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

2688 divided by 96 with remainder

Answers

Answer: OK, the answer is 28.

Step-by-step explanation: Also there is no remainder for this division problem, you could have the remainder if the numbers are not the same as a multiplication problem, so did you get it?

The GCF of 15 and 27

Answers

answer : 3
the greatest common factor of 15 and 27 is 3

Can someone help? I don't really understand this question...

Answers

7 1/2 - 5 5/8 but you need to find a common denominator, so
7 1/2 x 4 = 7 4/8
7 4/8 - 5 5/8 = 1 7/8

Which angles are adjacent angles to 3? Select all that apply

Answers

Two Answers: Angle 1, Angle 4

Adjacent angles share a common segment, line, or ray. Think of two adjacent rooms sharing a common wall.

9x+6+4x-2x+1-15
What is the answer?

Answers

Answer: 3x - 8

Hope it helps!

Answer:

9 + 6 + 4 − 2 + 1 − 1 5

9x+{\color{#c92786}{6}}+4x-2x+{\color{#c92786}{1}}{\color{#c92786}{-15}}

9x+6+4x−2x+1−15

9 − 8 + 4 − 2

Step-by-step explanation:

how do you find the distance between two negative fractions

Answers

Answer:

Use the number line and split the whole numbers into fractions

Step-by-step explanation:

Example: If a number line goes from -10 all the way to +10, and you are trying to find the distance between -2 1/4 and -7 3/4. You would split the number line into fourths and then locate -7 3/4. You would then count up to -2 1/4 to get 4 3/4.

Hopefully this makes sense!

What do you call a female bug that floats?

Answers

Answer:

A buoyant girl ant

Step-by-step explanation:

A um gashsvwhqjqkqjqbwbqbqhwuwbw

Are they equal or diffrent angles

Answers

equal because the parallel lines :)

Students will be going to the zoo in a field trip entrance fee is $6.00 and you will be able to purchase drinks or food items for $2.00 each write an equation indicating the total cost of going to the zoo

Answers

Answer:

c = 6+2x

Step-by-step explanation:

c = total cost, 6 = entrance fee, 2x = 2 dollars per food/drink item

The cost of an item is $0.30 per ounce. If total cost of the item is $3.60, how many ounces are in the item?

Answers

Answer:

Example 1: - If the item's label displays the weight as 3 lb 2 oz, type the shop name and item's brand, enter 3 in the pounds field, leave the 00 (decimal) value unchanged, enter 2 in the ounces field, leave the 00 (decimal) value unchanged, fill out the Price field and Calculate to get the price per ounce

Answer:

12 ounces

Step-by-step explanation:

3.60 = .3x

divide by .3 on both sides

12 = x

Which phrase describes how to divide a complex number z by r(cos θ + i sin θ)?

Scale by a factor of StartFraction 1 Over r EndFraction and rotate clockwise by θ.
Scale by a factor of r and rotate clockwise by θ.
Scale by a factor of StartFraction 1 Over r EndFraction and rotate counterclockwise by θ.
Scale by a factor of r and rotate counterclockwise by θ.

Answers

Answer:

its a

Step-by-step explanation:

The phrase is Scale by a factor of 1 /r and rotate clockwise by θ.

What is complex number?

Complex numbers are numbers that consist of two parts — a real number and an imaginary number.

Given:

z=r(cos θ + i sin θ)

So, to divide a complex number the best phrase to describe is Scale by a factor of 1 /r and rotate clockwise by θ.

Learn more about complex number here:

https://brainly.com/question/28007020

#SPJ2

Find the slope using the formula.
(-2,-9) and (-6,-6)

Answers

Answer:(3,-4) you just have to follow the equation.

Slope = change in y over change in x.

Slope = (-6 - -9) / (-6 - -2)

Slope = (-6 + 9) / (-6 + 2)

Slope = 3/-4

Slope = -3/4

What are all of the possible classifications for a 3 × 3 system? Check all of the boxes that apply.

consistent and dependent

consistent and independent

inconsistent and dependent

inconsistent and independent

Answers

Answer:

consistent and dependent

consistent and independent

inconsistent and independent

Step-by-step explanation:

Answer:

1

2

4

Step-by-step explanation:

has nice day

Evaluate the function for x = 2,3,4
F(x) =2x-7-3

Answers

Answer:

below in bold

Step-by-step explanation:

f(x) = 2x - 7 - 3

~Combine like terms

f(x) = 2x - 10

When x = 2...

f(x) = 2(2) - 10

f(x) = 4 - 10

f(x) = -6

When x = 3...

f(x) = 2(3) - 10

f(x) = 6 - 10

f(x) = -4

When x = 4...

f(x) = 2(4) - 10

f(x) = 8 - 10

f(x) = -2

Best of Luck!

What is the place value of 3 of 652.4397. N Place Value: Select an answer Select an answer Get help: Vi tenths Points possible hundredths This is attemp Post this questhousandths ten thousandths Submit . hundred thousandths​

Answers

Answer:

100 thousandths

Step-by-step explanation:

Peter collected 171 marbles but lost 3/4 of them on his way home through of hole in his bag when he arrived at home now many marbles did Peter have left?​

Answers

The answers is 43 since 171 divided by 4 is 42.75. So then multiply that by 3. and subtract that from 171. and u get ur answer which is 43

The number of marbles Peter had when he arrived home was 43 marbles

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

The number of marbles Peter had on his way home = 171

The amount of marbles he lost on his way home = ( 3/4 ) th

Now , the amount of marbles Peter have left = 1 - amount of marbles he lost on his way home

The amount of marbles Peter have left = 1 - 3/4

                                                                = ( 1 / 4) th

So , The number of marbles Peter had left when he arrived home is =

Amount of marbles Peter have left x Number of marbles Peter had

The number of marbles Peter had left when he arrived home is = (1/4) x 171

= 171 / 4

= 42.75

≈ 43 marbles

Hence , the number of marbles Peter had left when he reached home is 43

To learn more about percentage click :

https://brainly.com/question/12861068

#SPJ2

Check the picturee need helppp

Answers

You didn’t post a picture??

Evaluate the expression 8-3×2+5

Answers

Answer:

7

Step-by-step explanation:

First do 3x2 to get 6, and then do 8-6, which is 2, and add that to 5 to get 7


If 6 x 7 = 26 +0, find the number that belongs in the box.
211

Answers

Answer: 185 sorry if wrong

You can tell if the value of a function for a certain interval is positive just by 2 points looking at its graph. If the value is positive that part of the graph will:

a: be to the right of the y-axis
b: be above the x-axis
c: intersect the x-axis
d: be below the x-axis

Answers

it is b. above the x axis


5. Cherries are on sale for $16 for 4 pounds. Jordyn pays $28.00 for
cherries to make a cobbler. How many pounds of cherries does she buy? *

Answers

Answer:

7 pounds

Step-by-step explanation:

1 pound is $4 28/4 is 7

Find the value of this question ​

Answers

Answer:

the expression is equal to 0

Karen spent 39 minutes knitting 3 hats. In all, how many hats could Karen knit in 117 minutes

Answers

9 because 39\3 =13 and 13 divide by 117 =9

Please help geometry find the solution

Answers

Answer:

Directions Unclear:

Step-by-step explanation:

I am now drowning on air.

Answer:

ok

Step-by-step explanation:

Out of 1,200 students surveyed, 92% of them like country music. How many students like rap music?

Answers

Answer:

96

Step-by-step explanation:

1200*92=110400/100=1104

1200-1104=96

Answer:

1152 students like rap just take the numbers n divide

Suppose that Y has density function
f(y) = ky(1 − y) if 0 ≤ y ≤ 1 0, elsewhere
A) Find the value of k that makes f (y) a probability density function.
B) Find P(Y ≤ .4|Y ≤ .8).
C) Find the .95-quantile, i.e., find a point φ.95 such that P(Y ≤ φ.95) = .95.

Answers

I'm assuming

[tex]f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}[/tex]

(a) f(x) is a valid probability density function if its integral over the support is 1:

[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1[/tex]

Compute the integral:

[tex]\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16[/tex]

So we have

k / 6 = 1   →   k = 6

(b) By definition of conditional probability,

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)

It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).

We have

[tex]\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y<0\\3y^2-2y^3&\text{for }0\le y<1\\1&\text{for }y\ge1\end{cases}[/tex]

Then

P(Y ≤ 0.4) = F (0.4) = 0.352

P(Y ≤ 0.8) = F (0.8) = 0.896

and so

P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393

(c) The 0.95 quantile is the value φ such that

P(Y ≤ φ) = 0.95

In terms of the integral definition of the CDF, we have solve for φ such that

[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95[/tex]

We have

[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95[/tex]

which reduces to the cubic

3φ² - 2φ³ = 0.95

Use a calculator to solve this and find that φ ≈ 0.865.

Using probability concepts, it is found that

a) The value is k = 6.

b) P(Y ≤ .4|Y ≤ .8) = 0.554.

c) The 95th percentile is x = 0.86465.

The density function is:

[tex]f(y) = ky(1 - y)[/tex]

Item a:

The condition that makes it a probability density function is:

[tex]\int_0^1 f(y) dy = 1[/tex]

Thus:

[tex]\int_0^1 f(y) dy = \int_0^1 ky - ky^2 dy[/tex]

[tex]\int_0^1 f(y) dy = k(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0}^{y = 1}[/tex]

[tex]\int_0^1 f(y) dy = k(\frac{1}{2} - \frac{1}{3})[/tex]

Then

[tex]k(\frac{1}{2} - \frac{1}{3}) = 1[/tex]

[tex]k(\frac{3-2}{6}) = 1[/tex]

[tex]k = 6[/tex]

The value is k = 6.

Item b:

This probability is:

[tex]\int_0.4^0.8 f(y) dy = 6(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0.4}^{y = 0.8}[/tex]

Then

[tex]p = 6\left(\frac{0.8^2}{2} - \frac{0.8^3}{3} - \frac{0.4^2}{2} + \frac{0.4^3}{3}\right)[/tex]

[tex]p = 0.554[/tex]

Thus, P(Y ≤ .4|Y ≤ .8) = 0.554.

Item c:

This is x for which:

[tex]\int_0^x f(y) dy = 0.95[/tex]

Thus:

[tex]6(\frac{x^2}{2} - \frac{x^3}{3}) = 0.95[/tex]

[tex]-2x^3 + 3x^2 - 0.95 = 0[/tex]

Solving a cubic equation with the help of a calculator, and considering [tex]0 \leq x \leq 1[/tex], this is x = 0.86465.

A similar problem is given at https://brainly.com/question/22223588

If the simple interest on ​$3000 for 3 years is ​$720 ​, then what is the interest​ rate?

Answers

Answer:

8%

Step-by-step explanation:

Starting Principal: $  

3,000.00

Years:    

3

Annual Interest Rate:    

8

%

 

Results

Future Value, using...

 Simple Interest: $  

3,720.00

 Annually Compounded Interest: $  

3,779.14

PLEASE HELP QUICKLY!!!!! PLZZZZZZ!!!!!!!

Answers

(4)=34 (3/2)=67 sorry if I am wrong.

Bella wants to create a tea-mix. She can buy Asian Treasure tea for $7.50 per ounce and Paradise tea for $5.00 per ounce. If she wants to make 60 ounces of tea-mix at a cost of $6.00 per ounce, how many ounces of Asian Treasure tea and how many ounces of Paradise tea should she buy?

Answers

9514 1404 393

Answer:

24 oz Asian Treasure36 oz Paradise

Step-by-step explanation:

The proportion of Asian Treasure is the difference in price of the mix and Paradise tea, divided by the difference in price of Asian Treasure and Paradise tea. So the amount of Asian Treasure is ...

  (6.00 -5.00)/(7.50 -5.00)(60 ounces) = 24 ounces . . . Asian Treasure tea

The remaining 60-24 = 36 ounces will be Paradise tea.

__

Using an equation

You can get the same result if you define a variable (a) to the amount in ounces of the higher-priced contributor. Then the lower-priced contributor will be in the amount (60-a) ounces. The total cost of the mix is ...

  7.50a +5.00(60 -a) = 60(6.00)

  (7.50 -5.00)a +60(5.00) = 60(6.00) . . . rearrange the left side

  (7.50 -5.00)a = 60(6.00 - 5.00) . . . . . .  subtract 60(5.00)

  a = 60(6.00 -5.00)/(7.50 -5.00) . . . . . . divide by the coefficient of 'a'

Note that this last expression is identical to the one we used above to find the quantity of Asian Treasure tea.

How many solutions does the absolute value equation have?

I x - 3 I + 2 = -2

Answers

9514 1404 393

Answer:

  the correct answer is marked

Step-by-step explanation:

When the graph of the left side of the equation does not intersect the graph of the right side of the equation, there are no solutions.

__

Additional comment

Even if you extend the domain to complex numbers, there are no solutions. The f(x) = |x| function always returns a positive real value, even for complex numbers.

Other Questions
Read the text carefully, then answer the question located beneath:Time to "Bee" Wary, by Gordon WintersAfricanized honey bees were created in Brazil in 1957. Scientists mixed local bees with African ones to create a bee that would make more honey. They ended up with something much different. The new bees evolved in unexpected ways. They multiplied and migrated north. These Africanized honeybees are now known as killer bees for several scary but legitimate reasons.Killer bees are far more aggressive than their relatives. They have been known to attack in great numbers, even when there has been no direct threat on their hives. They have swarmed because of loud noises, dark clothing, bright jewelry, and even strong perfume. They will chase a person for more than a quarter of a mile and remain angered for up to 24 hours.Killer bees are also dangerous because of their sting. While most bees take up to 30 seconds to attack, killer bees sting in just 3 seconds. Their venom is no stronger than a regular bee's, but when one killer bee stings, others follow. With up to 80,000 members in a colony, victims are quickly overwhelmed. So many stings in such a short time can cause allergic reactions. Victims enter a state of shock, lose blood pressure, and in many cases, die.A final reason why "killer" has been added to their name is the unfortunate number of deaths they have caused. Experts estimate that the Africanized honeybee moves at a rate of about 200 miles each year. As the bees claim new territory, they claim new victims as well. More than 1000 people have been stung to death in South and Central America. There have been rising numbers of attacks in Mexico and a handful in the United States. Once a swarm sets sights on a victim, it is very difficult for the victim to escape. Once attacked, it is very difficult to survive.Thankfully, there has been no killer bee invasion as some once predicted. Although there is no need for panic, the threat of the killer bee is real and should be taken seriously. It is good practice to call a professional to remove beehives in your area. If you are stung multiple times by any insect, you should always seek medical attention. You may not be expert enough to tell the difference between a killer bee and a less dangerous one, so be smart. It is better to be safe than sorry.Which sentence from the conclusion paragraph best rephrases the author's thesis? in the following chemical reaction between H_2 and Cl_2 to produce HCl, what is the sum of the mass of HCl produced plus the mass of left over reactants when 0.40 g of H_2 completely reacts with 12.35 g of Cl_2?H_2(g) + Cl_2(g) 2HCl(g) A punter kicks a football into the air. The pathway of the football can be represented by the equation h=-16t^2+82t (where t= time in seconds and h= height in feet.) what was the maximum height of the ball and what time was the maximum height reached? Which financial statement would include a listing of a companies assets I really need a 100 I'm felling in all my classes, please Select the fraction that is equivalent to one-sixth. The Creek resistance was led byA. Chitto HarjoB. Archibald S. McKennonC. Pleasant PorterD. Henry L. Dawes 4. The value of a copy machine is $8500 when it is purchased. After two years its value is $7475. What is its value after 8 years? In the diagram, AB= DC and AC= DB. Why does m What are 1. Dynamic character2. Static character3. Flat character4. Round character5. Theme A balance uses small metal weights of known mass to determine the mass of a substance. Where would a balance NOT function correctly?A balance scale.A.in a vacuum on EarthB.on the Moon's surfaceC.on the Earth's highest mountainD.in a zero gravity environment how do i find my sister's math question she just posted how do i find it Please answer FAST i need your help and when you put your answers put them like 1. 2.3.4.5. Can someone tell me about kinetic, potential, and gravitational energy? What was the significance of Frances Perkinss role in the Roosevelt administration? A. She was the first female Vice President. B. She was the first female leader of the Democratic Party. C. She was the first female Democratic representative. D. She was the first female Cabinet member. Which of the following are electromagnetic waves? *Water wavesSound wavesRadio wavesSeismic waves Overtime our bodies age and are less and less able to deal with stress from inside and outside of our body true or false? Pls someone help. I have no idea. A(n)______ dot on the graph of an inequality shows that the points IS a solution of the inequality. A) flat B) open C) closed D) invisible I'll give brainless The Northwest Ordinance of 1785 reserved some land in each township for______ use. What is x- value of point A