The ratio of pineapple juice to sparkling water that Sylvia and her
friends used to make punch last week was 3 : 2. They used 4 quarts of
water last week. This week, Sylvia and her friends want to make three
times as much punch.
PART A
Is the relationship between the amount
of pineapple juice and the amount of
sparkling water proportional? Explain.
PART B
How much pineapple juice do Sylvia and
her friends need for this week’s punch?
18 quarts
12 quarts
6 quarts
3 quarts

Answer:

Hello, I am not sure if you mean a dilation by 1/4. If it is, this will be the answer:

B (1, 1)

C (2, 3.5)

D (3, 0)

Step-by-step explanation:

Just divide each number by 4. B (4, 4) = B (4/4, 4/4) = B (1, 1)

Continue to do this for each coordinate set given.

Hope this helps!

The vertices of triangle B'C'D' are:

B'(-1, -1/2)

C'(0, 2)

D'(1, -3/2)

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To find the vertices of triangle B'C'D', which is a dilation of triangle BCD with center at the origin and a scale factor of 1/4,

We can follow these steps:

Find the coordinates of the centroid of triangle BCD.

The coordinates of the centroid G are:

[tex]x_G = (x_B + x_C + x_D) / 3 = (4 + 8 + 12) / 3 = 8[/tex]

[tex]y_G = (y_B + y_C + y_D) / 3 = (4 + 14 + 0) / 3 = 6[/tex]

Translate triangle BCD so that its centroid is at the origin.

We can do this by subtracting the coordinates of the centroid from the coordinates of each vertex:

B(4, 4) → [tex]B_1(4 - 8, 4 - 6) = B_1(-4, -2)[/tex]

C(8, 14) → [tex]C_1(8 - 8, 14 - 6) = C_1(0, 8)[/tex]

D(12, 0) → [tex]D_1(12 - 8, 0 - 6) = D_1(4, -6)[/tex]

Dilate the translated triangle [tex]B_1C_1D_1[/tex] by a scale factor of 1/4.

To do this, we can multiply the coordinates of each vertex by 1/4:

[tex]B_1[/tex](-4, -2) → B'(-4 x 1/4, -2 x 1/4) = B'(-1, -1/2)

[tex]C_1[/tex](0, 8) → C'(0 x 1/4, 8 x 1/4) = C'(0, 2)

[tex]D_1[/tex](4, -6) → D'(4 x 1/4, -6 x 1/4) = D'(1, -3/2)

Therefore,

The vertices of triangle B'C'D' are:

B'(-1, -1/2)

C'(0, 2)

D'(1, -3/2)

Learn more about triangles here:

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#SPJ2

Answer:

A

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

2 43/45

Step-by-step explanation:

Answer:

6 7/45

or

6 and 7/45

Step-by-step explanation:

8 3/5 - 2 4/9

= 43/5 - 2 4/9

= 43/5 - 22/9

= 277/45

= 6 7/45

1 = 84

3 = 252

7 = 588

10 = 840

Answer:

Step-by-step explanation:

Cheese

We want to find the total number of people that Annette surveyed given that we know a percentage and the number that the percentage represents.

We will find that the number of people that Annette survey is 480.

To get the solution:

Let's assume that she surveyed a total of X people.

Then we can write the equivalence:

100% = X

We know that the 37.5% is equivalent to 180 people, then we can write:

37.5% = 180

The two equations are:

100% = X

37.5% = 180

Now we can take the quotient between these two equations to get:

(100%/37.5%) = X/180

Solving for X we get:

(100%/37.5%)*180 = X = 480

So the total number of people surveyed is 480.

Answer:

480 people

180/X × 100 = 37.5%

180 × 100 = 37.5 × X

18000 ÷ 37.5 = 37.5 × x ÷ 37.5

480 people = x

Let the required no. be x

Then the equation is-

(150/100)x = 750

=> x = 750 × (100/150)

=> x = 500

Ans- 750 is 150 percent of 500.

Answer:

35

Have a nice day

Answer:

35

Step-by-step explanation:

35 is the biggest number that you can multiply to get both 35 and 70

35 x 1 = 35

35 x 2 = 70

Answer: S1:E7 ; S2:E1 ; S3:E5

Step-by-step explanation:

What we know:

**A lot of info is problem-specific.

How to solve:

Since we only need to write the equations, we simply need to find the x and y variables, and the total.

Process:

Problem 1:

Problem 2:

Problem 3:

Solution: S1:E7 ; S2:E1 ; S3:E5

Answer:

S1:E7  S2:E1  S3:E5 Have a great day...

Step-by-step explanation:

Answer:

1) 2² + 3² - 2 = 4 + 9 - 2 = 11

3² + 2² - 3 = 9 + 4 - 3 = 10

2) 4(3²) + 3(2) + 3 = 36 + 6 + 3 = 45

4(2²) + 3(3) + 3 = 16 + 9 + 3 = 28

3) 2(3) + 3 + 1 = 10

4) 3(2²) + 2(3) + 2 = 12 + 6 + 2 = 20

3(3²) + 2(2) + 3 = 27 + 4 + 3 = 34

5) 2⁴ - 3² + 3 = 16 - 9 + 3 = 10

6) 2³ - 2(3)(3) - 5 = 8 - 18 - 5 = -15

3³ - 2(3)(3) - 5 = 27 - 18 - 5 = 4

1) x = 3, y = 2

2) neither

3) x = 2, y = 3

4) neither

5) x = 2, y = 3

6) neither

Answer:

247/100

Step-by-step explanation:

can be writen as 2.47 in dedimal form

247/100, I believe it's the answer, I'm not sure

Answer:

you can basically graph different points to form a decagon so you can have a 10 point combination and then say the order you went in.

Step-by-step explanation:

Answer:

4) 11.75   6) 23   10) 14

Step-by-step explanation:

4) To find the mean, you would find the average of all the data. To do that, you add all the numbers together, then divide them by the number of numbers there are. So: (14+14+10+12+11+13+11+11+14+10+13+8)/12=141/12=11.75

6) To find the median, you would find the number in between all the numbers. So: 16,20,22,22,22,24,26,26,28,28,28. The median of all of this would be between 22 and 24, so it would be 23.

10) Since one week has 7 days, and the cat drank 2 cups per day, you can multiply 7 and 2 to get 14, and that would be your answer.

Answer:

D

Step-by-step explanation:

20/5=4

28/7=4

Answer:

y=(x*9)-4

Step-by-step explanation:

for example:

0*9=0

0-4=-4

4*9=36

36-4=32

2*9=18

18-4=14

hope this helped ;)

Answer:

radius (r)= 2.25

Step-by-step explanation:

area (A)=16cm^2

A = πr^2

16= (22/7)r^2

(16*7)/22=r^2

√5.09= r

r=2.25

Answer:

A

Step-by-step explanation:

60/15=4 0.4

90/15=6 0.46

90/15=6 0.466

The 6 is repeating, so it can only be D and A.

The number at the top is divided by the number at the bottom in a fraction.

We are dividing 7 by 15, so it can not be D and must be A.

Answer:

5:3

Step-by-step explanation:

The ratio is 5 to 3

chocolate being 5 and oatmeal being 3

Answer:

50

Step-by-step explanation:

34%=34/100

34/100 = 17/50

Answer:

D. y=100-30x

Step-by-step explanation:

Every fpm (Feet Per Minute), the man is descending 30 feet

x = feet per minute

y = total amount

Answer:

7 units from (-3,2)(,2)and(,2)

Step-by-step explanation:

The purpose of this task is for students to solve a mathematical problem using points in the coordinate plane. This task also helps lay the foundation for understanding operations on signed numbers without formally introducing those notions, which are not expected until 7th grade (see 7.NS.1). Students will not have the full machinery needed to find distances between two arbitrary points in the plane until they have studied the Pythagorean Theorem in 8th grade. However, it is straightforward for them to find horizontal and vertical distances, which mirrors how one might represent sums and differences of signed numbers on a number line. The solution for the first part shows how these questions can be represented using absolute values (as described in standard 6.NS.C.8), although students are unlikely to make this connection without being asked to do so. If students are asked to solve this problem on their own first, it could be used to launch a discussion of the relationship between the the absolute value of coordinates of points in the plane and their distance to the respective axes.

Please note that students will have to assume that the points have integer coordinates, which is reasonable but worth mentioning.

Solution

The distance between points B and C is 5 units, as indicated below.

We can determine the distance between points B and C by counting the units between the two points since they are on the same vertical line which happens to be a grid line.

We can also note that the coordinates for B are (3,2) and so it is |2| units above the x-axis. Similarly, the coordinates for C are (3,−3), so it is |-3| units below the x-axis. Thus, the distance between B and C is

|2|+|−3|=5

units.

The distance between points D and B is 7 units, as indicated below.

The distance between points D and E is 4 units, as indicated below.

Point C is the only one of points A,…E that is both 4 units away from (−1,−3) and 2 units away from (3,−1). There is another point that satisfies these two criteria (which is the other intersection point of the circle of radius 4 and circle of radius 2 shown below), but it does not have integer coordinates and is not one of the points identified in the task

Answer:

The volume in Cubic feet is 60 cft.

Step-by-step explanation:

we have to divide 20 by 120. 120 ÷ 20 = 60. Even though 5 is divisible by 60, we won't be doing that. 60 cft. is the answer.

Hope this helps!

Answer:

it is 500 cubic feet, when it is a triangle or triangular prism we divide it in half since its half a square, 120 inches=10 feet. 10ftx20x1/2=100. 100x5=500

Answer: The answer will be created shortly.

We want to see if the relationship between the number of weeks and the money put in the jar is linear or not, we will see that this is not a linear equation (it is exponential).

So a linear relation is something like:

y = a*x + b

Note that for any value of x, an increase of 1 unit gives:

y = a*(x+ 1) + b = (a*x + b) + a

So for increases of 1 unit in the x-value, we have increases of "a" units on the y-value.

In the given situation we have:

and so on.

Writing that as points we have:

(1, $1)

(2, $3)

(3, $7)

(4, $15)

Notice that for equal increases in the x-value, (increases of 1 unit) we don't equal increases in the y-value (first increases by $2, then by $4, etc...) So this is not a linear equation, this is actually exponential.

If you want to learn more, you can read:

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The relationship of the ordered pair that represents Mallory savings is a nonlinear relationship.

Let x represents the number of weeks, and y represents the amount put in the jar, each week.

So, we have the following highlights for 6 weeks.

The ordered pairs can then be represented as:

[tex](x,y) = (1,1)(2,2)(3,4)(4,8)(5,16)(6,32)[/tex]

As the x values increase, the y values increase too, but the y values do not increase at a constant rate.

This means that the relationship is not linear; it is an exponential relationship.

Hence, the relationship is a nonlinear relationship.

Read more about linear relationships at:

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Answer:

  4188.79 yd^3

Step-by-step explanation:

The formula for the volume of a sphere is ...

  V = 4/3πr^3

A sphere with a diameter of 20 yards has a radius of 10 yards, so its volume is ...

  V = 4/3π(10 yd)^3 = 4000π/3 yd^3 ≈ 4188.79 yd^3

Rounded to tenths, that's approximately 4188.8 yd^3.

Answer: 4200? or 10 because there is a minus sign

Step-by-step explanation:

if we start with the parentheses you can see 4 x 15 = 60 and your subtracting 70 minus 60 so it would be 10

Step-by-step explanation:

Given expression:

It has two terms:

If we need to solve it then: