Activity 4: Fair Share!

Directions: apply the rules in multiplication of integers in answering the following activity.
​

Answer: 8x + -31 + 5y + 35 + 6x + 3 = 180. Reorder the terms: -31 + 35 + 3 + 8x + 6x + 5y = 180.

Answer:

y + 10 =2( x +1)

or

y -2 + 2( x -5)

These both name the same line.

Step-by-step explanation:

First we need to find the slope.  The slope is the change in y over the change in x.  In the point (-1,-10)

-1 is the x and -10 is the y.

In the point (5,2)  

5 is the x and 2 is the y.

[tex]\frac{2- -10)}{5 - -1)}[/tex]  Subtracting a negative is the same as adding a positive.

[tex]\frac{2+ 10}{5+1}[/tex] = [tex]\frac{12}{6}[/tex] = 2

We know know the slope.  We will use the form

y - [tex]y_{1}[/tex] = m (x-[tex]x_{1}[/tex])  we will plug in the numbers that we know.  

If we use point (-1, -10)

y -- -10 = 2(x - -1)

y + 10 = 2( x+1)

If we use the point (5,2)

y -2 = 2(x -5)

Both equations mean the same thing.

Part a

Let [tex]a=2[/tex]. Then, we have that

[tex]7+2=\sqrt{7b+c}\\\\81=7b+c[/tex]

We can let [tex]b=11[/tex] and [tex]c=4[/tex], meaning the equation is [tex]x+2=\sqrt{11x+4}[/tex].

Part b

[tex]x+2=\sqrt{11x+4}\\\\x^2 +4x+4=11x+4\\\\x^2 -7x=0\\\\x(x-7)=0\\ \\ x=0, 7[/tex]

Substituting both of these values into the equation, we see they are both solutions.

Part c

[tex]x+10=\sqrt{10x+219}[/tex]

If we define x as the number of goals that she needs to do, we can write the inequality:

x  ≥ 10.

And to graph that we need to use a closed dot at x = 10.

We know that Lesley wants to have an average of 4 games per day.

Until now she played:

Now we assume that on game 5 she does x goals, and if we want the average to be 4 or larger, then we can write:

(6 + 1 + 0 + 3 + x)/5  ≥ 4

Now we need to solve that inequality, we can rewrite:

(6 + 1 + 0 + 3 + x)/5  ≥ 4

(10 + x)/5  ≥ 4

(10 + x) ≥ 4*5

(10 + x) ≥ 20

x ≥ 20 - 10

x ≥ 10

So she needs to do at least 10 goals on the next game.

Now, when graphed we will have an open or a closed circle? In the inequality we have the symbol " ≥ " so x = 10 is a solution, then we need to use a closed circle.

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a)Percentage increase is 23.07%.

b)Percentage increase is 28.5%.

Percentage is a relative value that represents hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is

([tex]\frac{value}{total value}[/tex])100%.

Given Data

Percentage increase = [tex]\frac{final value - starting value}{starting value}[/tex]× 100

a) Cost = $65

New cost = $70

Difference = 5

Equating,

Percentage increase = [tex]\frac{70-65}{65}[/tex] × 100

Percentage increase = [tex]\frac{15}{65}[/tex] × 100

Percentage increase = 23.07%

Percentage increase is 23.07%.

b) Cost = $45

New cost = $35

Equating,

Percentage increase = [tex]\frac{45-35}{35}[/tex] × 100

Percentage increase = [tex]\frac{10}{35}[/tex] × 100

Percentage increase = 28.5%

Percentage increase is 28.5%.

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When the radius of the snowball is 4 and shrinks at a rate of 2 inches per hour then the rate of change of the surface area s is equal to 64π in²/hr

As the radius r is shrinking at the rate of two inches per hour, it can be represented as;

dr/dt = -2 in / hr

Here, the negative sign represents the shrinking of the snowball with time t.

The surface area of a sphere can be represented by the formula;

S = 4πr²

Now we differentiate S with respect to t by keeping radius (r) as a variable as follows;

dS/dt = d/dt (4πr²)

dS/dt = 4π (d/dt) (r²)

dS/dt = 4π × 2r (dr/dt)

Putting the value of r = 4 and calculated value of dr/dt = -2 in the equation as follows;

dS/dt = 4π × 2(4)(-2)

dS/dt = -64π

Therefore, the rate of change of surface area s is calculated to be 64π in²/hr.

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The graph shown below represents the equation y =[tex]3\sqrt{x+6} -3[/tex]

Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.

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Answer:

8x6y12

Step-by-step explanation:

Answer: if the j is supposed to be there, the answer is -9+24j. if the j is not there then just -9+24.

Step-by-step explanation: we distribute the -3 to the 3 and the -8. (-3x3=-9) and (-3x-8=24). when you multiply for divide by a single negative it is negative. when there are two negatives the answer will come out positive.

The value of x if H is the midpoint of GJ is 31 units.

The midpoint is the middle point of a line segment.

It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

The midpoint is halfway between the two end points.

Therefore, H is the midpoint of GJ

Hence,

GJ = GH + HJ

GJ = 4x - 8

GH = 120

Therefore, GH and HJ are congruent because H is the midpoint of GJ

GH = HJ

Hence,

4x - 8 = 120 + 120

4x - 8 = 240

4x = 240 + 8

4x = 248

x = 248 / 4

x = 31

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Answer: 40

Step-by-step explanation:

The smallest number that all three numbers go into evenly is 40.

Therefore the LCM of 8, 11, and 20 is 40.

Answer:

440

Step-by-step explanation:

To find the Least common multiple (L.C.M) of 8, 11 and 20, it means that:

8 = 2,2,2

11 = 1, 11

20= 2,2,5

LCM of 8,11,20 = 2× 2 × 2 × 11 × 5

= 440

The equation that represents the line is,

y+3 = 3/4(x-2)

We are asked to find the equation that represents the line shown in the figure.

We need the slope of the line and a point on the line to find the equation of the line.

The equation of a line can be written in the slope-intercept form given below as,

 y-y₁ = m(x-x₁),

where m is the slope of the line and (x₁, y₁) is a point on the line.

From the figure we can find two points on the line which are (x₁ ,y₁) = (2, -3) and (x₂, y₂) = (-2, -6).

Hence slope, m = (y₂-y₁)/(x₂-x₁)

                          = (-6- -3)/(-2-2)

                          = 3/4

So the equation that represents the line is

 y - -3 = 3/4(x-2)

⇒ y+3 = 3/4(x-2)

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Answer:

4s² (s + 5)(s − 3) ​

Step-by-step explanation:

Factor [tex]4s^{4} +8s^{3}-60s^{2}[/tex]

45² (s - 5)(s + 3)

This polynomial does not factor.

4s² (s 15)(s + 4)

4s² (s + 5)(s − 3) ​

The common term is [tex]4s^{2}[/tex] so:

[tex]4s^{2} (s^{2} +2s-15)[/tex]

assume:

a = 1

b = 2

c = -15

Find two numbers that sum to 2 and multiply to -15:

-3+5 = 2

-3 × 5 = -15

so [tex](s^{2} +2s-15) = (s-3)(s+5)[/tex]

Plug in to [tex]4s^{2} (s^{2} +2s-15)[/tex]

to get: [tex]4s^{2} (s-3)(s+5)[/tex]

Answer:

Rectangle

Step-by-step explanation:

It is because the length and breadth are not equal

Answer:

Step-by-step explanation:

- 4 ≤ 3 , then f(- 4) = [tex]\frac{1}{2}[/tex] ( - 4) + 1 = - 1

2 ≤ 3 , then f(2) = [tex]\frac{1}{2}[/tex] (2) + 1 = 2

3 ≤ 3 , then f(3) = [tex]\frac{1}{2}[/tex] (3) + 1 = 2.5

5 > 3 , then f(5) = 9×5 - 4 = 41

Answer:

[tex]4r - 9s = k \\ ➪4r = 9s + k \\➪ r = \frac{9s + k}{4} [/tex]

Hope it helps

On her way to work each morning, Alexia purchases a small cup of coffee for $6.50 from the coffee shop. So the

Independent Quantity: time,    Units: days

Dependent Quantity: cost,    Units: dollar($)

The dependent and independent quantity or variable are the two main factors in an experiment.

In a scientific experiment, the variable that is altered or controlled to examine the effects on the dependent variable is referred to as an independent quantity.

In a scientific experiment, the variable under test and the measurement is the dependent quantity.

On the independent quantity, the dependent quantity is said to be "dependent." The impact on the dependent quantity is seen as the experimenter modifies the independent quantity, and this effect is noted.

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Answer:

2

Step-by-step explanation:

Given, cosx+cos

2

x=1

⇒cosx=1−cos

2

x

⇒cosx=sin

2

x

Squaring both sides we get

⇒cos

2

x=sin

4

x .....(1)

⇒sin

4

x−cos

2

x=0

Adding both side 1, we get

⇒sin

4

x+1−cos

2

x=1

∴sin

2

x+sin

4

x=1 Proved.

The expression will be (2.99c + 20 = Total cost) and the total cost of Sam's consumption will be $30.465.

So, the expression for the total cost of the person using c pounds of clay:

Total cost when Sam uses 3.5 pounds of clay:

Therefore, the expression will be (2.99c + 20 = Total cost) and the total cost of Sam's consumption will be $30.465.

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On solving the simultaneous equations 3x+2y=7 and 2x-3y=-4 , the value of x is 1 and the value of y is 2  .

In the question,

it is given that the simultaneous equations are

3x+2y=7   ....(i)

and

2x-3y=-4    ...(ii)

to solve these equations ,

we multiply equation(i) with 2 and

multiply equation(ii) with 3 .

So , the equations become

6x+4y=14 ...(iii)

and

6x-9y=-12 ....(iv)

we subtract equation (iv) from  (iii) ,

So,

(6x+4y)-(6x-9y)=14-(-12)

Solving further ,

6x+4y-6x+9y = 14+12

4y+9y = 26

13y = 26

y = 26/13

y = 2

Substituting the value of y as 2 in equation (iii) , we get

6x+4(2) = 14

6x + 8 = 14

6x = 14-8

6x = 6

x=6/6

x=1

hence x=1 and y=2 .

Therefore , On solving the simultaneous equations 3x+2y=7 and 2x-3y=-4 , the value of x is 1 and the value of y is 2  .

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The inequality expression given has a solution of 1 < x < 5.

Inequality are expressions not separated by an equal sign. Given the inequality expression below;

|x − 3| + 8 > 6

The expression can be divided into x − 3 + 8 > 6 and -(x - 3) + 8 > 6

For the inequality x − 3 + 8 > 6

x - 3 > 6 - 8

x - 3 > -2

x > 1

For the inequality -(x - 3) + 8 > 6

-(x - 3) > 6 - 8

-(x - 3) > - 2

x - 3 < 2

x < 5

Hence the solution to the given inequality is 1 < x <5

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The percentage of population of those knowing neither Hindi nor English is 43%.

The outcome of multiplying a given number by a percentage is the percentage. Since a percentage is a portion of a number or quantity, they are typically smaller than the actual number. There are instances, though, where the percentage exceeds the number. If the percentage is greater than 100%, this would occur.

A percentage is simply a certain proportion of a number.

Typically, the phrase "percent of" comes after the quantity.

So, 70% of 50 is 35, for instance.

50 is the quantity, 35 is the percentage, and 70% is the percent in this sentence.

The total percentage of population is represented by 100%, so let the population be 100

No. of population that knows only Hindi = 34 - 23

                                                                   = 11

No. of population that knows only English = 46 - 23

                                                                      = 23

No. of population that knows both = 23

The sum = 11 + 23 + 23

              = 57

No. of population that knows neither Hindi nor English = 100 - 57

                                                                                           = 43

And percentage = 43%

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Answer:

A)

Step-by-step explanation:

vertical angle rule

Answer:

5) a) x=55

Step-by-step explanation:

x=55

2x + 15 = 110 + 15

=125

The equation of the line passing through (0, 0) and (2, –3) is y = - 3 / 2 x

The equation of a line can be described as follows:

y = mx + b

where

Therefore, using (0, 0)(2, -3)

m = y₂ - y₁ / x₂ - x₁

m = -3 - 0 / 2 - 0

m = - 3 / 2

Therefore, the y-intercept is 0.

The equation of the line is y = - 3 / 2 x

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y = -5/2x-8 is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.

Given that, the line 5x+2y = 10 passes through the point (-6,7) and is parallel to the given equation. Now, we have to write an equation in the slope-intercept form.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as: y = mx + b.

where, m is the slope of the line and b is the y-intercept of the line.

Let's proceed to find the equation.

5x+2y = 10

2y = -5x+10

y = -5/2x+10/2

y = -5/2x+5

Now, comparing with y = mx+b (slope-intercept form)

m = -5/2 and b = 5

As the two lines are parallel with each other then the slope of other line will also be same as m = -5/2

Now, the line passing through the point (-6,7)

⇒ x₁ = -6 and y₁ = 7

y-y₁ = m(x-x₁) ..........(1)

putting values in equation (1), we get

y-7 = -5/2(x-(-6))

⇒ y-7 = -5/2(x+6)

⇒ y = -5/2x-15+7

⇒ y = -5/2x-8

This is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.

Hence,  y = -5/2x-8 is the required answer.

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Correct option is B)

Put x=3y=4

(3x+4y):(5x+6y)=(3×3+4×4):(5×3+6×4)

                                      =(9+16):(15+24)

                                      =25:39

Answer:

b is -4

Step-by-step explanation:

we're given:

|2b + 2| = 6

substituting b for -4 :

|2(-4) + 2| = 6

|-8 + 2| = 6

|-6| = 6

any negative number between absolute value becomes positive.

Hence b is -4

She should try to stop the car.

We will discuss the possibilities of trying to stop and trying to speed up in 2s and find the distance she travels to get into a conclusion.

If she try to stop, then the acceleration, a = -5.8 m/s²

Initial velocity, v₀ = 12.5 m/s

Final velocity, v₁ = 0 m/s   [Since the car is stopped]

Let d be the distance the car travels before stopping.

Then, we have, v₁² = v₀² + 2ad

Therefore, d = v₁²-v₀²/2a

                     =  0-(12.5)²/2 x (-5.8)

                     = 156.25/11.6

                     = 13.47 m

So she can stop in time as she is 28m far from the beginning of the intersection.

If she try to speed up, then the acceleration of the car, a = 3.5 m/s²

Initial velocity of the car, v₀ = 12.5 m/s

Time she have, t = 2 s

Let d be the distance the car travels in 2 s.

Then, d = v₀t +(1/2)at²

            = 12.5 x 2 + (1/2) x 3.5 x 2²

            = 25 + 7

            = 32 m

She is 28 m before the beginning of the intersection which is 15 m wide. So if she speed up she will be in the middle of the intersection when the light turns red and may have to stop.

Hence as a legal driver, she should try to stop the car.

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