Please help worth 25 points

A rectangle has a base that is three feet longer than its height. The area of the rectangle is 54 square feet. What are the dimensions of the rectangle?

Answers

Answer 1

Answer:

h=6 feet

Step-by-step explanation:

Given: 1. The base of a rectangle is three feet longer than its height.

2.Are of the rectangle=54 square meters

Let us say the rectangle has height h and base(breadth) b.

Since, the base of the rectangle is three feet longer than the height, we have b=h+3.

Also, Area of the Rectangle= hb

therefore, 54=h(h+3)

54= h2+ 3h

h2+3h-54=0 (Subtract 54 from both the sides)

To find the value of h we have to solve the quadratic equation.

[We have the equation in the form ax2+bx+c=0, to factorise the equation-

Step1. Find two numbers such that their multiplication is equal to ac and their addition is equal to b.

Step2. Replace b with these numbers.

Step3. Simplify the equation]

So, h2+3h-54=0

h2+9h-6h-54=0

h(h+9)-6(h+9)=0

(h+9)(h-6)=0

Which gives-

h= -9 or h= 6

As h is the height of the rectangle, h can not be -9.

so h=6 feet

and b=h+3=9 feet

So the dimensions of the rectangle are 6 feet for the height and 9 feet for the base.


Related Questions

Question 6
Which expression is equivalent to the expression shown?
2
7147²
712
17
716
77

Answers

Answer:

7^12

Step-by-step explanation:

if you are dividing the base numbers then you are subtracting the exponents

HELPPP please!!! need answer fast, very confused

Answers

Answer:

I think D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Its d

State the Postulate or Theorem

Answers

Answer:

7. Corresponding Angles Theorem

8. Alternate Interior Angles Theorem

9. Alternate Exterior Angles Theorem

10. Supplementary Angles Theorem

Step-by-step explanation:

The ratio of squirrels to pigeons in the park is 15 to 125. Which statement describes this relationship?

Answers

Answer: A. There are 3 squirrels for every 25 pigeons in the park

Step-by-step explanation:

The options include:

A) There are 3 squirrels for every 25 pigeons in the park.

B) There are 3 squirrels for every 5 pigeons in the park.

C) There are 5 squirrels for every 3 pigeons in the park.

D) There are 25 squirrels for every 3 pigeons in the park.

Since the ratio of squirrels to pigeons in the park is 15 to 125. The common factor we have here is 5. We can then divide the figures given by 5. This will be:

= 15/125 = (15/5)/(125/5) = 3/25

This mean that for every 3 squirrels, there are 25 pigeons in the park.

Therefore, the correct answer is A.

Use substitution to solve the following system of equations.
x + 4y = 8
2x - 5y = 29
I

Answers

Answer:

(12, - 1 )

Step-by-step explanation:

Given the 2 equations

x + 4y = 8 → (1)

2x - 5y = 29 → (2)

Rearrange (1), expressing x in terms of y by subtracting 4y from both sides

x = 8 - 4y → (3)

Substitute x = 8 - 4y into (2)

2(8 - 4y) - 5y = 29 ← distribute and simplify left side

16 - 8y - 5y = 29

16 - 13y = 29 ( subtract 16 from both sides )

- 13y = 13 ( divide both sides by - 13 )

y = - 1

Substitute y = - 1 into (3) for corresponding value of x

x = 8 - 4(- 1) = 8 + 4 = 12

solution is (12, - 1 )

[tex]x = 8 - 4y \: \: eqn \: 1[/tex]

now in eqn 2

[tex]2(8 - 4y) - 5y = 29[/tex]

[tex]16 - 8y - 5y = 29[/tex]

[tex]16 - 13y = 29[/tex]

[tex]16 - 29 = 13y[/tex]

[tex]13 = 13y[/tex]

[tex] \frac{13}{13} = y[/tex]

[tex]y = 1[/tex]

Now in eqn 1

[tex]x = 8 - 4y[/tex]

[tex]x = 8 - 4 \times 1[/tex]

[tex]x = 8 - 4[/tex]

[tex]x = 4[/tex]

therefore x=4 & y=1 answer

PLEASE HELP DUE AT MIDNIGHT

Answers

Answer:

268.1

Step-by-step explanation:

Area of Sphere =

[tex] \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi {4}^{3} \\ = 268.1 {units}^{3} (nearest \: tenth)[/tex]

Find the area and circumference of the circle from the problem to the left. h 14 in Area= Circumferencer​

Answers

Answer:

r is 14÷2=7in

r is 7

area of circle is pie R square

22÷7×7×7

154 in

since area = circumference

154=154

hope it helps

12
11
10
9
8
4
3
-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8 9 10 11 12
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12

Answers

Answer:

You didn't say what the question was

Answer: 3

Step-by-step explanation:

Reparte 280 euros entre 3 personas, de forma que la 1º reciba el triple que la 2º y esta el doble de la3º

Answers

Answer:

x = 31.11

Step-by-step explanation:

Let us assume the third person receives be  x

Now the second person receives be 2x

And, the second  be 3(2x) = 6x

The total is 280

Now the equation is

x + 2x + 6x = 280

9x = 280

x = 31.11

Find the value of x in the isosceles triangle shown below.
V74
V74

Answers

Answer:

C. x = 10

Step-by-step explanation:

By Pythagoras Theorem:

[tex] \bigg( \frac{x}{2} \bigg)^{2} = {( \sqrt{74} )}^{2} - {7}^{2} \\ \\ \frac{ {x}^{2} }{4} = 74 - 49 \\ \\ \frac{ {x}^{2} }{4} = 25 \\ \\ {x}^{2} = 25 \times 4 \\ \\ {x}^{2} = 100 \\ \\ x = \sqrt{100} \\ \\ x = 10[/tex]

Answer:

C. x = 10

Step-by-step explanation:

Use Pythagorean theorem.

(x/2)² = (√74)² - 7²(x/2)² = 25x/2 = √25x/2 = 5x = 10

Correct choice is C

Can someone help please!

Answers

Answer:

Step-by-step explanation:

extend the line on the 5ft side to create a triangle and a rectangle.

Area of a rectangle is l x b

10 x 4 = 40ft^2

Area of a triangle is 1/2 base x height

the height of the triangle will be 10 - 5 = 5ft

the base of the triangle will be 12 - 4 = 8

1/2 (8) x (5)

20ft^2

Total area = area of triangle + area of rectangle

Total area  = 20ft^2 + 40ft^2

Total area = 60 ft^2

Answer this Quickly Please 50 points !!!!!!!!!!!!!!!
A seagull is flying in the sky 10 meters above sea level. Directly below the
seagull, a dolphin is jumping 2.5 meters above sea level. Directly below these
animals, is an octopus, swimming 10 feet below sea level. Select all the true
statements. *
10
k
S
vertical position (meters)
-5
-10
The difference in height between the seagull and the dolphin is -7.5 feet.
The difference in height between the seagull and the dolphin is 7.5 feet.
The difference in height between the dolphin and the octopus is -12.5 feet.
The difference in height between the dolphin and the octopus is 12.5 feet.

Answers

Nsnananqnqnqnnqnqnqnqnkkkk

Samuel needs 233 feet of wood to build a fence.The wood comes in lengths of 11 feet. How many prices will samuel need to buy?

Answers

Answer:

21 pieces

Step-by-step explanation:

Given that,

Length of wood needed = 233 feet

The wood comes in lengths of 11 feet.

We need to find the number of pieces samuel need to buy. It can be done as follows :

Let he needed x peices. So

[tex]x=\dfrac{233}{11}\\\\x=21.18\\\\or\\\\x=21[/tex]

So, he will need approx 21 peices.

(10pts) find all the solutions to the equations.

Answers

all of your solution is right
I think they are all correct

Round your answer to the nearest hundredth if necessary. A figure is shown. 8X 44.49 What is the measure, in degrees, of the shaded angle?​

Answers

You can download answer here

tinyurl.com/wpazsebu

PLEASE HELP...!!!!!!!!!!

Answers

Answer:

5 and 10

Step-by-step explanation:  

You have all the information you need to find the area of the circle and then subtracting that from 77 you'll have the area of the rectangle and will be able to figure out the length and height by looking at the answer options.

So the area of a triangle is 1/2(b x h) or (b x h)/2 so the base is 6 and the height is 9 so the area is 54/2 which equals 27. 77 - 27 = 50 so the area of the rectangle is 50. With the answer options provided I can see that the height of the rectangle is 5 and the length is 10.

What is the volume of this composite solid?
4 m
6 m
10 m
6 m
O A. 372 cubic meters
B. 144 cubic meters
Ο Ο Ο Ο
O C. 600 cubic meters
D. 480 cubic meters

Answers

D. 480 cubic meters. Using the volume formula LxWxH we can find the volume of the rectangular prism on the bottom. Using the triangle area formula, we know the face of the triangle has an area of 12. Multiply this twelve by 10 and you get 120. 120+360 = 480

Answer:

its D. 480 cubic meters for Ape.x

Step-by-step explanation:

Will give Brainliest, A car wash has a weekly ad in the local newspaper that is 2 inches wide and 4 inches high and costs $36.75 per week. The cost of each ad is based on its area. If the owner of the car wash decides to double the width and height of the ad, how much will the new ad cost?

Answers

Answer:

4+2+$36.75= $42.75

Step-by-step explanation:

4+2+36.75

6+36.75

42.75

Alternative Form

171/4,42 3/4

Answer:

4+2+$36.75=$42.75.

Step-by-step explanation:

6+36.75=42.75

Jenna's only source of income is from her job at a car wash, where she works 25 hours each week. She is paid $9.90 per hour. What is her net weekly income if she pays $30.70 in payroll tax each week?

Answers

Answer: 216.8$

Step-by-step explanation:

25 x 9.9 = 247.5

247.5 - 30.70 = 216.8

Help me with this!!!

Answers

Answer:

15

Step-by-step explanation:

Answer:

TW= 15

Step-by-step explanation:

If UV ≈ VW it means the two triangles shown are congruent (or equal).

So if they are equal it means TU will equal TW.

TU = 15 = TW

A child has a box of colored building blocks. He will choose one block without looking. The odds against choosing a blue block are 13/4. What is the probability of choosing a blue block?

Answers

Answer:

The answer is "0.2352".

Step-by-step explanation:

Given:

The chance of selecting a odds blue block [tex]= \frac{13}{4}[/tex]

[tex]=\frac{\text{Amount of unfavourable blue block evets} \ (13)}{\text{Amount of unfavourable blue block evets} \ (4)}[/tex]

total number of events are 13+4= 17

Calculating the probability of choosing the blue block  

[tex]=\frac{\text{Amount of unfavourable blue block evets} }{\text{Amount of unfavourable blue block evets} } \\\\ = \frac{4}{17} \\\\ =0.2352[/tex]

5/x+4=9/x-8. Solve for x.

Answers

Answer: x = 1/3

Step-by-step explanation:

5/x - 9/x = -8 - 4

-4/x = -12

x = -4/-12

x = 1/3

Answer:

-19

Step-by-step explanation:

symbolab- a website that you enter an equation in and it solves it for you it's free and no videos or anything :)

These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?

Answers

Answer:

2/10 * 2/10 = 1/25

Step-by-step explanation:

Suppose you have 10 marbles in a bag. 5 black , 2 pink and 3 blue

As if two pink marbles are selected then for one pink marble probability = event occurred / total outcome = 2/10

Similar probability for an other pink marbles Probability for the drawing two pink marbles is P = 2/10 * 2/10  = 1/25

Which of these is a unit of density?
Please help.

Answers

Answer:

I think is C.

Step-by-step explanation:

Hope it's help you ❤️❤️❤️❤️❤️❤️❤️

C

SI unit of density
= kilogram per cubic meter

x: y = 8:1
Which is the correct equation?
A. y=8x
B. x=8y
C. y=7x

Answers

B) x*1=y*8 -> x=8y that’s the right answer

Answer:

B. x=8y

Step-by-step explanation:

X*1=y*8

X=8y

I hope so that i help you

Someone please please..help me I don’t want to fail this..

Answers

Step-by-step explanation:

hope it helps you........

Alyssa is going to invest in an account paying an interest rate of 4.3% compounded daily. How much would Alyssa need to invest, to the nearest dollar, for the value of the account to reach $330 in 17 years?

Answers

Answer:

159

Step-by-step explanation:

158.877856673=P

round:

P=159

Answer:

159  

Step-by-step explanation:

Calculate the unknown sides and angles of the triangle ABC given.
Given the final answer correct to three significant figures.
C= 25.7° , b= 3.5cm, a = 6cm​

Answers

Answer:See below

Step-by-step explanation:

to understand thisyou need to know about:law of sinelaw of cosinePEMDASlet's solve:

there are 3 ways to solve SAS triangle

use The Law of Cosines to calculate the unknown side,then use The Law of Sines to find the smaller of the other two anglesand then use the three angles add to 180° to find the last angle.

first figure out [tex]\angle C [/tex]

to do so we will use the formula of law of cosine of C angle

[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2ab.\cos(C) [/tex]

substitute the given values of a,b and [tex]\angle C[/tex]

[tex] \sf{c}^{2} = {6 }^{2} + {3.5}^{2} - 2.6.(3.5). \cos( {25.7}^{ \circ} ) [/tex]

simplify squares:

[tex]c^{2}=36+12.25-42.\cos(25.7^{\circ})[/tex]

simplify addition:

[tex]c^{2}=48.25-42.\cos(25.7^{\circ})[/tex]

square root both sides

[tex] \sf \: \sqrt{ {c}^{2} } = \sqrt{ 48.25-42. \cos(25.7^{\circ})}[/tex]

simplify:

therefore

[tex]\bold{c=3.23}[/tex]

use law of sine to figure out angle A

[tex] \dfrac{6}{\sin( \angle \: A) } = \dfrac{3.23}{\sin(25.7)} [/tex]

therefore

[tex]\bold{\angle A=53.66°}[/tex](use calculater to simplify it)

therefore

[tex]\angle B\: is\: 180^{o}-25.70^{o}-53.66^{o}[/tex]

[tex]\bold{= 100.64}[/tex]

Choose the system of equations to solve the following: Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Determine the total number of adult and student tickets. *

A: 7.25a + 5.50s = 8 and a + s = 52.75
B: 7.25a + 5.50s = 52.75 and a + s = 52.75
C: 7.25a + 5.50s = 52.75 and a + s = 8

Answers

UMMMMMMMMMMMMMMM I don't know

Find two integers whose sum is -20 and product is 99

Answers

Answer:

Step-by-step explanation:

let the integers be x and y

x+y=-20

y=-20-x

xy=99

x(-20-x)=99

-20x-x²=99

x²+20x+99=0

x²+11x+9x+99=0

x(x+11)+9(x+11)=0

(x+11)(x+9)=0

x=-11,-9

when x=-11

-11+y=-20

y=-20=11=-9

when x=-9

-9+y=-20

y=-20+9=-11

so integers  are -11,-9

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