,3
Step-by-step explanation:
The Bedroom is in the Shape of Rectangle
Area of Rectangle = LW
Perimeter of Rectangle = 2(L+W)
Since the Area = 24
Then LW=24 --->1
Since the Perimeter = 22
Then 2(L+W)=22, Then L+W=11 --->2
Substitute by L=11-W from Equation 2 into Equation 1
(11-W)*W=24
[tex]11W-W^{2} =24[/tex]
[tex]W^{2} -11W+24=0[/tex]
(W-3)(W-8)=0
W=3 or W=8
Substitute in Equation 1 to Find L
at W=3 , L=24/3=8
at W=8 , L=24/8=3
so the Dimension of the Door is 8 and 3 feet
Is triangle EJH congruent to triangle EIH?
Yes or No?
Answers
Answer:
Yes
Step-by-step explanation:
I need to increase the numbers of customers I talk to daily by 20%. I talk to an average of 8 customers per hour during an 8 hour shift so now I’ll need to talk to ____ customers per day”
Answers
Answer:77
Step-by-step explanation:Talk to 8 customers per hour, work 8 hours, so:Talk to 8*8 = 64 customers.
Has to increase by 20%, so 64 is multiplied by 1 + 0.2 = 1.2. Then64*1.2 = 76.8Rounding up, 77 is the answer.
1)0.1x+0.2=0.3x+0.4
2)0.4x-0.7=0.2x+0.3
3)1/4x+1/2=1/5x+3/5
4)2/3x+4/5=1/6x+3/10
5)2/5x-5/6=3/10x+4/7
Answers
Answer:
as the following table?y 4 32 7 56 8 64. Choose 3 answers: 1.Step-by-step explanation:
In the figure, m ║ n and p is a transversal. Which of the following are alternate interior angles?
A. ∠1 and ∠7, ∠2 and ∠8
B. ∠2 and ∠8, ∠1 and ∠6
C. ∠3 and ∠5, ∠4 and ∠6
D. ∠3 and ∠7, ∠4 and ∠8
Answers
Please put the letter and the answer choice that goes with it so i know which answer is for that question. (example 1. 3+3=6 or 2.T)
Answers
Answers:
Choice DChoice DChoice C=======================================================
Explanations:
Problem 1
A = (4,4)
B = (-12,8)
Vector u starts at A and ends at B. The arrow points to B.
Subtract x coordinates: xB - xA = -12-4 = -16
Subtract y coordinates: yB - yA = 8-4 = 4
The vector is u = <-16, 4> which is in quadrant Q2.
Use the pythagorean theorem to find the length of the vector.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
||u|| = sqrt( (-16)^2 + 4^2 )
||u|| = 16.492
Now compute the angle
theta = arctan(b/a)
theta = arctan(4/(-16))
theta = -14.036
Add on 180 degrees so the angle lands in Q2.
-14.036+180 = 165.964
The angle is roughly theta = 165.964 degrees
------------------------------
Problem 2
A = start point = (4, 3)
B = end point = (-4, -1)
Subtract x coordinates: xB - xA = -4 - 4 = -8
Subtract y coordinates: yB - yA = -1-3 = -4
v = <a, b> = <-8, -4> which is in Q3
Use the pythagorean theorem to find the length of the vector.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
||v|| = sqrt( (-8)^2 + (-4)^2 )
||v|| = 8.944
And,
theta = arctan(b/a)
theta = arctan(-4/(-8))
theta = 26.565
We need to add on 180 so we move from Q1 to Q3
26.565+180 = 206.565
------------------------------
Problem 3
The notation <-3, 4> means "move 3 units left, 4 units up".
Only vector r fits the description as we move from the initial point (5,3) to the terminal point (2,7)
HELP!! I dont know which one is the correct answer. I'll give brainliest
Answers
Answer:
[tex]\sf g = 13.18 \ units[/tex]
explanation:
the "g" refers to the opposite side of angle G
First solve for angle E:
E + 60° + 45° = 180°
E = 180° - 105°
E = 75°
Then using sine rule:
[tex]\sf \dfrac{a}{sin(A)} = \dfrac{b}{sin(B)}[/tex]
[tex]\rightarrow \sf \dfrac{18}{sin(75)} = \dfrac{g}{sin(45)}[/tex]
[tex]\rightarrow \sf \dfrac{18*sin(45)}{sin(75)} = g[/tex]
[tex]\rightarrow \sf g = 13.18 \ units[/tex]
Please can someone help me
Answers
Answer:
[A] $1500
[B] 1/4
[C] 375
Step-by-step explanation:
Given:
Priced at $1499.80
Sale for 25% off
Solve:
[A] Rounded MacBook Price:
$1499.80 → $1500
Hence, Rounded MacBook Price is $1500
[B] Estimated Discount Price:
25% ⇒ 25/100
Simplify
1/4
Hence, Estimated Discount Price: 1/4
[C] Estimated Sale Price AFTER DISCOUNT ( Do NOT include tax):
$1500 x 1/4 = 375
Hence, Estimated Sale Price after discount( not include tax) is 375.
[RevyBreeze]
R=
[tex]{ [/tex]
(x,y):y=
[tex] {x}^{2} [/tex]
[tex]}[/tex]
Step-by-step explanation:
Amongal medhanite motwal
3. Margaret has a container on her dresser in the shape of a cube. It holds her earrings. Each
edge of the container is 6 cm long. What is the volume of the container?
clo
Answers
Step-by-step explanation:
Volume of cube = 6 × 6 × 6 cm³
= 216 cm³
The monthy net gains sales for a new sporting goods store were: $7195, $1484, $3224, $8807, $7185, $1730, $2573, $7071, $5360, S4331. Find the median
Answers
Answer:
$7,185 see below ↓
explanation:
With median, it is about the number that appears the most, and since the closest it gets is between $7,071 and $7,195, we have to pick the number that averages in-between which in this case is 7,185.
Below, this ↓ array proves the logic.
[tex]\left[\begin{array}{ccc}7195&7185&7071\end{array}\right][/tex]
A 20,000 m^3 rectangular cistern is to be made from reinforced concrete such that the interior length will be twice the height. If the cost is $40/m^2 for the base, $100/m^2 for the side walls, and $200/m^2 for the roof, find the interior dimensions (to one decimal place) that will keep the cost to a minimum. To protect the water table, the building code specifies that no excavation can be more than 22m deep. It also specifies that all cisterns must be at least 1m deep
Answers
The volume of 20,000 m³, and the cost of $40/m², $100/m², and
$200/m², give the dimensions that give minimum cost as follows;
The height of the cistern is approximately 20.4 metersThe length is approximately 40.8 metersThe width is approximately 24.029 metersHow can the dimensions of the cistern be found?The dimensions of the cistern = L × W × H
L = 2·H
L × W × H = 20000
2·H² × W = 20000
[tex]W = \mathbf{ \dfrac{20000}{2 \cdot H^2}}[/tex]
Therefore;
A = 40·L·W + 200·L·W + 100·2·L·H + 100·2·W·H
A = 400·H² + 680·W·H
Given that the leading coefficient is positive, the function has a minimum point.
[tex]A = \dfrac{400 \cdot H^4 + 6800000 \cdot H}{H^2}[/tex]
[tex]\dfrac{d}{dH} A = \mathbf{\dfrac{d}{dH} \left( \dfrac{400 \cdot H^4 + 6800000 \cdot H}{H^2} \right)} = 0[/tex]
Which gives;
800·H⁵ - 6800000·H² = 0
800·H⁵ = 6800000·H²
H³ = 6800000 ÷ 800 = 8500
H ≈ 20.4 m
Which gives;
L ≈ 2 × 20.4 m = 40.8 m
[tex]W = \dfrac{20000}{2 \times 20.4^2} \approx \mathbf{24.029}[/tex]
The interior dimensions of the cistern are;
The height, H ≈ 20.4 m.The length, L ≈ 40.8 mWidth of the cistern, W ≈ 24.029 mLearn more about minimum value of a function here:
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1) What is the area of square of length 5cm?
2) The length and breadth of a rectangular garden are 25m and 2500cm
respectively. Find its perimeter.
Answers
Answer:
20 is my answer and the question is somehow confusing
Jeff can ran 3 miles in 22 minutes. Assuming he can run at a constant rate, how long would it take Jeff to run 8 miles?
Answers
Write the ratio as a ratio of whole numbers in lowest terms $1.50 to $1.20
Answers
Hope this helps! If you found my answer helpful, please mark brainliest! Thanks!
Answer:
[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Ratio of $1.50 to $1.20
=[tex]\frac{1.50}{1.20}[/tex]=[tex]\frac{1.5}{1.2}[/tex]=[tex]\frac{15}{12}[/tex]=[tex]\frac{5}{4}[/tex]
Ratio will be [tex]\frac{5}{4}[/tex]
Solve for x. Please look at the picture and answer it. Thank you.
Answers
Hope it helps ~
Answer:
x=24
Step-by-step explanation:
i cant quite explain how i did it
Solve equation by using the quadratic formula. 15x² + 31x = -10
Answers
use the quadratic formula
a=15 b = 31 c = 10
Which tables could be used to verify that the functions they represent are inverses of each other? Select two
options.
X
-120
27
-110
2
y
-100 -95 -90
27 227627
х
- 120
-110
27
y
2
100
27
-95
227
-90
627
х -120
y 627
-110
227
-100
27
-95
2
-90
27
х
y
627 227 27
-120 -110-100
2
-95
27
-90
627
227
y -90-110
27
-100
2 27
- 110 -120
Mark this and return
Save and Exit
Next
Submit
Answers
Answer:
options. X -120 27 -110 2 y -100 -95 -90 27 227627 х - 120 -110 27 y 2 100 27 -95 227 -90 ... - did not match any news results.
Step-by-step explanation:
Based on the tables given and the functions represented, the two functions that are inverses of each other are tables 3 and 4. Therefore, the options 3 and 4 are correct answers.
What is inverse function?Inverse function is represented by f⁻¹ with regards to the original function and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.
When two functions are said to be inverses of each other, it means that the value of x is one is the corresponding value of y in the other function.
For instance, when the point is (5, 16) in one function, the other function's point would be (16,5).
Therefore, the options 3 and 4 are correct answers.
Learn more about the inverse function here:
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#SPJ7
QRST WXYZ. The area of QRST is given. Find the area of WXYZ.
Answers
Answer:
b. 1296 in^2
Step-by-step explanation:
The area of a rectangle is calculated by multiplying width and length:
The length of the QRST is 144 since its width is given as 8 to find the length:
144/8 = 18 is the length of the QRST
it is stated that the two rectangles are similar so their widths and lengths are proportional.
Let x represent the width of WXYZ:
8/24 = 18/x cross multiply expressions
8x = 432 divide both sides by 8
x = 54 now we can calculate area of WXYZ
24*54 = 1296
Make [tex] u [/tex]the subject of formula
[tex] \frac{1}{v} + \frac{1}{u} = \frac{2}{f} [/tex]
Answers
Step-by-step explanation:
hello I hope this will help you.
a number less than 45
Answers
Answer:
A number less than 45 would be
n<45
n=the number, and the sign is less than
7) Explain how to divide $53.56 by 10 WITHOUT USING A CALCULATOR
Write down the final answer as well.
Answers
Answer: Okay first think back you surely have divided whole numbers by 10 it is the same with decimals for each 0 in the thing you are dividing it by you move the dot one to the left. So if you divide it by 10 it is 5.356 by 100 it would be 0.5356.
Hence the answer is 5.356.
Step-by-step explanation:
Hope it helps
Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
cos(B) = 4/5 a=90
Answers
Answer:
Step-by-step explanation:
cosB = a/c = 4/5
so c = 5a/4 = 5*90/4 = 112.5
b² = c² - a² = 112.5² - 90² = 4556.25
b = 67.5
I need help with this question please
Answers
Answer : It Is B Reflection Across The Y Axis
Explanation : The Triangles Are At The Exact Same Spot On The Negative And Positive Sides
Hope This Helps
◊ YusuCr ◊
Can somebody help me figure out the tax bracket please!
Answers
Answer:
Hmmmm, very tricky question but I'll figure it out and type it in the comments
Write the following statement in symbolic form: If you qualify for a loan, then you completed the application and have the minimum gross income.
Answers
Answer:
I did not mean to send this blank
Step-by-step explanation: