Mathematics College

Determine which expression is equivalent to 15a + 6. (5 points)

a
3(5a + 6)

b
3(5a + 2)

c
5(3a + 6)

d
5(3a + 2)

Question 2 (5 points)
(03.01 LC)

Excellence Middle School charges $6.25 for students from all grade levels to attend the school dance. If s represents the number of seventh grade students who came to the dance and g represents the number of eighth grade students at the dance, which expression best represents the total money collected for attending the dance. (5 points)

a
6.25s + g
b
6.25(s + g)

c
13.50(s + g)

d
13.50s + g

Question 3 (5 points)
(03.01 LC)

Ken and Paul have been mowing lawns to earn extra money. Their jobs earn $65 per week. Ken worked for x weeks and earned an extra $18. Paul worked for y weeks. From the expressions below, select one that determines the total amount that Ken and Paul earned mowing lawns. ? (5 points)

a
83x + 65y

b
65x − 18 + 65y

c
60x + 83y

d
65x + 18 + 65y

Question 4 (5 points)
(03.02 MC)

Michelle and her friends wondered who had the most pop albums in their music collection. She recorded the information below:


Music Collection Survey
Name Number of Pop Albums Total Number of Albums in the collection
Michelle 33 60
Sasha 36 78
Kat 40 89
Monica 24 59


Based on the survey, which friend had the greatest percentage of pop albums? (5 points)

a
Michelle

b
Sasha

c
Kat

d
Monica

Question 5 (5 points)
(03.02 MC)

Lynne was wondering which game was more popular so she aksed her friend which they liked to play more, FortNite or Among Us. She found that of the 80 people who responded, 0.55 of them preferred FortNite, and 30% of them preferred Among Us. How many more of her friends prefer FortNite than Among Us? (5 points)

a
30

b
20

c
44.45

d
5

Question 6 (5 points)
(03.02 MC)

Hulk, Iron Man, Thor, and Captain America together clean out evil from 60 cities. Hulk cleaned up 0.25 of the cities, Iron Man cleaned up 12 of the 60 cities, Thor cleaned 35% of the cities, and Captain America cleaned up the the remaining cities. Who cleaned up the most cities? (5 points)

a
Hulk

b
Iron Man

c
Thor

d
Captain America

Question 7 (5 points)
(03.04 MC)

Solve for x: (5 points)





a
12

b
−12

c
-35

d
35

Question 8 (5 points)
(03.04 MC)

Clark Kent needs to buy some new glasses. He has $70 to spend and the glasses that he wants only costs $30. He wants to spend the remainder of his money on new capes. Each cape costs $8. Which inequality represents the number of capes he can purchase? (5 points)

a
x ≥ 5

b
x ≤ 11

c
x ≤ 5

d
x ≥ 11

Question 9 (5 points)
(03.04 LC)

Find the equation that can represent the situation if the sum of two numbers is 32. We also know that the greater number is 5 more than the smaller number. (5 points)

a
x + (x + 5) = 32

b
x − (x + 5) = 32

c
x(x + 5) = 32

d
x(x − 5) = 32

Question 10 (5 points)
(03.05 MC)

SpongeBob needs $44 to buy a new pair of rectangle pants. He has already been able to save $9 and plans to work as a cook where he can earn $7 per hour. Which inequality shows the minimum number of hours, n, that SpongeBob will have to work as a cook to earn enough to buy the rectangle pants? (5 points)

a
9 + 7n ≤ 44, so n ≤ 5

b
9 + 7n ≥ 44, so n ≥ 5

c
7n ≥ 44 + 9, so n ≥ 7.8

d
7n ≤ 44 + 9, so n ≤ 7.8

Question 11 (5 points)
(03.05 MC)

Jesse sells clothes in the Yee Haw! Western Clothing store and earns $40 per day. She earns an extra $5 for each lasso she sells. If Jesse wants to earn at least $70 per day, which inequality shows the minimum number of lasso, n, that she would need to sell? (5 points)

a
40 + 5n ≤ 70, so n ≤ 6

b
40 + 5n ≥ 70, so n ≥ 25

c
40 + 5n ≤ 70, so n ≤ 25

d
40 + 5n ≥ 70, so n ≥ 6

Question 12 (5 points)
(03.05 MC)

Defne was looking online and saw some some cakes that looked delicious. Each cake costs $10.01 and has a shipping cost of $9.96 per order. If Defne wants to spend no more than $50 for the cakes, which inequality shows the maximum number of cakes, c, Defne can buy?(5 points)

a
9.96p − 10.01p ≤ 50, so p ≤ 1

b
9.96p + 10.01p ≤ 50, so p ≤ 2

c
9.96 − 10.01p ≤ 50, so p ≤ 3

d
9.96 + 10.01p ≤ 50, so p ≤ 4

I NEED HELP (ASAP)

Answers

Answer 1

Answer:

1. [tex]Expression: 3(5a + 2)[/tex]

2. [tex]Total\ charges = 6.25(s+g)[/tex]

3. [tex]Total = 65x + 18 + 65y[/tex]

4. Michelle

5. 20 friends

6. Thor

8. [tex]x\leq 5[/tex]

9. [tex]x + x + 5 = 32[/tex]

10. [tex]7n + 9 \leq 44[/tex] so: [tex]n \leq 5[/tex]

11. [tex]40 + 5n \leq 70[/tex] So: [tex]n \leq 6[/tex]

12. [tex]10.01 p + 9.96 \leq 50[/tex] so [tex]p \leq 4[/tex]

Step-by-step explanation:

1. Given

[tex]Expression: 15a + 6[/tex]

Required

Determine the equivalent expression

[tex]Expression: 15a + 6[/tex]

Expand:

[tex]Expression: 3 * 5a + 3 * 2[/tex]

Factorize:

[tex]Expression: 3(5a + 2)[/tex]

Hence, the equivalent expression of the given expression is [tex]3(5a + 2)[/tex]

2.

Given

[tex]Charges = \$6.25[/tex]

s = seventh grade students

g = eight grade students

Required

Determine the total charges

First, we need to calculate the total number of charges:

[tex]Total=s+g[/tex]

[tex]Total\ charges = Charges * Total[/tex]

[tex]Total\ charges = 6.25(s+g)[/tex]

3. Given

Ken

[tex]Duration = x\ weeks[/tex]

[tex]Extra\ Earnings = \$18[/tex]

[tex]Weekly\ Earnings = \$65[/tex]

Paul

[tex]Weekly\ Earnings = \$65[/tex]

[tex]Duration = y\ weeks[/tex]

Ken's total charges is:

[tex]Weekly\ Earnings * Duration + Extra\ Earnings[/tex]

[tex]65 * x + 18[/tex]

[tex]65x + 18[/tex]

Paul's total charges is:

[tex]Weekly\ Earnings * Duration[/tex]

[tex]65 * y[/tex]

[tex]65 y[/tex]

[tex]Total = Ken + Paul[/tex]

[tex]Total = 65x + 18 + 65y[/tex]

4.

To calculate the percentage, we simply divided the number of pop albums by the total number of albums.

For Michelle.

[tex]\%Pop = \frac{33}{60} * 100\%[/tex]

[tex]\%Pop = \frac{3300\%}{60}[/tex]

[tex]\%Pop = 55\%[/tex]

For Sasha

[tex]\%Pop = \frac{36}{78} * 100\%[/tex]

[tex]\%Pop = \frac{3600\%}{78}[/tex]

[tex]\%Pop = 46.2\%[/tex]

For Kat:

[tex]\%Pop = \frac{40}{89} * 100\%[/tex]

[tex]\%Pop = \frac{4000\%}{89}[/tex]

[tex]\%Pop = 44.9\%[/tex]

For Monica:

[tex]\%Pop = \frac{24}{59} * 100\%[/tex]

[tex]\%Pop = \frac{2400\%}{59}[/tex]

[tex]\%Pop = 40.7\%[/tex]

From the calculation above, Michelle has the highest percentage of Pop music

5.

[tex]People = 80[/tex]

[tex]Fortnite = 0.55[/tex]

[tex]Among\ Us = 30\%[/tex]

Required

Determine number of friends that prefer fortnite more than among us

First, we need to calculate the number of people that prefer Fortnite.

[tex]Fortnite = 0.55 * 80[/tex]

[tex]Fortnite = 44[/tex]

Next, we need to calculate the number of people that prefer Among Us.

[tex]Among\ Us = 30\% * 80[/tex]

[tex]Among\ Us = 24[/tex]

The difference is:

[tex]Difference = 44 - 24[/tex]

[tex]Difference = 20[/tex]

Hence, 20 more people preferred Fortnite to Among Us

6.

[tex]Hulk = 0.25[/tex]

[tex]Iron\ Man = 12[/tex]

[tex]Thor = 35\%[/tex]

Captain America cleaned the rest

[tex]Total = 60[/tex]

Number of cities by each is:

[tex]Hulk = 0.25 * 60[/tex]

[tex]Hulk = 15[/tex]

[tex]Iron\ Man = 12[/tex]

[tex]Thor = 35\%[/tex]

[tex]Thor = 35\% * 60[/tex]

[tex]Thor = 21[/tex]

[tex]Captain\ America = 60 - 15 -12 - 21[/tex]

[tex]Captain\ America = 12[/tex]

By comparison, Thor cleaned the highest number of cities

7. This question is not clear

[tex]Total = \$70[/tex]

[tex]Glass = \$30[/tex]

[tex]Each\ Cape = \$8[/tex]

Let the number of cape be x.

We have that:

[tex]8 * x + 30 \leq 70[/tex]

[tex]8 x +\leq 70 - 30[/tex]

[tex]8 x +\leq 40[/tex]

[tex]x\leq 5[/tex]

9.

Let the first number be x and the second be y

[tex]x + y = 32[/tex]

[tex]y = x + 5[/tex]

Substitute x + 5 for y in the first equation

[tex]x + x + 5 = 32[/tex]

10.

[tex]Savings = \$9[/tex]

Earnings = $7 per hous

Total = $44

The inequality is:

[tex]7 * n + 9 \leq 44[/tex]

[tex]7n + 9 \leq 44[/tex]

[tex]7n \leq 44 - 9[/tex]

[tex]7n \leq 35[/tex]

[tex]n \leq 5[/tex]

11.

Earnings = $40

Extra = $5 per lasso

Total Earnings = At least $70 daily

The inequality is:

[tex]40 + 5n \leq 70[/tex]

[tex]5n \leq 70 - 40[/tex]

[tex]5n \leq 30[/tex]

[tex]n \leq 6[/tex]

12.

[tex]Each\ Cake = \$0.01[/tex]

[tex]Shipping = \$9.96[/tex] per order

[tex]Available = \$50[/tex] --- maximum

The inequality is:

[tex]10.01 * p + 9.96 \leq 50[/tex]

[tex]10.01 p + 9.96 \leq 50[/tex]

[tex]10.01 p \leq 50 - 9.96[/tex]

[tex]10.01 p \leq 40.04[/tex]

[tex]p \leq 4[/tex]

Related Questions

Iwefwegweg weg ewgwewegw egwe gwe gwe weg weg w

Answers

Answer:

gweew gshbx

Step-by-step explanation:

AYYYY HOLMES 100 POINTS BOISSS

Answers

Answer:

1) A

2) B

3) D

4) B

Step-by-step explanation:

1) Because 1 mile is 5280 feet one half of the proportion has to be 1/5280. The other half is 5/x

2) Multiply 1/2 * (10/2.5). This gets you 2

3) First find 4.5% of 545.00 (Multiply 545*.045) This gets you 24.525. Add this to 545, and you get 569.525. This can be rounded to $569.53

4) There seem to be 5 players for each coach. If there are 80 players, divide 80 by 5 to get the number of coaches. The final answer is 16

Answer:

1.) A.-  [tex]\frac{5}{x}[/tex]

2.) B.-  2

3.) D.- 569.53

4.) B.- 16

Step-by-step explanation:

-1.) His placement needs to be the denominator To be counted, Only Option "A." Has his value

-2.) Pints = 0.125-US liquid Gallon- For 10 gallons of gas he would need 2 Pints

-3.) Bringing 545.00 up by 45% Would leave us with- 569.53

-4.) We would need 16 couches for 80 softball players

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

Proportions are the same ratios written in different forms. A proportional relationship is states that they are the same. For example, 1/2 and 6/12 have a proportional relationship, which means they are the same. I hope this helps!!

Will give brainlist to who finds this out!

Answers

Answer:

1

2

4

Step-by-step explanation:

Answer:

[tex]\sqrt{1}, \sqrt{4}, \sqrt{9}[/tex]

Step-by-step explanation:

First, remember that rational numbers either terminate or have repeating decimals. Those three are the only answers with perfect squares, [tex]\sqrt{1} = 1, \sqrt{4} = 2, \sqrt{9} = 3[/tex]. As you can see all of these answers terminate and therefore are rational, the rest go one forever while never repeating.

i need help plzzzzzzzzz

Answers

Answer:

1 2 5 . 6 9

1 2 5 . 6 7 0

125.69 Would be Greater.

Step-by-step explanation:

First number to the right of the decimal is the tenths place 2nd number would be hundredths and you'd increase etc.

Solve for x
2x+5 = 32

Answers

Answer:

x=13.5

Step-by-step explanation:

Perform the same operation on each side:

2x+5 = 32

2x     = 27

x       = 13.5

So, x is 13.5

Describe the graph of x > 2 and x < 5

Answers

Answer:

y=(x−5)2

The graph of y is the standard parabolic, concave up curve of y=x2 shifted ("transformed") by 5 units right ("positive") on the x−axis,

The graph of y is shown below.

graph{(x-5)^2 [-10, 10, -5, 5]}

Answer:

I'm prettyy sure you already figured this out knowing you, so thanks;)

Step-by-step explanation:

question below please answer

Answers

Answer:

the awenser  is D

Step-by-step explanation:

took the test lolz

In AGHI, the measure of

Answers

Answer:

yes

Step-by-step explanation:

Feet thats the answer noooo problem

A manufacturer wants to produce an ice cream cone with the same volume and diameter of a spherical scoop of ice cream 6cm in diameter. What should the height of the cone be?

Answers

Answer:

IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?

Step-by-step explanation:

IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?IS THIS NIKHIL GARG?!?!?!?!?!? THE FORTNITE PRO?!?!?!?!?!?!??!?!?!?

Answer: HEY NIKHIL GARG MR. FORTNITE BATTLE ROYALE THE ANSWER IS 12

Step-by-step explanation:

TRUST BRO IF THE HEIGHT IS 12 THEN ITLL HAVE THE SAME VOLUME AS THE SPHERE, WHICH IS 36 PI

How to solve
2(-3x + 4) = 5x + 2

Answers

Answer:

x = 6/11

Step-by-step explanation:

2(-3x + 4 ) = 5x + 2  

    -6x + 8 = 5x + 2      

           - 2          - 2

    -6x + 6 = 5x

   +6x         +6x

             6 = 11x

            /11   /11

           6/11 = x

The original quantity is 5 and the new quantity is 3. What is the percent change?

Answers

Answer:

Step-by-step explanation:

Percentage change= New number/ original x 100

3/5=0.6

0.6 x 100= 60%

100-60=40%

Help Lesson 11 & 12: A shop sells bagels for $5 per dozen. At this rate, how much would 6 bagels cost? Your answer is a dollar amount, so it must have a number to the left of the decimal and two numbers to the right of the decimal. (Example: $5.50 would be entered as 5.50) *

Answers

2.5 dollars because if one dozen is 5 dollars and we divide 12 by 2 we get 6 witch is also how much we need so we also divide 5 dollars by 2 because 5 dollars = 12 bagels.

The probability of two events A and B happening simultaneously is 0.17. The probability of only event A happening is 0.34. Find the probability of event B happening, if event A has already happened

Answers

Answer:

because is the probability is 0.17 and 0.34 is fair

You can use the multiplication rule of probability.

The probability of event B happening if event A has already happened is 0.5

What does general multiplication rule of probability says for 2 events A and B?

[tex]P( A \: \rm and \: B) = P(A)P(B|A) = P(B)P(A|B)[/tex]

Since we've to find the probability of B given that A has already happened, we need [tex]P(B|A)[/tex]

Since the probability of both event A and event B happening simultaneously is 0.17, thus:
[tex]P(A \: \rm and \: B) = 0.17\\ [/tex]

Since the probability of only event A happening is 0.34, thus:

[tex]P(A) = 0.34[/tex]

Thus, from the multiplication rule, we have:
[tex]P(A \: \rm and \: B) = P(A)P(B|A)\\ 0.17 = 0.34 \times P(B|A)\\\\ \dfrac{0.17}{0.34} = P(B|A)\\\\ P(B|A) = \dfrac{1}{2} = 0.5[/tex]

Thus, we have the probability of event B happening when A has already happened as 0.5

Learn more about multiplication rule of probability here:

https://brainly.com/question/14450597

HELP AND YOU WILL GET BRAINLIEST!!!!!!!!

4 liters of oil cost $10.00. Find the cost per liter of oil.
Group of answer choices

$2.00

$3.00

$10.00

$2.50

$400

Answers

Answer: $2.50

$10.00 per 4 liters

10/4=2.5

I hope this is good enough:

Answer:  because i just want points and 1 +2= 3

Step-by-step explanation: because  if u add 2 with 1 u will get 3

8 1/3 divided by 5 5/7
In simplest form

Answers

Answer:

35/24

Step-by-step explanation:

8 1/3= 25/3  5 5/7= 40/7

(25/3) divided by (40/7) is equal to (25/3) x (7/40) using Keep Change Flip (KCF) where you keep the initial value, switch the sign from dividing to multiplying, and then flip the other value. Then, multiply across to get 175/120 which simplifies to 35/24.

What is the formula for the area of a square?

Answers

Answer:

Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared. If a square has one side of 4 inches, the area would be 4 inches times 4 inches, or 16 square inches. (Square inches can also be written in2.)

Answer:

lxwxtor you can up it in the calculator

How far does the tip of the minute hand of a clock move in 20 minutes if the hand is 10 inches long?

Answers

Answer:

20.95 inches

Step-by-step explanation:

The complete revolution of the minute hand forms a circle in 60 minutes.

circumference of a circle = 2[tex]\pi[/tex] radius

i.e C = 2[tex]\pi[/tex]r

But from the question, r = length of the minute hand = 10 inches

⇒ C = 2[tex]\pi[/tex] x 10

  = 20[tex]\pi[/tex]

C = 20[tex]\pi[/tex] inches

Also, 20 minutes = [tex]\frac{20 minutes}{60 minutes}[/tex] = [tex]\frac{1}{3}[/tex] of the circumference.

So that,

the distance of the tip of the minute hand = [tex]\frac{1}{3}[/tex] x C

                                                                     = [tex]\frac{1}{3}[/tex] x 20[tex]\pi[/tex]

                                                                     = [tex]\frac{1}{3}[/tex] x 20 x [tex]\frac{22}{7}[/tex]

                                                                     = 20.9524

                                                                     = 20.95 inches

Thus, the distance of the tip of the minute hand is 20.95 inches

Louis owns a rectangle price of property with an area of 1 3/4 square miles. The length of the property is 2 1/3 miles. What is the width of the property?

Answers

Answer:

1/4

Step-by-step explanation:

Divide the area by the length and you will find the width.

what is the difference of the fractions? use the number line to help find the answers. 4/7 - 10/7​

Answers

Answer:

This means that the fraction 3/4 is 3 out of 4 equal parts. So, count 3 parts from 0 and you will get 3/4. That's it! You've shown the fractions 1/4 and 3/4 on a number line!

Step-by-step explanation:

It is.

Answer:

This means that the fraction 3/4 is 3 out of 4 equal parts. So, count 3 parts from 0 and you will get 3/4. That's it! You've shown the fractions 1/4 and 3/4 on a number line!

Step-by-step explanation:

The math is just correct

In 2007, the average e-mail user sent 578 personal and business e-mails each week. The number of personal e-mails was 30 fewer than the number of business e-mails. How many personal e-mails were sent?

Answers

Answer:

548

Step-by-step explanation:

it would be 578 - 30 which equals 548

I put it at 50 pts because it will take a while plz help me

Answers

Answer:

well i am not that smart sorry i really wish i could help but i know one of the things  

Step-by-step explanation:

3. what causes wind

Gases move from high-pressure areas to low-pressure areas. And the bigger the difference between the pressures, the faster the air will move from the high to the low pressure. That rush of air is the wind we experience.

sorry it took so long for me to type it

hope you have a good day sir/ma'am!!!

20POINTS WILL MARK BRANLIEST PLSS
The layout of a city park is pictured in the figure above. Park managers would like to find the distance of segment DE, in order to build a walkway across the middle of the park. The park managers look up the distance of segments BC and AB in the city records. If the length of segment AB is determined to be 562 feet, what is the distance of mid-segment DE in feet?

Select one:
A. 220
B. 244
C. 276
D. 281

Answers

244 is the correct answer

Which equation represents a lineThat passes through (-2, 4) and has a slope of 2/5

Answers

Answer:

-2,4

Step-by-step explanation:

Solve:
5y + 3y +1+1 = 2y + 6y +6 +2

Answers

Answer:

0=6

There are no solutions to this answer.

Step-by-step explanation:

Answer:

There is no solution.

Step-by-step explanation:

A child’s wading pool has a diameter of 5 feet and a height of 2 feet. How much water would it take to fill the pool?

Answers

Answer:

12.5π or ≈39.27

Step-by-step explanation:

The formula for finding the volume is V=πr^2*d (where h is the height and r is  the radius).

Plug in the values: V=π(2.5)^2*2 (Diameter=2*Radius)

Solve: V=6.25π*2

V=12.5π

V≈39.27

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? ​

Answers

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.

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

Three times one number is equal to two times the larger one and their difference is 1. What are the numbers?

Answers

Answer:

Y=3

X=2

Step-by-step explanation:

There are ten toppings available to make an ice
cream sundae. How many ways can Max choose
two?

Answers

Answer:

There will be 56 possible combinations if he is allowed to choose the same topping twice.

There will be 47 if he is not allowed to choose the same topping twice.

Step-by-step explanation:

Number of ways max choose two are 45

What are combinations?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of both the selection is irrelevant. You can choose the components of combos in any order;

Permutations and combinations can be mixed up. The sequence in which the chosen components are chosen is crucial in permutations, too. For instance, the configurations ab and ba are distinct in permutations but equivalent in combinations (regarded as one arrangement);

Given;

Toppings available to make an ice cream sundae = 10

The  number of ways can Max choose 2;

= 10C2

=10! / [(10-2)! X 2!]

=45

Therefore, Max can choose toppings is 45 by combination

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These two triangles are similar. What are a and b? Note: the two figures are not drawn to scale. Please help with this!!!

Answers

9514 1404 393

Answer:

a = 6b = 22.5

Step-by-step explanation:

The ratio of smallest sides in the two triangles is ...

  smaller / larger = 4/10

To find A and B, we write proportions involving corresponding side lengths.

__

Side A in the smaller triangle is ...

  A/15 = 4/10

  A = (4/10)(15) = 6

__

The ratio of larger to smaller is the inverse of the above ratio, so ...

  B/9 = 10/4

  B = (10/4)(9) = 22.5

Find the Y intercept of the graph

Answers

Answer:

6

Step-by-step explanation:

The intercept would be 6 because that's the point on the Y line or the line going vertically.    

Answer:

6

Step-by-step explanation:

Hello!

The y-intercept of the graph is when the graph touches the y-axis.

As you can see the graph intersects the y-axis at point (0,6), indicating the y-intercept of the graph to be 6.

y - intercept: 6

The x-intercepts of the graph are when the graph intersects the x-axis. There are three roots for the graph: -1, -3 and 2.

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