Which is the graph of the line with equation y−6=4(x−3)+2?


Number graph ranging from negative four to three on the x axis and negative five to two on the y axis. A line is drawn on the graph that passes through the points (zero, negative four) and (one, zero).


Number graph ranging from negative three to three on the x axis and negative seven to one on the y axis. A line is drawn on the graph that passes through the points (zero, negative six) and (three, zero).


Number graph ranging from negative three to three on the x axis and negative two to five on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four).


Number graph ranging from negative three to three on the x axis and negative two to five on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, four).

The potential roots of the function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex] are -10,-5,3,15.

Given function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex]

We have to find the potential roots of the function according to rational root theorem.

Root is the solution of an equation usually expressed as a number or an algebraic formula.

The rational root theorem is used to find the potential roots of function.

For a polynomial function:

p(x)=p[tex]x^{n}[/tex]+..............................+q

The potential roots are:

Roots =±factors of q/factors of p

Th factors of 60 are =±1,±2,±3,±4,±5,±6,±10,±12.

The factors of 1 is ±1.

So we have factors are:±1,±2,±3,±4,±5,±6,±10,±12,±15,±20/±1

The  roots are =±1,±2,±3,±4,±5,±6,±0.

Factors:-10,-5,3,15.

Hence the potential roots are -10,-5,3,15.

Question is incomplete as it should includes options :-10,-7,-5,3,15,24

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The number of homes sold in the Southwest region in 2017was B. 102.

Regional sales refer to the sales recorded by marketing and sales regions through which an organization distributes its products and services.

Recording sales by region helps management to determine regional managers' performances and contributions to the sales efforts.

Sales in Washington county:

Southeast = 48%

Southwest = 12%

Northwest = 25%

Northeast = 15%

Sales of homes in the Southwest region = 102 (850 x 12%)

A. 1,020

B. 102

C. 588

D. 1,231

Thus, the homes sold in the Southwest region in 2017 were B. 102.

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Using the normal distribution, the probabilities are given as follows:

a) 0.6517 = 65.17%

b) 0.0823 = 8.23%.

c) 0.6109 = 61.09%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 8.9, \sigma = 2.8[/tex]

Item a:

The probability is the p-value of Z when X = 10, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 8.9}{2.8}[/tex]

Z = 0.39

Z = 0.39 has a p-value of 0.6517.

0.6517 = 65.17% probability that the time is less than 10 minutes.

Item b:

The probability is the one subtracted by the p-value of Z when X = 5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 8.9}{2.8}[/tex]

Z = -1.39

Z = -1.39 has a p-value of 0.0823.

0.0823 = 8.23% probability that the time is more than 5 minutes.

Item c:

The probability is the p-value of Z when X = 15 subtracted by the p-value of Z when X = 8, hence:

X = 15:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{15 - 8.9}{2.8}[/tex]

Z = 2.18

Z = 2.18 has a p-value of 0.9854.

X = 8:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8 - 8.9}{2.8}[/tex]

Z = -0.32

Z = -0.32 has a p-value of 0.3745.

0.9854 - 0.3745 = 0.6109 = 61.09%.

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Answer:

5

Step-by-step explanation:

Each trip adds up to 8/4 = 2 km

According to this, to travel 10 km is required:

10/2 = 5 trips

Hope this helps

[tex] \sf{\red{ANSWER \: \: :}}[/tex]

x = 18 1/3

[tex] \sf{\purple{EXPLANATION \: \: :}}[/tex]

x - 20 + 2x = 35

- 20 + 3x = 35

3x = 35 + 20

3x = 55

x = 55/3

x = 18 1/3

Answer:

$2.55

Step-by-step explanation:

2d + $14.00 – $7.00 = $12.10; $2.55

Answer:

3x+13 units

Step-by-step explanation:

square perimeter of 12x +52 units

perimeter= 12x +52

12x + 52= 4(sides)

divide both sides by 4 = 12x/4 + 52/4= 3x+13

which give you 3x +13 units

Answer: Digit Place Value

                7                Tens

                5                Ones

                 .  

                7                Tenths

                3                Hundredths

                3                Thousandths

Step-by-step explanation: this should help its not the answer but it's support

Step-by-step explanation:

assuming you are looking for angles and not angels:

Zero Angle (0° in Measure)

Acute Angle (0 to 90° in Measure)

Right Angle (90° in Measure)

Obtuse Angle (90 to 180° in Measure)

Straight Angle (180° in Measure)

Reflex Angle (180 to 360° in Measure)

Complete Angle (360° in Measure)

The measure of <2 is 92 degrees

The complete question is in the attached image

The angles are given as:

<1 = 4x - 4

<2 = 4x

The sum of angles on a straight line is

<1 + <2 = 180

So, we have:

4x - 4 + 4x = 180

Evaluate the like terms

8x = 184

Divide by 8

x = 23

Substitute x = 23 in <2 = 4x

<2 = 4 * 23

Evaluate

<2 = 92

Hence, the measure of <2 is 92 degrees

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Using compound interest, it is found that $390.6 was earned in interest in the next 90 days.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

In this problem, the parameters are:

P = 28214.35, r = 0.055, n = 365, t = 3/12 = 0.25.

Hence the amount after 90 days is:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(90) = 28214.35\left(1 + \frac{0.055}{365}\right)^{365 \times 0.25}[/tex]

A(90) = $28,604.95

28604.95 - 28214.35 = $390.6 was earned in interest in the next 90 days.

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Answer:

I believe the answer to be c 75°

Step-by-step explanation:

a 4 sided shape is 360 total degrees

Considering the given probability distribution, distribution D is valid.

A probability distribution is valid if:

In this problem:

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Answer:

B

Step-by-step explanation:

first for the easy one : the curve line is dotted, if the line points are NOT part of the solution. and it is solid, if the points are included.

you know what the curve line indicates ? it indicates the points for which there is equality.

so, if there is a ">=" or "<=" relation, then that includes equality, and the curve is solid.

if there is only a true inequality ("<", ">"), then the curve is dotted, as the equality is not included.

so, I how this is now really clear.

in our case here (I suspect it really looks like this)

y + 4x <= x² + 2

we have a "<=" sign, so, the curve is ..., well ? ... well ? ...

well ? ... well ? ... solid !

and we still treat inequalities as much as possible as regular equalities.

so,

y <= x² - 4x + 2 (after subtracting 4x from both sides).

and now you see it, right ?

all y values that are smaller or equal to the quadratic expression.

SMALLER ! so, BELOW the curve (as the smaller y values are represented by the lower part of the y-axis).

The type of function that these sets of points are known to produce is the cubic function.

This is a function that is known to be a polynomial of degree 3. This type of polynomial is one that the coefficients are known to be complex numbers.

This is a cubic function given that the x axis is known to go through these points (-3,0), (-1,0), (2,0).

b. Given the sets of pints that we have, we have the equation

f(x) = a(x+3)(x+1)(x-2)

Such that

f = -2 =

4 = a x 1 x -1 x -4

4 = 4a

a = 1

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Thus, the required equation is given by Y = 5/2X.

Given data can tabulate is
Days overdue(x)  = 0  2  4  6  8  10

Amount of fine(y) = 0  5  10  15  20  25

equation is the relationship between variable and represented as     is example of polynomial equation.

Since, the as for every value of x, y grows linerely.

Equation can be given as for every 2 step of x, y increase 5 steps
therefore, y = 5/2x

Thus, The required equation is given by  y = 5/2x

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Answer:

[tex]\huge\boxed{\sf 900}[/tex]

Step-by-step explanation:

Sides of the figure = n = 7

(n - 2)×180

Where n is the number of sides in the polygon

So,

= (n - 2) × 180

= (7 - 2) × 180

= 5 × 180

= 900

[tex]\rule[225]{225}{2}[/tex]

Answer: 720°

Step-by-step explanation:

- Assuming this is a regular hexagon, all the sides are equal and all the angles are equal

- One of the properties of a regular hexagon is that the sum of all the interior angles is 720°

- Since the sum of all the interior angles is 720°, this means each interior angle is 120°

hope this helps :)

Answer:

Recognize the equation as that of a vertical line passing through the x-axis at 8

Answer:

the first option : vertical line passing through the x-axis at 8.

Step-by-step explanation:

x = 8

is a special case of a line equation.

it means that it contains all points for which x = 8.

so, e.g.

(8, -26), (8, - 7), (8, 0), (8, 3), (8, 57), ...

in other words, any y value is possible, but x is constant 8.

therefore, it is one vertical line going through 8 on the x-axis.

the is therefore no y-intercept.

this line equation maps all y values from -infinty to +infinity to the x value of 8. and FYI - it is therefore not a function (where each x value has exactly one assigned y value).

the slope of such a line is infinite or even more accurate undefined.

as the slope is y difference / x difference, x difference is always 0. something divided by 0 is officially undefined and often considered as infinite.

the opposite extreme is something like

y = 8

this is now the line that contains all points with y = 8.

any x-value is possible, but y is always 8.

that is a horizontal line that goes through the y-axis at 8.

and in fact, this is a function, as every x value has exactly one assigned y value (they are all 8, but that does not matter).

there is no x-intercept, of course.

and the slope is 0, as the slope is y difference / x difference, and the y difference is always 0. 0 divided by something is 0.

Answer:

60%

Step-by-step explanation:

There are 6 professors younger than 55 (49, 43, 53, 41, 33, 34).

6/10 = 60%

The mortgage that will give the lowest monthly payment is EMI1 which translates to $ 1,708.16; and method one will require payment of the highest interest.

A mortgage is an arrangement between you and a lender that provides the lender the right to repossess your property if you fail to repay the loan plus interest.

Mortgage loans are used to purchase a property or to borrow money against the value of an existing home.

Given that:

Total amount = $525,000

Down payment = 20% = 0.2

Method 1: Time is 30 years and rate is 2.72%

Method 2: Time is 15 years  and the rate is 2.25%

Loan amount  = total amount less down-payment

= 525,000  - (0.2 * 525,000)

= $420, 000

Given that t = 30 year or 360 months

r = 2.72% or 0.0272

EMI1 =  [ 420, 000 * (0.0272/12) * ( 1 + (0.0272/12)³⁶⁰]/ [( 1 + (0.0272/12)³⁶⁰ -1]

= [952  * 2.259]/1.259

EMI1 = $ 1,708.16

t = 15 years or 180 months

Rate = 2.25% or 0.0225

EMI2 =  [420,000 * (0.0225/12) * ( 1 + (0.0225/12)¹⁸⁰]/ [( 1 + (0.0225/12)¹⁸⁰ --1]

= [787.5 * 1.401]/0.401

EMI2 = $2,751.34

Method 1

Interest = EMI1 x total months - loan amount

=  1,708.16 x 360 - 420,000

= $194, 937.6

Method 2

Interest = EMI2 x total months - loan amount

2,751.34 x 180 - 420,000

= $75,241.2

From the above method 1 requires the highest interest.

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The function r =f(t) is f(t) = 1 - 8t/3

The function is given as:

3r + 8t = 3

Make r the subject

3r = 3 - 8t

Divide by 3

r = 1 - 8t/3

This means that:

f(t) = 1 - 8t/3

To calculate f(-3), we have:

f(3) = 1 - 8 * 3/3

Evaluate

f(3) = -7

Also, we have:

1 - 8t/3 = 2

Add 2 to both sides

-8t/3 = 3

Solve for t

t = -9/8

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Complete question

Consider the relationship 3r+8t=3

Write the relationship as a function  r = f(t)

Evalute f(-3)

Solve for f(t) = 2

The formula that calculates the compound rate from the given values is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]

The compound interest formula is:

[tex]I = P(1 + \frac rn)^{nt} - P[/tex]

Where:

We start by adding P to both sides

[tex]P + I = P(1 + \frac rn)^{nt}[/tex]

Divide through by P

[tex]\frac{P + I}{P} = (1 + \frac rn)^{nt}[/tex]

Take the nt-th root of both sides

[tex]\sqrt[nt]{\frac{P + I}{P}} = 1 + \frac rn[/tex]

Subtract 1 from both sides

[tex]-1 + \sqrt[nt]{\frac{P + I}{P}} = \frac rn[/tex]

Multiply through by n

[tex]r = n(-1 + \sqrt[nt]{\frac{P + I}{P}})[/tex]

In this case, t = 10

So, we have:

[tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]

Hence, the formula that calculates the compound rate is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]

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Answer:

5.71428571429

Step-by-step explanation:

Answer:

  (c)  0

Step-by-step explanation:

The answer to this question requires that you read a graph.

Finding the value of h(2) means finding the value of "y" that corresponds to x=2.

The x-axis of this graph is identified by the "x" at the right side, under the arrow at the end of the x-axis. The y-axis is similarly identified by the "y" to the right of the y-axis at the top of the graph.

Each axis is labeled with numbers.

To find the y-value associated with x=2, first find the vertical line labeled 2 on the x-axis. It is 2 grid squares to the right of the y-axis.

Follow this vertical line until you reach the point where it intersects the line segment(s) representing h(x). At one of these, you encounter a solid dot. At the other point of intersection, you see an open circle (empty dot). The open circle means the point is not included in the function graph.

The value of h(2) is the y-value at the point where the vertical line x=2 meets the defined point on the function graph, the solid dot. The y-value is found by following the horizontal grid line to the y-axis, and reading the y-value there.

The point on this graph where the axes cross, the "origin," has no markings indicating the x- and y-values are zero there. You must infer that from the markings that are shown.

The point on the graph where x=2 lies on the horizontal line y=0. That is ...

  h(2) = 0

Answer:

  (a)  I, III, and IV

Step-by-step explanation:

We want to identify areas on a graph where the solutions to an inequality might be found.

The boundary line for the inequality y ≤ 2/3x -4 has a positive slope and a negative y-intercept. That means it must pass through quadrants I, III, and IV.

Quadrant II is above the line, but the y ≤ () inequality tells you the shading is below the line, where y-values are less than those on the line. There can be no solutions in quadrant II.

Solutions are found in quadrants I, III, and IV.

___

For reference, the second attachments shows the quadrant numbering.

Answer:

124

Step-by-step explanation:

1^3-1=0

2^3-1=7

3^3-1=26

4^3-1=63

5^3-1=124

Hence the next one in the pattern is 124.

The option that's true regarding the sum and difference of the polynomial p(x) and b is B. The sum and difference of p(x) and b are polynomials.

From the information given, it was stated that p(x) is a polynomial and is given as p(=) = a₁ + a₁ + a₂=² + ... + an.

In this case, it should be noted that the sum and difference of p(x) and b are polynomials.

They can't be integers as the function given is represented as a polynomial.

In conclusion, the correct option is B.

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The graph of the given equation is given below.

We have given the equation of the line is f(x)=-1/5x+4f(x)

We have to determine the coordination.

line coordinates are used to specify the position of a line just as point coordinates (or simply coordinates) are used to specify the position of a point.

Therefore we get f(x)=y

y=-1/5x+4....(1)

Plug x=0 in (1) then y=4

Plug x=5 in (1) then

y=-1/5(5)+4

=-1+4

=3

Therefore we get the coordinates (0,4) and (5,3)

Therefore the graph is given below,

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The difference between m and r from the given expressions is 8

Given the following exponents

x^m/x^5=x^7

x^m = x^5 * x^7

x^m = x^12

Equate the powers

m = 12

For the expression

(x^r)³ = x^12

x^3r = x^12

3r = 12

r = 4

Take the difference

m - r = 12 - 4

m - r = 8

Hence the difference between m and r is 8

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No, John is incorrect.

[tex]\sf x^2 - 6x - 7 = 0[/tex]

[tex]\sf x^2 - 6x = 7[/tex]

[tex]\sf x^2 - 6x + 9= 7 + 9[/tex]

[tex]\sf (x-3)^2= 16[/tex]

[tex]\sf x-3=\pm \sqrt{16}[/tex]

[tex]\sf x-3= \pm 4[/tex]

[tex]\sf x= + 4 + 3 \quad or \quad x = -4 + 3[/tex]

[tex]\sf x= 7 \quad or \quad x = -1[/tex]

The correct answer should be x = 7 or x = -1