One base of a trapezoid is 8 cm longer than the other. The height of the trapezoid is 2 cm longer than the shortest base. If the area is 48 cm2, what are the height and bases?
A. The height is 6 cm, and the bases are 4 cm and 12 cm.
B. The height is 12 cm, and the bases are 10 cm and 18 cm.
C. The height is 4 cm, and the bases are 2 cm and 10 cm.
D. The height is 10 cm, and the bases are 8 cm and 16 cm.

Answers

Answer 1

Answer:

B

Step-by-step explanation:

Let's call the shortest side a. The longest base, b, is 8cm longer than a. The height, h, is 2cm longer than a.

b = a + 8

h = a + 2

A = (a + b)h/2

48 = (a + (a+8))(a+2)/2

     = (2a+8)(a+2)/2

     = (2a^2+12a+16)/2

48 = a^2+6a+8

a^2+6a-40=0

Now, we factor this:

(a + 4)(a - 10)=0

a = -4, 10

a (length) cannot be a negative no. so the only possible answer is a = 10.

b = 10 + 8 = 18

h = 10 + 2 = 12

The answer is B

Hope this helps!


Related Questions

The surface area of a three-dimensional object is the sum of the area of the faces. If represents the length of the side of a cube, write a formula for the surface area S of the cube.

Answers

Answer:

S = 6e²

I don't know what variable you're using here.

Step-by-step explanation:

There are 6 faces on a cube and they are all the same. Because of this, 6 is the coefficient in this equation.

A square's area can be found by squaring the side length (Which I'll represent with e). So e² is the variable.

Thus, the equation is S = 6e²

Which of the following statements is true about the graphs of a linear function (x) = mx + b and that of an exponential function g(x) = a*, where a > 0 and a = 1?

Answers

Answer:

the answer a is the correct answer

3,3 x,y 6,9 what is x,y 

Answers

answer:

answer:

answer:

Monica can clean the house in 5 hours by herself. When Monica and Sydney
work together, it takes 3 hours. How long would it take Sydney to clean the
house by herself?
A. 5.5 hours
B. 7.5 hours C. C: 2.0 hours
D. 4.7 hours

Answers

Answer:

The answer is B 7.5 hours.

Step-by-step explanation:

A. P. E. X

Sydney can clean her house in 7.5 hours.

What is Efficiency?

Efficiency is often measured as the ratio of useful output to total input, which can be expressed with the mathematical formula r=P/C, where P is the amount of useful output ("product") produced per the amount C ("cost") of resources consumed.

Here, Monica can clean her house in 5 hours

Monica's efficiency = 1/5

Let, Sydney cleans the house in x hours.

Sydney's efficiency = 1/x

They both together complete their work in 3 hours

Combined efficiency = 1/3

Now, according to question;

1/5 + 1/x = 1/3

(x+5)/5x = 1/3

3x + 15 = 5x

5x - 3x = 15

2x = 15

x = 15/2

x = 7.5

Thus, Sydney can clean her house in 7.5 hours.

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Juan pago $50.00 pesos por 3 cajas de paquetes y 5 cajas de clavos, mientras que Pedro compró 5 cajas de taquetes y 7 cajas de clavos y tuvo que pagar $ 74.00 pesos . ¿ Cual es el precio de cada caja de taquetes y clavos ?
a) ¿ Cuantas incógnitas hay en el problema ?
b) ¿ Cuántas ecuaciones puedes construir según el texto?
c) ¿ Cuales son esas ecuaciones?

Answers

A) confusión al encontrar la suma de la diferencia de precios
B ) dos
C ) 50 dividida 8, 74 dividida 12


espero que esto haya ayudado!
te agradecería que me dieras un gracias y brainliest (:

Evaluate the following expression using the values given:

Find 5x − 3y − z if x = −2, y = 2, and z = −3

Answers

Answer: -13

Step-by-step explanation:

just substitute the letters for the numbers.

5(-2) - 3(2) -(-3)

then, remove the parenthesis.

-10 - 6 + 3

finally, just calculate it.

-13

15 points theres an image to help you guys out too i need it ASAP though.. please

Answers

Answer:

16

Step-by-step explanation:

8-1+9

7+9=16

the answer is=16

Answer:

16

Step-by-step explanation:

(8-1) = 7 + 9

= 16

D ......

Manuel ate lunch in 5 minutes. How many seconds is this?

Answers

Answer:

300 seconds

Step-by-step explanation:

1 minute= 60 seconds

5 x 60 = 300

Answer:

1 minute is 60 seconds, so 60 x 5 is 300. So your answer is 300 seconds

5.00 minus2.40minus1.33= plz show me how you got that answer step by step

Answers

Answer:

5.00 -2.40= 2.60

2.60-1.33= 1.27

The answer is 1.27

Step-by-step explanation:

Polly buys 14 cupcakes for the party. the bakery puts them into boxes that hold 4 cupcakes each.
how many boxes will be needed for Polly to bring all the cupcakes to the party? Explain

Answers

Answer:

11 boxes

Step-by-step explanation:

14 didived by 4 is 10.25 so if you round you should get 11 .

Answer:

4, If you round.

Step-by-step explanation:

If you divide the 14 by 4, you get 3.5 and you can't really break the box in half.

So, you would have to use 5.

Please help me answer this:)
I will give you braisnlt

Answers

Answer:

B, E, F

Step-by-step explanation:

they are linear because there are no fractions or exponents  

Answer:

B, E, F

Step-by-step explanation:

For a linear function, you can have x multiplied by a number, but you cannot have x multiplied by a variable. Also you can't have x in denominator or an exponent on x other than 1.

For a linear equation, y must equal a first degree polynomial or a constant.

Answer: B, E, F

Debra needs to make a total of 40 deliveries this week. So far she has completed 6 of them. What percentage of her total
deliveries has Debra completed?

Answers

6/40=0.15 = 15% of her deliveries
debra has completed 15 percent

Ben earns an annual income of $12,800 a year. The income tax he has to pay is 15%. What is the amount of income tax in dollars and cents that Ben has to pay? A $1,664 B $10,880 C 12,000 D $1,920

Answers

Answer:

$

1

,

920

Explanation:

Find  

15

%

×

12800

15

100

×

12800

1

=

$

1

,

920

Step-by-step explanation:

Answer:

D $1,920

Step-by-step explanation:

$12,800 annual income he has to pay 15%

EASYYYYYYYYYYYYYYYYYYYY'

just get

12,800 DIVIDE BY 100

12,800/100

128=1 percent

now multiply by 15

128*15=

1920

small bottle of Gatorade holds 75% as much as the large bottle of Gatorade. If the small bottle holds 36 units, how many units does the large bottle hold?

Answers

Answer:

48 unit

Step-by-step explanation:

36=x75%

x=36/75% = 48

double check just in case :)

_9) What are the solutions of the equation (x – 3)2 + 2(x – 3) - 8 = 0?
A) x = -5 and x = 1
B) x = -1 and x = 5
C) x = -1 and x = -7
D) x = 1 and x = 7
Help please

Answers

Answer:

Step-by-step explanation:

Two numbers r and s sum up to \frac{1}{2} exactly when the average of the two numbers is \frac{1}{2}*\frac{1}{2} = \frac{1}{4}. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C.

Name the corresponding an

Answers

Answer:

what do you want to say?

umm girll what? lol i’m so confused

WILL MARK BRAINLIEST
what type of transformation is described by (x,y) —> (x+2, y+16)?

Answers

This transformation takes a vector (x,y) and maps it to the vector (x+2, y+16). In other words, it moves the X coordinate of the vector 2 units to the right, and the Y coordinate of the vector is moved 16 units upwards.

If you would take a set of points and apply this transformation, you would see the entire set moving upwards and to the right, with no stretching ou rotating. This type of transformation is called a translation transformation.

Last year 950 people attended a town's annual parade. This year 1,520 people attended. What was the percent increase in attendance from last year to this year?

Answers

Answer: 60% increase

Step-by-step explanation: look up calculator soup if you have more questions like this

Find -8 1/4 divided (-2 5/12) write your answer as a mixed number in simplest form

Answers

Answer:

I believe the answer is 3 12/29

59:41 To build the roof for a paper house, a rectangular paper is cut to form a trapezoid. Which diagram shows the correct cuts? Save and Exit Mark this and return Nes Submn K​

Answers

Answer:

Step-by-step explanation:

wheres the diagram?

Answer:B

Step-by-step explanation:

Please Help Friends !!!

Answers

Answer:

A=4 B=1 C=2 D=5 E=3

Step-by-step explanation:


If the radius is 21 cm and the angle at
center of circle is 140° then the length of
the arc is ?

Answers

Step-by-step explanation:

Given: Radius , r =21 cm

The angle at the center of the circle, n° =140°

Length of an arc =?

W.K.T Formula, Length of an arc = 2πr( n°÷360°) units

= 2*(22/7)*21*(140°/360°)

= 154/3

= 51.33cm

Answer:

2*(22/7)*21*(140°/360°)

= 154/3

= 51.33cm

Step-by-step explanation:

solve (x – 3)2 = 81 quadratic equation​

Answers

Answer:

x = 43.5 or x = 87/2

Step-by-step explanation:

(x - 3)2 = 81

2x - 6 = 81

2x = 87

x = 43.5

A bank deposit paying simple interest at the rate of 8%/year grew to a sum of $1300 in 6 months. Find the principal. (Round your answer to the nearest cent.)

Answers

Answer:

$1,250

Step-by-step explanation:

The rate is 8%

= 8/100

= 0.08

Time is 6 months

= 1/2 year

Therefore the principal can be calculated as follows

Principal × (1+0.08(1/2) = 1300

Principal × 1+ 0.04 = 1300

Principal × 1.04= 1300

Principal= 1300/1.04

Principal = $1,250

Hence the principal is $1,250

In the diagram, line p(perpendicular) line r. Which must be true?

Answers

s+t =90 is a required answer

Help plz the problem is in the photo

Answers

Answer:

25 = 50%

37.50 = 75%

75 = 150%

Step-by-step explanation:

We know that 50 is 100% so we can work with that.

We also know the percentages increase by 25% for every $12.5.

12.50 + 12.50 = 25

25 + 12.50 = 37.50

62.50 + 12.50 = 75

25 = 50%

37.50 = 75%

75 = 150%

I hope this helps and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

first line is- first blank is 25 second blank is 37.5 third blank is 75

bottom line is- first blank is 50%. second blank is 75%. third blank is 150%

The null hypothesis for an ANOVA is that all treatments/samples come from populations with the same mean. The alternative hypothesis is best stated as:____________

Answers

Answer:

At least one of the population means is different from the others.

Step-by-step explanation:

ANOVA is a short term or an acronym for analysis of variance which was developed by the notable statistician Ronald Fisher. The analysis of variance (ANOVA) is typically a collection of statistical models with their respective estimation procedures used for the analysis of the difference between the group of means found in a sample. Simply stated, ANOVA helps to ensure we have a balanced data by splitting the observed variability of a data set into random and systematic factors.

In Statistics, the random factors doesn't have any significant impact on the data set but the systematic factors does have an influence.

Basically, the analysis of variance (ANOVA) procedure is typically used as a statistical tool to determine whether or not the mean of two or more populations are equal through the use of null hypothesis or a F-test.

Hence, the null hypothesis for an ANOVA is that all treatments or samples come from populations with the same mean. The alternative hypothesis is best stated as at least one of the population means is different from the others.

A chain letter starts when a person sends a letter to five others. Each person who receives the letter either sends it to five other people who have never received it or does not send it to anyone. Suppose that 10,000 people send out the letter before the chain ends and that no one receives more than one letter. How many people receive the letter, and how many do not send it out?

Answers

Answer:

50,001 people sent out the letter.

40,001 did not send it out

also can i get brainliest???

Step-by-step explanation:

780 people receive the letter before the chain ends.

9,220 people do not send out the letter.

We have,

In the given scenario, the chain letter starts with one person sending it to five others.

Each recipient of the letter has the option to either send it to five new recipients or not send it to anyone.

Let's analyze the chain letter progression:

The first person sends the letter to 5 recipients.

Each of those 5 recipients has the choice to send the letter to 5 new recipients or not send it.

If each of the 5 recipients sends the letter to 5 new recipients, we have a total of 5 x 5 = 25 new recipients.\

If any of the 5 recipients choose not to send the letter, they are out of the chain.

Now, we have 25 recipients who received the letter and have the same choice: send it to 5 new recipients or not send it.

If each of the 25 recipients sends the letter to 5 new recipients, we have a total of 25 * 5 = 125 new recipients.

If any of the 25 recipients choose not to send the letter, they are out of the chain.

This process continues until the chain ends.

To determine how many people receive the letter and how many do not send it out, we can observe the pattern:

After the first step, there are 5 recipients.

After the second step, there are 5 + (5 * 5) = 30 recipients.

After the third step, there are 5 + (5 * 5) + (5 * 5 * 5) = 155 recipients.

After the fourth step, there are 5 + (5 * 5) + (5 * 5 * 5) + (5 * 5 * 5 * 5) = 780 recipients.

We can see that the number of recipients follows a geometric progression with a common ratio of 5.

The formula for the sum of a geometric progression is:

[tex]Sum = a (r^n - 1) / (r - 1)[/tex]

Where:

a = initial term = 5

r = common ratio = 5

n = number of steps

We are given that the chain ends after 10,000 people send out the letter. Let's calculate the number of recipients:

[tex]Sum = 5 (5^4 - 1) / (5 - 1)[/tex]

= 5 (625 - 1) / 4

= 5 624 / 4

= 780

Therefore, 780 people receive the letter before the chain ends.

To find the number of people who do not send it out, we subtract the number of recipients from the total number of people who sent out the letter:

Number of people who do not send it out = Total number of people - Number of recipients

= 10,000 - 780

= 9,220

Therefore, 9,220 people do not send out the letter.

Thus,

780 people receive the letter before the chain ends.

9,220 people do not send out the letter.

Learn more about geometric sequence here:

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What is the unit cost of the olives at Mangio's​

Answers

Answer:

$6

Step-by-step explanation:

18/3=6

24/4=6

30/5=6

36/6=6

Find the volume and solve the application.

A mason's assistant's rate of pay is $0.95 per cubic foot of earth moved. He digs a trench 1.5 ft. wide by 1 ft. deep by 150 ft. in length. What is his pay for this job?

Answers

1.5ft * 1ft * 150ft = 225ft^3

225 *  $0.95 = $213.75 pay for the job

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