15 POINTS!

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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

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:

Option D: [tex]\frac{2}{5}[/tex] is the x-coordinate

Explanation:

It is given that the coordinates of the line segment are A(3,2) and B(6,11).

Since, the line is partitioned by the point C by the ratio AC : BC = 2 : 3

The distance between the x-coordinates is 3 units.

To determine the value of the x-coordinate for point C, let us divide the value of x-coordinate from the ratio divided by the sum of ratio.

The value of x-coordinate from the ratio is 2.

Sum of the ratio is 2 +3 = 5

Thus,

The x - coordinate = value of x-coordinate from the ratio / Sum of ratio = 2/5

Substituting the values, we have,

The x - coordinate of the Point C = [tex]\frac{2}{5}[/tex]

Thus, Option D is the correct answer.

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.

Martina runs 10.5 miles in 75 minutes

Solution:

Given that,

Martina runs 7 miles in 50 minutes

Therefore, miles ran in 1 minute is:

[tex]Miles\ ran\ in\ 1\ minute = \frac{7}{50}\ miles[/tex]

At the same rate how many miles will she run in 75 mins

Thus, to find the miles ran in 75 minutes:

[tex]Miles\ ran\ in\ 75\ minute = \frac{7}{50}\ \times 75\\\\Miles\ ran\ in\ 75\ minute = 0.14 \times 75\\\\Miles\ ran\ in\ 75\ minute = 10.5[/tex]

Thus she runs 10.5 miles in 75 minutes

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:

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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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:

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:

B: 2

Step-by-step explanation:

2 is the y-intercept of the given line.

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:

1,864

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

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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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

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:

D. or 5(w+10)

Hope this helps :)

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.

Answer:

12 m squared

Step-by-step explanation:

area of triangle is 1/2 base x height

base x height is 28 so 1/2 is 14

the area of the rectangle is base x height

1 x 2 = 2

14-2 = 12

Answer:

138/11

Step-by-step explanation:

5 3/4 * 2 2/11

23/4 * 24/11

(552/44)/4

138/11

The number of coins Sparrow has at the beginning of the game is 92 coins.

How many coins did Sparrow have at the beginning of the game?

Total number of coins = 210.

Ratio of coins belonging to Ahab, Sparrow and Davy = 4 : 5 : 6

Let

x = multiplying factor

The number of coins to Ahab = 4x

The number of coins to Sparrow = 5x

The number of coins to Davy = 6x

Since, total number of coins = 210

So

4x + 5x + 6x = 210

15x = 210

Divide both sides by 15

x = 16

Therefore,

The number of coins to Sparrow = 5x

= 5 × 16

= 80 coins

At the end Ahab and Davy wins 5 and 7 coins respectively

So at the beginning of the game, the number of coins Sparrow has = 80 + 7 + 5

= 92

Step-by-step explanation:

The second one is the first claim, because it is a traingles and one square.

The third one is the sond claim because they are a part of the rectangular so moving them outside of it would increase the area, I think, if that makes sense.

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.

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:3

Step-by-step explanation:

5,7,12

The answers are option C) segment and option D) ray

Step-by-step explanation:

Line :

Point :

Segment :

Ray :

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:

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:

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