Graph the line that passes through the points (3,-7) and (-3, 5) and determine
the equation of the line.

The coordinates of the polygon before and after dilation is below

preimage      image

J (2, 4)           J' (4, 8)

K (4, 4)           K' (4, 4)  

P (3, 2)            P' (6, 4)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we have

preimage                           image

J (2, 4)   → (2 * 2, 4 * 2) →   J' (4, 8)

K (4, 4)  → (4 * 2, 4 * 2) →    K' (8, 8)  

P (3, 2)  → (3 * 2, 2 * 2) →    P' (6, 4)

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Answer:

[tex]\boxed{\sf x=\cfrac{5}{6}}[/tex]

Step-by-step explanation:

[tex]\sf -\cfrac{5}{6}=-\cfrac{1}{4}-\cfrac{7}{10}x[/tex]

[tex]\sf -\cfrac{1}{4}-\cfrac{7}{10} \; x=-\cfrac{5}{6}[/tex]

Add 1/4 to both sides:-

[tex]\sf -\cfrac{1}{4}-\cfrac{7}{10}x+\cfrac{1}{4}=-\cfrac{5}{6}+\cfrac{1}{4}[/tex]

Simplify:-

[tex]\sf -\cfrac{7}{10}x=-\cfrac{7}{12}[/tex]

Multiply both sides by 10:-

[tex]\sf 10\left(-\cfrac{7}{10}x\right)=10\left(-\cfrac{7}{12}\right)[/tex]

Simplify:-

[tex]\sf -7x=-\cfrac{35}{6}[/tex]

Divide both sides by -7:-

[tex]\sf \cfrac{-7x}{-7}=\cfrac{-\cfrac{35}{6}}{-7}[/tex]

Simplify:-

[tex]\sf x=\cfrac{5}{6}[/tex]

____________________

Hope this helps!

Have a great day! :)

Answer:

x = 5/6

Step-by-step explanation:

Given equation,

→ (-5/6) = (-1/4) - (7/10)x

Now the value of x will be,

→ (-5/6) = (-1/4) - (7/10)x

→ (-7/10)x = (-5/6) + (1/4)

→ (-7/10)x = (-10 + 3)/12

→ x = (-7/12) × (-10/7)

→ x = 10/12

→ [ x = 5/6 ]

Hence, the answer is 5/6.

The other coordinate is x = [tex]\sqrt{3} /2[/tex].

Given:

A point (x, y) is on the unit circle. If its y-coordinate is 1/2 and the point lies in Quadrant I.

we know that :

In unit circle radius r = 1.

[tex]x^{2} +y^{2} = r^{2}[/tex]

[tex]x^{2} +(1/2)^2 = 1^2[/tex]

[tex]x^{2} +1^2/2^2 = 1[/tex]

[tex]x^2 + 1/4 = 1[/tex]

[tex]x^{2} = 1-1/4[/tex]

[tex]x^{2} = 4- 1 / 4[/tex]

[tex]x^{2} =3/4[/tex]

[tex]x =[/tex] ±[tex]\sqrt{3/4}[/tex]

[tex]x =[/tex] ±[tex]\sqrt{3} /2[/tex]

since x is in first quadrant it has only positive value

[tex]x =\sqrt{3} /2[/tex].

Therefore the other coordinate is x = [tex]\sqrt{3} /2[/tex].

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Answer:

The points ​(6​,​7) and ​(​36,​42) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.

Step-by-step explanation:

to find slope from 2 points you do delta y over delta x meaning

42 - 7 over 36 - 6 which equals to 35/ 30 which simplifies down to 7 over 6 or 7/6 so the slope of the line is 7/6 to graph it you need the b to get the b you take one of the points and the slope and do y = mx + b.

42 = 7/6(36) + b

42 = 42 + b

subtract 42 from both sides right to left to get variable alone

0 = b so

y = 7/6x + 0 but you never put the 0 you just leave at

y = 7/6x and graph. Start at 0 go up 7 to the right 6  

P.S. I was bored so I felt like doing the rest of it  ^_^

60.59 seconds  will pass before the planes are at the

same altitude.

5953.79 ft  is the altitude when they're at the same

altitude.

What is altitude?

The height at which something is relative to a planet's or a natural satellite's surface, like sea level or land

To answer this question, you need to determine the altitude difference and speed difference between plane B and plane A.

The initial altitude difference should be: 3500 feet-1970  feet= 1530 feet.

The speed difference should be: 65.75 ft/s - 40.25 ft/s= 25.5 ft/s

After that, you can determine how long will pass before the plane at the same altitude. The calculation would be:

Final altitude difference= Initial altitude difference + speed difference*time

0 ft= 1530 ft + (25.25ft/s * time)

25.25 time= -1530

time= 60.59 second

To determine the altitude you just need to sample either plane A or plane B. Let's use plane B for an easier initial altitude. The calculation would be:

Final altitude= initial altitude + speed*time = 1970 +  65.75 ft/s *60.59s= 5953.79 ft

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Answer:

3

Step-by-step explanation:

3 x 3 = 9

Answer: 70 liters of gas

Step-by-step explanation:

Answer:

Jesse will use 70 liters of gasoline to travel 700 kilometers.

Step-by-step explanation:

Step one: Find how much gasoline is used for one kilometer.

20/200 = 0.1

0.1 liters of gasoline is used for every kilometer traveled.

Step two: Multiply by 700

0.1 x 700 = 70

Step three: Get your Answer!

Jesse will use seventy liters of gasoline to travel seven hundred miles.

Hope my answer helped, have a great afternoon!

Using the concepts of ratio and proportion, we got that $6.4 as the money will be added onto the bill for the tip to the the waitress at the restaurant who provided really good service.

We are given that we are giving the waitress 20% tip, means that apart from the actual bill we give her 20% of actual bill cost

So, 20%of $32 is given by

=(20/100)×32

=32/5

=$6.4

Hence, if the waitress at the restaurant provided really good service, so me and my friends  decided to add on an 20% tip to your $32 bill, the money that  will be added onto the bill for the tip is $6.4

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Solving the proportion using the multiplication property of equality gives

The both ratio showing fractions of one-fifth on the left hand side of the equation is equal to the right hand side of the equation which have t as the numerator and 3 as the denominator

The fractions will be solves by cross multiplying as below

1/5 = t/3

5 * t = 3 * 1

5t = 3

dividing through by 5

5t / 5 = 3 / 5

t = 3/5

plugging in t back to the initial equation gives

1/5 = t/3

1/5 = 3/5 / 3

1/5 = 1/5

Therefore t = 3/5

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The Taylor has to pay $8.95 as shipping charge for his total purchase of some dog grooming and pet supplies for $140.

To Determine Percent

Here given shipping charge ,

Shipping charge = $8.95 or 5.5% of total purchase, which is greater.

Total purchase of Taylor = $140.

Here given shipping charge = 5.5 % of $140.

5.5 % of 140

= (5.5 /100)*140

= (5.5*140) / 100

= 770 / 100

= 7.7

5.5 % of total purchase = $7.7

Since $8.95 is greater that $7.7.

They take $8.95 as shipping charge.

Therefore the Taylor pay's $8.95 as shipping charge .

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The first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The first system of equations:

4x + y = 8

x + 3y = 8

4/1 ≠ 1/3 = 1  (consistent independent)

The second system:

-4x + 6y = 2

2x - 3y = 1

-4/2 = -6/3 = 2  (incosistent)

The third system:

5x - 2y = 4

5x - 2y = 6

5/5 = -2/-2 ≠ 4/6 (consistent dependent)

Thus, the first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.

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The number of real solution of the system y = [tex]3x^2[/tex] and y = 3x - 2 is zero

The system of equations are

y = [tex]3x^2[/tex]

y = 3x - 2

Then the equation will be

[tex]3x^2[/tex] = 3x - 2

Move 3x - 2 to the left hand side of the equation

[tex]3x^2[/tex] - 3x + 2  = 0

Find the value of [tex]b^2[/tex] - 4ac

Here value of a = 3

The value of b = -3

The value of c = 2

Substitute the values in the expression

= [tex](-3)^2[/tex] - 4×3×2

= 9 - 24

= -15

Here the value of  [tex]b^2[/tex] - 4ac is -15

Therefore there is no real valued solution

Hence, the number of real solution of the system y = [tex]3x^2[/tex] and y = 3x - 2 is zero

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The equation of the line is y = -x +3

We need to calculate the line which is perpendicular to y = x +4 and passes through the point (1, 2)

The given equation is y = x +4

Comparing this equation with the general equation of the line, y = mx +c, we get the slope of the equation as 1

Now, When two lines are perpendicular to each other, the product of their slopes is -1.

So, the slope of the required equation is -1.

Now, the equation of the line which passes through the points,  and has slope m, is given by

[tex]y - y_{1} = m(x -x_{1} )[/tex]

Putting the values in the general equation, we get,

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

y - 2 = -x +1

y = -x +3

The equation of the line is y = -x +3.

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The height in terms of x is 4/x², the cost function is C(x) = 7x² + 16/x, and the dimensions for minimum cost are 2/∛7 and ∛14.

a)

It is given that we need to consider the length of the square side to be x ft and the height to be h ft.

The volume of any cuboid

= Length X breadth X height

Here,

length = breadth = x ft

height is h ft.

Volume id 4 ft³

Hence,

x²h = 4

or, h = 4/x²

b)

Since this is a box for the kitten to sleep in, it cannot have any lid.

Hence it will have one square side of area x²  and 4 rectangular sides each of area xh

h = 4/x²

Hence,

xh = 4/x

The square bottom costs $7 per ft and the sides cost $4 per sq. ft

Hence cost to make the box

= 7x² + 4 X 4/x

= 7x² + 16/x

Hence, C(x) = 7x² + 16/x

c)

Here,

C(x) = 7x² + 16/x

Hence, to minimize the cost we will equate its first-order derivative with 0 to get

C'(x)= 0

or, 14x - 16/x² = 0

or, 14x³ - 16 = 0

or, 14x³ = 16

or, x³ = 16/14

or, x = 2/∛7

Hence h = 4∛14/4

= ∛14

Therefore, the dimensions are 2/∛7 and ∛14

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Complete Question

You are constructing a box for your cat to sleep in. The plush material for the square bottom of the box costs 7 dollars per square foot and the material for the sides costs 4 dollars per square foot. You need a box with a volume of 4 ft³. Use x to represent the length of the square base, and use h to represent the height of the box.

(a) Determine a formula for the height h in terms of x.

(b) Determine a formula for the total cost C(x) of the materials for the box.

(c) Find the dimensions (in ft) of the box that minimize cost. (length of base and height)

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Based on the sum of their ages, Mark's brother is 14 years old.

Let us assume the age of Mark be x. Now forming the equation based on mentioned information.

Mark's age = x

Mark's brother's age = x + 5

x + x + 5 = 23

Performing addition on Left Hand Side of the equation

2x + 5 = 23

Shifting 5 to Right Hand Side of the equation

2x = 23 - 5

Performing subtraction on Right Hand Side of the equation

2x = 18

Shifting 2 to Right Hand Side of the equation

x = 18a1 ÷ 2

Performing division on Right Hand Side of the equation

x = 9

So, Mark's age = 9

Mark's brother's age = 9 + 5

Mark's brother's age = 14

Hence, Mark's brother's age is 14 years.

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Linear pair of x for the given figure will be 33

Linear pair:

                 Linear pair of angles are formed when two lines intersect each other at a single point.

                                  The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.  

                                   The sum of angles of a linear pair is always equal to 180°.

For the given figure,

                             m ||n

given angles are (x-17)° and (5x-1)° ,both the angles are linear pair.

using the properties of linear pair,

Sum of the angles will be equal to 180°

that is,

         (x-17)° +   (5x-1)° =180°

        (x + 5x) + (-17 -1) = 180

                         6x - 18 = 180

                         6x = 180 + 18

                         6x =198

                           x = 198/6

                          x =33

Thus, the value of x will be 33

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The expression (3⁴)² in repeated multiplication is (3⁴) * (3⁴)

From the question. the expression is given as

(3⁴)²

The task is that we rewrite the expression as products i.e. repeated multiplication

This in other words means that:

We rewrite the (3⁴)² as repeated multiplication

To do this, we apply the exponent rule of indices

This rule states that:

a^m = a * a * a .... in m places

So, we have

(3⁴)² = (3⁴) * (3⁴)

Hence, the equivalent expression is (3⁴) * (3⁴)

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The weight of each of his checked bags will be; 15.5 kg.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that; Number of checked bags = 2

Backpack weight = 4 kg

The total weight of Carl's baggage 35kg

Let w be the weight of each checked bag.

Weight of 2 checked bags = 2w

It can be found as; Weight of 2 checked bags + Backpack weight =  Total weight of Carl's baggage

Then;

2w + 4 = 35

Subtract 4 from both sides;

2w + 4 = 35

2w  = 31

Divide 2 from both sides;

w = 15.5

Therefore, the weight of each of his checked bags will be; 15.5 kg.

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Using the formula of speed, the speed of first trains is 45 mph and the speed of second train is 60 mph.

In the given question, we have to find the speed of each.

Two trains going in opposite directions leave at the same time.

One train tavels 15 mph faster than the other.

In 6 hours the trains are 630 miles apart.

Let the speed of the first vehicle be s mph, then according to the question, the speed of the second vehicle would be (s+15) mph.

Let the first vehicle covers the distance D(1) and the second one D(2) in the prescribed time.

So, find the distance covered by the first vehicle in 6 hours by using the formula

Distance = Speed × Time

So the distance D(1) is;

D(1) = s*6

D(1) = 6s

So the distance D(2) is;

D(2) = (s+15)*6

D(2) = 6s+90

Since, after 6 hours both the vehicles are at the distance 630 miles. So, the sum of the two distances D(1) and D(2) will be equal to 630.

D(1)+D(2) = 630

Puttimg the value of D(1) and D(2)

6s+6s+90=630

Simplifying

12s+90=630

Subtract 90 on both side we get

12s=540

Divide by 12 on both side we get

s=45 mph

So the value of speed of the faster vehicle

s+15 = 45+15

s+15 = 60 mph

Hence, the speed of first train is 45 mph and the speed of second train is 60 mph.

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Answer:

  x ∈ {2, 3, 4, 5, 6}

Step-by-step explanation:

You want the positive integer solutions of ||x²-2x|-|3x-20|| = |x²+x-20|.

Each of the absolute value functions has turning points where the argument is zero. Those turning points are ...

  x²-2x   ⇒   x(x-2) = 0   ⇒   turning points at x=0 and x=2

  3x-20   ⇒   x -20/3 = 0   ⇒   turning point at x=20/3

  x²+x-20   ⇒   (x+5)(x-4) = 0   ⇒   turning points at x=-5 and x=4

In numerical order, the turning points are ...

  x ∈ {-5, 0, 2, 4, 20/3}

These divide the domain of the equation into 6 intervals. Since we are concerned only with positive integer solutions, we are only interested in the intervals ...

  [0, 2), [2, 4), [4, 20/3), [20/3, ∞)

In this domain, x²-2x < 0, 3x-20 < 0, and x²+x-20 < 0. This means the equation becomes ...

  |-(x² -2x) +(3x -20)| = -(x² +x -20)

The difference in the absolute value bars is negative, so we get the equation ...

  -(-x² +2x +3x -20) = -x² -x +20

  2x² -4x = 0 . . . . . . . add x²+x+20

  x = 0 . . . . . x = 2 is not in the domain

There are no positive integer solutions in this domain.

In this domain, x²-2x > 0, 3x-20 < 0, and x²+x-20 < 0. This means the equation becomes ...

  |(x² -2x) +(3x -20)| = -(x² +x -20)

The difference in the absolute value bars is negative, so we get the equation ...

  -(x² -2x +3x -20) = -x² -x +20

  0 = 0 . . . . . . . . . . . . add x² +x -20

  2 ≤ x < 4 . . . . . . . . all x-values in the domain are solutions

The positive integer solutions are x = 2, x = 3.

In this domain, x²-2x > 0, 3x-20 < 0, and x²+x-20 > 0. This means the equation becomes ...

  |(x² -2x) +(3x -20)| = x² +x -20

The difference in the absolute value bars is positive, so we get the equation ...

  (x² -2x +3x -20) = x² +x -20

  0 = 0 . . . . . . . subtract x² +x -20

  4 ≤ x < 6 2/3 . . . . . . . . . all values of x in the domain are solutions

The positive integer solutions are x = 4, x = 5, x = 6.

In this domain, x²-2x > 0, 3x-20 > 0, and x²+x-20 > 0. This means the equation becomes ...

  |(x² -2x) -(3x -20)| = x² +x -20

The difference in the absolute value bars is positive, so we get the equation ...

  x² -2x -3x +20 = x² +x -20

  -6x +40 = 0 . . . . . . . subtract x² +x -20

  x = 6 2/3 . . . . . . . add 6x, divide by 6

There are no positive integer solutions in this domain.

The positive integer values of x are {2, 3, 4, 5, 6}.

The median of the given data is 88.5

The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.

Given the numbers of pairs of shoes sold during the 10 days of the sale were:

86 84 100 97 96 88 89 60 78 99

We have to determine the median for the given data

The data given must be arranged in ascending order.

60, 78, 84, 86, 88, 89, 96, 97, 99, 100

median = middle most value

∴ 88,89 are middle values

∴ Median =(88+89)/2

= 177/2

= 88.5

Therefore the median of the given data is 88.5

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The y-intercept of this situation is -20 and it means, the remaining budget balance is -20 dollars if no printing  presentation handouts

In this question, we have been given a function 2x+y=20 that represents the relationship between the remaining budget balance(y) dollars in dollars if printing x presentation handouts.

We write given equation in slope-intercept form,

y = -2x - 20

when x = 0,

y = -20

So, y-intercept is -20

This means, the remaining budget balance is -20 dollars if no printing  presentation handouts (x = 0).

Therefore, the y-intercept of this situation is -20 and it means, the remaining budget balance is -20 dollars if no printing  presentation handouts

Given question is incomplete.

The complete question is:

A company has a small budget for printing presentation handouts for an important meeting. The function 2x+y=20 represents the relationship between the remaining budget balance, y, in dollars if printing x presentation handouts. What is the y-intercept of this situation and what does it represent?

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a manufacturing machine has a 1% defect rate. if 8 items are chosen at random, then the probability that at least one will have a defect is 0.077255 or 7.72 %

Given data

defect rate = 1%

no of sample = 8

to find out

probability at least one will have a defect solution

we know here probability of defect is

Probability (defect) = 0.01

and n is 8

so

probability (at least one defect is) = 1 - probability (none)

we know probability (none)  = 0.99^n

probability (none)  = 0.99^8

put this in equation 1

probability (at least one defect is) = 1 - 0.99^8

probability (at least one defect is) is 0.077255 or 7.72 %

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For conducting experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.

As given in the question,

To conduct a experiment based on the effect of net force applied to an object the dependable quantities are as follow:

Force = mass × acceleration

As object remain same ⇒ mass is constant as object remain same.

And there is change in the acceleration.

Acceleration depends change in velocity over total time taken.

Acceleration depends on velocity and time.

Net force also depends on velocity and time.

Two measurements need to know  while conducting trail experiments are velocity and time.

Therefore, to conduct experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.

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am answering from two to ten

Answer:

factors of 20: 1, 2, 4 , 5, 10, 20

factors of 25: 1, 5, 25

gcf: 5

Step-by-step explanation: the common factors of 20 and 25 is 1 and 5. the greater one is 5, therefore the gcf is 5.

hope this helps!! :)

Answer:

√12 is between 3 and 4.

Explanation

The number [tex]\sqrt{12}[/tex] is an irrational number that is between 3 and 4.

The given number is [tex]\sqrt{12}[/tex]

The irrational number is such a number that cannot be expressed in the form of p/q, and are nonterminating and non-repeating.

The number 12 is an irrational number since its value, 3.4641016, has no repeating or ending digits after the decimal, and it cannot be represented as a fraction.

The value  [tex]\sqrt{12}[/tex] is 3.464101

So, the value [tex]\sqrt{12}[/tex] is between 3 and 4.

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Answer:

380.2 hours

Step-by-step explanation:

find how much he receives an hour:

$50/10min × 6 = $300/hr

find out the number of hours it takes:

$114,058 ÷ $300 = 380.19hours

≈ 380.2 hours (to 1 decimal point)

The outcomes in the collection for event E is four and they are  (1, 4) (2,3) (3,2) (4, 1).

Two number cubes, each of which has its faces numbered from 1 to 6 is rolled.

The cubes will be rolled and the sum of the numbers landing face up will be recorded.

The total sample space for two cubes = 6² = 36

Let the event E represent the event of rolling a sum of 5

Total possible outcomes for a sum of 6 is (1, 4) (2,3) (3,2) (4, 1)

We need to find the probability of event E, P(E)

P(E) = possible outcomes/ sample space

P(E) = 4/ 36 = 1/9

Therefore, the outcomes in the collection for event E is four and they are  (1, 4) (2,3) (3,2) (4, 1).

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