E 4) In the diagram below, the dimensions of the large rectangle are (3x-1) by (3x+7) units. The dimensions of the cut-out rectangle are x by (2x+5) units. Which choice expresses the area of the shaded region, in Square units? ​

E 4) In The Diagram Below, The Dimensions Of The Large Rectangle Are (3x-1) By (3x+7) Units. The Dimensions

Answers

Answer 1

Answer:

Option (D)

Step-by-step explanation:

Area of a rectangle = Length × width

Area of large rectangle = (3x - 1)(3x + 7) square units

                                       = (9x² + 21x - 3x - 7)

                                       = 9x² + 18x - 7

Area of small rectangle = (2x + 5)x

                                       = (2x² + 5x) square units

Area of the shaded region = Area of large rectangle - Area of small rectangle

= (9x²+ 18x - 7) - (2x² + 5x)

= (9x² - 2x²) + (18x - 5x) - 7

= (7x² + 13x - 7) square units

Therefore, Option (D) will be the correct option.

Answer 2

The expression that represents the area of the shaded region is:[tex]7x\² + 13x - 7[/tex]

The dimension of the big rectangle is given as:

Length: 3x - 1Width: 3x + 7

So, the area of the rectangle is:

[tex]Area = Length \times Width[/tex]

[tex]Area= (3x - 1) \times (3x + 7)[/tex]

Expand

[tex]Area = 9x\² + 21x - 3x - 7[/tex]

[tex]Area = 9x\² + 18x - 7[/tex]

The dimension of the small rectangle is given as:

Length: 2x + 5Width: x

So, the area of the rectangle is:

[tex]Area = Length \times Width[/tex]

[tex]Area= (2x + 5) \times x[/tex]

Expand

[tex]Area = 2x\² + 5[/tex]

The area of the shaded region is the difference between the area of the big and small rectangles.

So, we have:

[tex]Area = (9x\²+ 18x - 7) - (2x\² + 5x)[/tex]

Expand, and collect like terms

[tex]Area = 9x\²- 2x\² + 18x -5x- 7[/tex]

[tex]Area = 7x\² + 13x - 7[/tex]

Hence, the area of the shaded region is [tex]7x\² + 13x - 7[/tex]

Read more about areas at:

https://brainly.com/question/24487155


Related Questions

Zoey wants to use her iPad throughout a 6-hour flight. Upon takeoff, she uses the iPad for 2 hours and notices that the battery dropped by 25%, from 100% to 75%. How many total hours can Zoey expect from the iPad on a full battery charge?

Answers

Answer:

6 hours more

Step-by-step explanation

When Zoey started the flight the battery was 100%, then it dropped to 75% in 2 hours. So each 25% will last 2 hours and there is 75% remaining which if you divide by 3 it will give 1. And each 25% will last 6 more hours until the battery dies.

John has $200 in his bank account he made a purchase at the grocery store that was $1.50 more than he had in his bank account select the point on the number line that represents the balance of his bank account after buying groceries.​

Answers

Answer: You are right

Step-by-step explanation:

You are in charge of food shopping for a party. You need to buy snacks and soda. A bag of snacks costs $2 and a pack of soda $3.5. If your mom gives you $25 to buy groceries and you buy 8 bags of snacks, how many packs of soda can you buy?

Answers

Answer:

2 bags

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

2x8=16

25-16=9

3.5+3.5=7

Rochelle received a $15 gift card to an online music store. She downloaded 12 songs that each cost the same price. After the gift card was applied, her total was $8.88. Which equation can be used to find , the price of each song?

Answers

Answer:

15 + 18.88 ÷ 12 = p

if p were price of each song

p= 1.99

BIG POINT
Describe the significance of the unit circle to Trigonometry. Make connections to solving, graphing, identities, and other key concepts included in this course. Provide at minimum of 4 connections with an explanation of the connections.
Write in paragraph please.

Answers

Answer: (compiled from google)

One radian is the measure of the central angle of a circle such that the length of the arc is equal to the radius of the circle.

A full revolution of a circle ( 360 ∘ ) equals  2 π   r a di a n s. This means that  1  radian = 180 ∘ π .  

The formula used to convert between radians and degrees is  angle in degrees = angle in radians ⋅ 180∘ π .

The radian measure of an angle is the ratio of the length of the arc to the radius of the circle  ( θ = sr ) . In other words, if  s  is the length of an arc of a circle, and  r  is the radius of the circle, then the central angle containing that arc measures radians.

Key Terms

arc: A continuous part of the circumference of a circle.

circumference: The length of a line that bounds a circle.

radian: The standard unit used to measure angles in mathematics. The measure of a central angle of a circle that intercepts an arc equal in length to the radius of that circle.

The  x – and  y -coordinates at a point on the unit circle given by an angle  

t  are defined by the functions  x = cos t  and  y = sin t .

Although the tangent function is not indicated by the unit circle, we can apply the formula  

tan  t = sin  t  cos  t  to find the tangent of any angle identified.

Using the unit circle, we are able to apply trigonometric functions to any angle, including those greater than  90 ∘ .

The unit circle demonstrates the periodicity of trigonometric functions by showing that they result in a repeated set of values at regular intervals.

Key Terms

periodicity: The quality of a function with a repeated set of values at regular intervals.

unit circle: A circle centered at the origin with radius 1.

quadrants: The four quarters of a coordinate plane, formed by the  x – and y -axes.

If this doesn't help I appologize

PLEASE HELP ME ASAP​

Answers

Answer:

The answer is Option D

Step-by-step explanation:

Supplementary angles are angles that sum up to 180 °

Enter the ordered pair for the vertices for Rx-axis(QRST).

The graph with X-coordinate marks -4, -2, 0, 2, 4 and Y-coordinate marks -4, -2, -1, 0, 2, 4, 6. There is a polygon QRST with coordinates T at (-2, 3), Q at (1, 5), R at (3, -1) and S at (0, 0).

Answers

Given:

The vertices of a polygon QRST are T(-2, 3), Q(1, 5), R(3, -1) and S(0, 0).

To find:

The vertices for [tex]R_{x-axis}(QRST)[/tex].

Solution:

The rule [tex]R_{x-axis}(QRST)[/tex] represents refection of polygon QRST across the x-axis.

If a figure is reflected across the x-axis, then

[tex](x,y)\to (x,-y)[/tex]

Using this rule, we get

[tex]T(-2,3)\to T'(-2,-3)[/tex]

[tex]Q(1,5)\to Q'(1,-5)[/tex]

[tex]R(3,-1)\to R'(3,1)[/tex]

[tex]S(0,0)\to S'(0,0)[/tex]

Therefore, the vertices for [tex]R_{x-axis}(QRST)[/tex] are T'(-2, -3), Q'(1, -5), R'(3, 1) and S'(0, 0).

Rx-axis means that the polygon QRST is reflected across the x-axis.

The ordered pair after Rx-axis is Q'(1,5), R'(3,1), S'(0,0) and T'(2,3)

The points are given as:

[tex]\mathbf{Q = (1,5)}[/tex]

[tex]\mathbf{R = (3,-1)}[/tex]

[tex]\mathbf{S = (0,0)}[/tex]

[tex]\mathbf{T = (-2,3)}[/tex]

The rule of reflection across the x-axis is:

[tex]\mathbf{(x,y) \to (x,-y)}[/tex]

So, we have:

[tex]\mathbf{Q' = (1,-5)}[/tex]

[tex]\mathbf{R' = (3,1)}[/tex]

[tex]\mathbf{S' = (0,0)}[/tex]

[tex]\mathbf{T' = (-2,-3)}[/tex]

Hence, the ordered pair after Rx-axis is Q'(1,5), R'(3,1), S'(0,0) and T'(2,3)

Read more about reflections at:

https://brainly.com/question/938117

Which step will get you closest to the solution of this equation?
5.2 – 2)=7
(Imagine math)

Answers

Answer:

I'm pretty sure it's the to right one

Step-by-step explanation:

5x-10=7 because you have to distribute the left side

Example of a balance point

Answers

a home's loss of heat is equal to heat created in the home or when both sides of a seesaw are at an equal level.

What is the coefficient of 4x^2 ?

Answers

It has a coefficient of 4 :)

If the Washington Monument is 3025 square feet and an average gallon of paint covers 400 square feet, how much paint would it take to cover it all up? PLEASE HELP WILL GIVE BRAINLIEST. I’m also wondering how I would go about solving this? I have a lot more.

Answers

Divide total area by area of a gallon of paint:

3025 / 400 = 7.56

Because there is a decimal answer you need to round up tot he next whole number.

You would need 8 gallons of paint.

Help me please pleasessssss

Answers

0.2 because 0.02 times 10 makes it 0.2

Bus X travels 224 miles in 4 hours. Write the equation of the line that describes the relationship between distance y and time x.

Answers

Answer:

The answer is 56

Step-by-step explanation:

The equation is Y=56x+4 I think

The equation of the line that describes the relationship between distance y and time x from the given graph is y=56x.

Given that, bus X travels 224 miles in 4 hours.

What is slope of a line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The coordinate points of a line from the given graph are (4, 224) and (1, 56).

Here, slope (m) = (56-224)/(1-4)

= -168/(-3)

= 168/3

= 56

Put m=56 and (x, y)=(4, 224) in y=mx+c, we get

224=56(4)+c

⇒ c=0

Substitute m=56 and c=0 in y=mx+c, we get

y=56x+0

⇒ y=56x

Therefore, the equation of the line that describes the relationship between distance y and time x from the given graph is y=56x.

To learn more about the slope of a line visit:

https://brainly.com/question/14511992.

#SPJ2

Find the volume of the sphere. Sorry the pic isn’t the best! I tried lol!

Answers

Answer:

4,186.6 repeated (just round to .7 if it asks for it)

Step-by-step explanation:

The volume of a sphere is 4/3 pi r^3

plug in the radius and simplify that expression

If f(x) = 4x^5 + 5x^3 +3, then what is the remainder when f(x) is divided by
X+2?

Answers

Answer: x2 + 4x + 9 on top, with a remainder of r(x) = 30

Step-by-step explanation:

The remainder of the division of the given polynomial by (x +2) is; -165.

What is the remainder of the division of the Polynomial by (x -2)?

It follows from the task content that the remainder of the polynomial division is required.

On this note, the remainder of the division is the f(x) at x= -2.

f(-2) = 4(-2)⁵ + 5(-2)³ +3 = 4(-32) + 5(-8) + 3

f(-2) = -165.

Read more on remainder from polynomial division;

https://brainly.com/question/24662212

Use the variable, n, to write an expression for seven less than a number.

Answers

Answer:

n-7 would be the equation

Answer:

n - 7

Step-by-step explanation:

n - 7

4n + 1= 25 how do I solve this and show my work?​

Answers

Answer:

n=6

Step-by-step explanation:

4n + 1= 25

Move constant to the right

4n=25-1

Calculate

4n=25-1

Then divide on both sides

Answer:

Today: Friday, 06 November 2020

Hour: 09.44 WIB (Indonesia)

_______________________________

4n + 1 = 25

4n = 25 - 1

4n = 24

n = 24/4

n = 6

I need a girl and yes I understand I’m on the wrong website please don’t report smh

Answers

Answer:

lol, what for?

Step-by-step explanation:

Answer:

So the answer would be B.

Step-by-step explanation:

This is not the right site like you said also no one knows your age or what you look like so good luck buddy.

James determined that these two expressions were equivalent expressions using the values of x - 4 and x - .6
Which statements are true? Check all that apply.
7x+4 and 3x+5+4x-1
When x = 2, both expressions have a value of 18.
The expressions are only equivalent for x = 4 and x = 6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When x = 0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if x = 8.

Answers

Answer:2 4 and 5

Step-by-step explanation:

PLEASE IM BEGGING YOU please answer i’ll do anything i need in 10 minutes please

Answers

Answer:

1.                           2.

   -3, 4                      -3,  2

   -1,  2                       0,  1

   0, 1                         3,  0

   4, -3                      6,  -1

Step-by-step explanation:

kala is saving money to buy a bike that cost $125. She has $60 and will save an additional $5 each week. In how many weeks will she have enough money to buy the bike?

Answers

In exponential form it’s: 125=60(1.05)^x
So it should be around 15.043 weeks
If you have to round up to then next week then the answer is 16 weeks she will have enough money to buy the bike. I’m

The rabbit population in a forest area grows at the rate of 9% monthly. If there are 242 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected next September. Use
y
=
242
(
2.7
)
0.09
t
y
=
242
(
2.7
)
0.09
t

Answers

Answer:

503 should be the answer

Step-by-step explanation:

Answer:

i think its 503

Step-by-step explanation:

242 multiplied by 0.09 = 21.78

21.78 multiplied by 12 = 261.36

added by 242 = 503.36

Solve one fourth plus ten sixteenths

Answers

Answer:

The answer is 0.875

Answer:

13

Step-by-step explanation:

How do you write 3.684 × 103 in standard form?

Answers

The answer is 379.452

ill give brainliest please help.

Answers

Answer:

A = 5

Step-by-step explanation:

hhhhhhhhhhhhhhhhhelp hhhhhhhhhhhhhhhhhelp hhhhhhhhhhhhhhhhhelp hhhhhhhhhhhhhhhhhelp hhhhhhhhhhhhhhhhhelp

Answers

Answer:

B is the answer

Step-by-step explanation:

hey luv the answer is (d.) :)

Find the value of x. Then find the measure of each labeled angle.

Answers

Answer:

1. 70

2. 30

Step-by-step explanation:

ok, so we first know that x+(x-40)+90+90=360, so if we simplfy, we will get x+x+40=180, and 2x=140, so x is 70. 70-40 is 30.

solve for x and y
x +2y= -6
-5x+4y=2

Answers

Answer:

y=1/2+5x/4

x=−6−2y

Step-by-step explanation:

i hope this helped :)

The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 240 bacteria, and the population after 12 hours is double the population after 1 hour. How many bacteria will there be after 3 hours

Answers

Answer:

240

Step-by-step explanation:

According to law of exponential growth,

[tex]y=y_0e^{kt}[/tex]

Here, [tex]y_0[/tex] denotes the initial amount and k is the rate constant of the equation.

Now, the initial population is 240 bacteria.

Put [tex]y_0=240[/tex]

So,

[tex]y=240e^{kt}[/tex]

The population after 12 hours is double the population after 1 hour.

[tex]y(12)=2y(1)[/tex]

[tex]240e^{12k}=240e^{k} \\e^{12k}=e^{k} \\e^{12k-k}=1\\e^{11k}=1\\11k=log 1=0\\k=0[/tex]

(Formulae used: [tex]\frac{e^x}{e^y}=e^{x-y}\,,\,log 1=0[/tex])

So,

[tex]y=240e^{0}=240\\y=240[/tex]

Therefore,

Number of bacteria after 3 hours = 240

What's the range in the question below. Please answer one of the answer choices.

Answers

Answer:

yo I'm doing the same thing

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