Using this picture, describe what we are doing with the factored form of p(x) shown in the image in order to create a sketch of the function.
Answers
Given:
[tex]p(x)=(x-1)(x+1)(x-4)^2[/tex]Sol:
[tex]\begin{gathered} p(x)=(x-1)(x+1)(x-4)^2 \\ \\ p(0)=(0-1)(0+1)(0-4)^2 \\ \\ p(0)=-16 \end{gathered}[/tex]X-intercept is at p(x) = 0 then,
[tex]\begin{gathered} p(x)=0 \\ \\ p(x)=(x-1)(x+1)(x-4)^2 \\ \\ 0=(x-1)(x+1)(x-4)^2 \\ \\ x=-1,1,4 \end{gathered}[/tex]At y- intercept the value of x is zero and at x = 0 function value is:
[tex]\begin{gathered} y=-16 \\ \\ \text{ The point is:} \\ (0,-16) \end{gathered}[/tex]At x-intercept y value is zero and x-intercept is -1,1,4 is:
[tex]\begin{gathered} \text{ At }x=-1 \\ \\ the\text{ value of }y=0 \\ \\ (-1,0) \\ \\ At\text{ }x=1 \\ \\ \text{ The value of }y=0 \\ \\ (1,0) \\ \\ \text{ At }x=4 \\ \\ \text{ The value of }y=0 \\ \\ (4,0) \end{gathered}[/tex]So all point is (-1,0) ,(1,0) and (4,0)
Related Questions
what is 1x2x3x4x5x6x7x8x9
Answers
Answer:
1x2x3x4x5x6x7x8x9 = 362880
you could also break it down
1x2x3=6
4x5x6=120
7x8x9=504
6 x 120 x 504 = 362880
The solution to the given question [tex]1\times 2\times {3\times 4\times \5\times 6\times 7 \times \ 8\times 9\times 10[/tex] will be[tex]3,628,800[/tex].
The process of making a mathematical expression simpler (usually shorter) is termed simplification.
example :
37 - [5 + {28 - (19 - 7)}]
here using the BODMAS rule we will get the simplified value of this expression.
[tex]=[1\times 2\times {3\times 4\times (5\times 6\times 7 )\times \ 8\times 9\times 10][/tex]
firstly we will solve the small brackets, thus we get the value
[tex]=[1\times2\times3\times{4\times210 \times8}\times9\times10][/tex]
on multiplying again all the terms by itself we get
=[tex]3,628,800[/tex]
thus the solution of the given expression using simplification will be [tex]3,628,800[/tex].
Learn more about Simplification here:
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help 25 points
A line includes the points (10,6) and (2,7). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
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Answer:
y = (-1/8)x + (29/4)
Step-by-step explanation:
(10, 6), (2, 7)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 7 - 6 1 -1
m = ------------ = ----------- = ----------- = ---------
x₂ - x₁ 2 - 10 -8 8
y - y₁ = m(x - x₁)
y - 6 = (-1/8)(x - 10)
y - 6 = (-1/8)x + (5/4)
+6 +6
-------------------------------
y = (-1/8)x + (29/4)
I hope this helps!
What is the solution to 4x-8=12 please explain
Answers
Given the equation 4x-8=12 you need to clear the value of x.
First step is to leave the value of x in one side of the equation and the integers in the other side, to do so you have to add 8 to both sides of the equation
[tex]\begin{gathered} 4x-8=12 \\ 4x-8+8=12+8 \\ 4x=20 \end{gathered}[/tex]Next you have to divide both terms of the equation by 4 to get the value of x
[tex]\begin{gathered} 4x=20 \\ \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]The value of x=5
Use the distributive property and simplify: 3n+4-5(n+6)
Answers
By distributing the number -5 into the parentheses, we have
[tex]3n+4-5n-30[/tex]Now, by collecting similar terms, we get
[tex]-2n-26[/tex]Therefore, the answer is: -2n-26
49x^2 + 16y^2 - 392x +160y + 400 = 01. give the coordinates of the upper vertex2. give the coordinates of the lower vertex3. give the coordinates of the upper focus(round to the nearest hundredths)4. give the coordinates of the lower focus(round to the nearest hundredths)5. give the eccentricity
Answers
we have
49x^2 + 16y^2 - 392x +160y + 400 = 0
Complete the square
Group terms
[tex](49x^2-392x)+(16y^2+160y)=-400[/tex]Factor 49 and 16
[tex]49(x^2-8x)+16(y^2+10y)=-400[/tex][tex]49(x^2-8x+16)+16(y^2+10y+25)=-400+16(49)+25(16)[/tex][tex]\begin{gathered} 49(x^2-8x+16)+16(y^2+10y+25)=784 \\ 49(x^{}-4)^2+16(y+5)^2=784 \end{gathered}[/tex]Divide by 784 both sides
[tex]\begin{gathered} 49(x^{}-4)^2+16(y+5)^2=784 \\ \frac{49(x^{}-4)^2}{784}+\frac{16(y+5)^2}{784}=1 \end{gathered}[/tex]simplify
[tex]\frac{(x^{}-4)^2}{16}+\frac{(y+5)^2}{49}=1[/tex]we have a vertical elipse
the center is the point (4,-5)
major semi axis is 7
we have
a^2=16 --------> a=4
b^2=49 ------> b=7
Find the value of c
[tex]\begin{gathered} c=\sqrt[]{b^2-a^2} \\ c=\sqrt[]{33} \end{gathered}[/tex]see the attached figure to better understand the problem
How much did he invest in Fund B, if both guns together returned a 8% profit.
Answers
Find the exact length of the arc intercepted by a central angle on a circle of radius . Then round to the nearest tenth of a unit.
Answers
Given:
Angle subtended at the center = 135 degrees
radius (r) = 4 yd
Solution
The formula for the length (l) of an arc is given as:
[tex]\begin{gathered} l\text{ = }\frac{\phi}{360^0}\text{ }\times\text{ 2}\pi r \\ \text{where }\phi\text{ is the angle subtend}ed\text{ at the center} \end{gathered}[/tex]When we substitute the given parameters, we can find the length (l) of the arc:
[tex]\begin{gathered} l\text{ = }\frac{135}{360}\text{ }\times\text{ 2 }\times\text{ }\pi\text{ }\times\text{ 4} \\ =3\pi \\ \approx\text{ 9.4 yd (nearest tenth)} \end{gathered}[/tex]Answer: 9.4 yd or 3.0 pi
A cab company charges a flat rate of $2 plus an additional $0.50 for every mile traveled. Use this information for Items 12 and 13. 12. a. Write an expression that can be used to determine the total cab fare for a distance of m miles. b. When Sara arrived at your destination, her cab fare was $7.50. Write an equation to represent this situation. How many miles did Sara travel?
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The cost for each travel on this cab company can be expressed as a sum of the fixed fee and the price per mile multiplied by the distance in miles of the travel. Therefore:
[tex]c(m)=2+0.5\cdot m[/tex]If Sarah paid $7.5 for her cab, then c(m)=7.5 and we can use this value on the expression above to solve for "m". We have:
[tex]\begin{gathered} 7.5=2+0.5\cdot m \\ 0.5\cdot m=7.5-2 \\ 0.5\cdot m=5.5 \\ m=\frac{5.5}{0.5}=11 \end{gathered}[/tex]She traveled 11 miles.
Classify the following triangle. Check all that apply.- A. AcuteB. ObtuseC. Right. D. Isosceles. E. EquilateralF. Scalene
Answers
The triangle above is
Acute since the other angles are less the 90°
Can not be obtuse since non of the angles is greater than 90°
Is a Right angle since one of the angles is 90°
Is isosceles since two of it side are equal
Is not equilateral because all its side and angle are not equal
Is not Scalene since two of its side are equal.
Hence the Triangle is Acute, Right and Isosceles
Valentina opened a savings account and deposited 1,000.00 as principal the account earns 3%interest compounded monthly what is the balance after 8 years
Answers
According to the problem, the principal is $1,000, the interest is 3% compounded monthly and the time is 8 years.
We have to use the compounded interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Replacing the given information, we have
[tex]A=1,000\cdot(1+\frac{0.03}{12})^{12\cdot8}[/tex]Now, we solve for A
[tex]\begin{gathered} A=1,000(1+0.0025)^{96} \\ A=1,000(1.0025)^{96} \\ A\approx1,270.87 \end{gathered}[/tex]Hence, she will have $1,270.87 after 8 years.find the midpoint of PQ. P(6,4) and Q(4,3)
Answers
the midpoint between two points has the following formula
[tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]replace in the formula using P as point 1 and Q as point 2
[tex]\begin{gathered} (\frac{6+4}{2},\frac{4+3}{2}) \\ (\frac{10}{2},\frac{7}{2}) \\ (5,\frac{7}{2}) \\ (5,3.5) \end{gathered}[/tex]Graph the solution set of each system of inequalities. Graph the solution set of each sx+2y ≤ 63x- 4y < 2
Answers
Given:
[tex]\begin{gathered} x+2y\le6\ldots\text{ (1)} \\ 3x-4y<2\ldots(2) \end{gathered}[/tex]We have to take the value of x as zero and to find the value of y in bothe the equations to plot the graph.
By taking the value of x as zero in the first equation,
[tex]\begin{gathered} 2y\le6 \\ y\le3 \end{gathered}[/tex]By taking the value of y as zero in the first equation,
[tex]x\le6[/tex]By taking the value of x as zero in the second equation,
[tex]\begin{gathered} -4y<2 \\ -2y<1 \\ y>-\frac{1}{2} \end{gathered}[/tex]By taking the value of y as zero in the second equation,
[tex]\begin{gathered} 3x<2 \\ x<\frac{2}{3} \end{gathered}[/tex]if you copy a page on a machine at 60%, you should get a similar copy of the page. What is the corresponding setting to obtain the original from the copy? The corresponding setting to obtain the original from the copy is _______%
Answers
Answer:
The corresponding setting to obtain the original from the copy is 166.67%
[tex]166\frac{2}{3}\text{\%}[/tex]Explanation:
Let c and x represent the copy and original respectively;
[tex]c=60\text{\% of x}[/tex]making x the subject of formula;
[tex]\begin{gathered} c=0.6x \\ x=\frac{c}{0.6} \\ x=1\frac{2}{3}c \\ in\text{ percentage;} \\ x=1\frac{2}{3}c\times100\text{\%} \\ x=166.67\text{\% of c} \end{gathered}[/tex]Therefore, The corresponding setting to obtain the original from the copy is 166.67%
[tex]166\frac{2}{3}\text{\%}[/tex]Select three equations that could represent a step in solving this system using the substitution method. 4x+y = 6 x = 8 0.00 0:52 9 1x 2 4(8)+y=6 o y = 18
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the first step is replacing x=8 on the first equation, so
[tex]4(8)+y=6[/tex]the second step is do the multiplication
[tex]\begin{gathered} 32+y=6 \\ y+32=6 \end{gathered}[/tex]and the last step is place the 32 on the other side substracting
[tex]\begin{gathered} y=6-32 \\ y=-26 \end{gathered}[/tex]a national survey of 1517 respondents reached on landlines a and cell phones found thas t the percentage of adults who favor legalized abortion has dropped from 53% a yeas r ago to 44% the study claimed that the error attributable to sampling is +5 percentage points would you claim that a majority of people are not in favor of legalized abortion. the confidence interval for the study is _% to _%
Answers
Answer:
You can claim that the majority of people are not in favor of legalized abortion.
39% < p < 49%
Explanation:
The confidence interval for the study can be calculated as:
44% - 5% < p < 44% + 5%
39% < p < 49%
Where p is the percentage of people that are in favor of legalized abortion and 5% is the error attributable to sampling.
Since the upper limit of the confidence interval is 49% (less than 50%), you can claim that a majority of people are not in favor of legalized abortion.
Wich situation can be represented by 3 + 3s =5s - 7
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3 + 3s = 5s - 7
A. Three times a number increased by 3 ( can be represented by 3s + 3 ) is the same as ( = ) five times a number decreased by 7 ( can be represented by 5s -7 ). 3s + 3 = 5s - 7
Answer: A
Patrice found airpods on sale for $84. The sale sales tax is 5%. What is the total Patrice will pay for the airpods?
Answers
To find the final cost with tax. You find the 5% of $84 and add that result to the initial cost:
[tex]84\cdot\frac{5}{100}=4.2[/tex][tex]84+4.2=88.2[/tex]Then, Patrice will pay $88.2 for the airpods
Algebraically manipulating the formula FV = P(1 + p", how much money is needed as an initial deposit to reach a future value of $8,700, if the account isearning 7%, compounded quarterly, for 6 years to the nearest whole dollar)?$6,154.33$5,737.11$5,432.19$4,908,66None of these choices are correct.
Answers
The future value formula, given by
[tex]FV=P(1+\frac{r}{n})^{nt}[/tex]Can be used to obtain the Principal by substituting other values into the equation and solving for P
Step 1: List out the parameters given
FV =$8,700
r=7%=0.07
n=4 (since there are 4 quarters in a year)
t=6 (since it will be compounded 6 times a year)
Step 2: Substitute the values into the formula
[tex]8700=P(1+\frac{0.07}{4})^{4\text{ x 6}}[/tex][tex]8700=P(1+0.0175)^{24}[/tex][tex]\begin{gathered} 8700=P(1.0175)^{24} \\ 8700=1.5164P \end{gathered}[/tex]Solving for P
[tex]\begin{gathered} 1.5164P=8700 \\ P=\frac{8700}{1.5164} \end{gathered}[/tex]P=$5737.11
Option B is correct
two seventh of a number is 30 less than the number . find the number
Answers
Let x = the number
So, the given situation can be expressed as:
[tex]\frac{2}{7}x=30-x[/tex]Then, solve for x:
[tex]\begin{gathered} \frac{2}{7}x+x=30-x+x \\ \frac{9}{7}x=30 \\ \frac{7}{9}\cdot\frac{9}{7}x=30\cdot\frac{7}{9} \\ x=\frac{210}{9}=\frac{70}{3} \end{gathered}[/tex]Answer: the number is 70/3
Male and female populations of elephantsunder 80 years old are represented by age inthe table below. Completo parts (a) through(d)(a) Approximate the population mean and standard deviation of age for males)(Round to two decimal places as needed.) )
Answers
Solution:
Given:
From the table of values derived above;
The mean for males is;
[tex]\begin{gathered} \bar{x}=\frac{\sum ^{}_{}fx}{n} \\ \bar{x}=\frac{5774.5}{141} \\ \bar{x}=40.95 \end{gathered}[/tex]The standard deviation is;
Hence,
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{300115.25-\frac{5774.5^2}{141}}{141}} \\ \sigma=\sqrt[]{\frac{300115.25-236488.2996}{141}} \\ \sigma=\sqrt[]{\frac{63626.95035}{141}} \\ \sigma=\sqrt[]{451.25497} \\ \sigma=21.243 \\ \\ To\text{ two decimal places,} \\ \sigma=21.24 \end{gathered}[/tex]Therefore, the population standard deviation for males is 21.24
the sum of x and 3/5 is 5/7what is the value of x?
Answers
Explanation
the sum of x and 3/5 is 5/7
Step 1
convert the words into math terms
Let
the sum= addition
is= "="
[tex]x+\frac{3}{5}=\frac{5}{7}[/tex]Step 2
to find the value of x, isolate
[tex]\begin{gathered} x+\frac{3}{5}=\frac{5}{7} \\ \text{subtract }\frac{3}{5}in\text{ both sides} \\ x+\frac{3}{5}-\frac{3}{5}=\frac{5}{7}-\frac{3}{5} \\ x=\frac{5}{7}-\frac{3}{5} \\ x=\frac{25-21}{35} \\ x=\frac{4}{35} \end{gathered}[/tex]f(x) =-x² + 2x + 6
Find f(-7)
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Find du and v. Treat a and n as constants.
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Stated that;
[tex]u=x^n[/tex]Then, differentiating u with respect to x using the power rule where n is a constant is;
[tex]\begin{gathered} du=(n\times1)x^{n-1} \\ du=nx^{n-1} \end{gathered}[/tex]Also,
[tex]dv=e^{ax}[/tex]Then, we can find v by integrating, we have;
[tex]\begin{gathered} \int dv=\int e^{ax}dx \\ v=\frac{1}{a}e^{ax} \\ \end{gathered}[/tex]
In circle G with m_FGH = 150 and FG = 12 units find area of sector FGH.Round to the nearest hundredth.Fa.
Answers
The formula for the area of sector is,
[tex]A=\frac{\theta}{360}\pi(r)^2[/tex]Substitute the values in the formula to obtain the area of sector FGH.
[tex]\begin{gathered} A=\frac{150}{360}\cdot\pi(12)^2 \\ =188.4955 \\ \approx188.50 \end{gathered}[/tex]So area of sector FGH is 188.50.
A baseball card store prints a total of 15,363 cards on Tuesday and Wednesday. It printed 3,978 cards on Wednesday. How many cards did the store print from Tuesday through Thursday?
Answers
The stored printed 34,704 cards from Tuesday through Thursday.
How to find the total number of cards printed?To find the total number of cards printed through a series of n days, we add the amounts printed on each day.
In the context of this problem, from the text presented, the daily amount of cards printed on Tuesday, Wednesday and Thursday is given as follows:
Tuesday: 15,363 cards.Wednesday: 15,363 cards.Thursday: 3,978 cards.Hence the total number of cards printed by the store from Tuesday through Thursday is calculated by the addition presented as follows:
15,363 + 15,363 + 3,978 = 2 x 15,363 + 3,978 = 34,704 cards printed by the store from Tuesday through Thursday.
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factor the equationx^2-17x+42
Answers
To factor an expression of the form:
[tex]x^2+Bx+C[/tex]we need to find two integers a and b that fullfil:
[tex]\begin{gathered} a+b=B \\ ab=C \end{gathered}[/tex]then we write the expression as:
[tex]x^2+ax+bx+C[/tex]and factor by agrupation.
Let's do this with the expression:
[tex]x^2-17x+42[/tex]In this case B=-17 and C=42.
If we take a=-14 and b=-3, then:
[tex]\begin{gathered} (-14)(-3)=42 \\ -14-3=-17 \end{gathered}[/tex]then we write the expression as:
[tex]\begin{gathered} x^2-14x-3x+42=x(x-14)-3(x-14) \\ =(x-3)(x-14) \end{gathered}[/tex]Therefore, the factorize expression is:
[tex](x-3)(x-14)[/tex]The table shows the linear relationship between the average height in feet of trees on a tree farm andthe number of years since the trees were planted,Average Tree HeightNumber of Years Sincethe Trees were planted1361115Average Height (ft)10244580108m
Answers
Rate of change = change in y / change in x
From the table, number of years since the tree are planted are the x
They are; 1, 3, 6, 11 , 15
Average height are y, and they are;
10, 24, 45, 80, 105
Now, to calculate the rate of change, we will find the difference between two values of y then divide it by the difference between 2 values of x
If we are going to pick the first and second value of y, we must also pick the first and second value of x
If we are to pick the second and 3rd value of y, we must then pick the 2nd and 3rd value of x
That is;
rate of change = 24 -10 / 3-2
= 14/2
= 7 ft/yr
The two-way table represents the number of clubs that two hundred high school studentswere involved in.One Club Two clubsBoys 17Girls 28Total 45256893Three or more clubs Total50126292108200What is the probability that a student will be in two clubs only and a girl?
Answers
Given:
The two-way table represents the number of clubs that two hundred high school students
We will find the probability that a student will be in two clubs only and a girl
From the table, we will select the number that represents the number of girls that will be in the two clubs
so, the number = 68
the total number of students = 200
So, the probability will be =
[tex]\frac{68}{200}*100=34\%[/tex]So, the answer will be 34%
Brianna's teacher asks her if these two expressions 3x + 5 and 4x are equivalent.Brianna says the expressions are equivalent because the value of each expression is 20 when x = 5.Is Brianna correct synlainthink ASAP please
Answers
Step 1
Given data
Expression 1 = 3x + 5
Expression 2 =
· A) A highway noise barrier is 120 m long is constructed in 2pieces. One piece is 45 m longer than the other one. Findthe length of each piece. B) If you are to construct arectangle with each of the sizes of the pieces being thelength and width then what is the perimeter? c) What would bethe area of that rectangle? (Note: Use an Equation to solve)
Answers
A) Let the length of one piece be x. if one piece is 45 m longer than the other one, it means that the length of the other one would be (x + 45) m
Given that the total length of both pieces is 120m, then the equation would be
x + x + 45 = 120
2x + 45 = 120
2x = 120 - 45 = 75
x = 75/2
x = 37.5
Thus, the length of each piece are
37.5 m
37.5 + 45 = 82.5 m
B) The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
Given that
length = 82.5
width = 37.5
then
perimeter = 2(82.5 + 37.5) = 2 * 120
perimeter of rectangle= 240 m
C) the formula for determining area of a rectangle is expressed as
Area = length * width
Area of rectangle = 82.5 * 37.5 = 3093.75 cm^2