The graph shows a proportional relationship between the number of workers and weekly cost in dollars for a company. Use the points ​(6​,3600​) and ​(12​,7200​) to find the weekly cost for the company for each worker. Use pencil and paper. Describe what a unit rate is used for.

The magnitude of the vector JK is estimated to be  2√13.

The given vector JK's direction is - Ф = 33.69° (angle lies in the fourth quadrant with having direction in clockwise)

The algebraic demonstration of the coordinate-based distances between two points (in coordinate system). Using rectangular coordinates, the Pythagorean theorem is employed to determine distances among points in 2- and 3-dimensional Euclidean space.

Now, in answer to your questioning;

J and K have coordinates of (8,1) & (2,5), respectively.

The following is the distance formula for the points J & K:

JK² = (x₂ - x₁)² + (y₂ - y₁)²

JK = √[(x₂ - x₁)² + (y₂ - y₁)²]

The given of coordinates of J and K's  are-

(x₁,y₁) = (8,1)   and (x₂,y₂) = (2,5).

Substituting the given values in the distance formula;

JK = √[(2 - 8)² + (5 - 1)²]

JK = √[(-6)² + (4)²]

JK = √[36 + 16] = √52

JK  = 2√13 (magnitude of the vector JK)

Now, estimate the vector JK's direction.

The angle formed by a vector with a horizontal line defines its direction.

Use one of the given equation to find the direction of a vector.

tan Ф = Δy/Δx

Where, x = horizontal change

and, y = vertical change

tan Ф = (y₂ - y₁)/(x₂ - x₁)

        = (5 - 1)/(2 - 8)

tan Ф = 4/(-6) = -2/3

Ф = 33.69° (angle lies in the fourth quadrant with having direction in clockwise)

As a result, the distance between J and K is found to be 2√13, that is the same as a magnitude of the given vector JK.

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The find two consecutive odd integers is 7 and 9

These are functions that has a linear degree of 1. Let the two consecutive odd numbers be 2x + 1 and 2x + 3

If their product is the same as fifteen more than three times their sum, then;

(2x+1)(2x+3) = 3(2x+1+2x+3) +15

4x²+6x+2x+3 = 3(4x+4)  +15

4x²+8x+3 = 12x+12 + 15

4x² - 4x + 3 = 27

4x² - 4x - 24 = 0
x² - x - 6 = 0

On factorizing, the value of x is 3 and -2

First number = 2(3) + 1 = 7

Second number = 2(3) + 2 = 9

Hence the find two consecutive odd integers is 7 and 9

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The length of slant height l is √98 ft. when diameter of cone and  height of cone is 7 ft.

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.

Here, the diameter of cone is given as : 14ft.

also, the height of cone is : 7 ft.

the radius r of base will be half of diameter :

r = b/2  

r = 14/2 = b

Now to find the slant height of the cone we use Pythagoras theorem between the base of cone b, height of cone h and slant height l that is :

h² + r² = l²

7² + 7 ² = l²

l² = (2x7²)

l = 7 √2 ft. or √98 ft.

Therefore, the length of slant height l is √98 ft.

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We can use the pythagorean theorem to answer this question.

We know that [tex]l[/tex] is the hypotenuse, and the 2 sides are 7 and 7.

So, we can build the equation:

[tex]7^2+7^2 = l^2[/tex]

[tex]98 = l^2[/tex]

[tex]\sqrt{98} = l[/tex]

.

The local gym holds three 45-minute workout sessions and two 30-minute sessions each week. Then the, total number of minutes Judy worked out for the week was 155 minutes.

We are to determine the total number of minutes Judy worked out for the week.

The gym holds three 45-minute workout sessions and two 30-minute sessions each week

So,

We can write,

The total number of minutes the gym holds workout sessions is

3 × 45 + 2 × 30

= 135 + 60

= 195 minutes

Also, from the information,

Judy left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions.

The total number of minutes Judy didn't attend is

= 3 × 10 + 2 × 5

= 30 + 10

= 40 minutes

Then,

The total number of minutes Judy worked out for the week was,

= 195 minutes - 40 minutes

= 155 minutes

Therefore,

The total number of minutes Judy worked out for the week was 155 minutes.

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The person that is most likely considered the authority on the subject is A. a zoologist.

It should be noted that a zoologist simply means the individual that study animals and how they interact with their ecosystem.

In this case, Myra is reading an article about the success of introduced species of animals into the United States.

Therefore, the person that is most likely considered the authority on the subject is a zoologist.

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The line which has an undefined slope among the answer choices given in the task content as described is; the line R which is a vertical line.

It follows from the task content that the line which has an undefined slope is to.be determined among the answer choices.

Since, the slope of a graph is the rate of change in the vertical axis to that in the horizontal axis; it follows that the slope of vertical lines is undefined.

The statement above is true because, no change is recorded in the X axis of vertical lines. Hence, the denominator in the slope formula is; 0 and ultimately, the slope is undefined.

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Answer:

Step-by-step explanation:

The answer is R

By substitution, the solution of the system of equations, x + 12y = 68 and x = 8y - 12, is (20 , 4).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + 12y = 68     (equation 1)

x = 8y - 12     (equation 2)

Since the second equation is already expressed in x in terms of y, substitute the value of x to the first equation.

x + 12y = 68     (equation 1)

(8y - 12) + 12y = 68

8y - 12 + 12y = 68

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

8y - 12 + 12y = 68

8y + 12y = 68 + 12

20y = 80

y = 4

Substitute the value of y in the second equation and solve for x.

x = 8y - 12     (equation 2)

x = 8(4) - 12

x = 32 - 12

x = 20

Hence, the solution of the given system of equations is (20 , 4).

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The speed of the faster car is 15 miles per hour.

Two cyclists, 80 miles apart, start riding toward each other at the same time.

One cycles 3 times as fast as the other. If they meet 4 hours later

speed = distance  / time

distance = speed × time

let

speed of the slower cycle = x

speed of the faster cycle = 3x

Therefore,

4x + 3x(4) = distance

4x + 3x(4)  = 80

4x + 12x  = 80

16x  = 80

divide both sides by 16

x = 80 / 16

x = 5

Therefore, the speed of the faster car is 15 miles per hour.

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The number of chickens are J. 90.

Let the chickens be represented by x and the pigs be represented by y.

Forming the equation according to first information -

Equation 1 : x + y = 120

x = 120 - y

Both chicken and pig has one head. Chicken has 2 feet while pig has 4 feet. Forming the equation according to second information -

Equation 2 : 2x + 4y = 300

Simplifying the equation 2 by dividing by number 2

x + 2y = 150

Keep the value of x from equation 1 in equation 2

120 - y + 2y = 150

Performing subtraction

120 + y = 150

Further shifting the value and performing subtraction

y = 150 - 120

Performing subtraction

y = 30

Now, 30 is the number of pigs.

Number of chickens = 120 - y

Number of chickens =  120 - 30

Number of chickens = 90

Hence, the number of chickens the farmer has is J. 90.

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The value of z varies jointly with w and y.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx

Given relation is z = kxy        —-- 1

Also x varies directly with w i.e. x = k'w, where k' is constant of variation for x and w

Using in equation 1, we have,

z = k(k'w)y

z = kk'wy

z = Kwy, where K is constant of variation i.e. K = kk'

It shows that z varies directly with w and y.

Hence, z varies jointly with w and y.

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A. The percentage of standardized test scores is between 210 and 840 is 99.7%

B. The percentage of standardized test scores that is less than 210 or greater than 840 is 0.3%.

C. The percentage of standardized test scores that is greater than 735 is 2.2%.

a) The z score for 210 will be:

= (210 - 525)/105

= -3

The score for 840 = (840 - 525)/105 = 3

Hence,

Percentage between 210 and 840 will be:

= P(-3 < z < 3)

= 99.7%

b) The percentage of standardized test scores is less than 210 or greater than 840 will be:

= 100% - P(Between 210 and 840)

= 100% - 99.7%

= 0.03%

c) The z score for 735 = (735 - 525)/105

= 2

Hence, the percentage greater than 735

= P(z > 2)

= 2.2%

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Answer:

x = 24

Step-by-step explanation:

[tex]\frac{6+x}{3}[/tex]  = [tex]\frac{x}{4}[/tex] + 4  Multiply though by 12 to clear the fraction

4(6 + x) = 3x + 48  Distribute the 4)

24 + 4x = 3x + 48  Subtract 3x from both sides of the equation

24 + x = 48  Subtract 24 from both sides.

x = 24

Using translation concepts, the new coordinates of the point are given as follows:

(-2.5, 9.8).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

For this problem, the translation rule for each point is given as follows:

(x, y) → (x - 7.5, y + 6.8)

This translation rule means that the figure is shifted:

The original coordinate is given by:

(5,3), meaning that x = 5 and y = 3.

Applying the rule to the original coordinates, we have tat:

Hence the new coordinates, after the rule is applied to the original coordinates, are given as follows:

(-2.5, 9.8).

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We can say that ΔRUQ ≅ ΔTUS under RHS condition.

So,

Given: RQ ≅ ST and RQ || ST

To Prove: ΔRUQ ≅ ΔTUS

So, we can say that ΔRUQ ≅ ΔTUS under RHS.

Therefore, ΔRUQ ≅ ΔTUS.

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Using elimination method, the solution of the given system of equations is (-1, -2)

A system of equations can be solved using:

The given system of equations is:

8y + 10 = 6x   ..... (1)

8y - 4x = -12   ...... (2)

Re-arrange equation (1) to

8y - 6x = -10   ........ (3)

To eliminate variable y, subtract equation (3) from equation (2):

8y - 4x = -12

8y  - 6x = -10 –

      2x  = -2

         x = -1

Substitute  x = -1 into equation (2)

8y - 4x = -12

8y - 4. (-1) = -12

8y + 4 = -12

Add (-4) to both sides:

8y = -16

 y = -2

Hence, the solution is (-1, -2)

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Answer: 100 $

Step-by-step explanation:

300 divided by 3 is 100

The distance between the points R and S is 18.03 units.

We know that for points P(x1, y1) and Q(x2, y2) the distance between points is given as:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In this question, we have been given two points R(8,0), S(-9,6)

We need to find the the distance between the points R(8,0) and S(-9,6)

Let R(8,0) = (x1, y1) and S(-9,6) = (x2, y2)

Using distance formula the distance between the points R and S is:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\d=\sqrt{(-9-8)^2+(6-0)^2} \\\\d=\sqrt{(-17)^2+6^2}\\\\ d=\sqrt{289+36}\\\\ d=\sqrt{325}\\\\d=18.03~~units[/tex]

Therefore, the distance between the points R and S is 18.03 units.

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Answer:

Let P(h,k) be the point which is equidistant from the point (2,4) and the y-axis. The distance of point P(h,k) from the y-axis is h. ∴h=√(h−2)2+(k−4)2⇒h2−4h−4+k2−8k+16=h2⇒k2−4h−8k+20=0.

Hence,the locus of (h,k)is y2−4x−8y+20=0.

Step-by-step explanation:

Answer:uh I think its a carrot

Step-by-step explanation:

After evaluating the expression | - 3 d - 6 | + | - 5 - d² | for d = - 3, we get that the result is 17.

We are given the expression:

| - 3 d - 6 | + | - 5 - d² |

We need to evaluate the expression for d = - 3

Put the value of d as - 3 in the expression, we get that:

| - 3 ( - 3 ) - 6 | + | - 5 - ( - 3 )² |

Solving the expression further, we get that:

| 9 - 6 | + | - 5 - 9 |

| 3 | + | - 14 |

= 3 + 14

= 17

Therefore, after evaluating the expression | - 3 d - 6 | + | - 5 - d² | for d = - 3, we get that the result is 17.

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Answer:

B

Step-by-step explanation:

-3^2 =+8999999999999999999999(9())))))))(-"""&+(()))))(&&%422222222222223

The approximate value of negative seventeen plus square root of sixty to the nearest tenth is -9. 3 . Option A

From the information given, we have;

Substitute the values into the expression, we have;

- 17 + √60

Find the square root of 60 and add to the expression;

-1 7 + 7. 7459

Find the sum of the values

-9. 3

Thus, the approximate value of negative seventeen plus square root of sixty to the nearest tenth is -9. 3 . Option A

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Answer:

The GCF of 16 and 24 is 8. To calculate the GCF (Greatest Common Factor) of 16 and 24, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 16 and 24, i.e., 8.

Step-by-step explanation:

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Answer:

A) y=10x-4

Step-by-step explanation:

There are 10 full boxes which means 10x (since x is the boxes of pizza)

but there are 4 already eaten slices in one, which can be subtracted at the end, making the equation y=10x-4.

Hope this helped and feel better soon! :)

Chords within a circle can be related in a variety of ways. Parallel chords cut congruent arcs in the same circle. That is, the arcs whose endpoints include one of each chord's endpoints have equal measures.

Chords within a circle can be related in a variety of ways. Parallel chords cut congruent arcs in the same circle. That is, the arcs whose endpoints include one of each chord's endpoints have equal measures.

The lengths of the arcs connecting two parallel chords of a circle are equal. Similarly, if the lengths of the two arcs connecting two distinct chords are the same, the chords are parallel. If two chords have the same length, the arcs between their endpoints will have the same measure.

The term "parallel" refers to how each note in the chord rises or falls by the same interval.

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Answer:

4

[tex]4x6 \div 17 \\ [/tex]

Answer:

Step-by-step explanation:

19-22= -3 becuase

22-19=3 but the other way around is -3

x=567

Step-by-step explanation:

Answer: X=Time(Minutes) Y=Gallons Y= 8x+70. I used slope intercept form: My example point would be (6, 118) (9, 142) 142-118/9-6=24/3=8. Therefore 8 is your slope. or you cold see that it increases by 24 everytime it skips 3 times.

Step-by-step explanation: