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What are the zeros of the function?
Use the zeros to find all of the linear factors of the polynomial function.
Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in the previous question. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form.
Use the y-intercept of the graph and your equation from part E to calculate the value of a.
Given what you found in all of the previous parts, write the equation for the function shown in the graph.
Answers
Answer:
Step-by-step explanation:
The zeros of this cubing function are easily read from the graph: {-20, -5, 15}.
The factors of this polynomial are therefore (x + 20), (x + 5) and (x - 15).
The y-intercept is (0, 1).
The function is thus f(x) = a(x + 20)(x + 5)(x - 15).
According to the y-intercept, if x = 0, y = 1.
Thus, y = 1 = f(0) = a(20)(5)(-15), or 1 = a(100)(-15), or 1 = -1500a.
Then a = -1/1500, and the function is:
f(x) = (-1/1500)(x^3 + .. + .. + ... ). We must multiply out (x + 20)(x + 5)(x - 15) to obtain f(x) in finished form.
Answer:
zeros: (-20, 0), (-5, 0) and (15, 0)
factors: (x + 20), (x + 5) and (x - 15)
f(x) = a*(x + 20)*(x + 5)*(x - 15)
a = -1/1500
f(x) = -1/1500*(x + 20)*(x + 5)*(x - 15)
f(x) = -1/1500*x^3 - 1/100*x^2 + 11/60x + 1
Step-by-step explanation:
The zeros of the function are those points where the function intercepts the x-axis. They are: (-20, 0), (-5, 0) and (15, 0)
The zeros of a polynomial are expressed as factors as follows: (x - a) where a is a zero. Then, for this case, the factors are (x + 20), (x + 5) and (x - 15)
The equation of f(x) use the factors and the leading coefficient as follows: f(x) = a*(x + 20)*(x + 5)*(x - 15)
Applying the distributive property of multiplication, we get the expanded form:
f(x) = a*(x + 20)*(x + 5)*(x - 15)
(x + 20)*(x + 5) = x^2 + 5x + 20x + 20*5 = x^2 + 25x + 100
f(x) = a*(x^2 + 25x + 100)*(x - 15)
(x^2 + 25x + 100)*(x - 15) = x^3 - 15x^2 + 25x^2 - 15*25x + 100x - 100*15 = x^3 + 15x^2 - 275x - 1500
f(x) = a*(x^3 + 15x^2 - 275x - 1500)
The y-intercept of the graph is (0, 1). Replacing this point into the function equation:
1 = a*(0 + 20)*(0 + 5)*(0 - 15)
1 = a*20*5*(-15)
1 = a*(-1500)
a = -1/1500
Replacing this value into the function equation:
f(x) = (-1/1500)*(x^3 + 15x^2 - 275x - 1500)
f(x) = -1/1500*x^3 - 1/100*x^2 + 11/60x + 1
Related Questions
A lighting products company has put a new brand of solar lightbulbs on the market. The graph shows the estimated revenue, in millions of dollars, as the selling price of the lightbulb varies. What selling price is expected to produce the maximum revenue? A. $2 B. $8 C. $5 D. $3
Answers
Answer:
$5
Step-by-step explanation:
Answer:
the answer is 5$
Step-by-step explanation:
Sharon suspects that her brother's penny is unfair. She flips it 50 times and heads comes up 40 times. Based on these trials, the probability that a flip of this coin comes up TAILS is A) 1/5 B) 4/5 C) 4/9 D (5/9)
Answers
The correct answer is B. 4/5. Hope this helps! : )
Answer:
1/5
Step-by-step explanation:
it said so in usa testprep and i hope this helps you! ^-^
Joelle bought 20 lollipops and 6 bags of Doritos for a total cost of $8.20. She knows that each lollipop cost 25 cents and reasoned that two bags of chip must cost a little more than $1.00. Is this a reasonable guess? Why or why not?
Answers
I mean... I think it's a reasonable guess because not gonna lie- chips can get expensive. BUT- It doesn't really make sense because like, she bought so many lollipops. My brain isn't really functioning to do the math- but my best guess would beeeee... UNreasonble. I'm super super sorry if it's wrong. Math isn't my strong point, sorry. Have a nice day!
Answer:
no
Step-by-step explanation:
because 20×.25 = 5 so the lollipop cost $5.00 and then you only have 3.20 left over
Type the correct answer in each box. Consider the expressions shown below.
A -9x^2-2x+7
B 9x^2-2x+2
C 9x^2+2x-7
Complete the following statements with the letter that represents the expression.
(7x^2-5x+3)+(2x^2+3x-1) is equivalent to expression___ .
(3x^2-4x-4)+(-12x^2+2x+11) is equivalent to expression___ .
(4x^2-3x-9)+(5x^2+5x+2) is equivalent to expression ___ .
Answers
Answer:
B, A and C.
Step-by-step explanation:
(7x^2-5x+3)+(2x^2+3x-1) is equivalent to expression B .
(3x^2-4x-4)+(-12x^2+2x+11) is equivalent to expression A .
(4x^2-3x-9)+(5x^2+5x+2) is equivalent to expression C .
You combine like terms to arrive with the answer.
The answer is:
- The first operation match with the polynomial:
B. [tex]9x^{2} -2x+2[/tex]
- The second operation match with the polynomial:
A. [tex]-9x^{2}-2x+7[/tex]
- The third operation match with the polynomial:
C. [tex]9x^{2} +2x-7[/tex]
Why?In order to solve the given operations, we need to group the like terms.
Remember, like terms are terms that share the same variable and the same exponent.
For example:
[tex]x^{2} +2x^{2} +3x^{3} +2=3x^{2} +3x^{3} +2[/tex]
We only operate with the variables that shares the same exponent.
Also, we need to remember the distributive property:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
So, we are given the following polynomials:
[tex]A.9x^{2} -2x+7\\\\B. 9x^{2} -2x+2\\\\C. 9x^{2} +2x-7[/tex]
And we need to perform the following operations:
First operation,
[tex](7x^{2}-5x+3)+(2x^{2} +3x-1)=7x^{2} +2x^{2} -5x+3x+3-1\\\\7x^{2} +2x^{2} -5x+3x+3-1=9x^{2} -2x+2[/tex]
So, the first operation match with the polynomial:
B. [tex]9x^{2} -2x+2[/tex]
Second operation,
[tex](3x^{2}-4x-4)+(-12x^{2}+2x+11)=3x^{2} -12x^{2} -4x+2x-4+11\\\\3x^{2} -12x^{2} -4x+2x-4+11=-9x^{2}-2x+7[/tex]
So, the second operation match with the polynomial:
A. [tex]-9x^{2}-2x+7[/tex]
Third operation,
[tex](4x^{2} -3x-9)+(5x^{2} +5x+2)=4x^{2}+5x^{2} -3x+5x-9+2\\\\4x^{2}+5x^{2} -3x+5x-9+2=9x^{2} +2x-7[/tex]
So, the second operation match with the polynomial:
C. [tex]9x^{2} +2x-7[/tex]
Have a nice day!
$4386 + 25% of the amount over $31850 1) 3986 2) 426.25 3) 4650 4) 7750
Answers
Answer:
3.)
Step-by-step explanation:
PLEASE HELP!!!!
The table shows which color boys and girls from 8th grade picked as their favorite color
Answers
Answer:
It should be B I me
Step-by-step explanation:
To determine which percentage is higher, we need to calculate the percentage of boys who prefer green and the percentage of girls who prefer red.
Percentage of boys who prefer green:
Total number of boys = 2 + 4 + 4 + 5 = 15
Number of boys who prefer green = 5
Percentage of boys who prefer green = (5/15) x 100% = 33.33% (rounded to the nearest whole number, this is 33%)
Percentage of girls who prefer red:
Total number of girls = 4 + 3 + 1 + 3 = 11
Number of girls who prefer red = 4
Percentage of girls who prefer red = (4/11) x 100% = 36.36% (rounded to the nearest whole number, this is 36%)
Therefore, the percentage of girls who prefer red (36%) is higher than the percentage of boys who prefer green (33%).
The answer is B. At 36%, the percentage of girls who prefer red is higher.
State if each angle is an inscribed angle. If it is, name the angles and the intercepted arc.
Answers
Answer:
Part 1) The inscribed angle is the angle ∠TRS and the intercept arc is the arc LST
Part 2) The inscribed angle is the angle ∠YWX and the intercept arc is the minor arc XY
Part 3) The inscribed angle is the angle ∠YXZ and the intercept arc is the arc YBZ
Part 4) The figure does not show an inscribed angle
Step-by-step explanation:
Part 1) The figure shown a inscribed angle
The inscribed angle is the angle ∠TRS
The intercept arc is the arc LST
Remember that
The inscribed angle measures half that of the arc comprising
so
∠TRS=(1/2)[arc LST]
Part 2) The figure shown a inscribed angle
The inscribed angle is the angle ∠YWX
The intercept arc is the minor arc XY
Remember that
The inscribed angle measures half that of the arc comprising
so
∠YWX=(1/2)[minor arc XY]
Part 3) The figure shown a inscribed angle
The inscribed angle is the angle ∠YXZ
The intercept arc is the arc YBZ
Remember that
The inscribed angle measures half that of the arc comprising
so
∠YXZ=(1/2)[arc YBZ]
Part 4) The figure does not show an inscribed angle
The figure shown a interior angle ∠BAC
What are the solutions to the system of equations? y=− x 2 +5x+6 −6x+y=6
(0,−1) and (6, 0)
(−1, 0) and (0, 6)
(0, 6) and (1, 2)
(−1, 0) and (6, 0)
Answers
Answer:
option B
(−1, 0) and (0, 6)
Step-by-step explanation:
Given in the question two equations,
Equation 1
y =−x² + 5x + 6
Equation 2
−6x + y = 6
plug value of y in second equation
−6x −x² + 5x + 6 = 6
-x² -6x + 5x +6 - 6 = 0
-x² - x + 0 = 0
-x² -x = 0
-x(x+1) = 0
x = 0
and
x = -1
plug value of x in second equation to find y
x = 0
−6(0) + y = 6
0 + y = 6
y = 6
and
x = -1
−6(-1) + y = 6
6 + y = 6
y = 0
Answer:
(−1, 0) and (0, 6)
Step-by-step explanation:
The given system of equations is
[tex]y=-x^2+5x+6[/tex]
and
[tex]-6x+y=6[/tex]
Solve for y in this second equation
[tex]y=6x+6[/tex]
We equate the two equations to get;
[tex]-x^2+5x+6=6x+6[/tex]
[tex]x^2+x=0[/tex]
[tex]x(x+1)=0[/tex]
x=0,x=-1
When x=0,
y=6(0)+6
y=6
When x=-1
y=6(-1)+6
y=0
A chef has 6 cups of berries and will use 2/3 cups of berries for each serving of fruit salad how many servings can be made
Answers
Answer:
6*2/3 = 12/3 = 4
Step-by-step explanation:
For this case we have a total of 6 cups of berries and per serving of salad we use [tex]\frac {2} {3}[/tex]of cups.
Let "x" be the variable that represents the portions of fruit salad that can be made, then, to find it we divide the number of cups of berries among the amount that is used for a portion:
[tex]x = \frac {6} {\frac {2} {3}} = \frac {6 * 3} {2 * 1} = \frac {18} {2} = 9[/tex]
Thus, 9 portions of salad can be prepared.
Answer:
9 portions
What is the measure of B E
Answers
Answer:
8cm
Step-by-step explanation
In between AE and DE
May somebody help me with this question? (It’s number 3) I would really appreciate it ! :) it gives you up to 50 points
Answers
Answer: Option D.
Step-by-step explanation:
You need to remember that the circumference of a circle can be calculated with this formula:
[tex]C=2\pi r[/tex]
Where "r" is the radius of the circle and [tex]\pi =3.14[/tex]
In this case the distance 150 feet (From the edge of the track to the center of the circle) is the radius.
Since she walks her horse 4 times around the track, you need to multiply the circumference by 4 to calculate the approximate number of feet that she and her horse will travel:
[tex]C=4[2(3.14)(150ft)]=3,768ft[/tex]
What is (a+b)(a-b) equal
Answers
Answer:a squared-b squared
Step-by-step explanation:
Answer:
[tex](a+b)(a-b)=a^{2} -b^{2}[/tex]
Step-by-step explanation:
This is a example of remarkable identities.
We know that the result of multiplication is called product and the values that multiply are called factors.
We call remarkable identities to certain algebraic expressions with binomial products very frequent in the calculation.
For this example, we got a Product of the sum for the difference of two binomials.
[tex](a+b)(a-b)[/tex]
The product of the sum for the difference of two binomials is equal to the square of the first quantity, minus the square of the second.
[tex](a+b)(a-b)=a^{2} -b^{2}[/tex]
Demostration:
[tex](a+b)(a-b)= a^{2} -ab+ab-b^{2}=a^{2} -b^{2}[/tex]
.
Which sequences are arithmetic? Select three options.
Answers
Answer:
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Step-by-step explanation:
find the area of the shape
Answers
Answer:
A = 12.5 units ^2
Step-by-step explanation:
This figure is a trapezoid
The area of a trapezoid is given by
A = 1/2 (b1+b2) * h where b1 and b2 are the lengths of the bases and h is the height
b1 = 7.5 and b2 = 2.5 and h = 2.5
A = 1/2( 7.5 + 2.5) * 2.5
A = 1/2(10) * 2.5
A = 12.5
2.5x2.5=6.25
7.5-2.5=5/2=2.5
(1/2)x2.5x2.5=3.125x2=6.25
6.25+6.25=12.5
The answer is: 12.5 units^2
HELP PLEASE!!
What is the value of 18^2?
A) 36
B) 324
C) 360
D) 9
Answers
18² is the same as saying 18 * 18, which is 324
Graph the linear equation. Find three points that solve the equation, then plot on the graph. -3y=x-6
Answers
The linear equation -3y=x-6 can be graphed using the slope-intercept form y = -1/3x + 2. By choosing different values for x and solving for y, we can find three points that solve the equation. Plotting these points on a graph and connecting them with a line represents the linear equation.
Explanation:The linear equation -3y=x-6 can be rewritten in slope-intercept form as y = -1/3x + 2. This form allows us to easily determine the slope and y-intercept of the equation. The slope is -1/3, which means for every increase of 1 in x, y decreases by 1/3. The y-intercept is 2, which indicates that the line crosses the y-axis at the point (0, 2).
To find three points that solve the equation, we can choose different values for x and substitute them into the equation to solve for y. Let's choose x = 0, x = 3, and x = -3. Plugging these values into the equation, we get y = 2, y = 1, and y = 3, respectively.
Therefore, the three points that solve the equation are (0, 2), (3, 1), and (-3, 3). When we plot these points on a graph, we can then connect them with a straight line to represent the linear equation.
what value of x makes this equation true? justify your solution.
6x + 12 = -6x + 12
Answers
Answer
0
Solution
6x+6x=12-12
12x=0
X=0
30 points for this question!| Mr. O’Hara found that on a recent trip his car used 12 gallons of gas to drive 396 miles. Assume that m represents the number of miles driven and g represents the number of gallons of gas used. What value makes the equation m=_*g represent the relationship between gallons of gas and miles driven?
Answers
Answer:
m = 33*g.
Step-by-step explanation:
The consumption of gas = 396 / 12
= 33 miles / gallon.
m = 33*g (answer).
I need help ASAP.... please help....
Answers
Answer:
(7x-1)(x-3)
Step-by-step explanation:
7x^2 - 22x + 3
The factors have to add to -22, but multiply to equal 3. But since the "a" value has a number on it, you have to use it too.
(7x +/- [n1]) ( x +/- [n2]) = 7x^2 - 22x + 3
Since the two numbers multiply to a positive value, they have to have the same sign. (7x-1) (x-3) works to produce the expression when it's foiled.
Answer:
(7x-1)(x-3)
Look in the photos. I hope this helps!
Let me know if you're unsure about anything! Thanks! :)
There are 4 semi- trailer truck park a line at the stop. After the first truck, each in the line weights 2 tons more than the truck before it. The truck weight a total of 32 tons. How many pounds does each truck weight?
Answers
Let's say the first truck weighs x tons
Then, the weight of 2nd truck = x+2 tons
The weight of 3rd truck = (x + 2) + 2 = x+4 tons
The weight of 4th truck = (x + 4) + 2 = x+6 tons
Total weight of 4 trucks:
x + (x+2) + (x+4) + (x+6) = 32
which can be solved easily to give x = 5
What is the equation parallel to y= -1/5x + 3 and goes through the point (7,4)? Please show steps.
Answers
Answer:
Step-by-step explanation:
If it's parallel, that means it has the same slope: -1/5.
Use point-slope form to write the equation:
y - 4 = -1/5 (x - 7)
If you wish to write in point-intercept form:
y - 4 = -1/5 x + 7/5
y = -1/5 x + 27/5
If two lines are parallel, it means that they will have the same gradient:
And remember, the equation of a line is y = mx +c
-----------------------------------
So we know that the equation of the parallel line is:
y = - [tex]\frac{1}{5}[/tex]x + c through point (7, 4)
All we need to do now is to work out what c is
Note: at point (7, 4) x = 7 , and y = 4.
So to work out c, we substitute in the values of x and y, and solve:
y = - [tex]\frac{1}{5}[/tex]x + c
4 = - [tex]\frac{1}{5}[/tex] * 7 + c
4 = -1.4 + c
5.4 = c
----------------------------------
Finally, we just put the value of c back into the original equation
y = - [tex]\frac{1}{5}[/tex]x + 5.4
------------------------------------------
Answer:
The equation of the a line parallel to y = - [tex]\frac{1}{5}[/tex]x + 3 through point (7,4)
is: y = - [tex]\frac{1}{5}[/tex]x + 5.4
Evaluate 1/3m-1-1/2n, when m=21 and n
=12
Answers
Answer:
0
Step-by-step explanation:
= 7 - 1- 6
= 6 - 6
=0
To evaluate the expression 1/3m - 1 - 1/2n with m=21 and n=12, you perform a series of arithmetic operations, resulting in an evaluated expression of 0.
Explanation:To evaluate the expression 1/3m - 1 - 1/2n when m=21 and n=12, we substitute the given values of m and n into the expression.
Firstly, calculate 1/3 of m: (1/3) × 21 = 7.Secondly, subtract 1 from the result of the first step: 7 - 1 = 6.Thirdly, calculate 1/2 of n: (1/2) × 12 = 6.Finally, subtract the result of the third step from the result of the second step: 6 - 6 = 0.How do you solve this?
Answers
Answer:
There are 8 boys in the chorus and 16 girls in the chorus
The graph in the attached figure
Step-by-step explanation:
Let
x----> the number of boys
y----> the number of girls
we know that
[tex]y=2x[/tex] -----> equation A
[tex]x=y-8[/tex] ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (8,16)
see the attached figure
therefore
There are 8 boys in the chorus
There are 16 girls in the chorus
Find m∠1 if m∠2=73°, m∠3=107°, m∠4=92°. Justify your response!
Answers
Answer:
92°
Step-by-step explanation:
The supplementary relationship between angles 2 and 3 means lines a and b are parallel. Since those lines are parallel, corresponding angles 1 and 4 are congruent.
m∠1 = m∠4 = 92°
Find the volume of the rectangular prism
Answers
To find the volume of a rectangular prism, we use the formula
Volume = length × width × height.
Since the rectangular prism has a length of 4 m, a width of 2 m, and a height of 1 m we can plug this information into the formula.
(4 m) (2 m) (1 m)
4 m × 2 m = 8 m
8 m × 1 m = 8 m³
Therefore, the volume of the rectangular prism is 8 m³.
Answer:
8
Step-by-step explanation:
L=Length
W=Width
H=Height
L=4
W=2
H=1
4 x 2 x 1
4 x 2 = 8
8 x 1 = 8
Rearranging to check my work:
1 x 4 x 2
1 x 4 = 4
4 x 2 = 8
I was right.
Hope this answers your question.
A limited edition poster increases in value each year. After 1 year, the poster is worth $20.70. After 2 years, it is worth $23.81. What equation can be used to find the vale, y, after x years?
Answers
Answer:
y=3.11x
Step-by-step explanation:
Not sure if it's correct. But my reasoning behind it is that 23.81-20.70=3.11 which means every year the cost goes up by $3.11
Erica has a monthly budget of $300 to spend on all of her expenses. She uses 2/3 on rent, and 1/4 on food. How much money remains for her expenses
Answers
Answer: $25
Step-by-step explanation: 2/3 of $300 is $200. 1/4 of $300 is $75. The total money she used is $275. $300-$275= $25.
Answer:
$75
Step-by-step explanation:
2/3 of 300 is 200 which means $100 bucks is left and 1/4 on food is $25 so what is left over is $75
Identify GCF and LCM (1)
Identify the GCF or LCM for each pair of numbers.
2205
3570
1100
1576
1100
1576
456
4680
456
4680
Choices to choose from
GCF = 24
GCF = 4
LCM = 433400
LCM = 74970
LCM = 88920
Answers
Answer:
2205
3570
LCM = 74970
1100
1576
GCF = 4
1100
1576
LCM = 433400
456
4680
GCF = 24
456
4680
LCM = 88920
Step-by-step explanation:
18837429928373829193
Find the arc length of the semicircle?
Answers
Answer:
5(pi) (exactly) or 15.7 (approximately)
Step-by-step explanation:
The length of arc of an entire circle is the circumference of the circle.
The length of arc of a semicircle circle is half of the circumference of the circle.
C = pi * d
For a semicircle:
arc length = 0.5 * pi * d
arc length = 0.5 * pi * 10
arc length = 5(pi)
arc length = 15.7
line s passes through the points (2,7) and (6,1) line t passes through the point (5,2) and is perpendicular to line s what is the equation for line t
Answers
let's keep in mind that perpendicular lines have negative reciprocal slopes, hmmm what is the slope of line S anyway?
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-7}{6-2}\implies \cfrac{-6}{4}\implies -\cfrac{3}{2} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{2}{3}}}[/tex]
so, we're really looking for the equation of a line whose slope is 2/3 and runs through (5,2)
[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{2})~\hspace{10em} slope = m\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=\cfrac{2}{3}(x-5)\implies y-2=\cfrac{2}{3}x-\cfrac{10}{3} \\\\\\ y=\cfrac{2}{3}x-\cfrac{10}{3}+2\implies y=\cfrac{2}{3}x-\cfrac{4}{3}[/tex]