EASY QUESTION 20 POINTS

1. The line passing through (-14,-9) and (7,9) has the equation:

y = 6/7x + 3/2

2.The line passing through (0,-3) and (0,15) has the equation:

since the slope is undefined, hence equation of the line is not formed.

3.The line passing through (-24,-16) and (-8,-6) has the equation:

y = 5/8x - 1

4.The line passing through (-8,-12) and (12,13) has the equation:

y = 5/4x - 2.

Given we have the pair of points, through which we need to determine the equation of the line:

1.  (-14,-9) and (7,9)

first we need to find the slope

(-14,-9) = (x₁,y₁)

(7,9) = (x₂,y₂)

m= y₂₋y₁/x₂₋x₁

= 9-(-9)/7-(-14)

= 18/21

m= 6/7

Use the slope and one of the points to find the y-intercept b:

(7,9) and m= 6/7

substitute in y=mx+b

9=6/7(7) + b

b = 9/6

b= 3/2

now substitute m=6/7 and b= 3/2 in slope intercept form.

y = 6/7x + 3/2

2. (0,-3) and (0,15)

first we need to find the slope

(0,-3) = (x₁,y₁)

(0,15) = (x₂,y₂)

m= y₂₋y₁/x₂₋x₁

= 15-(-3)/0-0

= undefined

hence  we can't frame the equation of the line.

3.  (-24,-16) and (-8,-6)

first we need to find the slope

(-24,-16) = (x₁,y₁)

(-8,-6) = (x₂,y₂)

m= y₂₋y₁/x₂₋x₁

= -6-(-16)/-8-(-24)

= -6+16/-8+24

= 10/16

m= 5/8

Use the slope and one of the points to find the y-intercept b:

(-8,-6) and m= 5/8

substitute in y=mx+b

-6=5/8(-8) + b

b = -1

now substitute m=5/8 and b= -1 in slope intercept form.

y = 5/8x - 1

4. (-8,-12) and (12,13)

first we need to find the slope

(-8,-12) = (x₁,y₁)

(12,13) = (x₂,y₂)

m= y₂₋y₁/x₂₋x₁

= 13-(-12)/12-(-8)

= 25/12+8

= 25/20

m= 5/4

Use the slope and one of the points to find the y-intercept b:

(12,13) and m= 5/4

substitute in y=mx+b

13=5/4(12) + b

b = -2

now substitute m=5/4 and b= -2 in slope intercept form.

y = 5/4x - 2.

hence we get the acquired results.

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Answer: 21 degrees

Step-by-step explanation:

Since (2x + 9) + 129 = 180, we can get that 2x = 42 and x = 21. Hope this helped!

Answer: y2-y1 and x2-x1

Step-by-step explanation:

5-9=-4

2--6=8

-4,8

H = S/2πr + r or (S + 2πr²)/2πr simplified and solved for the value  S = 2πr² + 2πrh

Here given that S = 2πr² + 2πrh

Lets simply the equation

⇒ S = 2πr² + 2πrh

⇒ S = 2πr(r + h)

⇒ S/2πr = r + h

⇒ h = S/2πr + r or (S + 2πr²)/2πr

In mathematics, an equation is a formula that indicates the equality of two expressions by connecting them with the equals sign =.

The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.

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Equation has no solution  is |4x-2|=-6

checking option A

|4x-2|=-6  . . . .1

if 4x-2≥0

  4x≥2

  x≥1/2

then |4x-2| = 4x-2

So , .. . . 1 becomes

4x-2=-6

4x=-4

x=-1

But x≥1/2

So x=-1 is not a solution.

if   4x-2≤0

  4x≤2

  x≤1/2

then |4x-2| = -(4x-2)

So , .. . . 1 becomes

-4x+2=-6

4x=8

x=2

but x≤1/2

So x=2 is not a solution.

checking option B

|-2-x| = 9  . . . 2

if -2-x ≥ 0

   x≤-2

then

|-2-x| = -2-x

So,  . . .. . 2 becomes

-2-x=9

x=-11

so it has a solution .

checking option C

|3x+61| = 6 . . . . . 3

if 3x+61≥0

x≥-61/3

then

|3x+61| = 3x+61

So, . . .3 becomes

3x+61=6

x=-55/3

So it has a solution.

checking option D

|-2x+8|=0 . . . . .4

if -2x+8≥0

x≤4

then  |-2x+8| = -2x+8

So , .. . . . .4 becomes

-2x+8=0

x=4

So it has a solution.

Hence option A |4x-2|=-6

has not a solution.

Sometimes equations have no solution. This means that no matter what value is plugged in for the variable, you will ALWAYS get a contradiction.

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The lengths of the scaled copy of rectangle is 18 inches by 30 inches .

Scaled by a factor : Whenever something is scaled by a factor it means that it is multiplied by that factor .

For Example , if 3  is scaled by a factor of 2 , means 3 is multiplied by 2 that is 3*2=6.

In the given question

length of rectangle = 3inches

it is scaled by factor of 6 , that means

length of scaled copy of rectangle = 3*6= 18inches.

breadth of the rectangle = 5 inches

it is scaled by factor a factor of 6 , that means

breadth of scaled copy of rectangle = 5*6 = 30inches.

Therefore , the lengths of the scaled copy of the rectangle will be 18inches by 30inches.

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Function g(x) = 4x -13 after the graph is translated 1 unit right of the graph of f(x) = 4x - 9.

As given in the question,

Function f(x) = 4x -9

Graph g(x) get translated 1 unit right of the graph of function f(x)

It means change in the value of x  equals to x-1

g(x) = 4(x-1) -9

⇒ g(x) = 4x -4 -9

⇒ g(x) = 4x-13

Therefore, function g(x) = 4x -13 after the graph is translated 1 unit right of the graph of f(x) = 4x - 9.

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The component form of the given magnitude and direction is 7.4 +  6.7i.

To find the component form of  magnitude 10 and direction 42°:
component form = x + iy

Then,

Therefore, 7.4 + 6.7i is the component form of the given magnitude and direction

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Answer:

8

Step-by-step explanation:

sqrt 58 =7.62   closer to 8 than 7

The percentage increase is 103.7%.

Answer:

103.7%

Step-by-step explanation:

Given the following question:

Original price = $1.35
New price = $2.75

Find the percent change. To find the percent change we will use the formula to calculate the percent change of course rounding if needed.

[tex]\frac{np\times op}{op} \times100[/tex]
[tex]\frac{2.75\times1.35}{1.35} \times100[/tex]
[tex]2.75 - 1.35\div1.35\times 100% =[/tex]
[tex]=103.7037037037[/tex]

Round to the nearest tenth:
[tex]103.7037037037[/tex]
[tex]0 < 5[/tex]
[tex]103.7[/tex]

1.35 to 2.75 is a "103.7%" increase.

Hope this helps.

The total number of gumballs in the jar calculated using probability is about 181.

Probability is the study of chance. The likelihood of an event to occur given as a fraction is probability.

For a sure event the probability is 1 and for an impossible event the probability is 0.

Carlos draws a sample of 55 gumballs. Out of which the number of green gumballs is 44.

Probability of a green gumball= number of green gumballs ÷ total number of gumballs

P(green) = 44 ÷ 55 = 4/5

Now in the sample the number of green gumballs is 4/5 , and in the jar the number of green gumballs is 145 .

Let us consider there are x gumballs in total in the jar.

P(green)=145 ÷ x

We know that P(green)= 4/5

∴4/5 = 145 ÷ x

or, x = 145 × 5 ÷ 4

or, x = 181.25 gumballs.

or, x ≈ 181 gumballs(As the number of gumballs cannot be a fraction)

Therefore there are about 181 gumballs in total .

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Answer: 0

Step-by-step explanation: the slope intercept form is y= mx +b. The equation here is y = -19. It means that the slope, m, is 0. You can also think about it this way. y= -19 graph will show you that for every x value, the y is at -19 since there is no rise over run. it is just a straight line at y= -19

The weight of the original sample from which all 14 batches in the task content is;  65.8 x 10-8 grams.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

WE have been given that Eli broke a cell sample into 14 batches, each weighing 4.7 x 10-8 grams. which follows that the task content; the weight of the original sample from which the eight batches were obtained be determined.

Hence, since each of the 14 batches weighs;

[tex]4.7 \times 10^{-8}[/tex]

Therefore, the weight of the original sample can be obtained as;

[tex]4.7 \times 10^{-8} \times 14\\\\65.8 \times 10^{-8}[/tex]

However, when the weight is expressed in scientific notation, thus the weight of the original sample is;

[tex]65.8 \times 10^{-8}[/tex]

Hence, The weight of the original sample from which all 14 batches which each weighed  4.7 x 10-8 grams are obtained as required in the task content is;  65.8 x 10-8 grams.

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The monthly cost of 57 minutes calls is $12.55.

The monthly cost is $12.03 for 53 minutes and $ 13.59 for 65 minutes call

Therefore we have two points (53, 12.03) and ( 65, 13.59)

slope = (13.59 - 12.03)/ ( 65 - 53)

          = 1.56/ 12

          = 0.13

The intercept is

y = mx + c

12.03 = 0.13×53 + c

12.03 = 6.89 + c

c = 5.14

Equation:

cost = 0.13(minutes) + 5.14

       = 0.13×57 + 5.14

       = 7.41 + 5.14

       = 12.55

Therefore the monthly cost for 57 minutes is $12.55.

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Answer:

it 21

Step-by-step explanation:

rr

Answer: 54.9

Step-by-step explanation:

121 lb converted to kk is 54.885

54.885 rounded to the nearest tenth is 54.9

The fraction of the sweets that are blue given the ratios is 13/40.

A fraction is a non-integer that is made up of a numerator and a denominator. An example is 2/3. 2 is the numerator and 3 is the denominator.

Ratio shows the relationship between two or more numbers. It is the number of times that one value is contained in other value(s). Ratios are used to compare two or more numbers.

We would be assuming the numbers of sweet based on the given ratios.

The number of hard sweets = 30

The number of soft sweets = 50

Number of hard sweets that are blue = (1/5) x 30 = 6

Number of soft sweets that are blue = (2/5) x 50 = 20

Total number of blue sweets =20 + 6 = 26

Total number of sweets = 30 + 50 = 80

Fraction of blue sweets = 26/80 = 13 /40

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(a) The answer of (g.f)(2) is [tex]\sqrt{23}[/tex] .

(b)The answer of (g + f) (2) is [tex]\sqrt{3}[/tex] -  3 .

(c)The answer of  (g - f) (-1) is [tex]\sqrt{15}[/tex] .

(d)The answer of [tex]\frac{f}{g}(-1)[/tex] is 0 .

We have given two functions f(x) = [tex]1-x^2[/tex] and g(x) = [tex]\sqrt{11-4x}[/tex]

(a) Put x = 2 in f(x) we get  f(2) = 1 - 4 = -3

  (g.f)(2) =  g(f(2))

             = g(-3)

              [tex]=\sqrt{11-4(-3)}\\=\sqrt{11+12} \\=\sqrt{23}[/tex]

which is option (c) .

(b)  Put x = 2 in f(x) we get f(2) = 1 - 4 = -3 and g(2) = [tex]\sqrt{11-8} =\sqrt{3}[/tex]

(g + f) (2) = g(2) + f(2)

              = [tex]\sqrt{3}[/tex] + (-3)

               = [tex]\sqrt{3}[/tex] - 3

which is option (a)

(c) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]

(g - f) (-1) = g(-1) - f(-1)

              = [tex]\sqrt{15}[/tex] + 0

               = [tex]\sqrt{15}[/tex]

which is option (b)

(d) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]

[tex]\frac{f}{g}(-1)[/tex] = f(-1) / g(-1)

          = 0 / [tex]\sqrt{15}[/tex]

           = 0

which is option (d)

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Answer:

(-16, 0)

Step-by-step explanation:

The midpoint can be found using the formula below, where [tex](x_1,y_1)[/tex] is the first endpoint and [tex](x_2, y_2)[/tex] is the other endpoint.

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

Let the other endpoint be (x, y).

Substitute the given midpoint and one endpoint into the formula above:

(-6, 4)= [tex](\frac{x+4}{2},\frac{y+8}{2} )[/tex]

Comparing the x-coordinate:

[tex]-6=\frac{x+4}{2}[/tex]

Multiply both sides by 2:

x +4= -12

Subtract 4 from both sides:

x= -12 -4

x= -16

Comparing the y-coordinate:

[tex]4=\frac{y+8}{2}[/tex]

Multiply both sides by 2:

y +8= 8

Subtract 8 from both sides:

y= 8 -8

y= 0

Thus, the other endpoint is (-16, 0).

Supplementary:

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The difference between -4/5 and -3/5 will be -7/5.

It should be noted that the difference between 4/5 and 3/5 will be illustrated thus:

= 4/5 - 3/5

= 1/5

Subtracting -3/5 from -4/5 will be:

= -3/5 - 4/5

It should be noted that they both have negative signs.

Therefore, the value will be -7/5 or - 1 2/5.

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The $785 balance on Dan's credit card is currently due. The APR on his credit card is 24.42%. He has to pay the full balance that is $785.2442.

Given that,

The $785 balance on Dan's credit card is currently due.

The APR on his credit card is 24.42%.

We have to find what finance fee would he pay if he didn't pay the balance in full.

To find the balance full he has to pay.

We have to add the balance of current due and APR .

We get,

=$785+24.42%

=$785+0.2442

=$785.2442

Therefore, he has to pay the full balance that is $785.2442.

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Answer:

34

Step-by-step explanation:

Solution:

Inequality Form: [tex]4\leq x\leq 7[/tex]

Interval Notation: [tex][4,7][/tex]

_________________________________________________________

As for plotting on your line graph, one point should be a closed circle on 4, then the next should be a closed circle on 7.

__________________________________________________________

Hope this helps! If so, lmk! Thanks and good luck!

Answer:

8/5 or 1 3/5

Step-by-step explanation:

Answer:

Exact form: 8/5
Mixed Number form: 1 3/5

Step-by-step explanation:

First, let's cancel the common factor of 3

4/3 * 6/5
4 * (3*2/5)
4 * 2/5

Next, lets combine 4 and 2/5

4*2/5
8/5

We can finish this off by simplifying 8/5

8/5 = 1 3/5

Let's say you wanted to find the cube root of 8

You write it on your paper like this: [tex]\sqrt[3]{8}[/tex]

In your calculator, you'd type this in:  8^(1/3)

The exponent of 1/3 corresponds to a cube root.

In general, the exponent of 1/n is for the nth root

The connection is [tex]\sqrt[n]{\text{x}} = \text{x}^{1/n}[/tex]

The measure of the length PQ is 7.2

Figures are known to be similar if the ratio of the sides is equal to a constant "k".

In order to determine the value of k, we will use the following ratio as shown:
AB/BC = PQ/QR

Substitute the given parameters

6/2 = x/2.4

Cross multiply

2x = 2.4(6)

2x = 14.4

x = 14.4/2

x = 7.2

Hence the measure of the length PQ is 7.2

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An absolute value inequality for given graph is |x| ≤ 6

In this question, we have been given a graph of a number line.

We need to write an absolute value inequality for given graph.

From the given graph, we can observe that the value of x lies between -6 to 6.

i.e., -6 ≤ x ≤ 6

We know that, for a real number 'm', the absolute value function for m would be,

|±m| = m

So, -6 ≤ x ≤ 6

|x| ≤ 6, which is required inequality.

Therefore,  an absolute value inequality for given graph is |x| ≤ 6

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Answer:

-2, S, U, V. that was a good question.

Step-by-step explanation:

Thanks. You are known.

She should buy  five sweaters.

A rational consumer would purchase a good as long as marginal benefit is equal or greater than marginal cost.

Marginal cost is the additional cost generated by producing an additional unit of output. Marginal benefit is the benefit derived from consuming one extra unit of a good.

The marginal benefit of the first five sweaters is greater than the marginal cost. Thus, she should buy  five sweaters.

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