A cubic equation has zeros at -2, 1, and 3 a) Write an eqn for a polynomial function that meets the given conditions.b) Draw the graph of a polynomial function that meets the given conditions.
Answers
we know that
A cubic equation has zeros at -2, 1, and 3
so
the factors of the cubic equation are
(x+2), (x-1) and (x-3)
Part a
The equation of a polynomial is
[tex]P(x)=(x+2)\cdot(x-1)\cdot(x-3)[/tex]Applying distributive property
[tex]\begin{gathered} P(x)=(x^2-x+2x-2)\cdot(x-3) \\ P(x)=(x^2+x-2)\cdot(x-3) \end{gathered}[/tex]Applying distributive property again
[tex]P(x)=x^3-3x^2+x^2-3x-2x+6[/tex]Combine like terms
[tex]P(x)=x^3-2x^2^{}-5x+6[/tex]Part b
using a graphing tool
see the attached figure below
Related Questions
the difference between 58% of a number and 39% of the same number is 247. what is 62% of that number
Answers
Answer
62% of the number = 806
Explanation
We are told that that the difference between 58% of a number and 39% of the same number is 247.
We are then asked to compute 62% of the number.
Let the number be x.
From the first statement,
58% of x = 0.58 × x = 0.58x
39% of x = 0.39 × x = 0.39x
The difference between them is 247
0.58x - 0.39x = 247
0.19x = 247
Divide both sides by 0.19
(0.19x/0.19) = (247/0.19)
x = 1300
So, we can now calculate 62% of the number
62% of x = 0.62 × x = 0.62 × 1300 = 806
Hope this Helps!!!
Prove the Question according to the theorem of a Circle
Answers
Given -
P,Q,R and S are 4 points on the circle and PQRS is a cyclic quadrilateral
Prove -
[tex]\angle PQR\text{ + }\angle PSR\text{ = 180}[/tex]Explanation -
[tex]\angle1\text{ = }\angle6\text{ ------\lparen1\rparen \lparen Angles in same segment\rparen}[/tex][tex]\angle5\text{ = }\angle8\text{ ------\lparen2\rparen \lparen Angles in the same segment\rparen}[/tex][tex]\angle2\text{ = }\angle8\text{ ------\lparen3\rparen \lparen Angles in the same segment\rparen}[/tex][tex]\angle7\text{ = }\angle3\text{ -------\lparen4\rparen\lparen Angles in the same segment\rparen}[/tex]By using angle sum property of quadrilateral
[tex]\angle P\text{ + }\angle Q\text{ + }\angle R\text{ + }\angle S\text{ = 360}[/tex][tex]\angle1\text{ + }\angle2\text{ + }\angle3\text{ + }\angle4\text{ + }\angle5\text{ + }\angle6\text{ + }\angle7\text{ + }\angle8\text{ = 360}[/tex][tex](\angle1+\angle2+\angle7+\angle8)+(\angle3+\angle4+\angle5+\angle6)=360[/tex]By using equation 1,2,3 and 4
[tex]2(\angle3+\angle4+\angle5+\angle6)\text{ = 360}[/tex][tex]\angle3+\angle4+\angle5+\angle6\text{ = 180}[/tex][tex](\angle3+\angle4)+(\angle5+\angle6)\text{ = 180}[/tex][tex]\angle PQR\text{ + }\angle PSR\text{ = 180}[/tex]Hence Proved
X+87°2x⁰ i have to solve for x it’s a 180 angle
Answers
Answer:
31
Step-by-step explanation:
x + 87 and 2x are linear pair angles.
Sum of linear pair angles is 180,
x + 87 + 2x = 180
x + 2x + 87 = 180
3x + 87 = 180
3x = 180 - 87
3x = 93
x = 93 / 3
x = 31
What is the greatest common factor of 28y^2 and 49y^2?A. 196y^2B. 7y^2C. 21y^2D. 7y
Answers
the value is 7 and keep the y^2
so is
[tex]7y^2[/tex]the points E,F,G and H all lie on the same line segment, in that order, such that ratio of EG:FG:GH is equal to 4:1:5. If EH=10, find EG
Answers
You have that the ratio of EG:FG:GH = 4:1:5.
Moreover, segment EH = 10.
In order to find EG you consider the following ratios:
EG/FG = 4/1
FG/GH = 1/5
Furthermore, EH = EG + FG + GH
The table shows the numbers of ships that visited a port in the past 5 years. Identify a polynomial function for thenumber of ships in thousands that visited the port in a given year.
Answers
The function is f(x) = 1.3x^2 + 0.1X
2 x— =-------7 x+ 10x = ???
Answers
Answer:
x = 4
Explanation:
Given the expression;
2/7 = x/x+10
Cross multiply
2(x+10) = 7x
Expand the bracket
2x + 20 = 7x
Subtract 7x from btoh sides
2x+20-7x = 7x - 7x
2x-7x+20 = 0
-5x + 20 = 0
-5x = -20
Divide both sides by -5;
-5x/-5 = -20/-5
x = 4
hence the value of x is 4
given A(2, 3), B(8, 7), C(6 1), which will make line AB perpendicular to line CD?D(9, 3)D(4, 4)D(3, 3)D(8, 4)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
A(2, 3), B(8, 7), C(6 1)
Step 02:
Line AB
Slope formula
m = (y2 - y1) / (x2 - x1)
A (2 , 3) x1 = 2 y1 = 3
B (8 , 7) x2 = 8 y2 = 7
[tex]m\text{ = }\frac{7-3}{8-2}=\frac{4}{6}=\frac{2}{3}[/tex]Step 03:
Slope of the perpendicular line, m’
m' = -1 / m
[tex]m\text{'}=\text{ }\frac{-1}{m\text{ }}=\text{ }\frac{-1\text{ }}{\frac{2}{3}}\text{ = -}\frac{3}{2}[/tex]Step 04:
Line CD
m' = (y2 - y1) / (x2 - x1)
C (6 , 1) x1 = 6 y1 = 1
D ( x2, y2) x2 = x2 y2 = y2
[tex]-\frac{3}{2}=\text{ }\frac{y2-1}{x2-6}[/tex][tex]\frac{3}{2}=\frac{1-y2}{6-x2}[/tex]We must test the numerical values to verify equality,
x2 = 9
y2 = 3
[tex]\frac{3}{2}=\frac{1-9}{6-3}\text{ = }\frac{-8}{3}\text{ }[/tex]x2 = 4
y2 = 4
[tex]undefined[/tex]The table shows a linear relationship between x and y. Drag and drop the options provided into the correct boxes to complete the equation. х 1 0 6 -4 41 у 9 -39 The equation that represents the relationship Is y = -8 -41 ON 9 4 O?
Answers
To calculate the equation first we need to choose two points of the table
P1 (1,1)=(x1,y1)
P2(0,9)=(x2,y2)
then we calculated the slope m
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the points we have
[tex]m=\frac{9-1}{0-1}=\frac{8}{-1}=-8[/tex]then we can calculate the equation
[tex](y-y1)=m(x-x1)[/tex][tex](y-1)=-8(x-1)[/tex][tex]y-1=-8x+8[/tex][tex]y=-8x+8+1[/tex]the equation is
[tex]y=-8x+9[/tex]Write an equation of each circle described below. Show work! (Hint: find the coordinates of the center first)Given a circle with (5, 1) and (3,-1) as the endpoints of the diameter.(x − B1)² + (y - B2)² = (B3)²B1=B2=B3=Blank 1:Blank 2:Blank 3:Submit
Answers
Given:
It is given that a circle is represented by two end points (5,1) and (3,-1).
Find:
we have to find the equation of the circle, radius and center of the circle using end points.
Explanation:
The circle represented by two end points (5,1) and (3,-1) is drawn as
The diameter of the circle is
[tex]d=\sqrt{(5-3)^2+(1-(-1))^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}[/tex]Therefore radius of the circle is
[tex]B3=\frac{d}{2}=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex]The center of the circle is
[tex](B1,B2)=(\frac{5+3}{2},\frac{1-1}{2})=(\frac{8}{2},\frac{0}{2})=(4,0)[/tex]Therefore, the equation of the circle is
[tex](x-4)^2+(y-0)^2=(\sqrt{2})^2[/tex]where,
[tex]\begin{gathered} B1=4 \\ B2=0 \\ B3=\sqrt{2} \end{gathered}[/tex]Identify the leading coefficient, degree and end behavior. write the number of the LC and degree
Answers
Given
[tex]P(x)=-4x^4-3x^3+x^2+4[/tex]Solution
The LC is -4
End behavior is determined by the degree of the polynomial and the leading coefficient (LC).
TThe degree of this polynomial is the greatest exponent is
[tex]\begin{gathered} x\rightarrow\infty\text{ then P\lparen x\rparen} \\ p(\infty)=-4(\infty)^4-3(\infty)^3+\infty^2+4 \\ p(\infty)=-4\infty^4-3\infty^3+\infty^2+4 \\ P(\infty)=-\infty \\ \end{gathered}[/tex][tex]\begin{gathered} x\rightarrow-\infty \\ p(-\infty)=-4(-\infty)^4-3(-\infty)^3+(-\infty)^2+4 \\ P(-\infty)=-4\infty^4+3\infty^3+\infty^2+4 \\ P(-\infty)=-\infty \end{gathered}[/tex]The degree is even and the leading coefficient is negative.
The final answer
need help with this problem answer in a quick and clear response
Answers
Answer:
A system of inequalities with parallel boundaries doesn't have a solution when the regions for each inequality don't intersect. This region depends on the sign of inequality, so the signs of inequality determine if the system has solutions.
Select the correct answer from each drop-down menu.Glven: W(-1, 1), X(3, 4), Y(6, 0), and Z(2, -3) are the vertices of quadrilateral WXYZ.Prove: WXYZis a square.
Answers
ANSWER
all four sides have a length of 5
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is,
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Let's find the distance between each pair of points, WX, XY, YX, and WZ,
[tex]WX=\sqrt{(3-(-1))^2+(4-1)^2}=\sqrt{(3+1)^2+(4-1)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]XY=\sqrt{(6-3)^2+(0-4)^2}=\sqrt{(3)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex][tex]YZ=\sqrt{(2-6)^2+(-3-0)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]WZ=\sqrt{(2-(-1))^2+(-3-1)^2}=\sqrt{(2+1)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]Hence, using the distance formula we found that all four sides have a length of 5.
у = -3х5х + y = 14i need help finding the matrix of this
Answers
3x + y = 0
5x + y = 14
[tex]\Delta\text{ = }\begin{bmatrix}{3} & 1{} & \\ {5} & 1{} & {} \\ {} & {} & {}\end{bmatrix}\text{ = (3 x 1) - (5 x 1) = 3 - 5 = -2}[/tex][tex]undefined[/tex]
For one of the meals eaten duringthe field trip to Williamsburg, VA,WHMS will be charged $115.50 foradults to eat and $712.50 forstudents to eat WHMS will leave a10% tip. How much money willWHMS leave for the tip
Answers
The total amount the WHMS would be charged for adults and students to eat is
115.5 + 712.5 = $828
We were told that WHMS will leave a 10% tip. Recall that percentage is expressed in terms of 100. This means that the amount of money that WHMS will leave for the tip is
10/100 * 828 = $82.8
WHMS would leave $82.8 for the tip
Find all critical points of the function f(x) = x^3 + 5x^2 - 7x - 3.The critical point(s) is(are) =
Answers
We are given:
[tex]f(x)=x^3+5x^2-7x-3[/tex]Now, we know that in order to determine the critical points we derivate and the derivative is then equal to 0, that is:
[tex]f^{\prime}(x)=3x^2-10x-7=0[/tex]Now, we solve for x, that is:
[tex]3x^2+10x-7=0\Rightarrow x=\frac{-(10)\pm\sqrt[]{(10)^2-4(3)(-7)}}{2(3)}[/tex][tex]\Rightarrow\begin{cases}x=-\frac{5+\sqrt[]{46}}{3}\Rightarrow x\approx-3.9 \\ \\ x=\frac{-5+\sqrt[]{46}}{3}\Rightarrow x\approx0.6\end{cases}[/tex]So, the critical points of the function are:
[tex]\begin{cases}x=-\frac{5+\sqrt[]{46}}{3} \\ \\ x=\frac{-5+\sqrt[]{46}}{3}\end{cases}[/tex]Now, we determine the y-components of the points, that is:
[tex]\begin{cases}f(-\frac{5+\sqrt[]{46}}{3})=(-\frac{5+\sqrt[]{46}}{3})^3+5(-\frac{5+\sqrt[]{46}}{3})^2-7(-\frac{5+\sqrt[]{46}}{3})-3\Rightarrow f(-\frac{5+\sqrt[]{46}}{3})=41.03608735 \\ \\ f(\frac{-5+\sqrt[]{46}}{3})=(\frac{-5+\sqrt[]{46}}{3})^3+5(\frac{-5+\sqrt[]{46}}{3})^2-7(\frac{-5+\sqrt[]{46}}{3})-3\Rightarrow f(\frac{-5+\sqrt[]{46}}{3})=-5.184235498\end{cases}[/tex]So, the two critical points are:
[tex](-\frac{5+\sqrt[]{46}}{3},41.03608735)[/tex]and:
[tex](\frac{-5+\sqrt[]{46}}{3},-5.184235498)[/tex]This can be seing as follows:
The points (-6, -10) and (23, 6) form a line segment.
Write down the midpoint of the line segment.
Answers
Answer:
(8.5, - 2 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = (- 6, - 10 ) and (x₂, y₂ ) = (23, 6 ) , then
midpoint = ( [tex]\frac{-6+23}{2}[/tex] , [tex]\frac{-10+6}{2}[/tex] ) = ( [tex]\frac{17}{2}[/tex] , [tex]\frac{-4}{2}[/tex] ) = (8.5, - 2 )
Exam Content
Question 25
Approximately how many years would it take money to grow from $5,000 to $10,000 if it could earn 6% interest?
Answers
It would take 16.66 years to grow from $5,000 to $10,000 if it could earn 6% interest.
Time it would take money to grow from $5,000 to $10,000
The prinicipal amount is $ 5000
The total amount is $ 10000
The rate of interest is 6%
Interest = Amount - principal
interest = 10000 - 5000 = 5000
By putting the simple interest formula
SI = prt/100
where p is the principal, r is the rate of interest and t is the time period
SI = 5000 x 6% x t/100
5000 = 5000 x 6 x t / 100
5000 x 100= 5000 x 6 x t
t = 100/6
t = 16.66
Therefore, it would take 16.66 years to grow from $5,000 to $10,000 if it could earn 6% interest.
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How many values does the expression 6+(x+3)^2 have?
Answers
The solution of a quadratic equation is imaginary.
What are the solutions of a quadratic function?
A quadratic equation with real or complex coefficients has two solutions, called roots.
These two solutions may or may not be distinct, and they may or may not be real.
The solution of the given quadratic function is calculated as follows;
6 + (x + 3)² = 0
subtract 6 from both sides of the equation;
6 + (x + 3)² - 6 = 0 - 6
(x + 3)² = - 6
take square root of both sides
x + 3 = √-6
x + 3 = 6i
x = 6i - 3
Thus, the solution of a quadratic equation can be determined solving for the value of unknown in the equation.
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How many megagrams(Mg) are there in 3.6 tons?[ ? ] MgMass in MgEnter
Answers
Step 1
Given;
[tex]3.6\text{tons}[/tex]Required; To find how many megagrams(Mg) are in 3.6 tonnes
Step 2
Find how many megagrams(Mg) are in 3.6 tonnes
[tex]\begin{gathered} 1\text{ tonne=1000000}g \\ 1\text{ megagram=1}000000g \end{gathered}[/tex]Therefore,
[tex]1\text{ tonne = 1 megagram}[/tex][tex]\frac{1\text{ tonne}}{3.6\text{ tonnes}}=\frac{1\text{ megagram}}{x\text{ megagram}}[/tex][tex]\begin{gathered} x\text{ megagram(1 tonne)=1 megagram(3.6 tonnes)} \\ \frac{x\text{ megagram}(1\text{ tonne)}}{1\text{ tonne}}\text{=}\frac{\text{1 megagram(3.6 tonnes)}}{1\text{ tonne}} \\ x=\text{ 3.6 megagrams} \\ x=3.6Mg \end{gathered}[/tex]
The total fixed costs of producing a product is $36,000 and the variable cost is $124 per item. If the company believes they can sell 1,800 items at $170 each, what is thebreak-even point?667 items695 items705 items783 itemsNone of these choices are correct.
Answers
calculate the surface area of a hollow cylinder which is closed at one end if the base radius is 3.5 cm and the height is 8 cm
Answers
Answer:
A=2πrh+2πr2=2·π·3.5·8+2·π·3.52≈252.89821cm²
The surface area is 214.305cm².
What is surface area?The surface area is the area of the outer covering of the object.
It is given that radius, r=3.5 cm, and height, h=8 cm.
The surface area of the given object will be the sum of curved surface area and the area of the bottom, which is circle.
Surface Area = Curved Surface Area + Area of bottom circle
=2πrh+πr²
=2π(3.5)(8)+π(3.5)²
=56π+12.25π
=68.25π
Substitute π=3.14 to determine the surface area.
Surface Area = 68.25(3.14)
=214.305
So, the surface area will be 214.305cm².
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Looking to receive help on the following practice question thank you.
Answers
use the definition of sec and write it in terms of cos
[tex]r=4\cdot\frac{1}{\cos \theta}[/tex]multiply both sides by cos
[tex]r\cos \theta=4[/tex]then we know that r*cos is equal to x in the cartesian
[tex]x=4[/tex]if you run 5/6 of a mile in 1/12 of how hour how much is that
Answers
The entire miles that the person runs in 1 hour is 10 miles
What is a fraction?A fraction simply means the numbers that's expressed as a/b where a = numerator and b = denominator.
In this case, the person runs 5/6 of a mile in 1/12 of an hour.
The number of miles for the entire run will be the division of the fractions given. This will be illustrated as:
= 5/6 ÷ 1/12
= 5/6 × 12
= 5 × 2
= 10 miles
The entire race is 10 miles.
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3. (02.04 MC)
Choose the equation that represents a line that passes through points (-6, 4) and (2, 0).
Answers
The answer to the question is here
Enter an equation that passes through the point (12, 7) and forms a system of linear equations with no solution when combined with the equation y=−3/4x+8.
Answers
To answer this question, we need to know that two linear equation that does not have solutions must not cross to each other, that is, they do not have a common point. For this case, both lines must be parallel lines. So in the question, we need to find a parallel line to the given line. Two parallel lines have the same slope.
Then, we have that the line must pass through (12, 7), and, because it is parallel to y = -3/4x + 8, and the slope for this line is m = -3/4, then, the line equation is, applying the point-slope form of the line:
[tex]y-y_1=m(x-x_1)[/tex]And
x1 = 12
y1 = 7
m = -3/4
Then
[tex]y-7=-\frac{3}{4}(x-12)\Rightarrow y-7=-\frac{3}{4}x+\frac{3}{4}\cdot12\Rightarrow y-7=-\frac{3}{4}x+\frac{36}{4}[/tex][tex]y-7=-\frac{3}{4}x+9\Rightarrow y=-\frac{3}{4}x+9+7\Rightarrow y=-\frac{3}{4}x+16[/tex]Then, the line equation is y = -3/4 x + 16.
We can check this if we use the elimination method as follows:
This is a FALSE result, and we do not have solutions for this system. Therefore, the line equation is y = -3/4 x + 16.
What does 10 represent in 10/6
Answers
10/6
This is a fraction, in a fraction the bottom number represents the denominator and the top number represents the numerator.
So, in this case, 10 represents the numerator.
laws exponents multiplication band power to a power simplifymake it small steps please the smallest you canbare minimum of steps
Answers
Answer:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)=-12r^6s^{-4}[/tex]Explanation:
Given the expression:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)[/tex]This can be rearranged using law of multiplication (That multiplication is cummutative) to become:
[tex](4)(-3)(r^4rr)(s^{-2}s^{-3}s)[/tex]This becomes, using the law of exponents:
[tex]-12r^{4+1+1}s^{-2-3+1}[/tex]and finally, we have:
[tex]-12r^6s^{-4}[/tex]Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Answers
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
answer reflects:
3 dvds sold for d price - cost of headphones and a remaining $2.30
Which of the following could be the areas of the three squares below? A. 12ft^2, 16ft^2, 20ft^2B. 10ft^2, 18ft^2, 30ft^2C. 4ft^2, 5ft^2, 12ft^2D. 8ft^2, 16ft^2, 24ft^2i have to show work too :(
Answers
The correct option is D
8ft^2, 16ft^2, 24ft^2 could be the three areas of the given squares
Explanation:To know the area of the three squares, we need to know the side length of each square. This can be done by applying Pythagorean rule on the right-angle triangle formed in the middle.
The square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (legs).
The area of a square is the square of its side length.
Taking the square roots of each of the given options, which ever option has Pythagorean triple is the correct option.
A.
[tex]2\sqrt[]{3},4,2\sqrt[]{5}[/tex]This is NOT a Pythagorean triple.
B.
[tex]\sqrt[]{10},3\sqrt[]{2},\sqrt[]{30}[/tex]This is NOT a Pythagorean triple.
C.
[tex]2,\sqrt[]{5},2\sqrt[]{3}[/tex]This is NOT a Pythagorean triple
D.
[tex]2\sqrt[]{2},4,2\sqrt[]{6}[/tex]This is a Pythagorean triple.
CHECK[tex]\begin{gathered} (2\sqrt[]{2})^2+4^2=(2\sqrt[]{6})^2 \\ 8+16=24 \\ 24=24 \end{gathered}[/tex]