Given:
The length of a rectangle is 3 inches less than three times its width.
The perimeter of the rectangle is 34 inches.
To find:
The dimensions of the rectangle.
Solution:
Let x be the width of the rectangle. Then, the length of a rectangle is 3 inches less than three times its width.
Length of the rectangle = 3x-3
Now, perimeter of the rectangle is
[tex]Perimeter=2(Length + Width)[/tex]
[tex]Perimeter=2(3x-3+x)[/tex]
The perimeter of the rectangle is 34 inches.
[tex]34=2(4x-3)[/tex]
[tex]34=8x-6[/tex]
[tex]34+6=8x[/tex]
[tex]40=8x[/tex]
Divide both sides by 8.
[tex]\dfrac{40}{8}=x[/tex]
[tex]5=x[/tex]
The value of x is 5. So, width of the rectangle is 5 inches.
[tex]Length=3x-3[/tex]
[tex]Length=3(5)-3[/tex]
[tex]Length=15-3[/tex]
[tex]Length=12[/tex]
Therefore, the length of the rectangle is 12 inches and the width of the rectangle is 5 inches.
PLEASE HELP Review the equation, then complete the following. f(x)=1/x-4, g(x)=4x+1/x Use composition to prove whether or not the functions are inverses of each other. Express the domain of the compositions using interval notation.
Answer:A. Yes, they are inverse of each other.
B. Domain and range of the compositions is .
Step-by-step explanation:
A. We have, and .
Now, 'when two functions f and g are inverses of each other, they satisfy the property '.
So, we have,
Thus, we get for the given function f and g, .
Hence, they are inverse of each other.
B. Now, as we have,
That is, the composition of the functions is equal to the identity function.
Thus, the domain and range are the set of all real numbers respectively.
So, in the interval notation, we have,
Domain and range of the compositions is .
helpp with explanation:
a 25 foot telephone pole is to be secured with cable that will extend from the top of the pole to a stake in the ground 20 feet from the base of the pole. if y represents the length of the cable what is the approximate value of y?
Answer: 5
Step-by-step explanation:
Linear Equations Digital Escape! Can you find the slope-intercept equation of each line and type the correct code?
Answer: I can if there’s a picture...
Step-by-step explanation:
Answer: cgia
Step-by-step explanation:
how to solve 9x^2+9x+2
Answer:
factoring: ( 3 x + 1 ) ( 3 x+ 2 )
expressing/equation: 9x²= 81x
81x + 9x + 2=
9x+81x=90x
90x + 2
Step-by-step explanation:
Here is a story: Lin bought 4 bags of apples. Each bag had the same number of apples. After eating 1 apple from each bag, she had 28 apples left.
Answer:
she started with 32 apples and ended with 28
there were 8 apples in each bag but after she ate one from each bag, there are only 7 apples in each bag
Step-by-step explanation:
The estimate obtained from a sample of which size is likely to be closest to the actual parameter value of a population?
Answer:
184
Step-by-step explanation:
Answer: 184
Step-by-step explanation:
A P E X
please help me thank you
Answer:
7<x<14
Step-by-step explanation:
Answer:
heh heh that's a hard one
What number minus one-half is equals to negative one-half
Answer:
0
Step-by-step explanation:
please help!! Graph the line that has a slope of 3 and contains the point (3,0)
Answer:
Step-by-step explanation:
I'm so confused, cans omeone help it's a TEST!!
Answer:
Step-by-step explanation:
sin R = opp/hyp = 11/61 = .18
sinR =.18
the angle R = sin^-1 (11/61) = 10.39°
∠R = 10.39°
plzz help Solve the following equation using factoring and the Zero Product Property. Select the answer which is the sum of all solutions to this equation, rounded to the nearest tenth.
24x2 + 16x + 2 = 0
Find the mean and range of: 1.5, 0.5, 2, 3, 2.5
Answer:
mean 2 range2.5
Step-by-step explanation:
Solve for x (X-9)(x+5)=8(21)
what is 500/465 please
Answer:
1.075
in fraction form 100/93 but they are both equivalent
Step-by-step explanation:
Answer:
100/93
Step-by-step explanation:
decimal form- 1.075
mixed number- 1
7/93
The cylinder shown here has a height of 7 centimeters and a radius of 4 centimeters.
Part A. What is the area of the base of the cylinder? Express your answer in terms of π. options are: 15 pi cm, 14 pi cm, 16 pi cm, 17 pi cm.
Part B: How many cubic centimeters of fluid can fill this cylinder? Express your answer in terms of π. options are: 112 pi cm, 110 pi cm, 113 pi cm, 107 pi cm.
Part C: Give a decimal approximation of your answer to the second question using 3.14 to approximate π. options are: 351.68 cm, 368.15 cm, 386.51 cm, 315.68 cm.
Answer:
A: 16[tex]\pi[/tex][tex]cm^{2}[/tex]
B: 112[tex]\pi[/tex][tex]cm^{3}[/tex]
C: 351.68[tex]cm^{2}[/tex]
Step-by-step explanation:
The cubic inches that can fill the cylinder is [tex]112\pi[/tex] and the decimal approximation 351.68 cm^3
The given parameters are:
Radius (r) = 4 cm
Height (h) = 7 cm
The area of the baseThe area of the base is:
[tex]A = \pi r^2[/tex]
So, we have:
[tex]A = \pi *4^2[/tex]
[tex]A = 16\pi[/tex]
Hence, the area of the base is [tex]16\pi[/tex]
The cubic inches that can fill the cylinderThis is the volume of the cylinder.
So, we have:
[tex]V = \pi r^2h[/tex]
Substitute known values
[tex]V = \pi * 4^2 * 7[/tex]
[tex]V = 112\pi[/tex]
Hence, the cubic inches that can fill the cylinder is [tex]112\pi[/tex]
The decimal approximationWe have:
[tex]V = 112\pi[/tex]
Expand
[tex]V = 112 * 3.14[/tex]
Evaluate the product
[tex]V = 351.68[/tex]
Hence, the cubic inches that can fill the cylinder is 351.68 cm^3
Read more about volume at:
https://brainly.com/question/10171109
-4M = 48 What would you do to each side of the equation?
Pls responddd
Answer:
divide by - 4
Step-by-step explanation:
Given
- 4M = 48 ( isolate M by dividing both sides by - 4 )
M = - 12
PLEASE HELP!!!!!!!!!!!!!!!!ASAP!!!!!!!!!!NOW!!!!!!!!!!RIGHT AWAY!!!!!!!!
Answer:
(a)it is
Step-by-step explanation:
this is because ABC and SDC are both right angle triangles
(3) GEOMETRY IMAGE BELOW. 20 POINTS!!
Answer:
option D
Step-by-step explanation:
option D is the correct answer of this question.
the length of the mid segment was 42 option A
( previous question ) according to me and it is right so please recheck your previous answer as it was option A not D
hope this will be helpful to you.
and mark my answer as brainlist plzzzz.
Five chicken nuggets have 135 calories. How many calories are in 9 chicken nuggets
Answer:
243 calories
Step-by-step explanation:
The number of fish in a lake decreased by 25% between last year and this year. Last year there were 60 fish in
the lake. What is the population this year? If you get stuck, consider drawing a diagram.
There are
fish in the pond.
HELLPPP
Answer:
theres
4
Step-by-step explanation:
Tia earns $19.25 per hour she worked 36 hours.what is her straight time pay
Tia earns $693 in 36 hours
Simplify the following fraction:
18/66
Plz help
Answer:
[tex]\frac{3}{11}[/tex]
Step-by-step explanation:
What is the GCF of both numbers:
the GCF is 6.
6 goes into 18, 3 times
6 goes into 66, 11 times
so the simplified version is 3/11
Factorize 27x3 - 16y3
Answer:
27x3-16y3=
3x-4y
Step-by-step explanation:
I don't understand your question fully
I hope I helped you
Jonah deposited $80 in a savings account earning 5% interest, compounded annually. To the nearest cent, how much interest will he earn in 3 years?
find the volume of a rectangular block of ice 2 feet by 3 and 1/2 feet by 1 and 1/2 feet the volume of the rectangular block of ice is what simplify your answer please
Answer:
V = 10 1/2 ft³
Step-by-step explanation:
V = length • width • height
V = 2 • 3 1/2 • 1 1/2
V = 10 1/2 ft³
any help would be cool
Answer:
379.94
Step-by-step explanation:
Answer:
D. 69.08 meters
Step-by-step explanation:
The formula for solving circumference is 2 times pi times r(radius). Multiply 2 x 3.14 x 11 (the radius). You get 69.08 meters.
Hope it helps!
Please help me this is math 10, you need to find area of the shaded region in factored form.
Answer:
Express the fraction in its simplest form.

What is the missing number?
3x - 4.5 = -19.5
solve for x
Answer:
Step-by-step explanation:
3x=-15
x=-5
Answer:
-5
Step-by-step explanation:
Elise sold 110 total tickets for the football game. Adult tickets cost $2.50 and student tickets
cost $1.10. If she collected $212, how many of each kind of ticket did she sell? Define your
variables, write two equations and solve the system, showing all of your thinking
A=
S =
Answer:
A + S = 110
2.5A + 1.1 S = 212
S = 110-A
Put value of x in equation 2
A = 65......... S = 147
Step-by-step explanation:
what is .2735 rounded to the tenth, hundredths and thousandth place?
Answer:
Tenth: .2
Hundredths: .27
Thousandth: .273
Answer:
i fald
Step-by-step explanation:
