The height of a triangle is 4 feet less than the length of its base, b. The area of the triangle is 30 square feet.
Find the base and the height of the triangle.

Answers

Answer 1

Answer:

b = 10 ft , h = 6 ft

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

let base = b theh height h = b - 4

given A = 30 , then

[tex]\frac{1}{2}[/tex] b(b - 4) = 30 ( multiply both sides by 2 to clear the fraction )

b(b - 4) = 60 ← distribute parenthesis on left side by b

b² - 4b = 60 ( subtract 60 from both sides )

b² - 4b - 60 = 0

(b - 10)(b + 6) = 0

equate each factor to zero and solve for b

b - 10 = 0 ⇒ b = 10

b + 6 = 0 ⇒ b = - 6

however, b > 0 , then b = 10

and h = b - 4 = 10 - 4 = 6

then base is 10 ft and height is 6 ft


Related Questions

3x^2-2x+3
when x is 7???

Answers

Answer:

136

Step-by-step explanation:

Let's plug in 7 for x. 3(7)^2-2(7)+3. 7 to the second power is 49. 49*3 is equal to 147. 147-2(7) is 147-14, which is 133. 133+3=136, and therefore that is the answer.

Answer:

136

Step-by-step explanation:

substitute x = 7 into the expression

3x² - 2x + 3

= 3(7)² - 2(7) + 3

= 3(49) - 14 + 3

= 147 - 11

= 136

Everett bought a hat and a shirt that were both on sale. The hat was on sale for 2/5 off the original price, and the shirt was on sale for 1/10 off the original price. How much more was the discount on the hat than the discount on the shirt?

Answers

Answer: 3/10

Step-by-step explanation:

Hat price 3/5

Shirt price 9/10

Difference in Discount 2/5 - 1/10 = 4/10 - 1/10

On January 1st, 2003, Gerry opened a savings account that paid 3. 25% annual interest. His initial deposit was $1,100. If Gerry didn’t deposit or withdraw any additional money, what was his balance at the close of December 31st, 2012?

Answers

Answer:

1514.59

Step-by-step explanation:

The equation says
A=p(1+r)^t
A future value ?
P present value which is 1100
R interest rate 3.25%×100=0.0325
T time from January 1st, 2003 to December 31st, 2012 which is 10 years
Now apply them into the equation
A=1,100×(1+0.0325)^(10)
A=1514.59

Hope it helps!

Answer:$1,457.50

Step-by-step explanation:


The length of a box is twice the width and thrice the height. If the volume of the box is 288 m then find the dimensions of the box​

Answers

Answer:

length = 12 mwidth = 6 mheight = 4 m

Step-by-step explanation:

Let the height be x.

Length is 3 thrice the height, so length ⇒ 3xLength is twice the width, so width ⇒ 3x/2

We know the formula for volume of the box.

V = lwhV = (3x)(3x/2)(x)288 = 9x³/29x³ = 576x³ = 64x = 4 m

Dimensions

height = x = 4 mwidth = 3x/2 = 3(4)/2 = 6 mlength = 3x = 3(4) = 12 m

Please help don’t understand at alll

Answers

Answer:

47.3

Step-by-step explanation:

To find the standard deviation use this example formula

[tex]a =\sqrt{\frac{(x-u)^{2} }{N} }[/tex]

a = your answer, the standard deviation you are looking for

x = the value of each carrier

u = the carrier numbers mean (such as mean, median, and mode)

N = the overall total of the carriers

If you find this equation still confusing one of my favorite sites to use is Math.way, where you plug in each number with a comma in between and it solves it for you. Other sites work such as Calculatornet, Calculator.Soup, and Math.is.Fun.

Hope this helps :)

f(x) = x + 2
g(x) = x - 4
(f g)(x) =

Answers

Answer:

x2−2x−8

Step-by-step explanation:

Help me with this question, please

Answers

Answer:

x = 3 oz of seeds

y = 7 oz of seeds

Step-by-step explanation:

1. x + y = 10 oz (total amount of snack mix in ounces; oz)

2. $1.50x + $2.50y = $22 (how much the seeds and dried fruit costs)

3. Solve the system of equations using algebra.

$1.50 x + $1.50y = $15

$1.50 x + $2.50y = $22

There are $1.50x's in both of the equations, so cancel them out.

Subtract $2.50y by $1.50y and $22 by $15. y = 7

4. Plug in the y value in one of the equations.

x + 7 = 10; x = 3

Ansley went for a long hike and burned 452 calories in 2 1/4 hours. Bobbi decided to go for a jog and burned 1,045 calories in 3 1/2 hours. Who burned the most calories per hour

Answers

Answer:

Bobbi burned the most calories per hour.

Step-by-step explanation:

Ratio

452:2.25

1045:3.5

to simplify the ratios, divide to the unit rate.

452/2.25:2.25/2.25

≈201:1 hour, burned 201 calories in 1 hour

1045/3.5:3.5/3.5

≈299:1 hour, burned 299 calories in 1 hour

299 > 201

Answer:

Bobbi burned the most calories per hour.

Step-by-step explanation:

Ratio

452:2.25

1045:3.5

to simplify the ratios, divide to the unit rate.

452/2.25:2.25/2.25

≈201:1 hour, burned 201 calories in 1 hour

1045/3.5:3.5/3.5

≈299:1 hour, burned 299 calories in 1 hour

299 > 201

Scott invests $1000 at a bank that offers 6% compound annually

Answers

Answer:

A = 1000(1.06)^t     where A is the amount of the investment after t years.

Read more at Answer.Ya.Guru – https://answer-ya.com/questions/2080217-scott-invests-1000-at-a-bank-that-offers-6-compounded-annually.html

Find the volume ratio given:
Side ratio is 2:7

Answers

Step-by-step explanation:

2/7= 2*2*2/7*7*7

=8/343

The volume ratio is given as;

⇒ 8 : 243

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

Side ratio is,

⇒ 2 : 7

Hence, The volume ratio is given as;

⇒ 2³ / 7³

⇒ 2×2×2 / 7×7×7

⇒ 8 / 243

⇒ 8 : 243

Thus, The volume ratio is given as;

⇒ 8 : 243

Learn more about the ratio visit:

https://brainly.com/question/12024093

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How should the headings of a résumé be formatted so that they are clear and easy to find? a. bold and italicized b. capitalized and bold c. underlined and italicized d. capitalized and underlined

Answers

The headings of a résumé should be capitalized and bold formatted so that they are clear and easy to find.

What do you mean by headlines?

Headlines are the main topic or the highlighted part of any paragraph which indicates the nature of the article.

The headings of a résumé should be formatted so that they are clear and easy to find.

The headings indicate the nature of the article so it should be highlighted or different from the summary.

The heading must be capitalized and bold which makes the text different from the summary.

Learn more about headlines;

https://brainly.com/question/27224369

Answer:

B. EDG 2023

Step-by-step explanation:

Just took practice

one shot answer anyone know?

Answers

Answer:

786cm

Step-by-step explanation:

this should be right... hopefully

Which of the following is a simple event?

1.Getting a spade card
2.Getting a numbered card
3.All of the choices
4.Getting an ace of diamond card

Answers

number three is the best choice

100+345x94(56x23)095x234

Answers

Answer:

928,543,543,300

hi please help i’m having trouble solving these

Answers

Step-by-step explanation:

4) 36

5) 45⁰

6) 42⁰

I hope it helped you

Prism M is a dilation of Prism N. The height of Prism M is 434 ft, and the volume of Prism M is 6825 ft³. The height of Prism N is 238 ft. What is the volume of Prism N? Enter your answer as a mixed number in simplest form by filling in the boxes

Answers

Answer:

The answer is 8 11/20. Can I have brainliest?

Step-by-step explanation:

The table shows a schedule of jorge’s payment plan for a car. jorge’s payment plan year balance monthly payment end of year balance 1 $15,469.80 $257.83 2 $257.83 3 $257.83 4 $257.83 5 $257.83 6 $257.83 how many years will it take jorge to pay off the loan? 3 years 4 years 5 years 6 years

Answers

The number of the years is 5 which is taken by Jorge to pay off the loan. Then the correct option is C.

What is division?

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The table shows a schedule of Jorge’s payment plan for a car.

Jorge’s payment plan year balance monthly payment end of year balance.

The price of the car is $15,469.80

The monthly payment will be $257.83

Then the number of the years taken by the Jorge to pay off the loan will be

[tex]\rm \rightarrow \dfrac{15469.8}{257.83} \\\\\rightarrow 60 \ months \\\\\rightarrow 5 \ years[/tex]

More about the division link is given below.

https://brainly.com/question/369266

Answer:

The correct option is C  

Step-by-step explanation:

I took the unit test just 5 min ago god bless

#Chalnge share the favor who ever sees this find a question and answer it and say what this says

God loves you all no matter what you do just ask for forgiveness

God really loves us all

Solve for x. Round to the nearest tenth, if necessary.

Answers

x = 1.3 (to the nearest tenth)

Step-by-step explanation:

Missing angle is 20 degrees

CAH

hypotenuse = x

Adjacent = 3.6

Cos(20) = x/3.6

x3. 6

3.6 x (20) = x

x = 1.31029.....

Hope this helps!

62= -8(8x+4) - 2(5-6x)

Answers

Answer: x=-2

Step-by-step explanation:


Isolate the variables + divide each side.

Riddle: The more you take the more you leave behind you. What is the answer?

Answers

Answer:

Footsteps

Step-by-step explanation:

When you take footsteps, you leave them behind as well.

i need help 9th grade math

Answers

The answer is -4. Because there is 9 total negative and 5 total positive. So that means 5 - 9 = -4

how do i solve for x : x/3 = 5?

Answers

Answer:

x/3=5

cross multiply

x=3x5

x=15

Answer:15

Step-by-step explanation:

Step 1: Multiply both sides by 3.

x over 3 = 5

(x/3)*(3)=5*3

x=15

A school has 4 steps to the front door. Each step is 7 inches tall. Design a ramp for the

school.

Answers

The multiplication shows that the total steps for the ramp will be 28 inches.

How to calculate the steps for the ramp?

From the information given, the school has 4 steps to the front door and each step is 7 inches tall.

In this case, the total steps of the ramp will be gotten by multiplying the values. This will be:

= 4 × 7 = 28 inches.

Learn more about multiplication on:

https://brainly.com/question/10873737

Select the correct answer from the choices given (13 4i) n = 0 what is n? 0 1 –13 4i –13 - 4i

Answers

The correct answer from the choices given will be -13 - 4i. The numerical part is the real number while the term containing i is the imaginary part.

What is the complex number?

A complex number is one that both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.

The given complex number as;

[tex]\rm 13 + 4 i + n =0[/tex]

By transfeering the left-hand side term to the right-hand side the sign will change. We will get the value of n as;

[tex]\rm n=-13 - 4i[/tex]

Hence the correct answer from the choices given will be -13 - 4i.

To learn more about the complex number refer to the link;

https://brainly.com/question/10251853

Answer: Its D and for the second part its B

Step-by-step explanation:

Malika models the volume of a popcorn box as a right rectangular prism and the box can hold 35 cubic inches of popcorn when it is full. Its length is 22 in and its width is 2 1/2 in. Find the height of the popcorn box in inches. Round your answer to the nearest tenth if necessary.

Answers

Answer:

To find the height of this prism, let's use the formula for the volume of a rectangular prism:

V = l · w · h

And this is what we know:

Volume = 35 cubic inches.Length = 22 inches.Width = 2 1/2 inches, simplified would be 2.5 inches.

Now we are left to find the height, so plug in what we know into the formula I mentioned earlier:-

V = l · w · h

35 = 22 · 2.5 · h

Solve for 'h'!

35 = (22 · 2.5) · h

35 = 55 · h

35 = 55h

÷55  ÷55

35/55 = h

Which simplifies to:

7/11 = h, the height is 7/11 inches.

Double check;

V = l · w · h

V = 22 · 2.5 · 7/11

V = 35, which is correct!

Answer:21.1 in ^3

Step-by-step explanation:

Josh's club at school is selling lollipops for a fundraiser. They sold the lollipops for $.50 a piece but had to pay a shipping cost of $30. The function for their lollipop sales is P(s)=.50s−30, where s is the number of lollipops sold and P represents the profit made. If they sold 150 lollipops, how much profit would they make?

Answers

Answer:

they made $45

Step-by-step explanation:

divide 150 by 2 to get $75 - 30 = $45

4 + 6j + 5j - 5j.
I understand most questions like these but these ones are a little harder for me. I’ve already tried multiple times but I can’t get it yet

Answers

Answer:

j=4/6

Step-by-step explanation:

use sadmep to simplify the equation

What is the midpoint A (10,17) and B (-2,-1)

Answers

Answer:

(4,8)

Step-by-step explanation:

=(1+2/2,1+2/2)

=(10+−2/2,17+−1/2)

=(8/2,16/2)

=(4,8)


Kristen has been earning $170 per week by babysitting. She has been
working hard to save 25% of each week's earnings. If she continues to
save the same amount each week, how long will it take her to save $212.5?

Answers

25% of $175 is $42.5

$212.5 divided by $42.5 is 5.

It will take her 5 weeks

Answer:

5 weeks

Step-by-step explanation:

First we must turn the percentage into a decimal :)

170 x 0.25 = 42.50

Now we divide :)

212.5/42.50 = 5

She will take 5 weeks :)

Have an amazing day!!

Please rate and mark brainliest!!

From the observation deck of a skyscraper, Valeria measures a 67^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 945 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.

Answers

The horizontal distance from the base of the skyscraper out to the ship would be 401.1 feet.

What are the trigonometric ratios?

Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.

In a right-angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slanted side is called the hypotenuse.

Let d the horizontal distance from the base of the skyscraper out to the ship. Since the angle of depression is 67°, hence:

Angle = 90 - 67 = 23°

Using trigonometric ratio:

tan(23) = d/ 945

d = 401.1 feet

The horizontal distance from the base of the skyscraper out to the ship would be 401.1 feet.

Find out more on trigonometric ratio at:

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