Marilyn and Vanessa earn service points for every hour they volunteer at the local library. Marilyn
has earned 330 points, which is 165% of the number of points that Vanessa has earned. How
many points has Vanessa earned?

The solution is x = 2 and y = 4

Solution:

Given system of equations are:

y = 2x -------- eqn 1

x = -y + 6 ----------- eqn 2

We can solve the system of equations by substitution method

Substitute eqn 1 in eqn 2

x = -2x + 6

Move the variables to one side and constants to other side

x + 2x = 6

3x = 6

Divide both sides of equation by 3

x = 2

Substitute x = 2 in eqn 1

y = 2(2)

y = 4

Thus the solution is x = 2 and y = 4

Answer:

1,864

Step-by-step explanation:4 X 1398 would be 5592 then you divide it by 3 and get 1,864

Question

P c

4 14

5 17

6 20

7 23

There are 3 caterpillars on each plant, and there are 2 caterpillars on the ground. The table shows how the number of caterpillars, c, depends on the number of plants, p. Choose the equation which represents the rule.

A) c = 3p + 3

B) c = 2 − 3p

C) c = 3p − 2

D) c = 3p + 2

Answer:

c = 3p + 2 is the equation that shows relation between number of caterpillars and plants

Solution:

Given that,

There are 3 caterpillars on each plant

And there are 2 caterpillars on the ground

Let the number of plants be "p"

Let the number of caterpillars be "c"

The equation that shows relation between number of caterpillars and plants is:

If there are 3 caterpillars on each plant, then for "p" plants, there will be "3p" caterpillars

Number of caterpillars = 3p + 2 caterpillars on the ground

Therefore,

Number of caterpillars = 3p + 2

c = 3p + 2

Thus the equation is found

Answer:

180cm

Step-by-step explanation:

Vol of sphere = (4/3) pi r^3 and vol of cylinder = pi r^2 h

so

(4/3) pi 15^3 = pi (5)^2 h

(4/3) * 15^3 = 25h

h =  [(4/3) * 15^3 ] / 25  =  180 cm

Step-by-step explanation:

according to the question,

vol.of sphere = vol of cylinder

4/3πR³=πr²h

refer to the attached file.

thanks for the question!!

Answer:

[tex]x<5[/tex]

Step-by-step explanation:

we have

[tex]-7x+14>-3x-6[/tex]

Solve for x

Group terms that contain the same variable

[tex]-7x+3x>-6-14[/tex]

[tex]-4x>-20[/tex]

Divide by -4 both sides

Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol  

so

[tex]x<5[/tex]

The solution is the interval (-∞,5)

All real numbers less than 5

In a number line the solution is the shaded area at left of x=5 (open circle)

The value of x=5 is not included in the solution

See the graphs

First Case:

Here we have the following function:

[tex]h(x)=2sin(2x)-3[/tex]

In order to graph this function, first let's take:

[tex]f(x)=sin(x)[/tex]

Step 1. Compress horizontally this function by 1/2, so it becomes:

[tex]f_{1}(x)=sin(2x)[/tex]

Step 2. Stretch vertically this function, so it becomes:

[tex]f_{2}(x)=2sin(2x)[/tex]

Step 3. Shift the graph of the function three units down.

[tex]f_{2}(x)=2sin(2x)-3[/tex]

Second Case:

Applying a similar method, we get:

Step 1. Compress horizontally this function by 1/2, so it becomes:

Step 2. Stretch vertically this function, so it becomes:

Step 3. Shift the graph of the function tow units down.

Finally, the graphs are shown below.

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Answer:

The answer is D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Midpoint of AC = (–1, –1)

Solution:

In the given graph we can find the coordinates of A and C.

Coordinates of A = (–4, 2)

Coordinates of C = (2, –4)

Here, [tex]x_1=-4,x_2=2,y_1=2,y_2=-4[/tex]

Let us find the midpoint of the segment AC.

Midpoint formula:

[tex]$\text{Midpoint} =\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]

               [tex]$=\left(\frac{-4+2}{2}, \frac{2-4}{2}\right)[/tex]

               [tex]$=\left(\frac{-2}{2}, \frac{-2}{2}\right)[/tex]

               [tex]$=(-1, -1)[/tex]

Midpoint of AC = (–1, –1)

Option D is the correct answer.

Hence the coordinates of the midpoint of the line segment AC is (–1, –1).

Answer:

Step-by-step explanation:

x = small barrettes

y = large barrettes

13x + 11y = 142.......multiply by -1

13x + 12y = 149

-----------------------

-13x - 11y = -142 (result of multiplying by -1)

13x + 12y = 149

------------------------add

y = 7..........large barrettes used 7 yards

13x + 11y = 142

13x + 11(7) = 142

13x + 77 = 142

13x = 142 - 77

13x = 65

x = 65/13

x = 5........small barrettes used 5 yards

Final answer:

Kimberly uses 5 yards of ribbon for each small barrette and 7 yards of ribbon for each large barrette. The problem was solved using a system of equations and the elimination method.

Explanation:

To solve the problem using a system of equations and the elimination method, we first need to define variables for the unknown quantities we are trying to find. Let's let x represent the number of yards of ribbon used for each small barrette and y represent the number of yards of ribbon used for each large barrette.

From the information given, we can set up the following system of equations representing the two craft fairs:

For Rockport: 13x + 11y = 142

For Westminster: 13x + 12y = 149

Now, we will solve these equations using the elimination method. To eliminate one of the variables, we can subtract the first equation from the second equation.

13x + 12y - (13x + 11y) = 149 - 142This simplifies to:

y = 7

Using the value of y, we can substitute it back into either equation to find x. Plugging it into the first equation:

13x + 11(7) = 142

13x + 77 = 142

13x = 142 - 77

13x = 65

x = 65 / 13

x = 5

Therefore, Kimberly uses 5 yards of ribbon for each small barrette and 7 yards of ribbon for each large barrette.

Answer:

The value of y when x is 0 is 3

The value of x when y is 0 is 2

Step-by-step explanation:

3x + 2y = 6

3(0) +2y=6—> replace x with 0

2y=6—> divide both sides by 2

y=6

And do the same for y!

The equation 3x + 2y = 6 is a linear equation in standard form. Also, the equation y = 9 + 3x is an equivalent linear equation in slope-intercept form where b is 9 (y-intercept) and m is 3 (slope). A table of (x, y) values derived from this equation would plot as a straight line on a graph.

The equation you're looking at, 3x + 2y = 6, is indeed a linear equation in standard form. As a refresher, a standard form equation is written as Ax + By = C, where A, B, and C are constants, and x and y represent variables.

Let's consider another similar example, y = 9 + 3x. In this equation, which is in slope-intercept form, the b term has been set equal to 9 and the m term has been set equal to 3. We can fill out table A1 with different values for x and calculate the corresponding values of y. When plotted on a graph, these points will form a straight line, as dictated by the nature of linear equations.

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The notation V(r) actually gives the volume of air inside the basketball.  V(r) is volume as a function of radius, r  It can be written as:  V(r) = 4/3πr³  So, for any value of r, we can get the volume V.  For, example, when r = 7cm  we can say;  V(7) = 4/3 x 22/7 x 7³ = 1437.33 cm³

Answer:

47,754,000

Step-by-step explanation:

4 is located at thousand (place)

Answer:

b

Step-by-step explanation:

Answer:

The volume is 160 cubic units

Step-by-step explanation:

1. Information given to us to answer the question correctly:

8 = base length

5 = base width

12 = height

2. Let's recall the formula of the volume of a pyramid with rectangular base:

Volume = (Length * Width * Height)/3

Volume = (8 * 5 * 12)/3

Volume = 480/3 ?

Volume = 160 cubic units

The unknown resistance is approximately 0.44 Ω.

Solution:

Total (equivalent) resistance = 0.28 Ω

Resistance 1 = ?

Resistance 2 = 0.81 Ω

To find the unknown resistance.

Formula for determining equivalent resistance in a parallel circuit:

[tex]$\frac{1}{R_{e q}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}[/tex]

Substitute the given values in the formula.

[tex]$\frac{1}{0.28}=\frac{1}{R_{1}}+\frac{1}{0.81}[/tex]

[tex]$3.571=\frac{1}{R_{1}}+1.235[/tex]

Subtract 1.235 on both sides of the equation, we get

[tex]$2.282=\frac{1}{R_{1}}[/tex]

Take reciprocal to find [tex]R_1[/tex].

[tex]$R_{1}=\frac{1}{2.282}[/tex]

[tex]$R_{1}=0.44[/tex]

[tex]R_1[/tex] = 0.44 Ω

The unknown resistance is approximately 0.44 Ω.

Answer:

1. 8s-6

2. 13t-6

3. 32r

4. 5-4q+42r

5.no like terms

6. 107-106x

7. 16a2−15a

8. 28t

9. 4s+r+2rs

10. 7pt-3p+4t

11. 26x2−x

12. 107c

13. 16q+9

14. -23k

15. 151x

Step-by-step explanation:

Answer:

B: 2

Step-by-step explanation:

2 is the y-intercept of the given line.

Answer: a=-5

Step-by-step explanation:

2(a + 3) = −4

2a+6=-4

2a=-10

a=-5

Answer:

Your answer is a= -5. So A would be your answer.

Final answer:

The constant of proportionality is $0.833 per package, and the equation representing the cost C of sending p packages is C = 0.833p.

Explanation:

To find the constant of proportionality for the given shipping situation, we divide the total cost by the number of packages shipped. In this case, it costs $5 to send 6 packages, which gives us a constant of proportionality of $5 / 6 packages. This can be simplified to approximately $0.833 per package.

The equation to represent this relationship would be C = 0.833p, where C represents the total cost in dollars and p represents the number of packages. This shows that for each package sent, the cost will increase by approximately $0.833.

Step-by-step explanation:

Total Distance run by Katrina

[tex]=6 \times circumference \: of \: circular \: track \\ \\ = 6 \times 2 \pi \: r \\ = 6 \times 2 \times 3.14 \times 20 \\ = 240 \times 3.14 \\ = 753.6 \: m \\ [/tex]

Step-by-step explanation: Begin by studying the pattern.

Notice that the 1 + 1 is 2, 2 + 3 is 5, 5 + 5 is 10, and 10 + 7 is 17.

So thus far, we're adding 1, 3, 5, and 7. Notice that each of these numbers have a difference of 2 so we would add 9 to get to next number and so on.

Answer:

1. a) $ 25

b) $65

2) a) 246,000 followers

b) In 20 years

3a) $65

b) $85.25

Step-by-step explanation:

1. A linear equation is modeled by [tex]y=mx+b[/tex]

where b is the one time fee you pay and m=$8 is how much you pay per hour.

y is the total cost and x is the number of hours.

Hence the equation becomes: [tex]y=8x+b[/tex]

Since Jill rented for 3 hours and paid $49, x=3 and y=49.

We substitute and solve for the one-time fee, b.

This implies that:

[tex]49=8(3)+b[/tex]

49=24+b

b=49-24=25.

a) The fee is $25

b) We now write the equation in full to get: [tex]y=8x+25[/tex]

To find the cost for 5 hours we put x=5 into this equation and solve for y.

[tex]y=8(5)+25[/tex]

y=40+25=$65

2a) We still use the equation y=mx+b.

b is the number of followers he started with.

This time m=-12,000 because he is losing followers at the rate of 12,000

The equation becomes: y=-12,000x+b

After 4 years he was down to 198,000.

This implies that, when x=4,y=198,000

We substitute to get:

[tex]198,000=-12,000(4)+b[/tex]

[tex]198,000=-48,000+b[/tex]

[tex]b=198,000+48,000=246,000[/tex]

Hence he started with 246,000 customers

b) The equation now becomes [tex]y=-12,000x+246,000[/tex]

To find how many years he will have 6000 followers, we substitute y=6000 and solve for x.

[tex]6000=-12,000x+246,000[/tex]

[tex]6000-246,000=-12,000x[/tex]

[tex]-240,000=-12,000x[/tex]

[tex]x=\frac{240,000}{12,000}[/tex]

x=20.

3. We still use the equation: y=mx+b.

This time m=0.25 is the rate per mile.

This implies y=0.25x+b

Since Kyle drove 32 miles and spent $73, we have y=73 when x=32

We substitute these values and solve for x.

[tex]73=0.25(32)+b[/tex]

[tex]73=8+b[/tex]

[tex]b=73-8[/tex]

[tex]b=65[/tex]

Hence the one-time fee is $65

b) The equation now becomes:

[tex]y=0.25x+65[/tex]

To find how much it will cost to drive 81 miles, we substitute x=81 and solve for y.

[tex]y=0.25*81+65[/tex]

[tex]y=20.25+65[/tex]

[tex]y=85.25[/tex]

The cost for 81 miles is $85.25

Answer:

y = (2/3)x -3

Step-by-step explanation:

find the slope using ( y1 - y2 ) / ( x1 - x2)

slope: 2/3

y-intercept: -3

use y = mx + b

Answer:3

Step-by-step explanation:

5,7,12

To find the proportion of trick-or-treaters not dressed as knights, subtract the proportion dressed as knights from 1. Therefore, the proportion of trick-or-treaters not dressed as knights is 7/13.

To find the proportion of trick-or-treaters that were not dressed as knights, we need to subtract the proportion of trick-or-treaters who were dressed as knights from 1. If 6 out of every 13 trick-or-treaters were dressed as knights, then the proportion of trick-or-treaters not dressed as knights is 1 - (6/13) = 7/13.

In the realm of probability and proportions, calculating the proportion of trick-or-treaters not adorned in knightly attire involves a straightforward yet insightful approach. We initiate this quest by recognizing that the sum of all probabilities within a given context equals 1, which encapsulates all possible outcomes. Since we know that 6 out of every 13 trick-or-treaters don the guise of knights, we can deduce that the proportion of those not dressed as knights is the remainder of this whole, represented as 1 - (6/13). Simplifying this expression reveals that 7 out of every 13 trick-or-treaters fall into the category of not being attired as knights.

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Work Shown:

x - 3.4 > 17/68

x - 3.4 > 0.25

x - 3.4 + 3.4 > 0.25 + 3.4 .... add 3.4 to both sides

x > 3.65

Any number larger than 3.65 will work in place of x

Choice A does not work since 3.4 is not larger than 3.65

Choice B and choice C is the same story as well since 21/68 = 0.3088 approximately

Only choice D is larger than 3.65

1. The given squares perimeter after dilation is 16 cm. Perimeter is reduced by 48 cm due to dilation.

2. The squares area is 16 square centimeters after dilation. The area reduces by 240 square cm due to dilation

Step-by-step explanation:

Step 1; First, we determine the coordinates of the points given in the graph. By plotting we determine that the points are; K (-8, -8), L(8,-8), M(8, 8) and N(-8, 8).

Step 2; We calculate the new coordinates of the square KLMN by multiplying the scale factor with each of the coordinate's x and y values.

8 × [tex]\frac{1}{4}[/tex] = 2, -8  [tex]\frac{1}{4}[/tex] = -2 are the different values in the four coordinates.

So by multiplying the scale factor we get the dilated square's points as

K (-2, -2), L(2,-2), M(2, 2) and N(-2, 2).

Step 3; The perimeter of a square is given by 4 times its side length. As the units are in centimeters, we determine the side length is 4 cm whereas it is 16 cm for the undilated square.

Perimeter of original square = 4 × 16 cm = 64 cm

Perimeter of the dilated square = 4 × 4 cm = 16 cm.

Change in perimeter = Perimeter of original square - Perimeter of the dilated square = 64 cm - 16 cm = 48 cm.

Step 4; The area of any given square is the side length of the square squared. The side length of the original square is 16 cm whereas the side length of the dilated square is 4 cm.

Area of original square = 16 × 16 cm = 256 square cm

Area of the dilated square = 4 × 4 cm = 16 square cm.

Change in area = area of original square - area of the dilated square = 256 cm - 16 cm = 240 square cm.

Answer:

2 minuets

Step-by-step explanation:

Set up a ratio:

57 jumping jacks / 1 minute = 100 jumping jacks / x minutes

Cross multiply:

57x = 100

Divide both sides by 57:

X = 100/57

X = 1.754 minutes = 1 minute 45 seconds

Answer:

y = 8/3

Step-by-step explanation:

3(y + 2) = 14

3y + 6 = 14

3y = 14 - 6

3y = 8

y = 8/3

Answer:

Step-by-step explanation:

3(y + 2) = 14

3y + 6 = 14

3y = 14 - 6

3y = 8

y = 8/3 or 2 2/3

Answer:

138/11

Step-by-step explanation:

5 3/4 * 2 2/11

23/4 * 24/11

(552/44)/4

138/11