Expand and simplify:
a) -1/3{6(p+q)-3[p-2(p-3q)]}
A=-3p+4q

b) y-2/3(9x-3y)
A=-6x+3y

(The answer is written at the back of our books but I am struggling with the working I mean how to achieve the answer?)

Answers

Answer 1

Answer:

  a) -3p +4q

  b) -6x +3y

Step-by-step explanation:

Use the distributive property to eliminate parentheses. Use the properties of arithmetic to combine the numbers.

__

a)

The order of operations tells you to start with the inner parentheses and work outward.

  [tex]-\dfrac{1}{3}(6(p+q)-3(p-2(p-3q)))=-\dfrac{1}{3}(6(p+q)-3(p+(-2)(p) +(-2)(-3q)))\\\\=-\dfrac{1}{3}(6(p+q)-3(p-2p+6q))=-\dfrac{1}{3}(6(p+q)-3(-p+6q))\\\\=-\dfrac{1}{3}((6)(p)+(6)(q)+(-3)(-p)+(-3)(6q))=-\dfrac{1}{3}(6p+6q+3p-18q)\\\\=-\dfrac{1}{3}(9p -12q)=(-\dfrac{9p}{3})+(-\dfrac{-12q}{3})=\boxed{-3p+4q}[/tex]

__

b)

Same deal for the second expression: use the distributive property and combine like terms.

  [tex]y-\dfrac{2}{3}(9x-3y)=y+(-\dfrac{2\cdot9x}{3})+(-\dfrac{2(-3y)}{3})\\\\=y-6x+2y=\boxed{-6x+3y}[/tex]


Related Questions

what is the median in 72 77 75 72 70 69 71 78 75 68 62 69 65 63 68 53 57 79 77 75 80 73 71 64 71 64 50 50 55 55

Answers

Answer:

The median is 69.5

Step-by-step explanation:

The median is also known as the middle value. To find the median, you first arrange your data in numerical order.

Numerical order:

50, 50, 53, 55, 55, 57, 62, 63, 64, 64, 65, 68, 68, 69, 69, 70, 71, 71, 71, 72, 72, 73, 75, 75, 75, 77, 77, 78, 79, 80

There are 30 numbers, which means that the median is between the 15th and 16th value (69 and 70).

69 + 70 = 139

139/2 = 69.5

Therefore, the median of this data set is 69.5

Hope this helps!

P is a rectangle with length 40 cm and width x cm. Q is a rectangle with width y cm. P The length of Q is 25% more than the length of P. The area of Q is 10% less than the area of P. Work out the ratio x : y x cm Give your answer in its simplest form. 40 cm Q y cm

Answers

From rectangle P and Q, the ratio of x to y is 25/18

What is an equation?

An equation is an expression used to show the relationship between two or more numbers and variables.

Area of P = 40 * x = 40x cm²

Area of Q = y * (1.25 * 40) = 50y cm²

Given that area of Q = 90% if P = 0.9(40x) = 36x cm²

50y cm² = 36x cm²

x/y = 50/36 = 25/18

From rectangle P and Q, the ratio of x to y is 25/18

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27
5
to a mixed number
a
decimal.

Answers

Answer: 5.4 and 5⅖

Step-by-step explanation:

27/5 to a mixed number 5⅖

Decimal 5.4

Bob has 30 coins, which are all dimes and quarters. If the total amount of money he has
is $4.80, how many of each coin does he have?

Answers

Answer:

that means he will have 25.2

please solve for x 3x + 22

Answers

Answer:

The x intercept is [tex](-\frac{22}{3} ,~0)[/tex]

The y intercept is [tex](0,~22)[/tex]

Sally's soccer team played 25
games this season and lost 9 of
those games. What percent of the
games did the team win?

Answers

Answer:

64%

Step-by-step explanation:

25 - 9 = 16, so 16 of the games were won by Sally's team.

16/25 = 64% of the games were won

PLSSS HELP IF YOU TURLY KNOW THISS

Answers

Answer:

c

Step-by-step explanation:

because 3 x 3 = 9

               1 x 5 = 5

simplest form will be 1 4/5


I’m confused please help!

Answers

Answer:

See below

Step-by-step explanation:

c will be tha same as the labelled angle = 99 degrees

  then c + b = a straight line = 180

             99 + b   = 180

                    b = 81 degrees

Find the area of the sector of the circle.

A)40π
B)200π
C)60π
D)300π

Answers

Answer:

the answer is D) 300 π

Step-by-step explanation:

Formula for Area of sector is:

θ/360° * π * (r)^2

here,

θ= 30° and radius= 60 in

so, after we substitute, we get:

30/360* π* 60*60       after simplifying we get:

= 1/12* π* 5*60

=300π

Hope it helps.

Answer:

D

Step-by-step explanation:

area of sector=

[tex] \frac{theta}{360} \times \pi \: r {}^{2} \\ \\ \frac{30}{360} \times \pi \: (60) {}^{2} \\ \\ 300\pi[/tex]

360

The tank of a car holds 10 gallons of gas.
How many liters does the tank hold? Round to the nearest tenth.

Answers

Answer:

37.9 liters

Step-by-step explanation:

Multiply the number of gallons by 3.785 to convert to liters

Multiplying by ten moves the decimal point over to the right

3.785 * 10 = 37.85

The tenths place is where the 8 is, and since 5 is [tex]\geq[/tex] (greater than or equal to) 5 that makes the 8 round up to a 9

resulting in...

10 gallons = 37.9 liters

hope this helps:)

Look at the image for the instructions! I need this asap! I will give points, 5 stars and brainliest ((:

(This is an essay)

Answers

Answer:

1. one is smaller by 5 cm and one is larger by 5 cm

2. well they are similar to each other, but one is dilated and isn't

The graph of a linear function is shown on the grid.
Which equation is best represented by this graph?

Answers

Answer:

C

Step-by-step explanation:

Because thats the answer

6. A rectangle with a length of 15 feet has a
diagonal that measures 17 feet. Find the
perimeter of the rectangle.

Answers

Answer:

46 feet

Step-by-step explanation:

it is a 8-15-17 Pythagorean Triple (or you can use the Pythagorean theorem)

P=8+8+15+15=46

The perimeter of the rectangle with a length of 15 feet and has a diagonal that measures 17 feet is: A. 46 feet.

What is the Perimeter of a Rectangle?

To find the perimeter of the rectangle, we need to know the width of the rectangle. Let's call the width of the rectangle W.

In a rectangle, the diagonal, length, and width are related by the Pythagorean theorem:

Diagonal² = Length² + Width²

In this case, the diagonal (D) is 17 feet, and the length (L) is 15 feet. So we have:

17² = 15² + W²

289 = 225 + W²

Now, let's solve for W:

W² = 289 - 225

W² = 64

W = √64

W = 8 feet

Now that we know the width is 8 feet, we can calculate the perimeter (P) of the rectangle:

Perimeter = 2 * (Length + Width)

= 2 * (15 + 8)

= 2 * 23

Perimeter = 46 feet

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A vending machine that takes only dimes and
quarters contains 30 coins, with a total value of
$4.20. How many of each coin are there?

Answers

Answer: 22 dimes, 8 quarters
Explanation: You can guess and check. You know you need more dimes because they are worth less. It would take more dimes to make up 30 coins. And you also know that quarters cannot make .20 exactly. So your number of dimes must make .20. So I guessed numbers that would have .20 left over, and added quarters to get to $4.20.

Whats 38240 divided by 4

Answers

Answer:

9560

Step-by-step explanation:

Use a calculator or do long division.

You can also divide by 2 twice.

38240/2 = 19120

19120/2 = 9560

Answer: 9560

Answer:

9560

Step-by-step explanation:

30000÷4=7500

8000÷4=2000

200÷4=50

40÷4=10

0÷4=0

7,500+2,000+50+10+0=9,500+60=9,560

What's the range of f(x)=x+6 if x ∈(-4,-1)

Answers

Answer:

the range of is (2 , 5)

Step-by-step explanation:

f(x)=x+6

f is an increasing function then the range of is

f(-4,-1) = (f(-4) , f(-1))

f(-4) = -4 + 6 = 2

f(-1) = -1 + 6 = 5

Therefore

the range of is f(-4,-1) = (2 , 5)

Last year the depth of the river was 4.2 feet deep. This year it dropped 9% Find the depth of the river this year

Answers

Answer: 3.822

Step-by-step explanation: 9/100 × 4.2 = 0.378

Deduct from 4.2

Don't Send links, don't Write random things and get the points for free.

Answers

Answer:

2,714in^3

Step-by-step explanation:

V = pi*r^2*h
V = 3.14*6^2*24
V = 3.14*36*24
V = 2,714

The volume of the cylindrical fish tank is 2,714 inches cubed.

Answer:

Option A, [tex]2714\ in^3[/tex]

Step-by-step explanation:

Step 1:  Determine the volume of the cylinder

[tex]V=\pi r^2h[/tex]

[tex]V=\pi *(12\ in/2)^2*24\ in[/tex]

[tex]V=\pi *(6\ in)^2*24\ in[/tex]

[tex]V=\pi * 36\ in^2 *24\ in[/tex]

[tex]V = \pi *864\ in^3[/tex]

[tex]V=2,714\ in^3[/tex]

Answer:  Option A, [tex]2714\ in^3[/tex]

Brady dilates an oblique prism by a scale factor of 2/3. Determine the scale factors for perimeter, area, and Volume. (Answer as a fraction)

Answers

Using proportions, it is found that:

The scale factor for the perimeter is of [tex]\frac{2}{3}[/tex].The scale factor for the area is of [tex]\frac{4}{9}[/tex].The scale factor for the volume is of [tex]\frac{8}{27}[/tex].

What is a proportion?

A proportion is a fraction of a total amount.

For the perimeter, as it is given in units, the scale factor is the same, hence it is of [tex]\frac{2}{3}[/tex].

For the area, as it is given in units squared, the scale factor is squared, hence:

[tex]\left(\frac{2}{3}\right)^2 = \frac{4}{9}[/tex]

For the volume, as it is given in cubic units, the scale factor is eleveted to the third power, hence:

[tex]\left(\frac{2}{3}\right)^3 = \frac{8}{27}[/tex]

More can be learned about proportions at https://brainly.com/question/24372153

A notebook costs £1.60, a pen costs 37p, a pencil costs 21p and a sharpener costs 86p.
Remi buys 3 pencils, 2 pens, 3 sharpeners and some notebooks.
He pays with £8 and receives 85p change.
How many notebooks did he buy?
notebooks

Answers

£1.60 each notebooks
3 pencils times 21p= 63p
2pens times 37p=74p
3sharpeners times 86p=258p
63p+74p+258p=£3.95
£8-3.95=£4.05
£4.05-£1.60= £2.45
£2.45-£1.60=85p
So… he bought 2 notebooks

Answer:

2

Step-by-step explanation:

£1 = 100p

3*21p+2*37p+3*86p+x*160p (x is the number of notebooks)

63p+74p+258p+x*160p = 395p+x*160p

He paid £8 so he paid 800p

800p-395p = 405p

405p-85p = 320p

320p:160p = 2

He bought 2 notebooks

‼️⚠️⚠️‼️ HELP PLEASE WILL GIVE POINTS​

Answers

Answer:

m∠ABC=42°

Step-by-step explanation:

m∠ABD=70°

⇒m∠ABD=m∠ABC+m∠CBD

⇒70°=(3x+33°)+(5x+13°)

70°=8x+46°

70°-46°=8x

24°=8x⇒x=3°

x=3°

Then,

m∠ABC=3x+33°

put x=3°, we get

m∠ABC=3×3°+33°=9°+33°

m∠ABC=42°

f x + 12 ≤ 5 − y and 5 − y ≤ 2(x − 3), then which statement is true?

Answers

Interval notation for x+12<=5-y
y<=-x-7
(-infinity ,-x-7)

This is statement is true
Interval notation for 5-y<=2(x-3)
y=>11-2x
[11 - 2 x, ∞)


A sample of students is taken from the school's A honor roll. The school
estimates that there are 360 students on the A honor roll. Using this sample,
how many students on the A honor roll are 8th graders?

Answers

360 that is the answer to how many honors there are

Answer:

There are 126 8th grade A honor roll students.

Step-by-step explanation:

Tisha and her scout troop are heading to the Swing Time zipline park. They plan to purchase
the group package. With the package, the cost per person is $5 less than the normal cost for
an individual. There are 12 scouts in Tisha's troop. Her troop leader called ahead and found
that the total cost for the group will be $150. What is the normal cost for an individual?

Answers

Answer:

$17.5

Step-by-step explanation:

divide 150 by 12 to get 12.5. 12.5 is what they paid per-person with the discount. add 5 to get 17.5 and that is the on-discounted price

The normal cost for an individual is $17.50.

Let's denote the normal cost for an individual as "N."

According to the given information, with the group package, the cost per person is $5 less than the normal cost for an individual. So, the cost for each scout in Tisha's troop is "N - $5."

There are 12 scouts in Tisha's troop, so the total cost for the group is given as $150.

We can set up an equation based on the total cost:

Total Cost = Cost per Person × Number of People

$150 = (N - $5) × 12

Now, let's solve for the normal cost for an individual (N):

$150 = 12N - $60

12N = $150 + $60

12N = $210

N = $210 / 12

N = $17.50

So, the normal cost for an individual is $17.50.

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Can you please help me really quick I need help with this

Answers

Check the picture below.

Which equation represents the graphed function? –3x 2 = y –x 2 = y x – 3 = y 2x – 3 = y

Answers

Answer:

C) 3/2x-3=y

Step-by-step explanation:

-3 because that is the Y- intercept and 3/2 is the slope of the line. Y= mx +b is the formula and m is the slope and b is the y intercept.

In 2010, Cameron invested $10,000 in an account that earns 8. 5% interest compounded monthly. How much money would Cameron have gained by 2025?

Answers

Answer:

Step-by-step explanation:

First, we need to calculate how many years will earn percent.

2010---->2025= 15 years elapsed. Now we have our time, we need to plug it in our compound interest formula=

Principal(rate+1)^time or A=P(1+R)^t

10,000(0.085+1)^15

=$33,997.43

To calculate how much Cam earned, you need to subtract from original amount.

=$33,997.43-10,000=

---->$23997.43

Please mark me brainiest :)

30 points pls helppp

Select the equation of the line that passes through the point (2, –1) and has slope 3 in point-slope form.


(y + 1) = 3(x – 2)


(y – 1) = 3(x + 2)


(x + 2) = 3(y – 1)


(x – 2) = 3(y + 1)

Answers

Answer:

(y + 1) = 3( x +2)

Step-by-step explanation:

from equation,

y - y1 = m( x - x1)

given x1=2, y1= -1

m = 3 (slope)

substitute

y - (-1) = 3( x - 2)

ans: y+1= 3(x+2)

Draw a right trapezoid with bases of 8 and 10 cm

Answers

Answer:

Here is a picture of a right trapezoid with bases of 8 and 10 cm

Solve the following inequalities, if it is known that the function g is decreasing on its domain. g(5-x^2)≤g(3x-5), Dg=(-∞,4)

Answers

For the following inequalities, if it is known that the function g is decreasing on its domain. g(5-x^2)≤g(3x-5) the solution is mathematically given as

1 ≤ x < 6

What is the following inequalities g(5-x^2)≤g(3x-5)?

Generally, the equation for the inequalities is mathematically given as

g(5-x^2)≤g(3x-5)

therefore,

x^2<5x+6

-1< x <6

In conclusion, the solution to the inequalities are

1 ≤ x < 6

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