Find the slope for the following pair of points:

(10,4) and (-2, 17)

To find the number of items, x, for which the total daily cost, C, of each machine will be the same, we can set up an equation and solve for x. The number of items x for which the total daily cost C of each machine will be the same is 20. For 20 items produced, the total daily cost per machine is $60.

To find the number of items, x, for which the total daily cost, C, of each machine will be the same, we can set up the following equation:

40 + 1x = 30 + 1.5x

Simplifying, we get:

0.5x = 10

Dividing both sides by 0.5, we find:

x = 20

Therefore, the number of items x for which the total daily cost C of each machine will be the same is 20.

To find the total daily cost per machine for this number of items, we can substitute x = 20 into the equations for each machine:

Machine A: C = 40 + 1(20) = 60

Machine B: C = 30 + 1.5(20) = 60

So, for 20 items produced, the total daily cost per machine is $60.

Answer:22m+42

Step-by-step explanation:

7•2m =14m + 8m = 22m

7•6=42

Answer:

81.625

Step-by-step explanation:

a mean is the average. an average is calculated by adding up all the numbers and then dividing the sum by the amount of numbers there are. these numbers added up = 653. 653 divided by 8 = 81.625. since it only goes up to three decimal places, no need to round.

Final answer:

The mean of the given data set is calculated by summing all the values and then dividing by the number of values. The calculated mean for this data set is 81.625.

Explanation:

To find the mean of the data set, we need to add all the data values together and then divide by the number of data values.

Thus, the mean of the data set is 81.625, which when expressed to three decimal places is 81.625.

Answer: vertex

Step-by-step explanation:

Answer:

Vertex. The vertex is the point where two points meet, and the point 12 is where the lines meet.

The random variables in this situation will be:

It should be noted that a random variable simply means the numerical description of the outcome of a statistical experiment.

In this case, the distance that the basketball lands from the hoop and the distance the basketball lands from the person are the random variables.

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Answer:

The distance the basketball lands from the hoop.

The distance the basketball lands from the person.

Answer: X= 83°

Step-by-step explanation: If we observe closely, the angle between 41° and X° is an angle opposite angle 56° (opposite angles are equal)

So what we have are three angles on a straight line, which are

41°, 56° and X.

Sum of angles on a straight line = 180°

Therefore,

41 + 56 + X = 180

97 + X = 180

Subtract 97 from both sides of the equation

X = 180 - 97

X = 83°

Answer:

$68.60

Step-by-step explanation:

If the original price is $98

30% = 0.03

0.30*98=29.40

Then, 98−29.40=$68.60

Answer:

x = 6/1.1

Step-by-step explanation:

hello :

1,331x^3 -216=0  means : x^3 = 216/1.331

x^3 = (6^3)/(1.1)^3   because : 216 = 6^3  and  1.331 = (1.1)^3

so : x^3 = (6/1.1)^3

x = 6/1.1

Based on the image we can see that angle B and angle E will be the same so we can write this into an equation.

x + 4 = 48°

Now, we can solve for x.

x + 4 - 4 = 48 - 4

x = 44 (answer)

Best of Luck!

Answer:

x=44

Step-by-step explanation:

I know because I had it!

x+4=48

x=48-4

x=44

Step-by-step explanation:

Given by question,

(x, y) = (5, 15)

Here, x = 5 and y = 15

To find, the value of [tex]\tan \theta[/tex] = ?

We know that,

[tex]\tan \theta[/tex] = Sope = [tex]\dfrac{y}{x}[/tex]

∴ [tex]\tan \theta[/tex]  = [tex]\dfrac{15}{5}[/tex]

⇒ [tex]\tan \theta[/tex]  = [tex]\dfrac{3}{1}[/tex]

⇒ [tex]\tan \theta[/tex]  = 3

∴ The value of [tex]\tan \theta[/tex] = 3

Thus, the value of [tex]\tan \theta[/tex] is equal to 3.

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Answer:

12X+10

Step-by-step explanation:

It's easy. Just combine like terms. Like terms must have the same variable and to the same power in this case all the terms  have a power of 1, but it doesnt show it because it doesn't really matter. So 4x,6x, and 2x all have the same variable so add them together. That gets you 10x. Since nothing else in the expression has the same variable with 10, you leave the 10 at the end resolving in 12x+10

Answer:

12x+10

Step-by-step explanation:

Collect the like terms to one side.  

Answers:

x = -5

y = 9

============================================

Work Shown:

Start by solving the second equation for x.

3x = -15

3x/3 = -15/3 .... divide both sides by 3

x = -5

Then plug this into the first equation and isolate y.

6x + 4y = 6

6(-5) + 4y = 6 .... every x replaced with -5

-30 + 4y = 6

-30+4y+30 = 6+30 .... add 30 to both sides

4y = 36

4y/4 = 36/4 .... divide both sides by 4

y = 9

Answer:

Step-by-step explanation:

Step-by-step explanation:

Let he owes x amount in taxes

He made amount last year = $68,000

His tax rate = 27%

So, he pays tax = 27% of the earning

So, A.T.Q.

27% times 68000 = x

{27}{100} times 68000 = x

27times 68000 = 100 times x

Answer:

Step-by-step explanation:

1,3,9,27, and 81

Answer:

The perimeter of a rectangle is found by using this equation: P = 2 (L + W)

Step-by-step explanation:

I cannot see the picture that you posted, but that is the above equation. Take the length of the rectangle, and the width... plug that in for (L and W), and you have your formula! :)

Hope this helps!

Length = 34 cm

Width= 9 cm

Step-by-step explanation:

Let the width of the rectangle to be.........w

Length is 7 more than three times the width..........3w+7

Perimeter = 86 cm

Perimeter of a rectangle = 2(l+w)

Perimeter of the rectangle = 2 (w + 3w +7)

                                             = 2w +6w + 14

                                      86= 8w +14

                                       86-14 =8w

                                        72=8w

                                        72/8 =8/8w

                                          9=w

Width= 9 cm

Length = 3*9 + 7= 27+7 = 34 cm

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Answer:

(-∞,-3), (-1,2), and (4,∞)

Step-by-step explanation:

If f(x) is increasing on (a,b), then f(a)<f(b) on (a,b).

From the given graph, the graph is increasing on (-∞,-3), (-1,2), and (4,∞).

Think of it as the portion of the graph that slopes forward.

The correct options are A, C, an E

Answer:

(-∞,-3), (-1,2), and (4,∞)

Answer:

The answer is W

Step-by-step explanation:

The answer is W because it is included in both angles.

Answer:

Step-by-step explanation:

The length of the arc is 4π.

Step-by-step explanation:

Given,

Arc length = ∅/360° (2πr)

⇒ 60°/360° (2π[tex]\times[/tex]12)

⇒ 24π/6

⇒ 4π

∴ The length of the arc is 4π.

Two division expressions equivalent to 61.12 divided by 3.2 are 611.2 divided by 32 and 6.112 divided by 0.32. These are derived by scaling both numbers by the same power of 10, and such scaling does not change the value of the quotient.

When looking for division expressions that have the same value as 61.12 divided by 3.2, we want to maintain the ratio between the dividend and the divisor.

By multiplying both the dividend and the divisor by the same power of ten, we can create equivalent expressions without changing the actual value of the division.

For the given problem, 61.12 ÷ 3.2, two equivalent division expressions from the choices provided are:

Both of these are arrived at by multiplying the original dividend and divisor by 10 and 100 respectively. This operation does not change the value of the quotient but simply scales the numbers involved.

The expressions that have the same value as 61.12 divided by 3.2 are Option1. 611.2÷32 and Option 3.  6.112÷0.32

Given the choices, let's identify the equivalent expressions that will have the same value as [tex]\( 61.12 \div 3.2 \)[/tex]

The original division:

[tex]\[ 61.12 \div 3.2 = 19.1 \][/tex]

We need to find two expressions that also equal 19.1

Let's test the given options:

1. [tex]\( 611.2 \div 32 \)[/tex]

[tex]\[ 611.2 \div 32 = 19.1 \][/tex]

2. [tex]\( 6.112 \div 0.32 \)[/tex]

[tex]\[ 6.112 \div 0.32 = 19.1 \][/tex]

So, the two division expressions that have the same value as  are:

[tex]\[ 611.2 \div 32 \quad \text{and} \quad 6.112 \div 0.32 \][/tex]

Thus, the answers are: [tex]\[ \boxed{611.2 \div 32 \quad \text{and} \quad 6.112 \div 0.32} \][/tex]

Full question

Write two division expressions that have the same value as 61.12 divided by 3.2

the following are choice you can pick 2 from

The given image is a triangle.

Property of triangle:

A triangle has three sides.

A triangle has three angles.

A triangle has three vertices.

To find the sides, angles and vertices of the triangle RST:

Sides of the triangle SRT:

RS, ST and RT

Angles of the triangle RST:

∠A, ∠B and ∠C

Vertices of the triangle RST:

A, B and C

These are sides, angles and vertices of the triangle.

Answer:

x=15

Step-by-step explanation:

This is a simultaneous equation

2x-3y=45 ------------------------------ equation i

x+y=10    -------------------------------equation ii

from equation ii

x+y=10

make x the subject of the matter

we have,

x=10-y

in equation i

substitute x for 10-y

2x-3y=45----------------------i

since x=10-y

we have,

2(10-y) - 3y=45

20-2y=3y=45

collect like terms

-2y-3y=45-20

-5y=25

divide both sides by -5

we have y=-5

substitute y for-5 in equation i

x+y=10

x+-5=10

collect like terms

x=10+5

x=15

therefore

x=15

Answer:

  x = 15

Step-by-step explanation:

Use the second equation to write an expression for y:

  y = 10 -x

Then, substitute this into the first equation and solve for x.

  2x -3(10 -x) = 45

  5x -30 = 45 . . . . . eliminate parentheses

  x -6 = 9 . . . . . . . . .divide by 5

  x = 15 . . . . . . . . . . .add 6

Answer:

4 44/49

Step-by-step explanation:

7 7/9 is 70/9

then u use 70/9 multiply by 7/4(I call it keep, change, flip method for division of fraction)

You keep the 1st fraction and because it is a mixed fraction, changing it to improper fraction is easier to solve it later on.

after that, you change the division sign to multiply sign(÷ to ×)

then you flip the 2nd fraction, which means 7/4 becomes 4/7

So overall it becomes 60/7 × 4/7 =240/49,4 44/49 as a mixed fraction.

Answer is 4 44/49

Answer:

The answer would be 0.2

Step-by-step explanation:

Because there is five numbers and if you split 1 into five equal parts there is 0.2 which leads to the answer being 0.2

The required probability of Keisha first picking a yellow marble and then an orange marble is 0.04. Option c is correct.

A bag contains marbles and has an equal number of marbles in 5 colors.
The probability of Keisha first picking a yellow marble and then an orange marble is to be determined.

Probability is the ratio of a favorable number of events to the total number of events.

The total number of samples is = 5
Probability for yellow marble = 1/5 = 0.2
Probability for orange marble = 1/5 = 0.2
Probability for first picking yellow than orange = 0.2*0.2
                                                                                = 0.04

Thus, the required probability of Keisha first picking a yellow marble and then an orange marble is 0.04.

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Final answer:

To calculate the travel time from Lubbock to San Antonio at 60 miles per hour, divide the distance (394 miles) by the speed, resulting in about 7 hours when rounded to the nearest hour.

Explanation:

The question is about calculating the travel time from Lubbock to San Antonio when driving at a speed of 60 miles per hour. Based on the provided chart, the distance between Lubbock and San Antonio is 394 miles. To find the travel time, we use the formula time = distance ÷ speed. Therefore, the travel time is calculated as 394 miles ÷ 60 miles/hour = 6.5667 hours. Rounding this to the nearest hour gives us approximately 7 hours. So, it will take about 7 hours to drive from Lubbock to San Antonio at a speed of 60 miles per hour.

Answer:area = x^2 +15x +36

Step-by-step explanation:

17)

Find how many more pencils are needed:

250 - 108 = 142

Divide by the number of pencils in a box:

142 / 16 = 8.875 = 9 more boxes.

18) 5/4x - 3(8x-1/4)

Use the distributive property:

5/4x - 24x - 3/4

Rewrite 24x as 96/4x

Now you have:

5/4x - 96/4x-3/4

Combine like terms:

-91/4x - 3/4

19)

Car: 3 feet in 4 seconds

60 seconds / 4 = 15

3 feet x 15 = 45 feet per minute

Truck: 2 feet in 6 seconds

60 seconds / 6 = 10

2 feet x 10 = 20 feet per minute

45 - 20 = 25 feet

The car travels 25 feet per minute faster.

Final answer:

Mrs. Smith will donate $20 for Sam walking 20 miles, illustrating a direct proportional relationship with a constant of proportionality of $1 per mile, which is a simple yet effective example of how constants of proportionality function in everyday scenarios.

Explanation:

In the fundraiser mentioned, Mrs. Smith pledges $1 for each mile walked. If Sam walks 20 miles, Mrs. Smith will donate $20. The constant of proportionality in this problem is $1 per mile.

You can see this relationship as a simple formula: total donation = $1 × number of miles walked. So, if we replace "number of miles walked" with 20, the formula would be total donation = $1 × 20 = $20. This illustrates how the initial pledge creates a directly proportional relationship between the money donated and the miles walked.

The constant of proportionality here is crucial because it tells us how much money will be donated per mile that Sam walks. It is a straightforward example of how constants of proportionality work in real-life scenarios, similar to being paid for each call made in a phone drive or being charged per hour of tutoring.