The height of a triangle is 4 feet more than four times the length of the base. The area is 24 square feet. Find the base and the height. Show your work and explain the steps you used to find the solution in order to receive full credit.

Answers

Answer 1

Use the given information to create equations to help solve the problem.
H= 4+ 4B
A=24 square feet

Know that the area of a triangle formula is 1/2 x b x h.
A=1/2 x b x h

Plug in the known values and solve for the base.
24= .5 x B x (4+4B)
48=B(4+4B)
48=4B+4B^2
12= B + B^2
0=B^2 + B -12
0=(B+4)(B-3)
B= -4, 3

This solution gives us two answers, so plug both into the formula to find the correct answer.
24=.5 x -4 x (4+4(-4))
48= -4 x (-12)
48=48

24= .5 x 3 x (4+4(3))
48= 3 x (4+12)
48= 3(16)
48=48

It looks like both work, so either answer is correct.

Related Questions

BRAINLIESTTTT

A plane can fly 11 miles per minute. The plane will fly 6 trips, and each trip is 500 miles. How many hours will the plane fly? Show your work to receive full credit. (10 points)

Answers

So, we are given the speed in mi/min. We want to convert this to mi/hr. We can do this through cross multiplication.

(11 miles/1min) * (60min/hr) = 660 mi/hr

Now, we need to find the total distance flown:
TD= 6 trips*(500 miles/1 trip) = 3,000 mi

Lastly, we find total time using our converted speed and total distance.

speed = (total distance (in miles))/(total time (in hours))

660mi/hr= 3000mi / t
660t=3000
t=3000/660
t= 4.54 hrs

Answer: The plane will fly a total of about 4 and a half hours.

The sum of two numbers is $30$. the difference of twice the larger number and three times the smaller number is $5$. what is the positive difference between the two numbers?

Answers

The positive difference between the two numbers is 8, which is found by setting up a system of linear equations based on the sum of the numbers and the difference of twice the larger number and three times the smaller number.

To solve the system of equations given by the problem, we can set up two equations based on the information provided. Let x be the larger number and y be the smaller number. We are given:

The sum of two numbers is $30: x + y = 30.The difference of twice the larger number and three times the smaller number is $5: 2x - 3y = 5.

Solving this system of equations will allow us to find the values for x and y. From the first equation, we can express y in terms of x as y = 30 - x.

Substituting this into the second equation gives us 2x - 3(30 - x) = 5, which simplifies to 2x - 90 + 3x = 5 and further to 5x = 95.

Dividing both sides by 5, we find x = 19. Now we can determine y by plugging x back into the first equation, resulting in y = 30 - 19, so y = 11.

The positive difference between the larger and smaller number is 19 - 11 = 8.

What is 3x-9-5x=-7 if you solve for x

Answers

3x-9-5x = -7

combine like terms -9-2x = -7

add 9 to both sides

-2x = 2

divide both sides by -2

x - 2/-2 = -1

x = -1

Huilan is 15 years older than thomas. the sum of their ages is 55 . what is thomas's age?

Answers

55-15=40 Thomas is 35

In order to be elected to student council, Jeremy must have at least 50% of the current council members vote in his favor. If x represents the percent of favorable votes received, which inequality represents the percent of favorable votes that Jeremy needs for election to student council?

Answers

x = % of favorable votes received

x has to be at least 50% => 50% is the lower bound

=> x ≥ 50

Answer: x ≥ 50

Drag a statement or reason to each box to complete this proof.

If 3x−4=14, then x=6.

1. 3x−4=14 >>>> Given
2. 3x−4+4=14+4 >>>>?
3. Simplifying >>>>?
4. 3x3=183 >>>>?
5. >>>?

A. Simplifying
B. Division property of equality
C. Addition property of equality
D. x=6
E. 3x=18

Answers

The items below show the complete steps as to how this is being answered.

1. 3x - 4 = 14 >>>> Given
2. 3x - 4 + 4 = 14 + 4 >>>
Step number 2 above is an addition property of equality. Both sides of the equation are added with 4.
3. Simplifying >>>
3x = 18
4. 3x/3 = 18/3 >>>> Division property of equality
5. >>>> Simplifying,
x = 6

Hence, the order of the choices as answers is C, E, B, A, D.

Final answer:

In this proof, we use the Addition and Simplifying properties of equality to show that if 3x-4 equals 14, then x equals 6.

Explanation:

Given: 3x-4=14

3x-4=14 >> Given

3x-4+4=14+4 >> Addition property of equality

Simplifying >> Simplifying

3x=18 >> x=6

Answer: x=6

What is the height of the wall that is 30 feet long and that required 2310 bricks to build

Answers

(2310)=7(30)H
2310=210H

11=H

I hope this helps!

Answer:

11=h

Step-by-step explanation:

Hank's pickup can travel 64 miles on 4 gallons of gas. How many gallons will Hank's pickup need to travel 32 miles?

Answers

2 gallons... dude just divide by 2, are you sure this is high school math?

2 gallons of gas because it uses 1 gallon every 16 miles, so 32 it's half 64 which means that it uses half of the gallons.

Rick works two jobs to pay for college. he tutors for $20 per hour and also works as a bag boy for $7 per hour. due to his class and study schedule, rick is only able to work up to 25 hours per week but must earn at least $200 per week. if t represents the number of hours rick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario? t + b less than or equal to 25 20t + 7b greater than or equal to 200 t + b greater than or equal to 25 20t + 7b = 200 t + b less than or equal to 25 20t + 7b less than or equal to 200 none of the systems shown represent this scenario.

Answers

the answer is actually in the question, but you have to write it out mathematically.

he needs at least $200 per week:

20t + 7b > 200 (greater than or equal to)

he can work up to 25 hours per week:

t + b < 25

so this is your system of inequalities. hope this helps!

7x to the second power - x=6 find the solution set

Answers

7x^2 - x = 6
7x^2 - x - 6 = 0
(7x + 6 )(x - 1) = 0
7x + 6 = 0; x = -6/7
x - 1 = 0; x = 1

answer
x = -6/7; x = 1

Becky created a graph to represent her distance away from home one afternoon. She left home and ran to the park, met some friends and stayed at the park, and then walked back home using the same route. Which graph could Becky have created?

Answers

Answer: The first graph is the right graph according to the given situation.

Step-by-step explanation:

Given: Becky created a graph to represent her distance away from home one afternoon.

She left home and ran to the park⇒ She started running from zero distance from the home .⇒the second and fourth graphs are wrong .

After that she met some friends and stayed at the park, then walked back home using the same route.⇒ The first one is correct because there we can see the graph is parallel to time axis for a interval but in the third one it shows that she she hasn't took rest .

If parallelogram rstu has all sides the same length then it would be true that rs = st

Answers

of course rs=st but it wouldn't be a parallelogram anymore but it would be a rhombus

I need work shown please
Q:
x^2+3x-28
________

x^2-7x+12

A:
x+7
___

x-3

I just need work shown

Answers

see the attached picture showing the work:

Hisham is saving to buy a video game system. every month he spends $30 of what he earns. after four months, he has saved $300. how much money does hisham earn every month?

Answers

i think its $75 per month cause 300÷4 equals 75

If your sample mean is 25, your population average is 5, and your standard error of the mean is 10, what is your observed z value?

Answers

10 divided by 5 times 10

Find the height of the pole if the shadow of a boy 6 ft. tall is 3 ft. and the shadow of the pole is 2 1/3 yards. 1 yards 4 feet 14 feet

Answers

Hi there! To solve this question, we can write and solve a proportion. We put shadow/height = shadow/x. We do this, because we're looking for the height of the pole and we already know the how big the shadow of the pole is. The yards need to be converted to feet. There are 3 feet in one yard and 3 * 7/3 is 21/3 or 7 in simplest form. The pole casts a shadow 7 feet tall. Plug in the numbers like this: 3/6 = 7/x. Cross multiply the values in order to get 3x = 42. now, you divide each side by 3 to isolate the "x". When you, you get x = 14. There. The height of the pole is 14 feet. The answer is C: 14 feet.

Answer:

14 feet

Step-by-step explanation:

Which of the following is the inverse of the statement, "If it is an orange, then it is a citrus fruit"? A.If it is a citrus fruit, then it is not an orange. B.If it is a citrus fruit, then it is an orange. C.If it is not an orange, then it is not a citrus fruit. D.If it is not a citrus fruit, then it is not an orange.

Answers

Your answer would be D.If it is not a citrus fruit, then it is not an orange. The reason why is because there are multiple citrus fruit. A does not make sense because they just told you that an orange is a citrus fruit so that statement is invalid. B and C does not make sense because it's not always a true statement because of the multiple citrus fruit situation I explained earlier.

C is the answer i think.

What is the least common denominator (LCD) of 1/2 and 3/5 ?

Answers

Im pretty its 1 and 5

expand (2x + 3)^5 can you please show your work because i am still very confused on how to do this.

Answers

Product of two binomials.
You can use the FOIL method which means First, Outer, Inner, Last.
Essentially, you are multiplying (2x+3) by itself, 5 times.
It is a very cumbersome solution, but at the end I have this answer:

32x^5+250x^4+720x^3+1080x^2+810x+243

CAN ANYONE HELP ME WITH THIS QUESTION!!!!!??? The length of a string in yards is a function f(n) of the length n in inches. Write a function rule for this situation.

A. f(n)=36n

B. f(n)=1/36 n

C. f(n)=12n

D. f(n)=n/12

Answers

Your answer would be B f(n)= 1/36 n

Two fair dice are rolled. find the probability of a "double" given that the sum is 11.

Answers

Star with the statement: "Given that the sum is 11"
which may seem a bit odd considering its the last part of the problem

The "given" is important as it sets up the constraints of what we're dealing with. In this case, we know 100% (we can see or someone told us without lying) that the sum is 11. We don't know what the individual values are but we know they add to 11.

What are the ways to add to 11? Well they are...
5+6 = 11
6+5 = 11
so there are 2 ways to do it. As you can see, none of those ways involve a double. A double is where we have two of the same values (eg: snake eyes which is 1 and 1 giving 1+1 = 2 as the sum). It turns out that it's impossible to have doubles add to any odd number.

So if we know the sum is 11, and we're asking "what is the probability of rolling doubles", then the answer is 0.
The 0 indicates "impossible" or "certainty of it never happening".

There are 0 (zero) probability of a "double" given that the sum is 11.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

Two fair dice are rolled.

And, The probability of a "double" given that the sum is 11.

Now,

Since, The the probability of a "double" means;

''Two fair dice after rolled gives the same numbers.''

Since, The sum of two same number is always gives the even number.

So, We cannot get the sum 11.

Hence, There are 0 (zero) probability of a "double" given that the sum is 11.

Learn more about the probability visit:

https://brainly.com/question/13604758

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If y = 5/17 when x = 10, find y when x=5

Answers

5/34 is the answer for this problem

Final answer:

To find y when x = 5, you can substitute x = 5 into the given equation. Let's substitute x = 5 into the equation y = -173.5 + 4.83x - 2(16.4) to find y = -182.15.

Explanation:

To find y when x = 5, we can substitute x = 5 into the given equation. Given that y = 5/17 when x = 10, we can find the value of y when x = 5. Let's substitute x = 5 into the equation y = -173.5 + 4.83x - 2(16.4):

y = -173.5 + 4.83(5) - 2(16.4)
y = -173.5 + 24.15 - 32.8
y = -182.15

Learn more about Algebra here:

https://brainly.com/question/24875240

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Which of the following is the solution to 3/5 = 20/(x+3)?

3/91

-91/3

-3/91

91/3

Answers

Answer:

91/3

Step-by-step explanation:

Multiply by 5(x+3) and you get ...

3(x +3) = 100

x +3 = 100/3 . . . . . . . . . . divide by 3

x = 100/3 -3 = 91/3 . . . . subtract 3

Find the mean of this data: 37, 36, 40, 36, 40, 36, 38. If necessary, round to the nearest tenth.

Answers

Add all the numbers together, and divide your total by the number of value there (in this case, 7). The nearest tenth is to one place after the decimal.

you add them all up to get 263 then you divide by how many number there are which is 7 so 263 dived by 7 = 37.571 then you round up (tenths)37.6

Please help me thank you!

Answers

1 is BD
2 is 15
3 is y = 2
4 is 40
5 is 47

1) BD

2)
3x = 5x - 10
2x = 10
x = 5

GH = 5x - 10 = 5(5) - 10 = 15
answer: 15

3)
10y = 8y + 4
2y = 4
y = 2
answer: 2

4)
m<DBE = 2(8y+4)
m<DBE = 2(8*2 + 4)
m<DBE = 2(20)
m<DBE = 40
Answer
m<DBE = 40

5)
m<FBA = 7x+6y
m<FBA = 7(5) + 6(2)
m<FBA = 35 + 12
m<FBA =47

answer
m<FBA = 47

By graphing the system of constraints, find the values of x and y that maximize the objective function.
2<_x<_6
1<_y<_5
x+y<_8
Maximum for p=3x+2y
Answers:
A. (2,1)
B. (6,2)
C. (2,5)
D. (3,5)

Answers

First, we'd need to find the feasible region which is bounded by the constraints 2 ≤ x ≤ 6, 1 ≤ y ≤ 5 and x + y ≤ 8. Let's graph all of them and we'll get the feasible region as unshaded in the attached image. To find the maximum for p = 3x + 2y, we'll plug the coordinates of the vertices in and compare them.
p(6,1) = 3(6) + 2(1) = 20
p(2,1) = 3(2) + 2(1) = 8
p(2,5) = 3(2) + 2(5) = 16
p(3,5) = 3(3) + 2(5) = 19
p(6,2) = 3(6) + 2(2) = 22
So the maximum value of p is 22 as x = 6 and y = 2.

Answer: (6,2)

Step-by-step explanation:

Find the indicated real nth root(s) of a.

n=2, a=100

Answers

a=50 is the nth term for a to equal 100

1. ∠E and ∠F are vertical angles with m∠E=9x+12 and m∠F=3x+24
What is the value of x?

2. What is m∠KNL?

Answers

the value of x is 2 and KNL will be 102

50 pts.

Solve this algebraic equation.

-6x + 5 + 12x -6

Answers

−6x+5+12x−6 =−6x+5+12x+−6

=−6x+5+12x+−6 =(−6x+12x)+(5+−6)=6x+−1

6x−1 is your answer.

−6x+5+12x+−6

(−6x+12x)+(5+−6)

6x+−1

the answer is, 6x−1

Jim has a membership to a comic book club. He pays $9.00 per month for membership and $2.50 for each comic book he purchases. What are the parameters in this scenario?

A.) The parameters are not defined.

B.) The slope is 9 and the y-intercept is 2.5

C.) The slope is 2.5 and the y-intercept is 9.

D.) x and f(x)

Answers

The answer is C) the slope is 2.50 and the y-intercept is 9, assuming the question refers to the parameters of his monthly cost.

His cost function could be described as y= 2.5x + 9, where x is the number of comic books he purchases. If he buys no comic books, he still has to pay the $9 membership fee.

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