Find an equation of the line. Write the equation using function notation.Through (4, - 7); perpendicular to 6y=x- 12The equation of the line is f(x)=..

Answers

Answer 1

To determine the equation of the line you need to determine its slope first.

You know that the line 6y=x-12 is perpendicular to the line you have to determine, two lines that are perpendicular, their slopes are opposite reciprocals. For example, let "m" represent the slope of one of the lines and "n" represent the slope of the perpendicular line, you can express their relationship as follows:

[tex]m=-\frac{1}{n}[/tex]

To determine the slope of the given line, you have to write it in slope-intercept form:

[tex]y=mx+b[/tex]

Where

m represents the slope

b represents the y-intercept

Given the line:

[tex]6y=x-12[/tex]

-Divide both sides by 6

[tex]\begin{gathered} \frac{6y}{6}=-\frac{x}{6}=-\frac{12}{6} \\ y=-\frac{1}{6}x-2 \end{gathered}[/tex]

The slope of this line is the coefficient of the x-term, n=-1/6

Its opposite reciprocal is:

[tex]\begin{gathered} m=-\frac{1}{n} \\ m=-(-\frac{1}{\frac{1}{6}}) \\ m=-(-1\cdot6) \\ m=-(-6) \\ m=6 \end{gathered}[/tex]

The slope of the line you have to determine is m=6

Now that you have the slope of the line, using the point-slope form, you can determine the equation of the line:

[tex]y-y_1=m(x-x_1)[/tex]

Where

m represents the slope of the line

(x₁,y₁) represent the coordinates of one point of the line

Replace the formula with m=6 and (x₁,y₁)=(4,-7)

[tex]\begin{gathered} y-(-7)=6(x-4) \\ y+7=6(x-4) \end{gathered}[/tex]

The next step is to write the equation in slope-intercept form:

-Distribute the multiplication on the parentheses term:

[tex]\begin{gathered} y+7=6\cdot x-6\cdot4 \\ y+7=6x-24 \end{gathered}[/tex]

-Pass "+7" to the right side of the equation by applying the opposite operation "-7" to both sides of it:

[tex]\begin{gathered} y+7-7=6x-24-7 \\ y=6x-31 \end{gathered}[/tex]

Finally, write the equation of the line using function notation:

[tex]f(x)=6x-31[/tex]


Related Questions

What is the first step for finding the quotient of 3x^3 z^5/5y * x^2 z^6/20y^3

Answers

The initial expression is:

[tex]\frac{3x^3z^5}{5y}\text{ / }\frac{x^2z^6}{20y^3}[/tex]

So the first step is to multiply the numerator of the second fraction with the denominator of the first franction and the denominator of the second fraction by the numerator of the first fraction so:

[tex]\frac{3x^3z^6}{5y}(\frac{20y^3}{x^2z^6})[/tex]

So is option C)

1. Sketch the graph of y = x that is stretched vertically by a factor of 3. (Hint: Write the equation first, then graph) Sketch both y = x and the transformed graph.

Answers

ANSWER and EXPLANATION

We want to stretch the graph of:

y = x

A vertical stretch of a linear function is represented as:

y' = c * y

where c is the factor

The factor from the question is 3.

So, the new equation is:

y' = 3 * x

y' = 3x

Let us plot the functions:

Help asp show your work you’ll get brainliest

Answers

The information given in the table on the Value of a Car and the Age of the Car, gives;

First Part;

The dependent variable is; The Value of Car

The independent variable is; The Age of Car

Second part;

The situation is a function given that each Age of Car maps to only one Value of Car.

What is a dependent and a independent variable?

A dependent variable is an output variable which is being observed, while an independent variable is the input variable which is known or controlled by the researcher.

First part;

The given information in the table is with regards to how the car's value decreases with time, therefore;

The dependent variable, which is the output variable, or the variable whose value is required is the current Value of the Car (Dollars)The independent variable, which is the input variable, or the variable that determines the value of the output or dependent variable, is the Age of Car (Years)

Second part;

A function is a relationship in which each input value has exactly one output.

Given that the Values of the cars are all different, and no two car of a particular age has two values, therefore;

The situation is a function

Given that the first difference varies depending on the age of the car, the function can be taken as a piecewise function

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help meeeeeeeeee pleaseee !!!!!

Answers

The composition of the function (g o f)(5) is evaluated as: (g o f)(5) = g(f(5)) = 6.

How to Determine the Composition of a Function?

To find the composition of a function, we have to first evaluate the inner function for the given value of x that is given as its input. After that, the output of the inner function would then be used as the input for the outer function, which would now be evaluated for the composition of the function.

Given the functions:

f(x) = x² - 6x + 2

g(x) = -2x

We need to find the composition of the function, (g o f)(5), where the inner function is f(x), and the outer function is g(x).

Therefore:

(g o f)(5) = g(f(5))

Find f(5):

f(5) = (5)² - 6(5) + 2

f(5) = -3

Substitute x = -3 into g(x) = -2x:

(g o f)(5) = -2(-3)

(g o f)(5) = 6

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f(x)A6X-868Which of the given functions could this graph represent?OA. f(t) = (x - 1)(x - 2)(x + 1)(x + 2)O B. f(x) = x(x - 1)(1 + 1)Oc. /(x) = x(x - 1)(x - 2)(x + 1)(x + 2)OD. (r) = x(x - 1)(x - 2)

Answers

The Solution:

Given the graph below:

We are required to determine the function that best describes the above graph.

Step1:

Identify the roots of the function from the given graph.

[tex]\begin{gathered} x=-2 \\ x=-1 \\ x=1 \\ x=2 \end{gathered}[/tex]

This means that:

[tex]\begin{gathered} x+2=0 \\ x+1=0 \\ x-1=0 \\ x-2=0 \end{gathered}[/tex]

So, the required function becomes:

[tex]f(x)=(x-1)(x-2)(x+1)(x+2)[/tex]

Therefore, the correct answer is [option A]

If you select one card at random from a standard deck of 52 cards, what is the probability of that card being a 5, 6 OR 7?

Answers

To solve this question we will use the following expression to compute the theoretical probability:

[tex]\frac{\text{favorable cases}}{total\text{ cases}}.[/tex]

1) We know that there are 4 fives, 4 sixes, and 4 sevens in a standard deck of 52 cards, then, the probability of selecting a 5, 6, or 7 is:

[tex]\frac{4+4+4}{52}\text{.}[/tex]

2) Simplifying the above expression we get:

[tex]\frac{12}{52}=\frac{3}{13}\text{.}[/tex]

Answer:

[tex]\frac{3}{13}\text{.}[/tex]

Use the remainder theorem to find P(-2) for P(x) = x³ + 3x² +9,Specifically, give the quotient and the remainder for the associated division and the value of P(-2).QuotientRemainder =P(-2)=

Answers

Answer:

Quotient:

[tex]x^2+x-2[/tex]

Remainder:

[tex]13[/tex]

P(-2):

[tex]13[/tex]

Step-by-step explanation:

Remember that the remainder theorem states that the remainder when a polynomial p(x) is divided by (x - a) is p(a).

To calculate the quotient, we'll do the synthetic division as following:

Step one:

Write down the first coefficient without changes

Step two:

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 3:

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 4:

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Now, we will have completed the division and have obtained the following resulting coefficients:

[tex]1,1,-2,13[/tex]

Thus, we can conlcude that the quotient is:

[tex]x^2+x-2[/tex]

And the remainder is 13, which is indeed P(-2)

A circle has a circumference of 10 inches. Find its approximate radius, diameter and area

Answers

Answer:

Radius = 1.59 in

Diameter = 3.18 in

Area = 7.94 in²

Explanation:

The circumference of a circle can be calculated as:

[tex]C=2\pi r[/tex]

Where r is the radius of the circle and π is approximately 3.14. So, replacing C by 10 in and solving for r, we get:

[tex]\begin{gathered} 10\text{ in = 2}\pi r \\ \frac{10\text{ in}}{2\pi}=\frac{2\pi r}{2\pi} \\ 1.59\text{ in = r} \end{gathered}[/tex]

Then, the radius is 1.59 in.

Now, the diameter is twice the radius, so the diameter is equal to:

Diameter = 2 x r = 2 x 1.59 in = 3.18 in

On the other hand, the area can be calculated as:

[tex]A=\pi\cdot r^2[/tex]

So, replacing r = 1.59 in, we get:

[tex]\begin{gathered} A=3.14\times(1.59)^2 \\ A=3.14\times2.53 \\ A=7.94in^2 \end{gathered}[/tex]

Therefore, the answer are:

Radius = 1.59 in

Diameter = 3.18 in

Area = 7.94 in²

Find the formula for an exponential function that passes through the 2 points given

Answers

The form of the exponential function is

[tex]f(x)=a(b)^x[/tex]

a is the initial value (value f(x) at x = 0)

b is the growth/decay factor

Since the function has points (0, 6) and (3, 48), then

Substitute x by 0 and f(x) by 6 to find the value of a

[tex]\begin{gathered} x=0,f(x)=6 \\ 6=a(b)^0 \\ (b)^0=1 \\ 6=a(1) \\ 6=a \end{gathered}[/tex]

Substitute the value of a in the equation above

[tex]f(x)=6(b)^x[/tex]

Now, we will use the 2nd point

Substitute x by 3 and f(x) by 48

[tex]\begin{gathered} x=3,f(x)=48 \\ 48=6(b)^3 \end{gathered}[/tex]

Divide both sides by 6

[tex]\begin{gathered} \frac{48}{6}=\frac{6(b)^3}{6} \\ 8=b^3 \end{gathered}[/tex]

Since 8 = 2 x 2 x 2, then

[tex]8=2^3[/tex]

Change 8 to 2^3

[tex]2^3=b^3[/tex]

Since the powers are equal then the bases must be equal

[tex]2=b[/tex]

Substitute the value of b in the function

[tex]f(x)=6(2)^x[/tex]

The answer is:

The formula of the exponential function is

[tex]f(x)=6(2)^x[/tex]

Angle RQT is a straight angle. What are m angle RQS and m angle TQS? Show your work.

Answers

11x + 5 + 8x + 4 = 180

Simplifying like terms

11x + 8x = 180 - 5 - 4

19x = 171

x = 171/19

x = 9

RQS = 11(9) + 5

= 99 + 5

= 104°

TQS = 8(9) + 4

= 72 + 4

= 76°

helppppppppppppppppppp

Answers

It’s a and then you multiply and you can go from there

Find the missing rational expression.382x + 6(x-3)(x + 1)X-332x + 6(x-3)(x + 1)(Simplify your answer.)X-3

Answers

[tex]\frac{3}{x-3}-\frac{2x+6}{(x-3)(x+1)}=\frac{3(x+1)-2x-6}{(x-3)(x+1)}=\frac{3x+3-2x-6}{(x-3)(x+1)}=\frac{x-3}{(x-3)(x+1)}=\frac{1}{x+1}[/tex]

The graph of f(x) is shown in black.Write an equation in terms of f(x) to match the redgraph.For example, try something like this:f(x)+3, f (x - 2), or 4f(x).

Answers

Notice that the red function is similar to the black function, which means the transformation applied was a translation.

The transformation is 5 units to the right, exactly.

Therefore, the function that represents the red figure is

[tex]f(x-5)[/tex]

2x - 6(x-3) ≥ 5

solve for x.

Answers

Answer:

It’s siu

Step-by-step explanation:

Answer:x≤4.6

Step-by-step explanation: 2x-6(x-3)≥5. 1).combine the like terms. 2x+x=3x & -6+-3=-9. 2). isolate the "x". 3x-9≥5. 3x≥14. 3). divide both sides by your coefficient. 3x≥14/ 3

x≥4.6

4) flip your sign. x≤4.6

Don’t get part b of the question. Very confusing any chance you may help me with this please.

Answers

To solve this problem, first, we will solve the given equation for y:

[tex]\begin{gathered} x=3\tan 2y, \\ \tan 2y=\frac{x}{3}, \\ 2y=\arctan (\frac{x}{3}), \\ y=\frac{\arctan(\frac{x}{3})}{2}=\frac{1}{2}\arctan (\frac{x}{3})\text{.} \end{gathered}[/tex]

Once we have the above equation, now we compute the derivative. To compute the derivative we will use the following properties of derivatives:

[tex]\begin{gathered} \frac{d}{dx}\arctan (x)=\frac{1}{x^2+1}, \\ \frac{dkf(x)}{dx}=k\frac{df(x)}{dx}. \end{gathered}[/tex]

Where k is a constant.

First, we use the second property above, and get that:

[tex]\frac{d\frac{\arctan(\frac{x}{3})}{2}}{dx}=\frac{d\arctan (\frac{x}{3})\times\frac{1}{2}}{dx}=\frac{1}{2}\frac{d\arctan (\frac{x}{3})}{dx}\text{.}[/tex]

Now, from the chain rule, we get:

[tex]\frac{dy}{dx}=\frac{1}{2}\frac{d\text{ arctan(}\frac{x}{3})}{dx}=\frac{1}{2}\frac{d\arctan (\frac{x}{3})}{dx}|_{\frac{x}{3}}\frac{d\frac{x}{3}}{dx}\text{.}[/tex]

Finally, computing the above derivatives (using the rule for the arctan), we get:

[tex]\frac{dy}{dx}=\frac{1}{2}\frac{\frac{1}{3}}{\frac{x^2}{9}+1}=\frac{1}{6}(\frac{1}{\frac{x^2}{9}+1})=\frac{3}{2(x^2+9)}.[/tex]

Answer:

[tex]\frac{3}{2(x^2+9)}.[/tex]

A pound of rice crackers cost 42.88 Jacob purchased a 1/4 pound how much did he pay for the crackers?

Answers

Answer:

10.72

Step-by-step explanation:

The price per pound is 42.88

We are getting 1/4 pound.

Multiply 42.88 by 1/4

42.88 * 1/4 =10.72

Answer:

So you know that a pound of rice crackers cost $42.88. You also know that Matthew bought 1/4 or 25% or 0.25 of a pound. This means that by 42.88 divided 4 will equal the answer.

42.88 ÷ 4 = 10.72

Therefore, Matthew paid or $10.72 for 1/4 pound of rice crackers.

12 = - 2/5 yI got -30 I want to see if I did the correct steps

Answers

Solution

[tex]12=-\frac{2}{5}y[/tex]

Step 1: Simplify the expression

[tex]\begin{gathered} 12=-\frac{2}{5}y \\ \text{cross multiply} \\ 12(5)=-2y \\ 60=-2y \end{gathered}[/tex]

Step 2: Divide the both side by -2

[tex]\begin{gathered} 60=-2y \\ \frac{60}{-2}=-\frac{2y}{-2} \\ y=-30 \end{gathered}[/tex]

Therefore the correct value of y = - 30

Need help !! Geometry unit 3 parallel and perpendicular lines

Answers

ANSWER;

Converse; Exterior alternate angles are equal

[tex]x\text{ = 3}[/tex]

EXPLANATION;

Here, we want to get the value of x given that the lines l and m are parallel

From the diagram given, we can see that;

[tex]15x\text{ +29 = 26x-4}[/tex]

The reason for this is that they are a pair of exterior alternate angles

Mathematically, exterior alternate angles are equal

From here, we can proceed to solve for the value of x;

[tex]\begin{gathered} 26x-15x\text{ = 29+4} \\ 11x=33 \\ x\text{ = }\frac{33}{11} \\ x\text{ = 3} \end{gathered}[/tex]

the length of a rectangle is 13 centimeters less then four times it’s width it’s area is 35 centimeters find the dimensions of the rectangle

Answers

Solution:

The area of a recatngle is expressed as

[tex]\begin{gathered} \text{Area of rectangle = L}\times W \\ \text{where} \\ L\Rightarrow\text{length of the rectangle} \\ W\Rightarrow\text{ width of the rectangle } \end{gathered}[/tex]

Given that the length of the rectangle is 13 centimeters less than four times its width, this implies that

[tex]L=4W-13\text{ ---- equation 1}[/tex]

Tha area of the rectangle is 35 square centimeters. This implies that

[tex]36=L\times W\text{ --- equation 2}[/tex]

Substitute equation 1 into equation 2. Thus,

[tex]\begin{gathered} 36=L\times W \\ \text{where} \\ L=4W-13 \\ \text{thus,} \\ 36=W(4W-13) \\ open\text{ parentheses} \\ 36=4W^2-13W \\ \Rightarrow4W^2-13W-36=0\text{ ---- equation 3} \\ \end{gathered}[/tex]

Solve equation 3 by using the quadratic formula expressed as

[tex]\begin{gathered} W=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}_{} \\ \text{where} \\ a=4 \\ b=-13 \\ c=-36 \end{gathered}[/tex]

thus, we have

[tex]\begin{gathered} W=\frac{-(-13)\pm\sqrt[]{(-13)^2-(4\times4\times-36)}}{2\times4}_{} \\ =\frac{13\pm\sqrt[]{169+576}}{8} \\ =\frac{13\pm\sqrt[]{745}}{8} \\ =\frac{13}{8}\pm\frac{\sqrt[]{745}}{8} \\ =1.625\pm3.411836016 \\ \text{thus,} \\ W=5.036836016\text{ or W=}-1.786836016 \end{gathered}[/tex]

but the width cannot be negative. thus, the width of the recangle is

[tex]W=5.036836016[/tex]

From equation 1,

[tex]\begin{gathered} L=4W-13 \\ \end{gathered}[/tex]

substitute the obtained value of W into equation 1.

Thus, we have

[tex]\begin{gathered} L=4W-13 \\ =4(5.036836016)-13 \\ =20.14734-13 \\ \Rightarrow L=7.14734 \end{gathered}[/tex]

Hence:

The width is

[tex]5.036836016cm[/tex]

The length is

[tex]7.14734cm[/tex]

Find the absolute maximum and minimum values of the following function on the given interval. f(x)=3x−6cos(x), [−π,π]

Answers

Answer:

Absolute minimum: x = -π / 6

Absolute maximum: x = π

Explanation:

The candidates for the absolute maximum and minimum are the endpoints and the critical points of the function.

First, we evaluate the function at the endpoints.

At x = -π, we have

[tex]f(-\pi)=3(-\pi)-6\cos (-\pi)[/tex][tex]\Rightarrow\boxed{f(-\pi)\approx-3.425}[/tex]

At x = π, we have

[tex]f(\pi)=3(\pi)-6\cos (\pi)[/tex][tex]\Rightarrow\boxed{f(\pi)\approx15.425.}[/tex]

Next, we find the critical points and evaluate the function at them.

The critical points = are points where the first derivative of the function are zero.

Taking the first derivative of the function gives

[tex]\frac{df(x)}{dx}=\frac{d}{dx}\lbrack3x-6\cos (x)\rbrack[/tex]

[tex]\Rightarrow\frac{df(x)}{dx}=3+6\sin (x)[/tex]

Now the critical points are where df(x)/dx =0; therefore, we solve

[tex]3+6\sin (x)=0[/tex]

solving for x gives

[tex]\begin{gathered} \sin (x)=-\frac{1}{2} \\ x=\sin ^{-1}(-\frac{1}{2}) \end{gathered}[/tex]

[tex]x=-\frac{\pi}{6},\; x=-\frac{5\pi}{6}[/tex]

on the interval [−π,π].

Now, we evaluate the function at the critical points.

At x = -π/ 6, we have

[tex]f(-\frac{\pi}{6})=3(-\frac{\pi}{6})-6\cos (-\frac{\pi}{6})[/tex][tex]\boxed{f(-\frac{\pi}{6})\approx-6.77.}[/tex]

At x = -5π/6, we have

[tex]f(\frac{-5\pi}{6})=3(-\frac{5\pi}{6})-6\cos (-\frac{5\pi}{6})[/tex][tex]\Rightarrow\boxed{f(-\frac{5\pi}{6})\approx-2.66}[/tex]

Hence, our candidates for absolute extrema are

[tex]\begin{gathered} f(-\pi)\approx-3.425 \\ f(\pi)\approx15.425 \\ f(-\frac{\pi}{6})\approx-6.77 \\ f(-\frac{5\pi}{6})\approx-2.66 \end{gathered}[/tex]

Looking at the above we see that the absolute maximum occurs at x = π and the absolute minimum x = -π/6.

Hence,

Absolute maximum: x = π

Absolute minimum: x = -π / 6

Which number is greater in each set?

Answers

We have three set of numbers and we must choose the greater value in each set

1.

[tex]\frac{1}{3}or\frac{1}{4}or\frac{1}{5}[/tex]

When the numerator is 1, the greater fraction is the one that has the small denominator.

So, in this case the greater number is

[tex]\frac{1}{3}[/tex]

2.

[tex]\frac{1}{4}or\frac{4}{3}or\frac{5}{6}[/tex]

In this case we can rewrite the fractions as fractions with the same denominator

[tex]\frac{1}{4}=\frac{3}{12}[/tex][tex]\frac{4}{3}=\frac{16}{12}[/tex][tex]\frac{5}{6}=\frac{10}{12}[/tex]

Then, the greater number is the one that has the greater numarator

So, it is

[tex]\frac{16}{12}=\frac{4}{3}[/tex]

in this case the greater number is

[tex]\frac{4}{3}[/tex]

3.

[tex]\frac{16}{5}or3\frac{2}{5}or3.25[/tex]

In this case we can rewrite the numbers as decimal numbers

[tex]\frac{16}{5}=3.2[/tex][tex]3\frac{2}{5}=3.4[/tex][tex]3.25=3.25[/tex]

In this case the greater number is

[tex]3\frac{2}{5}[/tex]

Can someone help with this question?✨

Answers

The equation of the line that is perpendicular with y = 4 · x - 3 and passes through the point (- 12, 7) is y = - (1 / 4) · x + 4.

How to derive the equation of a line

In this problem we find the case of a line that is perpendicular to another line and that passes through a given point. The equation of the line in slope-intercept form is described below:

y = m · x + b

Where:

m - Slopeb - Interceptx - Independent variable.y - Dependent variable.

In accordance with analytical geometry, the relationship between the two slopes of the lines are:

m · m' = - 1

Where:

m - Slope of the first line.m' - Slope of the perpendicular line.

If we know that m = 4 and (x, y) = (- 12, 7), then the equation of the perpendicular line is:

m' = - 1 / 4

b = 7 - (- 1 / 4) · (- 12)

b = 7 + (1 / 4) · (- 12)

b = 7 - 3

b = 4

And the equation of the line is y = - (1 / 4) · x + 4.

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Which of the following statements must be true based on the diagram below!(Diagram is not to scale)O JL is a segment bisector.JL is a perpendicular bisector.OJT is an angle bisectora Lis the vertex of a right angle,Jis the midpoint of a segment in the diagramNone of the above.

Answers

From the diagram, we notice that the line JL bisects the angle J into two equal angles. Hence, we can conclude that the correct statement is this:

JL is an angle bisector

An angle bisector are

Need help with this question

Answers

Given: a quadratic function with vertex (2,3) opening upward .

Find: the given statement is true or false.

Explanation: if parabola has a vertex at (2,3) and opens upward, it has one real solution., (2,3) will be a lowest point. The vertex will be at lowest point, it will be minimum.

that means graph has no one real solution. hence it will never going to intersect. so this statement is false.

Final answer: the given statement is FALSE.

If each machine produces nails at the same rate, how many nails can 1 machine produce in 1 hour

Answers

Divide the number of nails by the number of minutes:

16 1/5 ÷ 15 = 1 2/25 per minute

48 3/5 ÷ 45 = 1 2/25 per min

59 2/5 ÷ 55 = 1 2/25 per min

We have the number of nails produced per minute, to calculate the number of nails in an hour multiply it by 60, because 60 minutes= 1 hour:

1 2/25 x 60 = 64 4/5

A window washer drops a tool from their platform 155ft high. The polynomial -16t^2+155 tells us the height, in feet, of the tool t seconds after it was dropped. Find the height, in feet, after t= 1.5 seconds.

Answers

The answer is is pie

a janitor had 2/3 of a cleaning solution. he used 1/4 of the solution in an day. how much of the bottle did he use?​

Answers

Answer:

5/12 of the cleaning solution.

Step-by-step explanation:

2/3 – 1/4

------------------------------------------

2 × 4            

              = 8/12

3 × 4  

------------------------------------------

1 x 3        

             = 3/12

4 x 3

------------------------------------------

8 – 3

  12

=  5/12

------------------------------------------

Hopefully this makes sense!

For p(2) = 7 + 10x - 12x^2 - 10x^3 + 2x^4 + 3x^5, use synthetic substitution to evaluate

Answers

Answer:

p(-3) = -428

Explanations:

Given the polynomial function expressed as:

[tex]p(x)=7+10x-12x^2-10x^3+2x^4+3x^5[/tex]

Determine the value of p(-3)

[tex]\begin{gathered} p(-3)=7+10(-3)-12(-3)_^2-10(-3)^3+2(-3)^4+3(-3)^5 \\ p(-3)=7-30-12(9)-10(-27)+2(81)+3(-243) \\ p(-3)=-23-108+270+162-729 \\ p(-3)=-428 \end{gathered}[/tex]

Hence the value of p(-3) is -428

you bought a car for $5000. each year it depreciates by 8.5%. Which equation can be used to find the value, v, of the car, x years after it was purchased?

Answers

We have the following:

In this case, we have the following formula:

[tex]v=C\cdot(1-r)^x[/tex]

Where C is the original value of the car, r is the depreciation rate and x is the time in years

ur answer as a polynomial in standard form.=f(x) = 5x + 1g(x) = x2 – 3x + 12=Find: (fog)(x)

Answers

Answer:

(fog)(x) = 5x² - 15x + 61

Explanation:

The given functions are:

f(x) = 5x + 1

g(x) = x² - 3x + 12

(fog)(x) = f(g(x))

This means that we are substituting g(x) into f(x)

(fog)(x) = 5(x² - 3x + 12) + 1

(fog)(x) = 5x² - 15x + 60 + 1

This can be further simplified as:

(fog)(x) = 5x² - 15x + 61

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