Patricia and her brother Ian help themselves to a pitcher of lemonade on the kitchen counter. Patricia takes a glass and fills it with p ounces of lemonade. Ian takes a bigger glass and pours himself 20% more lemonade than Patricia poured in her glass. Write an expression to represent the quantity of lemonade(in ounces) in Ian’s glass in terms of the quantity in Patricias glass (p).

Part A- Write an expressionism terms of p that shows how many more ounces Ian poured in his glass than Patricia poured in hers.

Part B-Write an expression in terms of p to represent the amount of lemonade (in ounces) Ian poured in his glass. Include two terms in your expression.

Part C- combine the like terms in the expression from part B to create an equivalent expression.

Part D- using the simplified expression you wrote in part C, and domain what it means to have 30% more of a given quantity.

Part E- suppose that Patricia drinks one-fourth of the lemonade in her glass. Write an expression in terms of p that represents the number of ounces Patricia drank.

Part F- in part E, Patricia drank one-fourth of the lemonade in her glass. Write and expression in terms of p that represents the number of ounces Patricia has left in her glass. Include two terms in your expression.

Part G- combine the like terms in the expression from part F to create an equivalent expression.

Part H- using the simplified expression you wrote in part G, explain what it means to have 1/4 less of given quantity.

Please help me I’m struggling on this!

Answer:

21/40

Step-by-step explanation:

Answer:

0.525 or 21/40. Find the LCM between the denominators which is 40.

pentagon for sure based on the options

Answer:

4 million a day, 28 million a week, 145,600,000 a year.

Step-by-step explanation:

6 million times 4 is 24 million. Which explains 4 million daily.

4 million times 7 days a week is 28 million weekly.

28 million times 52 weeks a year is 145,600,000.

Answer:

D is the answer

Step-by-step explanation:

A filled circle means "or equal to" in which this case the symbol is less than or equal to, making the dot filled. Since 2 is greater than x, the line would start on the two and continue farther down the line to show that anything 2 or greater is more than x.

Answer:

C.) 2.07 × 10^6

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The solution is Option C.

The value of the number 2,070,000 written in scientific notation is

A = 2.07 x 10⁶

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as A

Now , the value of A is

A = 2,070,000

Now , to write the number in scientific notation ,

Multiply the number 207 with powers of 10

So , the value of A will be

A = 207 x 10⁴

Now , the number 207 can be written as 2.07 x 10²

On simplifying the equation , we get

A = 2.07 x 10² x 10⁴

A = 2.07 x 10²⁺⁴

A = 2.07 x 10⁶

Therefore , the value of A is 2.07 x 10⁶

Hence , the value of the number is 2.07 x 10⁶

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Answer:

5

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

We will use the KFC method to figure out the answer:

3/5 ÷ 2/1

We keep the first fraction

3/5 ÷ 2/1

Flip the last fraction (swap the numbers)

3/5 ÷ 1/2

Change the sign (to a multiplication symbol)

3/5 x 1/2

Then, finally, to solve for the answer, we multiply across (3 x 1 and 5 x 2).

3 x 1 = 3

5 x 2 = 10

The answer is 3/10 because it cannot be simplified any further.

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Answer:

Step-by-step explanation:

307 divided by 7 is the number of students in each bus with the remainder 6. As the 6 students cannot be fit into the bus and had to travel by car.

Thus we can conclude that:

307= 7x + 6 (6 extra students)

Take away 6 on both sides

7x = 301

i hope this helps i tried my best

x= 43

There are 43 students on each bus.

Answer:

62 people on each bus

Step-by-step explanation:

316-6=310.

310÷5=62 so there will be 62 people riding on each bus.

Answer:

12

Step-by-step explanation:

He makes 5 scores.

5 x 3 = 15

He earns 15 points.

He misses 4 goals.

4 x 4/3 = 3

He loses 3 points.

15 - 3 = 12.

Answer:

12.

Step-by-step explanation:

I had took the test, and I had got it 100% right !!

Answer:

9

Step-by-step explanation:

If this is referring to plots on a grid the answer would be positive since your just counting the distance and its not an actual equation. 1 negative space plus 8 positive spaces equals 9

Answer:

9

Step-by-step explanation:

-1 is 1 away from zero and zero is 8 away from 8 adding this toghter your answer would be 9

Answer:

2(x+7)(x-7)

Step-by-step explanation:

1. In 2x^2-98, there is a common factor of 2

2. The equation therefore becomes 2 (x^2 - 49)

3. We know that x^-49 is a difference of two squares and can therefore be factored into (x+7)(x-7)

4. Therefore the fully factored answer is 2(x+7)(x-7)

Answer:

yes it's on a 1.5 scale factor.....I think. The question you put at the top threw me off at first but the picture makes sense. I'm not entirely sure if this is right but if you adjust the triangle to be the same way as the other one then you will see which sides correspond to each other. Each number can be multiplied by 1.5 to get the number that is on the side of the other triangle that corresponds with it....if that makes any sense

Answer:

$3.53

Step-by-step explanation:

hot dogs = $1.25 each

2 hot dogs = 1.25 × 2

= $2.50

A serving of onion rings = $2.99

Drink = $0.98

Total amount with Karen = $10.00

how much change will Karen receive?

Total cost = 2 hot dogs + A serving of onion rings + Drink

= $2.50 + $2.99 + $0.98

= $6.47

Karen's change = Total amount with Karen - Total cost

= $10.00 - $6.47

= $3.53

Answer:

First blank: 11 Second blank: 12

Step-by-step explanation:

Since this is a parallelogram AB is parallel to DC and AD is parallel to BC.

Another thing the image includes is the lengths from the points, the opposing points have equal distances from the midpoint.

Answer:

A. 11

B. 12

Step-by-step explanation:

The length AD of  is  11  centimeters and the length of DC is  12  centimeters.

Correct for plato

Answer:

x = 20

Step-by-step explanation:

The length of the segment EG can be obtained as the sum of the segments EF and FG, that is:

EG = EF + FG

We are given:

EF = 4x + 14

FG = 50

EG = 144

Thus, we set the equation:

144 = 4x + 14 + 50

Simplifying:

144 = 4x + 64

Subtracting 64:

80 = 4x

Dividing by 4:

x = 80/4 = 20

x = 20

300 meters per minute: 3600 meters per hour

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Answer: SAS

Explanation: There are two sides that are congruent and there is one vertical angle between them which are always congruent.

Answer:

3

Step-by-step explanation:

3

ΔBCE is half the base length and two third the height of ΔACF, therefore,

the area of ΔBCE is less than half the area of ΔACF.

The area of triangle ΔBCE is 60 cm².

Reasons:

In ΔACF, we have;

B = The midpoint of AC

Point E and point D are points on side CF

Distance C to D = Distance D to E = Distance E to F

Area of ΔACT = 180 cm²

Required:

Area of ΔBCE

Solution:

[tex]Area \ of \, \Delta ACF = \mathbf{\dfrac{1}{2} \times AC \times CF} = 180 \ cm^2[/tex]

[tex]In \ \Delta BCE, \, BC = \dfrac{1}{2} \times AC \ and \ CE = \dfrac{2}{3} \times CF[/tex]

Therefore;

[tex]Area \ of \ \Delta BCE = \dfrac{1}{2} \times BC \times CE = \dfrac{1}{2} \times \left(\dfrac{1}{2} \times AC \ \right) \times \dfrac{2}{3} \times CF[/tex]

[tex]\dfrac{1}{2} \times \left(\dfrac{1}{2} \times AC \ \right) \times \dfrac{2}{3} \times CF = \dfrac{1}{2} \times \dfrac{2}{3} \times \left(\dfrac{1}{2} \times AC \ \right)\times CF = \mathbf{\dfrac{1}{3} \times Area \ \Delta ACF}[/tex]

Therefore;

[tex]Area \ of \ \Delta BCE = \dfrac{1}{3} \times Area \ \Delta ACF = \dfrac{1}{3} \times 180 = 60[/tex]

The area of triangle ΔBCE = 60 cm².

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Answer:

3 min per lap

Step-by-step explanation:

15 (minutes)/5 (lap)= 3 minutes

Answer:3 minutes per lap

Step-by-step explanation:

Answer:

(3, 1), (6, 2), (9, 3)

Step-by-step explanation:

x = 3

[tex]y=\frac{1}{3} *\frac{3}{1}= \frac{3}{3} =1[/tex]

x = 6

[tex]y=\frac{1}{3} *\frac{6}{1} =\frac{6}{3}=2[/tex]

x = 9

[tex]y=\frac{1}{3}* \frac{9}{1}=\frac{9}{3} =3[/tex]

Answer:

x=-1

Step-by-step explanation:

3(x−4)=15x

Use the distributive property to multiply 3 by x−4.

3x−12=15x

Subtract 15x from both sides.

3x−12−15x=0

Combine 3x and −15x to get −12x.

−12x−12=0

Add 12 to both sides. Anything plus zero gives itself.

−12x=12

Divide both sides by −12.

x=  

−12

12

​  

Divide 12 by −12 to get −1.

x=−1

Answer:

[tex]3(x- 4)=15x[/tex]

[tex]3x-12=15x[/tex]

[tex]3x-12+12=15x+12[/tex]

[tex]3x=15x+12[/tex]

[tex]3x-15x=15x+12-15x[/tex]

[tex]-12x=12[/tex]

[tex]\frac{-12x}{-12}=\frac{12}{-12}[/tex]

[tex]x=-1[/tex]

Answer:

the answer is 5,500/p = 55/100

Step-by-step explanation:

Answer:

.the last one

Step-by-step explanation:

Answer:

dude I really wish I knew how to do this but if I try to help you I would be guessing and it would most likely be wrong.

Could you help me with my question?

it's for Agriculture

Answer:

y=2x (x=0)

Step-by-step explanation:

swap the sides of the equation 2x=0 then divide both sides of the equation by 2 nd you get your answer which would be x=0

Answer:

$70.80

Step-by-step explanation:

Answer:

$2.88

Step-by-step explanation:

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Answer:

7

Step-by-step explanation:

Answer:

m<2.5

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

15c + 25s ≤ 1500

Step-by-step explanation:

Let the number of stools be s

Let the number of chairs bought be c

If each tools cost $15, s stools will cost $15c

If a chairs cost $25, c chairs will cost $25s

Total costs = 15c + 25s

If the center cannot spend more than $1500, then the required equation will be 15c + 25s ≤ 1500

The inequality sign will be less than and equal to since they cannot spend an amount greater than $1500.

Hence the correct equation is  15c + 25s ≤ 1500

Answer:

40000 and 12.5% respectively

Step-by-step explanation:

soln:

given,

cost price(c.p)=320000

selling price(s.p)=280000

loss(l),loss percentage(l%)=?

we know,

l=c.p-s.p

or,l=320000-280000

•°•l=40000

now,

l%=l/c.p*100%

or,l%=40000/320000*100%

•°•l%=12.5%