For the polynomial function f(x) = x5-x4-9x3 + 9x2, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.
A.) x = -3, cross; x = 0, cross; x = 1, cross; x = 3, cross
B.) x = -3, cross; x = 0, cross; x = 1, cross; x = 3, touch
C.) x = -3, cross; x = 0, touch; x = 1, cross; x = 3, cross
D.) x = -3, cross; x = 0, cross; x = 1, touch; x = 3, touch
Answers
Answer:
C.) x = -3, cross; x = 0, touch; x = 1, cross; x = 3, cross
Step-by-step explanation:
You want the zeros and their multiplicity of f(x) = x^5 -x^4 -9x^3 +9x^2, along with a description of whether the graph crosses or touches the x-axis at each zero.
FactorsThe equation can be factored as ...
f(x) = x^2(x^3 -x^2 -9x +9)
The cubic can be factored as ...
x^3 -x^2 -9x +9 = x^2(x -1) -9(x -1) = (x^2 -9)(x -1)
and the quadratic factor can be factored as the difference of square. The complete factorization is then ...
f(x) = x^2(x -1)(x -3)(x +3)
ZerosThe zeros are the values of x that make the factors zero:
x = 0, multiplicity 2x = -3, multiplicity 1x = 1, multiplicity 1x = 3, multiplicity 1Touch/CrossWhen the multiplicity of a zero is even, the graph touches the x-axis. Here, that means the graph will touch at x=0, where the multiplicity of the zero is 2.
When multiplicity is odd, the graph will cross the x-axis. The graph crosses at the zeros -3, -1, +3.
__
Additional comment
As soon as you recognize that the x^2 factor means the multiplicity of x=0 is even, you can identify the correct answer choice: the only one that says "touch" for x=0.
Related Questions
What is median class example?
Answers
The continuous data that is presented as a frequency distribution makes up the median of the grouped data.
The center number in the set of data, known as the median, is what divides the data set's upper and lower halves. Since the data is divided into class intervals, the middle value is unknown when calculating the median of grouped data.
Let us understand this with the help of a median class example.
Consider the data as 48, 20, 59, 69,73. We have to calculate the median.
Arranging in ascending order we get, 20, 48, 59, 69, 73.
Here the number of observations is n = 5.
To find the median of odd data we will use the formula:
[(n+1)/2] = (5+1)/2 = 3.
Therefore, median = 3rd observation.
Median = 59.
Hence we got the idea of the median with the example of class.
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In a series of transformations, which transformation would make two figures similar as opposed to congruent? answer choices.
a. translation
b. dilation.
c. reflection.
d. rotation.
Answers
Reasoning:
By definition, translations, rotations, and reflections preserve the congruence and collinearity of points on figures transformed from the pre-image to the image. This means that the transformed figure has the exact same dimensions: congruent angles, sides, location of points. On the other hand, dilations are a type of transformation that create similar figures. Similar figures are proportional, so they have congruent angles, and thus they are the same shape, but their side lengths are proportional. So, they look like a copy of the original figure, but either enlarged or reduced by a factor, called the scale factor or “k.”
How do you find the mean grade 7?
Answers
We find the mean grade 7 by using formula Mean = ∑x / n
Where, ∑ represents the summation
x represents observations
n represents the number of observations .
What is mean?In addition to the mode and median, the mean is one of the measurements of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.
The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.
By dividing the sum of the given numbers by the entire number of numbers, the mean (the average of the given numbers) is determined.
Mean = (Sum of all the observations/Total number of observations)
The mean in grade 7 is calculated by using formula Mean = ∑x / n
Where, ∑ represents the summation
x represents observations
n represents the number of observations .
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A student uses a solution that contains 16 grams of water to conduct an evaporation experiment. At the end of one hour the amount of water in the solution has decreased by 3.5%
Answers
Answer:
Step-by-step explanation:
.035*16=.56 solution has decreased for this part
16 divided by 3.5⁶66677⁷54776367
Step-by-step explanation:
4_35665567
What are the 20 examples of idioms?
Answers
There are many common idioms. Following are the 20 idioms that is mostly used.
What is idiom?An idiom is a collection of words with a figurative, extraneous meaning that cannot be understood from the individual words alone. Idioms frequently began with literal meanings but lost them when they strayed from their original context.
Write your favorite idiom.Rome was not build in a day is my favorite idiom
Better late than never.Up in the airStabbed in the backTakes two to tangoKill two birds with one stonePiece of cakeCosts an arm and a legBreak a legUnder the weather.The ball is in your court.Spill the beans. Break a leg. Pull someone's leg. Sat on the fence. Through thick and thin. Once in a blue moon.Give someone the benefit of the doubt. Back to the drawing board.Get your act together. Hang in thereTo learn more about idiom visit the link:
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What is the relationship between volume and surface area?
Answers
The surface area of any particular thing is the area or region that the object's surface occupies. Volume, on the other hand, is the quantity of space accessible in an object. There are several forms and sizes in geometry, such as the sphere, cube, cuboid, cone, cylinder, and so on. Each form has both a surface area and a volume.
What is area?The area amount denotes the size of a region on a flat or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as surface area, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. The area is the region determined by the shape of an item. The area of a form is the space in a plane covered by a figure or other two-dimensional geometric object.
Here,
The surface area of any given thing is the area or region occupied by the object's surface. Volume, on the other hand, refers to the quantity of space accessible in an object. Shapes and sizes in geometry include the sphere, cube, cuboid, cone, cylinder, and so on. Each form has a surface area as well as a volume.
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Help me with this I will give brainliest
Answers
Answer:
1) x = 29; m∠3 = 6º
2a) scalene
2b) acute
Step-by-step explanation:
1) We can first solve for m∠3, as it is supplementary to 174º.
174º + m∠3 = 180º
m∠3 = (180 - 174)º
m∠3 = 6º
Then, we can solve for x by setting the sum of the measures of the interior angles of the triangle to 180º.
m∠1 + m∠2 + m∠3 = 180º
↓ substitute in given and solved values
(3x + 2)º + (5x - 60)º + 6º = 180º
↓ combine like terms
8xº - 52º = 180º
↓ add 52 to both sides
8xº = 232º
↓ divide both sides by 8º
x = 29
2a) We know that this triangle is not equilateral, as the measure of one of its interior angles (m∠3) is 6º. However, the triangle may be isosceles if m∠1 = m∠2. We can check for that by substituting x into each angle measure expression.
m∠1 ≟ m∠2
(3x + 2)º ≟ (5x - 60)º
↓ substitute in x-value
3(29)º + 2º ≟ 5(29)º - 60º
↓ simplify
(87 + 2)º ≟ (145 - 60)º
89º ≠ 85º
m∠1 ≠ m∠2; the triangle is not isosceles. Therefore, it must be scalene.
2b) All of the triangle's angles are less than 90º. Hence, it is an acute triangle.
Solving Systems by Substitution
y=-4
y=-2x-20
Answers
Step-by-step explanation:
To solve a system of equations by substitution, you can solve one of the equations for one of the variables and substitute this expression into the other equation. This will give you an equation with only one variable, which you can then solve to find the value of that variable. You can then substitute this value back into one of the original equations to find the value of the other variable.
In this case, the given system of equations is:
y = -4
y = -2x - 20
Since the second equation is already in the form y = ..., we can substitute the expression for y from the second equation into the first equation:
-4 = -2x - 20
Solving this equation for x, we get:
x = -12
Substituting this value of x back into the second equation, we get:
y = -2(-12) - 20
= 24 - 20
= 4
Therefore, the solution to the system of equations is (x, y) = (-12, 4).
Answer:
x = -8
Step-by-step explanation:
-2x - 20 = -4
-2x = 16
x = -8
2/9 x 1/3 =
Enter your answer as a mixed number in simplest form
Answers
Answer:
2 / 27
Step-by-step explanation:
2/9 * 1/3 = (2*1) / (9*3) = 2/27
S= n(n+1)/2 despejar para n
Answers
Por propiedades algebraicas, la ecuación de la variable n es función de la variable S es igual a n = - 1 / 2 ± (1 / 2) · √(1 + 8 · S).
¿Cómo despejar una variable en una ecuación?
En esta pregunta tenemos un ecuación donde la variable S en función de la variable n y debemos reescribir la expresión como una de la variable n en función de la variable S. Esto es posible mediante el uso de propiedades algebraicas. Primero, escriba la ecuación:
S = n · (n + 1) / 2
Segundo, utiliza la propiedad distributiva:
S = (n² + n) / 2
Tercero, aplica compatibilidad con la multiplicación, existencia del inverso multiplicativo y propiedad modulativa:
2 · S = n² + n
Tercero, construya una ecuación cuadrática:
n² + n - 2 · S = 0
Cuarto, utilice la fórmula cuadrática:
n = - 1 / 2 ± (1 / 2) · √[1² - 4 · (- 2 · S)]
n = - 1 / 2 ± (1 / 2) · √(1 + 8 · S)
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How do I do this question and I need answer please
Answers
Answer: x = 3/4
Step-by-step explanation:
1/3x + 3 = 4 - x
Subtract 3 from both sides
1/3x = 1 - x
Then times 3 from both sides
x = 3 - 3x
Add 3x on both sides
4x = 3
Divided by 4, both side
x = 3/4
help me with this please
Answers
The evaluated value of the expression b² - 4ac when a = -2, b = -4 and c = 1 is 24.
How to evaluate expression?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
Therefore, let's evaluate b² - 4ac when a = -2, b = -4 and c = 1.
Hence,
b² - 4ac = (-4)² - 4(-2)(1) = 16 + 8 = 24
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Draw a line representing the 'rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
Answers
Rise and Run of line's ratio gives the Slope of the line.
What is rise of line and run of line?Rise of a line is the how many units you move up or down to reach from one point to another point. Run of a line is the how many units you move left or right to reach from one point to another.
>Slope of a line is the ratio of the rise to the run of the line.
Calculation:
Let us assume the graph of y = x.
Now in the graph we take three points
let point 1 be (3,3) = (x1,y1)
point 2 be (5,5)= (x2,y2)
point 3 be (5,3)= (x3,y3)
Now the rise is y2 - y1 which is 2
Now the run is x2 - x1 which is 2
Slope is [tex]\frac{rise}{run}[/tex] = [tex]\frac{2}{2} =1[/tex], we know that slope of line y=x is 1 and here we get the same so it is proved that slope of line is [tex]\frac{rise}{run}[/tex] .
Rise and Run of line's ratio gives the Slope of the line.
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you are playing a game with your friend to see who can make the most baskets from the free throw line. each of you has 5 shots at the basket. how many ways are there for you to make exactly 4 shots?
Answers
The probability of making exactly 4 shots is 4/5, in where 4 is outcomes Favour to me and 5 is total possible outcomes.
what is probability?The probability is measured as the ratio of favorable outcomes of a particular event to the total possible outcomes of that event. The value of probability should be lies between 0 to 1.
what are favorable outcomes of an event?The term favorable outcome uses to determine the probability in mathematics. It is the possibility of happening expected incident of a particular event.
the ways in how i can make exactly 4 shots in the game = my favorable outcomes/total possible outcomes
=4/5
hence, the result is 4/5.
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Are there 2 answers to a quadratic equation?
Answers
The above quadratic equation has two solutions, as shown by the question Yes.
A quadratic equation is what?A second-order polynomial equation with a single variable, x, is known as a quadratic equation.
ax2 + bx + c = 0 is a quadratic equation in standard form.
x stands for an unknown (an variable)
With respect to known numbers, a, b, and c, where a 0
The polynomial's number of solutions is influenced by the equation's highest possible power given in the question.
The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation.
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jason sampled 60 smokers who were questioned about the number of hours they sleep each day. jason wants to test the hypothesis that the smokers need less sleep than the general public which needs an average of 7.5 hours of sleep with a population standard deviation of 0.7 hours. z equals fraction numerator x with bar on top minus mu over denominator begin display style fraction numerator sigma over denominator square root of n end fraction end style end fraction if the sample mean is 7.2 hours, what is the z-score? answers are rounded to the hundredths place.
Answers
The z-score of the sample research is calculated as; -3.32
What is the z-score of the distribution?We are given the formula for z-score as;
z = (x-bar - μ)/(σ/√n)
where;
x-bar is sample mean
μ is population mean
σ is population standard deviation
We are given;
Population mean; μ = 7.5 hours
Sample mean; x-bar = 7.2 hours
population standard deviation; σ = 0.7 hours
sample size; n = 60
Thus;
z-score = (7.2 - 7.5)/(0.7/√60)
z-score = -0.3/0.0903696
z-score = -3.32
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Please help. In plus only answer if know the answer
Answers
Answer:x-int=4 1/4 y-int=-5 1/3
Step-by-step explanation:[tex]4x-3y=17\\ +3y =+3y\\ 4x=3y+17\\4x/4=3y/4 +17/4\\x=\frac{3}{4}x+ 4 \frac{1}{4} \\\\4x-3y=17\\-4x=-4x\\-3y=-4x+17\\-3y/-3=-4x/-3+17/-3\\y=\frac{4}{3}x -5\frac{1}{3}[/tex]
Please help I will give brainliest
Answers
Answer:
cos(x) = r/t
sin(x) = s/t
tan(x) = s/r
Step-by-step explanation:
Background info:
This question becomes simple when we remember SohCahToa.
Soh stands for Sine = Opposite/ Hypotenuse
Cah stands for Cosine = Adjacent/ Hypotenuse
Toa stands for Tangent = Opposite/ Adjacent
Solving:
1. Cosine of angle x (think Cah)
The adjacent side is r and the hypotenuse is t.
so the answer is r/t
2. sine of angle x (think Soh)
The opposite side is s and the hypotenuse is t.
so the answer is s/t
3. Tangent of angle x (think toa)
The opposite side is s and the adjacent side is r.
so so the answer is s/r
ason has 2 hours of free time. He spent 20 minutes playing outside, 25 minutes on his phone, and the rest of the time practicing his instrument. What percent of his time was spent playing his instrument?
Answers
Answer:
62.5%
Step-by-step explanation:
Split the time up into 5 minute slots. That gives us 24 slots of 5 minutes.
20/5=4 of the 5 minute slots playing outside
25/5=5 of the 5 minute slots on his phone
5+4=9 out of 24 slots spent
24-9=15 slots remaining to play his instrument
15/24x100=62.5% time playing instrument
Answer:62.5%
Step-by-step explanation:
25. The manager of a coffee shop has Costa Rican coffee that sells for $7 per pound and Kenyan coffee that sells for $10
per pound. The manager wishes to mix 80 pounds of the Kenyan coffee with the Costa Rican coffee to get a mixture that
will sell for SS per pound. How many pounds of the Costa Rican coffee should be used?
Answers
The Costa Rican coffee should be used is 160 pound.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given that the cost of Costa Rican coffee that sells for $7 per pound and Kenyan coffee that sells for $10.
The cost of the mixture is $8.5 per pound.
Assume that the manager mixed 80 pounds of the Kenyan coffee with the x pound of the Costa Rican coffee to get a mixture.
The cost of 80 pound Kenyan coffee is $(80×10) = $800.
The cost of x pound Costa Rican coffee is 7x.
The cost of mixture coffee is (80 + x)8.5
According to the question:
800 + 7x = (80 + x)8
800 + 7x = 640 + 8.x
640 + 8x = 800 + 7x
x = 800 - 640
x = 160
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For what value of k (- 2 is a zero of the polynomial 3x² 4x 2k?
Answers
-2 is the zero of the polynomial 3x²+ 4x + 2k for the value of k equals to -2.
As given in the question,
Given polynomial is equal to :
3x²+ 4x + 2k
-2 is the zero of the given polynomial 3x²+ 4x + 2k
Compare with the standard quadratic equation ax² + bx + c
Let 'α' be the zero whose value is equal to -2.
And 'β' be the another zero.
Sum of the zeros of the polynomial = -b/ a
⇒ α + β = -4 / (3)
⇒α + β = -4/3 ___(1)
Product of the zeros = c/a
⇒αβ = 2k / 3
⇒(-2)β = 2k/3
⇒β = -k/3
Substitute the value of α and β in (1)
-2 + -k/3 = -4/3
⇒-k/3 = -4/3 + 2
⇒ -k/3 =2/3
⇒ k = -2
Therefore , the value of k for the given polynomial with the given condition is equal to -2.
The above question is incomplete , the complete question is :
For what value of k , - 2 is a zero of the polynomial 3x²+ 4x + 2k?
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D
.0
A
58d
B
A, B, C and D are points on a circle, centre O.
Angle ABC = 58°
Calculate the size of angle ADC.
(1 mark)
Diagram NOT
accurately drawn
Answers
Answer:
∠ ADC = 122°
Step-by-step explanation:
ABCD is a cyclic quadrilateral.
opposite angles in a cyclic quadrilateral sum to 180° , that is
∠ ADC + ∠ ABC = 180∠
∠ ADC + 58° = 180° ( subtract 58° from both sides )
∠ ADC = 122°
Your class has 18 students. Exactly 23 of them say that science is the subject they like the most. Which model shows 23 of 18 circled?
Answers
12 students like science the most and can draw a model having 18 things out of which 12 are circled.
What is model in mathematics?
In order to create a forecast or offer insight, mathematical modelling is the act of developing a mathematical representation of a real-world phenomenon. Applying a formula and really creating a mathematical relationship are two different things.Consider the provided information.
Your class has 18 students. Exactly 2/3 of them say that, out of all their subjects, they like science the most.
First calculate 2/3 of 18.
= (2/3) * 18
= 2 * 6
= 12
Hence, 12 students like science the most.
We can draw a model having 18 things out of which 12 are circled.
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Emma had to finish her 249-page novel by Friday. She had already read 166 pages. Write and solve an equation to show how many pages Emma had left to read by Friday.
p + 166 = 249; p = 83 pages
p − 166 = 249; p = 415 pages
p over 166 equals 2; p = 332 pages
83p = 166; p = 2 pages
Answers
Answer:
p + 166 = 249
p = 83 pages
Step-by-step explanation:
We know that she has to finish 249 pages novel and read 166.
So, let p represent the number of pages left to read; we have the equation
p + 166 = 249
Now let's solve by subtracting 166 from both sides
p = 83 pages
So, Emma had 83 pages left to read by friday
How do you determine if a triangle is SSS SAS or ASA?
Answers
SSS Stands on Side - Side - Side
SAS Stands on Side - Angle - Side
ASA Stands for Angle - Side - Angle.
There are three theorems that may be used to determine whether two triangles are similar: Angle - Side - Angle (ASA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).
SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.
That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle are the same as the two sides and included angle of another triangle. Any angle that is created by two specified sides is an included angle.
According to the ASA postulate of Euclidean geometry, two triangles are similar if their two corresponding angles are congruent and one side is equal to the corresponding side of the other triangles.
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If 3x + 5y = 25, what is the value of 3x + 5y/5 =
Answers
Answer: 5
Step-by-step explanation: if you do something to one side of the equation, it has to be done to the other side.
in this case, they divided the left side (3x+5y) by 5
so so make both sides equal, you'd have to divide the right side (25) by 5 as well which would give you 5
If PS= RS = 31, PQ = 2v, and QR = v + 23, what is the value of v?
Answers
The value of the v is 11.5 units.
What is a Line Segment?
A line segment is a portion of a straight line that is defined by two points. It is a one-dimensional geometric figure with no width or area. Line segments can be drawn in many ways, including straight, curved, or jagged. The length of a line segment is the distance between the two points that define it. Line segments are commonly used to measure distances, form shapes, and construct geometric figures. Line segments can be used to define polygons, circles, and other shapes. Line segments are also used in mathematics to represent vectors and calculate angles. Line segments are a fundamental element of geometry and are used in a variety of applications, including navigation, construction, engineering, and computer graphics.
We have,
PS= RS = 31,
PQ = 2v,
and QR = v + 23,
v = ?
If PS= RS = 31,
then PQ = QR,
so, 2v = v + 23,
v = 23/2
v = 11.5 unit
Hence, the value of the v is 11.5 units.
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A bakery sells muffins for $3. 50 each. A beverage is $1. 75. A class purchases 32 items and spends a total of $87. 50.
Answers
Answer:
Number of muffins= 18
Number of beverages= 14
Amount spent on muffins= $63
Amount spent on beverages= $24.50
Step-by-step explanation:
To find the number of muffins sold, we can first assume that all the 32 items purchased were beverages.
If the class bought 32 beverages,
Total spending
= 32($1.75)
= $56
Difference in total spending
= $87.50 -$56
= $31.50
The difference in the total spending is due to the number of muffins purchased that we had assumed they were beverages.
Difference in cost for each muffin vs beverage
= $3.50 -$1.75
= $1.75
Thus, for every incorrect assumption we made, the total spending will be $1.75 lesser than the actual amount.
Sets of wrong assumption
= $31.50 ÷$1.75
= 18
This means that out of the 32 items we previously assumed to be beverages, 18 were actually muffins. The remaining number of items were indeed beverages.
Number of muffins= 18
Number of beverages
= 32 -18
= 14
Amount spent on muffins
= 18($3.50)
= $63
Amount spent on beverages
= 14($1.75)
= $24.50
Total spending
= $63 +$24.50
= $87.50
please help me with this problem
Answers
Answer:
40 orange marbles
Step-by-step explanation:
We know for every 12 marbles, we have 5 orange marbles and 7 green marbles
Now we have 56 green marbles. To get from 7 to 56, we take 7 times 8.
So, we do the same take 5 times 8 = 40 orange marbles
So, it contains 40 orange marbles!
Find [g ο f](-4) given f(x) = x + 4 and g(x) = -2x2
Answers
Answer:
Step-by-step explanation:
(
1
)
.
plugging the
4
into
g
(
x
)
and then putting what you get from that in to
f
(
x
)
(
2
)
.
plug
g
(
x
)
into
f
(
x
)
and then plug in the
4
Option 1:
Plug
4
into
g
(
x
)
:
g
(
x
)
=
−
2
(
4
)
−
6
=
−
8
−
6
=
−
14
Then plug
g
(
x
)
into
f
(
x
)
:
f
(
x
)
=
3
(
−
14
)
−
7
=
−
42
−
7
=
−
49
Option 2:
Plug
g
(
x
)
into
f
(
x
)
:
f
(
x
)
=
3
(
−
2
x
−
6
)
−
7
=
−
6
x
−
18
−
7
=
−
6
x
−
25
Finally plug
4
into our current
f
(
x
)
:
f
(
x
)
=
−
6
(
4
)
−
25
=
−
24
−
25
=
−
49