On a coordinate plane, the position of two friends can be defined by the points A(1,3) and B(7,6). Their teacher is standing at point C, the teacher’s distance from point A is twice the distance from Point B. What are the coordinates of point C?

A.) (5,5)
B.) (-5,5)
C.) (4, 9/2)
D.) (8/3, 3)

Please show work if possible!

Answer: I believe the answer is (-7, 12)

Step-by-step explanation:

Answer:

-7,12

Step-by-step explanation:

Based on the equation, the minimum number of years an employee would have to stay to make a salary of over $40,000 per year is B. 12 years.

An equation is a mathematical statement that defines that two or more mathematical expressions are equal or equivalent.

Equations show equality using the equation symbol (=).

When one expression is more or less than, or not equal to another expression, it is an inequality.

If S = $33,113 + $600t

Where S = the salary before taxes

t = the time since the date of hire in years.

For S ≥ $40,000:

$33,113 + $600t ≥ $40,000

$600t ≥ $40,000 - $33,113

$600t ≥ $6,887

t ≥ 11.48

t = 12 years

Thus, using the given equation, an employee needs to stay at the work for 12 years to earn more than $40,000 a year.

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Answer:

d = -5

Step-by-step explanation:

[tex]\frac{4}{5}d + 3 = -2 -\frac{1}{5}d\\ \\ \frac{4}{5}d + \frac{1}{5} d = -3 -2\\\\\frac{4+1}{5}d = -5\\\\ \frac{5}{5} d = -5\\\\d = -5[/tex]

Check:

[tex](\frac{4}{5} )(-5) + 3 = (-2) - (\frac{1}{5})(-5)\\\\(\frac{-20}{5} ) + 3 = -2 - (\frac{-5}{5} ) \\\\-4 + 3 = -2 + 1\ = -1[/tex]

Answer: x = 0, 8, -5

Step-by-step explanation:

We are trying to solve what value we substitute x into to get the value of 0. We have x outside of (x² - 3x - 40), and we can set that equal to 0. That will be one value of x because we are still left with (x² - 3x - 40). To solve this, we can factor it out into (x-8)(x+5). Set each equal to 0, (x-8) = 0 which leaves us with x = 8, and (x+5) =0, which leaves us with x = -5.

Answer: 19.2, 1.7, 15.93, 0.0512

Step-by-step explanation:

We can multiply these straight across but the trick with decimals is that your answer needs to have the same decimal place distance as what you are multiplying. In the first question, we go one decimal place. In the second, we go two decimal places. In the fourth, we go four decimal places.

The equation in slope intercept form is y= (-3/4)x + 95.

An equation can be represented by a linear function. The standard form for the linear equation is:

y= mx+b , for example, y=x+4.

Where: m= the slope.

It can be calculated for Δy/Δx.b= the constant term that represents the y-intercept. For the given example: m=1 and b=4.

It is important to inform that the standard form for the linear equation can be called slope-intercept form.

For writing a linear equation, you need two points. From the given graph, it is possible to extract some points, such as: (20,80), (60,50). Then, you should replace the known points in the slope-intercept form (y=mx+b).

For the point (20,80),  you can write  80=m*20+b. And for the point (60,50), you can write 50=m*60+b.

Thus, you have:80=20m+b   (1)50= 60m +b (2)For solving the previous system, you have to multiply the equation 1 by -1.

Thus,-80=-20m-b   (1)50= 60m +b (2)

After that, sum equations 1 and 2.-80+50 = -20m+60m-30=40mm=-30/40m=-3/4

Now, you have y= (-3/4)* x+b.

For finding coefficient b, you should use one of the given points. For example:

(20,80).

y= (-3/4)*x+b for (20,80)80

= -3/4*(20) +b 80

= - 60/4+bb=80 + 60/4b=(320+60)/4b=380/4b

=95

Therefore, the equation in slope intercept form is y= (-3/4)*x + 95.

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The principal is 1900

From the question, we have

after 40 month amount of 2375 is received by 15/2% interest rate

T = 40/12 = 10/3

amount = 2375 = P+I

R = 15/2%

amount = P+I

2375 = P+(PRT)/100

2375 = P(1+(RT)/100)

substituting the value  we get

2375 = P(1+(25)/100)

2375 = P*125/100

P = 2375*100/125

P = 1900

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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The ratio of 6 cups of sugar to pie that Quinn needs to make 12 potato pies will be 6 cups.

Ratio basically compares quantities, that shows value of one quantity with respect to other quantity.

If a and b are two values, there ratio will be a:b.

Given that,

For 3 potato pies required sugar is 3/2,

For 5 potato pies required sugar is 5/2,

for 9 potato pies required sugar is 9/2,

From the given information,

For 1 potato pies required sugar is 1/2

⇒For 12 potato pies required sugar=12×1/2=6

To make 12 potato pies,  required sugar will be 6.

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The derivative of the natural log function y = e^(-1/x^2) is

The given function is

y = e^(-1/x^2)

The given function is rearranged as

y = e^(-1/x^2) = e^u such that u = (-1/x^2)

Applying chain rule

y = e^u

y' with respect to u = e^u

u = (-1/x^2) = -x^(-2)

u' with respect to x = 2x^(-3)

(y' with respect to u) *  (u' with respect to x)

= e^u * 2x^(-3)

plugging in the value of u

=  e^(-1/x^2) * 2x^(-3)

= 2x^(-3)e^(-1/x^2)

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Answer:

  XY is tangent to circle Z

Step-by-step explanation:

You want to know if segment XY, measuring 3.6 units, is tangent to circle Z at point X. Segment YZ has length 1.8 units outside the circle, which has radius 2.7 units.

If the triangle XYZ is a right triangle, then we have ...

  XY² +XZ² = YZ²

  3.6² +2.7² = (1.8 +2.7)²

  12.96 +7.29 = 20.25 . . . . . true

Segment XY is a tangent.

If segment YZ is extended across the circle, the lengths of the segments from Y to the circle intersection points are 1.8 and (1.8 +2·2.7) = 7.2. The relation between the secant and the "tangent" will be ...

  3.6² = (1.8)(7.2) . . . . . true

This means XY is a tangent.

The completion of the MACRS annual cost recovery on a straight-line basis is as follows:

Method Purchased  Cost      Recovery     Recovery          Cost

                                                  Class             Year           Recovery

MACRS July 20      $ 5,000           7                 6            A = $833.33

MACRS  Nov. 5      $ 11,000        20                 13           B = $846.15

Ordinarily, the MACRS (modified accelerated cost recovery system) depreciation method is the tax-allowed method that ensures that larger deductions for depreciation expense or cost recovery are made in the beginning years and lower deductions for later years.

However, the same deductions are made each year when the straight-line method is used.

The depreciation expense using the MACRS straight-line method is computed by dividing the asset's cost by the recovery year.

Method Purchased  Cost      Recovery     Recovery          Cost

                                                  Class             Year           Recovery

MACRS July 20      $ 5,000           7                 6            A = $833.33 ($5,000/6)

MACRS  Nov. 5      $ 11,000        20                 13           B = $846.15 ($11,000/13)

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Answer:

-4 is not a solution to the following equation.

Step-by-step explanation:

It you replace x with -4 on both sides of the equation you get -2=-12 and they are not equal to each other. Therefore, -4 is not a solution to the equation.

The dimensions of the rectangle is 83 feet x 46 feet

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

The perimeter P of the rectangle = 258 feet

Let the length of the rectangle be = L

Let the width of the rectangle be = W

And , The width is 37 feet less than the length. ,

So , W = L - 37

Perimeter P = 2 ( Length + Width )

Substituting the values of L and W in the equation , we get

Perimeter P = 2 ( L + L - 37 )

2 ( L + L - 37 ) = 258

( L + L - 37 ) = 129

2L - 37 = 129

Adding 37 on both sides , we get

2L = 166

Divide by 2 on both sides , we get

Length L of the rectangle = 83 feet

Substituting the value of L in equation ,we get

W = L - 37

Width W of the rectangle = 46 feet

Therefore , Length = 83 feet and Width = 46 feet

Hence , the dimensions of the rectangle is 83 feet x 46 feet

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The future value of the account in 3 years is $15,918.

What is a future value?

The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

Here, we have

FV  =C×[ ((1+i)ⁿ −1)/i]

where:

C = cash flow per period

i = interest rate

n = number of payments

By applying the future value formula, we get

= ​$5,000×[ ((1+0.06)³ −1)/0.06 ]

= $5,000×3.1836

= $15,918

​Hence, the future value of the account in 3 years is $15,918.

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The image point of the point (-3, -2) after the transformation r x-axis R 270° is; (3, -2).

It follows from the task content that the image point of the pair of coordinates given is to be determined.

Given point is; (-3, -2).

Hence, after a reflection over the x-axis; we have; (-3, 2).

Also, after a rotation of 270°, it follows that we have; (x, y) ==> (-x, -y).

Therefore, the image point is; (-(-3), -(2)).

The image point is therefore; (3, -2).

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The probability of drawing two queens without replacement from ths standard deck is 1/221.

Probability is the likelihood that an event will occur.

In a standard deck of cards, the total number of cards is 52.

There are 4 queens, the probability of drawing the first queen is 4/52.

After the first draw, there'll be 3 queens left and 52 cards. Therefore, the probability will be:

= 4/52 × 3/51

= 1/13 × 1/17

= 1/221

The probability is 1/221.

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In given word problem ,

a) 2040  more kilojoules of energy would you use in an hour of jogging than an hour of swimming .

b)  45 minutes 2 seconds of walking would you have to do to burn up the 1,130 kilojoules in a candy bar.

What is word problem ?

   Our extensive collection of math word problems ranges from addition, subtraction, multiplication, and division to more specialised operations. Mathematical questions that are written as one or more sentences and ask students to use their mathematical understanding to solve problems from "real-life" situations are known as word problems. As a result, for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are already used to.

Here the given ,

=> 1 minute walking = 25 kilojoules

=> 1 minute jogging = 84 kilojoules

=> 1 minute swimming = 50 kilojoules.

a) 1 hour = 60 minutes.

1 hour jogging = 60*84 = 5040 kilojoules.

1 hour swimming = 60*50 = 3000

Then , => 5040-3000=2040 kilojoules.

Therefore 2040  more kilojoules of energy would you use in an hour of jogging than an hour of swimming .

b) x minute of walking = 1130 kilojoules.

=> 25*x=1130

=> x = 1130/25 = 45minutes 2 seconds.

Therefore 45 minutes 2 seconds of walking would you have to

do to burn up the 1,130 kilojoules in a candy bar.

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The value of constant C is 50.

Equations with a maximum degree of one are referred to as linear equations. According to this rule, a variable in a linear equation cannot have an exponent greater than 1.

A linear equation's graph is always depicted as a straight line. There are linear equations for one variable and two variables, respectively.

Given, the linear equation is 12.5x+5y = C

Here, constant C.

Consider one points from given table x = -2 and y = 15,

Putting the value of x and y,

C = 12.5×(-2) + 5×15

   = -25 + 75

   = 50

For point, x = 0 and y = 10,

Putting the value of x and y,

C = 12.5×0 + 5×10

   = 50

For point, x = 2 and y = 5,

Putting the value of x and y,

C = 12.5×2 + 5×5

   = 25 + 25

   = 50

Given, x = 4 and y = 0,

Putting the value of x and y,

C = 12.5×4 + 5×0

   = 50

Therefore, the value of constant C was found to be 50.

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Answer:

B. 10

Step-by-step explanation:

[tex]\rm \implies 28 \div 7 + 2 \times 3 \\ \\ \rm \implies 4 + 2 \times 3 \\ \\ \rm \implies 4 + 6 \\ \\ \rm \implies 10[/tex]

Answer:

2nd

Step-by-step explanation:

Step-by-step explanation:

so there sre 104 postcards .so what we do is 104 ÷ 4 post cards on each page , it will then = to 26 pages

The required sum of the first twenty terms of the series ∑n=1log 5r are in AP will be 32.37.

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

We have been given that the terms of the series ∑n=1log 5r are in AP.

As per the given question,

∑n(log(5r)) = log(5·1)+log(5·2)+log(5·3)+...+log(5·n)

n = 20

∑log(5r) = log(5·1)+log(5·2)+log(5·3)+...+log(5·20)

Using the property of logarithmic logₐ(xy) = logₐx + logₐy,

∑log(5r) = (log(5)+log(1)) + (log(5)+ log(2))+(10g(5)+Log(3))+ ...(10g(5)+Log(20))

∑log(5r) = (log(5)+log(5)+log(5)+...+log(5)

∑log(5r) = 20·1og(5)+((log(1)+log(2)+log(3)+...+log(20)

Using property of logarithmic logₐ(xy) = logₐx + logₐy,

∑log(Sr)=20·1og(5)+log(1×2×3×...20)

∑log(5r) = 20-log(5)+log(201)

∑log(5r) = 32.365524703598

Rounded to the nearest hundredth decimal,

∑log(5r) = 32.37

Thus, the required sum of the first twenty terms of the series ∑n=1log 5r in AP will be 32.37.

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The measure of ∠QTS = 58°

Given; A triangle QPR

PQ = PR

this means that ∠ Q = ∠ R

and QR = QT this means ∠ R = ∠ T

And ST ║ QR

and QT is the transversal

From the above mentioned information we can conclude that

∠QTS = ∠TQR -------------- 1

Thus since ∠ Q = ∠ R  

by using angle sum property of triangle we can conclude that

∠ Q + ∠ R = 116  [ exterior angle sum property ]

2 ∠ Q = 116

∠ Q = 58°

this means ∠ TQR = 58°

And from 1 we know that this angle is equal to angle QTS

Thus ∠QTS = ∠TQR = 58°

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Answer:

70

Step-by-step explanation:

If lines l and m are parallel, then using the corresponding angles theorem, the angle that forms a linear pair with angle [tex]x[/tex] is [tex]110^{\circ}[/tex].

This means that [tex]x=70[/tex].

answer the answer is 200

Step-by-step explanation:

490-290

The range of the given function is:

Range: {-9,-3,0,5,7}

We are given ordered pair of set (x,y)

where, first value of ordered pair shows domain of function and second value of ordered pair shows range.

Range: It is output value of function.

Ordered pair: {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}

We can write as:

f(-2)=0,     f(-4)=-3,   f(2)=-9,   f(0)=5,    f(-5)=7

The values of f(x) are the range of function.

We will make a set of second value of all ordered pair of given set.

Range: {-9,-3,0,5,7}

Hence we get the required range of the function.

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Answer:

D

Step-by-step explanation:

supplementary angles sum to 180° , that is

∠ 1 + ∠ 2 = 180°

67° + ∠ 2 = 180° ( subtract 67° from both sides )

∠ 2 = 113°