What is the area of this trapezoid? 50 in² 108 in² 126 in² 192 in² Trapezoid A B C D with parallel sides D C and A B. Points F and E are between D and C. F E B A form a rectangle with 4 right angles. D F is 2 inches, F E is 12 inches, E C is 2 inches, A B is 12 inches., and E B is 9 inches.
Answers
Answer: 126 square inches
Explanation:
Trapezoid is a quadrilateral , shape with straight sides that has a pair of opposite sides parallel.
I already attached the image of trpazoid.
Now find the area of trapazoid.
We have a formula to find the area of trapezoid.
Area of trapezoid = [tex] \frac{a + b}{2} h [/tex]
where a & b are the parallel side ( here "a" represent the upper side and "b" represent the base)
h is the height of the trapezoid (always remember heigth is the perpendicular distance)
now a = 12 inches (AB)
b = 2 + 12 + 2 (CD = CE + EF + FD) = 16 inches
h = 9 (BE)
Now put all these values in the given formula
Area of trapezoid = [tex] \frac{12 + 16}{2} (9) [/tex]
= [tex] \frac{28*9}{2} [/tex]
= 14*9
Are of trapezoid = 126 sq in (3rd option is correct)
Related Questions
The students at Myer Park HS were given information about two linear functions. Function F had an X intercept of eight and a Y intercept of -6. Function G is shown in the graph below. What is the slope of the function with the greater slope.
Answers
Function G slope : 3/5
Ans : I think it's 3/4 cuz it's greater in value than 3/5.
(Sorry if I'm confusing.)
If a dozen eggs cost $1.35, what is the unit cost?
Answers
dozen eggs cost =1.35 dollars
one egg =12/1.35
=0.11 dollars
The yearbook staff enlarges a picture with a length of 5 inches and a width of 7
inches by a scale factor of 3. The staff decides the enlarged picture is too large and reduces it by a scale factor of 0.5. Will the final image of the picture fit in an area of 80 square inches?
No, the area of the picture is 315 square inches.
Yes, the area of the picture is 35 square inches.
No, the area of the picture is 157.5 square inches.
Yes, the area of the picture is 78.75 square inches.
Answers
present dimensions = 5*7
dimensions after scaling with factor 3 = 15*21
dimensions after reducing by scale factor 0.5 = 7.5*10.5
area of rectangle = length * breadth
so area of yearbook = 7.5*10.5 = 78.75
because, 78.75<80
so, the yearbook will fit in area of 80 inches^2
Gloria placed 2 apples into each of 14 boxes. Let a represent the total number of apples she had. which represents this situation?
Answers
each person in Ellen's family drinks 8 1/3 ounces of water. If 5 people are in Ellen's familly., how many ounces of watet do they drink altogethet?
Answers
graph the linear equation find three points that solve the equation then plot on the graph -3y=2x-7
Answers
[tex] - 3y = 2x - 7 \\ y = - \frac{2}{3} x - \frac{7}{3} [/tex]
[tex] \binom{1}{2} \: \: \: \: \: \: \binom{5}{ - 1} \: \: \: \: \: \: \binom{8}{ - 3} [/tex]
this is the line
Manuel has 13 granola bars to split among 5 people. Express the number of granola bars that each person receives as a quotient and remainder.
Answers
--------
5/ 13
-10
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3
Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers.
Answers
y= larger number
We will have two equations to work with so we can solve for the variables.
EQUATION 1:
3 * y= 4 * x
3y= 4x
subtract both sides by 3y
0= 4x - 3y
EQUATION 2:
21= x + y
SOLVE:
solve for one variable in equation 2
21= x + y
subtract both sides by y
21-y= x
Substitute x= 21-y in equation 1:
0= 4x - 3y
0= 4(21-y) - 3y
0= (4*21) + (4*-y) - 3y
0= 84 - 4y - 3y
0= 84 - 7y
add 7y to both sides
7y= 84
divide both sides by 7
y= 12
Substitute y=12 in either equation to solve for x:
21= x + y
21= x + 12
subtract both sides by 12
9= x
CHECK:
0= 4x - 3y
0= 4(9) - 3(12)
0= 36 - 36
0= 0
ANSWER: x=9 and y=12
Hope this helps! :)
Does 4.5, 6, 7.5 form a right triangle
Answers
a & b are the two legs
c is the hypotenuse (longest side)
a = 4.5
b = 6
c = 7.5
Plug those values into the pythaogrean theorem and let's see if we get a true equation or not
a^2 + b^2 = c^2
4.5^2 + 6^2 = 7.5^2
20.25 + 36 = 56.25
56.25 = 56.25 .... true equation
Since we get a true equation, this means the original equation is true for the given a,b,c values. So we do have a right triangle.
Final answer:
The numbers 4.5, 6, and 7.5 can form the sides of a right triangle as their squared lengths satisfy the Pythagorean theorem where 4.5² + 6² equals 7.5².
Explanation:
To determine whether the numbers 4.5, 6, 7.5 can form the sides of a right triangle, we can apply the Pythagorean theorem.
This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
According to the given numbers, if we assume that 7.5 is the length of the hypotenuse, then:
4.5² + 6² should equal 7.5²
Calculating each term gives us:
4.5² = 20.256² = 367.5² = 56.25Adding the squares of the possible legs:
20.25 + 36 = 56.25, which is indeed the square of the hypotenuse. This confirms that 4.5, 6, and 7.5 can indeed form a right triangle.
A rectangular park has an area of 64 square yards. If we multiply its length and width by 12, what will be the area of the new rectangle?
Answers
Answer:
9216 see explanation
Step-by-step explanation:
area of a rectangle =l×b
let the area and the breadth of the rectangle be x an y respectively
Now
x×y=64cm^2
as we have to multiply the length and breadth both by 12 the new area will be x×y=64×12×12 so the new area would be 9216
Answer:
[tex]\displaystyle 9126\:yd.^2[/tex]
Step-by-step explanation:
Explanation:
[tex]\displaystyle wl = A[/tex]
First, let us list the factours of 64:
[tex]\displaystyle 1, 2, 4, 8, 16, 32, 64[/tex]
Any two factours of 64 would do [two eights would wourk of cource, but the park is not square-shaped]:
[tex]\displaystyle 9126 = [2(12)][32(12)] \\ 9126 = [4(12)][16(12)][/tex]
Either way, you still get the same result. By the way, NO court will ever be one yard, so I never included it, but again, you get the overall idea.
I am joyous to assist you at any time.
when Raphael solved the system below by using the method of elimination, he changed the second equation to -8x-2y=-2 what property justifies this manipulation?
8x+3y=7
4x+y=1
Answers
Raphael used the Property of Equality to justify his manipulation of the second equation.
Explanation:The property that justifies Raphael's manipulation is the Property of Equality. According to this property, if two expressions are equal, then subtracting or adding the same quantity to both sides of the equation will still give you an equal equation. In this case, Raphael changed the second equation to -8x - 2y = -2 by subtracting 1 from both sides of the equation.
Learn more about Method of elimination here:https://brainly.com/question/13877817
#SPJ12
1.At a video arcade , Jenny buys 25 tokens.She uses two tokens for each game She plays.
a ) Write an expression for the number of tokens Jenny left after playing g games.
b) Find the number of tokens Jenny has left after playing 1,4,6,10 and 12 games.
Answers
b) 25-2(1)=23
25-2(4)=17
25-2(6)=13
25-2(10)=5
25-2(12)=1
Answer:
The required expression is [tex]25-2g[/tex]
She left with 23 tokens after playing 1 game.
She left with 17 tokens after playing 4 game.
She left with 13 tokens after playing 6 game.
She left with 5 tokens after playing 10 game.
She left with 1 tokens after playing 12 game.
Step-by-step explanation:
Consider the provide information.
Part (A)
At a video arcade, Jenny buys 25 tokens. She uses two tokens for each game She plays.
Let the number of games she plays represented by g.
For each game she need to use 2 tokens.
Thus for g games she will use 2g tokens.
Thus, the required expression is: [tex]25-2g[/tex]
Part (B) Find the number of tokens Jenny has left after playing 1,4,6,10 and 12 games.
The number of tokens Jenny has left after playing 1, is:
[tex]25-2(1)[/tex]
[tex]25-2[/tex]
[tex]23[/tex]
Hence, she left with 23 tokens after playing 1 game.
The number of tokens Jenny has left after playing 4, is:
[tex]25-2(4)[/tex]
[tex]25-8[/tex]
[tex]17[/tex]
Hence, she left with 17 tokens after playing 4 game.
The number of tokens Jenny has left after playing 6, is:
[tex]25-2(6)[/tex]
[tex]25-12[/tex]
[tex]13[/tex]
Hence, she left with 13 tokens after playing 6 game.
The number of tokens Jenny has left after playing 10, is:
[tex]25-2(10)[/tex]
[tex]25-20[/tex]
[tex]5[/tex]
Hence, she left with 5 tokens after playing 10 game.
The number of tokens Jenny has left after playing 12, is:
[tex]25-2(12)[/tex]
[tex]25-24[/tex]
[tex]1[/tex]
Hence, she left with 1 tokens after playing 12 game.
Please anyone help me simplify the answer
Answers
Assume that after t hours on the job, a factory worker can produce 100te^-.5t units per hour. How many units does the worker produce during the first three hours?
Answers
[tex]N(t)=100t e^{(-0.5t)} [/tex]
To find the number of units produced during first 3 hours, we can substitute 3 for t. This will give us the number of units produced by the worker during first 3 hours.
[tex]N(3)=100(3) e^{-0.5(3)} = 67[/tex]
Thus the worker will produce 67 units during the first 3 hours of the work.
Final answer:
To find the number of units that the worker produces during the first three hours, we need to calculate the integral of the production function from 0 to 3. The production function is given as 100te^-0.5t. Using the power rule and the exponential rule of integration, we can find that the worker produces approximately -300e^-1.5 units during the first three hours on the job.
Explanation:
To find the number of units that the worker produces during the first three hours, we need to calculate the integral of the production function from 0 to 3.
The production function is given as 100te^-0.5t.
To integrate this function, we can use the power rule and the exponential rule of integration.
Now, we can plug in the values from 0 to 3 in the integral and calculate the result.
First, plug in the value t=3 in the integral: -100(3)e^-0.5(3) = -300e^-1.5.Then, plug in the value t=0 in the integral: -100(0)e^-0.5(0) = 0.Finally, subtract the result from step 2 from the result from step 1: -300e^-1.5 - 0 = -300e^-1.5.Therefore, the worker produces approximately -300e^-1.5 units during the first three hours on the job.
what is the answer to this problem
Answers
5 x 70 = 35 tens = 350
Answer:
350Step-by-step explanation:
The completed problem is
[tex]5 \times 70=5\times 7 \ tens.\\5 \times 70=35 \ tens=350[/tex]
Basically, the process is only about separating tens from units, so basically "tens" represents the zero, that's why we only multiply 5 and 7 digits, and add the zero at the end. It's an easier way to multiply tens.
PLEASE HELP WILL GIVE BRAINLIEST AND 20 POINTS
1 cubic foot of sand weighs 100 pounds. A square sandbox with 5-foot side has half of a foot of sand in it. How many pounds of sand is the sandbox holding?
Answers
So first let's find the volume of the sand in the sandbox. You have a square sandbox, with a side length of 5, meaning you have a length and width of 5. You also have half a foot of sand in the sandbox, meaning that you have a height of 0.5. To find the volume of the sand, multiply the length by the width by the height:
[tex]5 * 5 * .5 = 12.5[/tex]
So you have 12.5 cubic feet of sand. If each cubic foot of sand is 100 lbs, then you just multiply the two:
[tex]12.5 * 100 = 1250.0 [/tex]
X=
A.100
B.120
C.140
Answers
.. 10 = (30 -(150 -x))/2
.. 20 = x -120
.. 140 = x
The 3rd selection is appropriate.
Number 5 and a. b. 6. a. b. is difficult who can help me?
Answers
5a. Okay. So $90 were paid for the two tickets, that's $45 per ticket. 452.50 was the amount per ticket. First, let's subtract 45 from 52.50. 52.50 - 45 is 7.5. That's $15 for two tickets, and $7.50 of a markdown per ticket.
5b. For this all we have to do is divide the difference by the original price. Let's do the cost per ticket. There is a difference of 7.5. The original price was $52.5. 7.5/52.5 is 0.142857 and other numbers behind it, or 14% when converted to percent and rounded to the nearest whole number. You can divde the difference for two tickets by the original price for two tickets and get the same answer. There. The percent markdown is approx.14%.
For this part, in order to find the sale price, what we have to do is subtract the markdown from 100%, and then multiply the remainder by the original price. This is because while you do get a discount, you still have to pay a portion of the original price.
6a. The discount is 35%. That means you pay 65% of the original amount, because 100 - 35 is 65. Let's multiply. 4,200 * 65% (0.65) is 2,730. There. The sales price is $2,730.
6b. The discount is 44%, 100 - 44 is 56. So 56% of the original price is paid. Once again, multiply the percent and the original price together. 5,000 * 56% (0.56) is 2,800. There. The sale price is $2,800.
resolva a seguinte equaçao -8x-13 = 3 por favor preciso da conta
Answers
Here is your answer:
The proper answer to this question is "x-=2".
-8x-13=3
Add 13 both sides:
13+3=16
Divide 8 on both sides:
16/8=2
X=2!
If you need anymore help feel free to ask me!
Hope this helps!
Name the like terms in the expression 5a + 8 – 3a + 11.
Answers
8 and 11 are like terms because they both are constants and don't have a variable.
5a and 3a are like terms because they both have the variable a in common.
you would combine these like terms
5a + 8 - 3a + 11
(5a - 3a) + (8 + 11)
2a + 19
Hope this helps :)
5a
3a
Find k so that 25x^2+40x+k is the square of a binomial
Answers
(5x+ )(5x+ )
The blanks must multiply to equal k and add together to equal 40 when multiplied by 5x.
(5x+4)(5x+4) = (5x+4)^2
Applying the FOIL method to the perfect square binomial shows that k=16
Final answer:
To find k to make a quadratic expression a perfect square of a binomial, we must compare coefficients and solve equations for a and b. Finally, by substituting the values of a and b, the value of k can be determined as 16.
Explanation:
To find k so that 25x^2 + 40x + k is the square of a binomial, we aim to express 25x^2 + 40x + k as the square of the binomial form (ax + b)^2. Comparing coefficients gives us:
2ab = 40 (from the linear term)
a^2 = 25 (from the quadratic term)
Solving these equations, we find a = 5 and b = 4. Therefore, the value of k is 16.
What does this mean I don’t quite get it.
Answers
To find circumference, the formula is
[tex]2\pi \times r[/tex]
So, the answer to this problem would be 31.42
Derrick lives 3 miles from the park. He rode his bicycle to the park at an average speed of 9 miles per hour. How many minutes did it take Derrick to ride his bicycle to the park?
Answers
Since we don't know how many hours it took, we'll say 9 mph = 3 miles/x hours. To solve, we multiply both sides by x. 9x = 3 Dividing both sides by 9, we get that it took 3/9 hours or 1/3 hours. How many minutes are 1/3 hours? 20, so it took Derrick 20 minutes. Hope this helps! :)
Hugs!
- Nicole
how many athletes exercised more than 40 but less than 60 minutes
Answers
The correct answer is:
4.
Explanation:
The number 40 is written in this stem-and-leaf plot as 4|0. 60 is written as 6|0. There are 4 leaves between these numbers; 5, 5, 5 and 5, with the stem of 4. This means the numbers are 45, 45, 45 and 45. There are only 4 between these two numbers.
unscramble each of the clue words.
tow-setp
pyorerpt
dodtiina
niiosdiv
labviera
aileyquitn
bistautornc
nuatieqo
tiulinticpolma
Answers
Second property
Third addition
Fourth division
Fifth variable
And the last is multiplication
Sorry I don’t know the rest
There are (53)2 ⋅ 50 hens in a bird enclosure. What is the total number of hens in the enclosure?
a) 0
b) 55
c) 56
d) 530
Answers
Answer:
c) [tex]5^{6}[/tex]
Step-by-step explanation:
We have been given that there are [tex](5^3)^2\cdot 5^0[/tex] hens in a bird enclosure. We are asked to find the total number of hens in the enclosure.
Using exponent property [tex]a^0=1[/tex], we will get:
[tex](5^3)^2\cdot 1[/tex]
[tex](5^3)^2[/tex]
Using exponent property [tex](a^b)^c=a^{b\cdot c}[/tex], we will get:
[tex]5^{3\cdot 2}[/tex]
[tex]5^{6}[/tex]
Therefore, there are total number of hens in the enclosure would be [tex]5^{6}[/tex].
Ivan has 8 marbles. Each marble weighs 1/3 ounce. What is the total weight of the marbles in ounces?
Answers
= 8/3
the answer is 8/3 ounces
If each marble is 1/3 of an ounce:
8/1*1/3= 8/3
Or, we could say 8*1= 8 Tyen our that over 3.
8/3= 2 2/3 ounces
I hope this helps!
~kaikers
This system of equations represents Reese’s pocket change. Let n represent the number of nickels and d represent the number of dimes Reese has in his pocket. n + d = 11 5n + 10d = 70 How many dimes are in Reese’s pocket?
Answers
Answer: 3 dimes
Step-by-step explanation:
Let n represent the number of nickels and d represent the number of dimes Reese has in his pocket.
Given system : [tex]n+d=11........(1)\\5n+10d=70............................(2)[/tex]
Divide equation (2) by 3 on both sides, we get
[tex]n+2d=14................................(3)[/tex]
Subtract equation (1) from (3), we get
[tex]d=3[/tex]
Hence, there are 3 dimes in Reese's pocket.
Answer:
3 dimes are in Reese's pocket.
Step-by-step explanation:
Here, n represent the number of nickels and d represent the number of dimes.
Given the system of equations:
[tex]n+d = 11[/tex] .....[1]
[tex]5n+10d = 70[/tex] .....[2]
Multiply both sides by 5 in [1] we have;
[tex]5n+5d=55[/tex] .....[3]
Subtract equation [3] from [2] we have;
[tex]5d = 15[/tex]
Divide both sides by 5 we have;
d = 3
Therefore, 3 dimes are in Reese's pocket.
Tell how you know when you need to use renaming when subtracting mixed numbers
Answers
Step 1: Keep the denominator the same. Step 2: Add or subtract the numerators. ...Step 1: Find the Lowest Common Multiple (LCM) between the denominators. ...Step 1: Convert all mixed numbers into improper fractions. ...In this second method, we will break the mixed number into wholes and parts. ...Thus, is equivalent to.
In Art class, Mr. Jocelyn gave everyone a1 foot stick to measure and cut. Vivian measured and cut her stick into 5 equal pieces. Scott measured and cut his into 7 equal pieces. Scott said to Vivian, "the total length of my stick is longer than yours because I have 7 pieces, and you only have 5" is that correct?
Answers
However, they all got a 1-foot stick. So, if you add them up you have an equal length.
Scott is incorrect thinking his stick is longer; both received identical 1 foot sticks, so total lengths remain the same despite the number of pieces they are cut into.
The student's question involves Scott believing that because he has more pieces, the total length of his stick is longer than Vivian's. Scott and Vivian both received a 1 foot stick and divided it into equal pieces; Scott into 7 pieces and Vivian into 5.
This problem is related to the concept of division where each person divides their total length equally among the number of pieces, which means the length of each individual piece changes, but the total length of the stick remains the same. Scott is not correct; the total lengths of their sticks are identical, each being 1 foot in length before cutting, regardless of the number of pieces they've been cut into.