Which of the following options correctly represents the complete factored form of the polynomial F(x)= x - x2 - 4x-6?
Answers
Notice that:
[tex]F(3)=3^3-3^2-4\cdot3-6=27-9-12-6=27-27=0.[/tex]Therefore 3 is a root of the given polynomial.
Now, we can use this root to factor the polynomial:
[tex]F(x)=(x-3)\frac{x^3-x^2-4x-6}{x-3}.[/tex]Using the synthetic division algorithm we get that:
[tex]\frac{x^3-x^2-4x-6}{x-3}=x^2+2x+2.[/tex]The roots of the above polynomial are:
[tex]\begin{gathered} x=-1+i, \\ x=-1-i\text{.} \end{gathered}[/tex]Therefore:
[tex]F(x)=\mleft(x-3\mright)(x+1+i)(x+1-i)\text{.}[/tex]Answer:
[tex]F(x)=(x-3)(x+1+i)(x+1-i)\text{.}[/tex]Related Questions
In a school, 10% of the students have green eyes. Findthe experimental probability that in a group of 4students, at least one of them has green eyes.The problem has been simulated by generating randomnumbers. The digits 0-9 were used. Let the number "9"represent the 10% of students with green eyes. A sampleof 20 random numbers is shown.
Answers
Given that in a group of 4 students at least one has green eyes.
Also, the number 9 represents the 10% of the students with green eyes.
From the 20 random experimental numbers given, the number 9 appeared in only nine of them.
The experimental probability in percentage will be:
[tex]\frac{9}{20}\ast100\text{ = }45\text{ percent}[/tex]ANSWER;
45%
In the picture shown below, a cube with a side of 5 inches is placed directly on top of a larger cube which has a side of 18 inches. Then, another cube with a side of 3 inches is placed directly to the side of the lower cube. What is the surface area of this assembly? (drawing below is not to scale)
Answers
For this problem, we are given three cubes. Cube A is on top of cube B, the cube C is glued to the side of cube B. We need to calculate the surface area for the whole piece.
The surface area of a cube is given by the following:
[tex]A_{\text{surface}}=6\cdot l^2[/tex]Where "l" is the measurement of the length of the side on each cube.
To calculate the whole surface area, we need to calculate each cube individually then sum them. Let's start with cube A, since this cube is on top of Cube b, one of its faces shouldn't count for the surface area, therefore we have:
[tex]\begin{gathered} A_{\text{cubeA}}=5\cdot5^2=125\text{ square inches} \\ \end{gathered}[/tex]Now we need to calculate the surface area for cube C, which is very similar to cube A, as shown below:
[tex]A_{\text{cubeC}}=5\cdot3^2=45\text{ square inches}[/tex]Finally, we need to calculate the area for cube B, this one is different because we need to subtract one face from cube A and one for group C.
[tex]\begin{gathered} A_{\text{cubeB}}=6\cdot18^2-5^2-3^2 \\ A_{\text{cubeB}}=6\cdot324-25-9 \\ A_{\text{cubeB}}=1994-25-9=1910 \end{gathered}[/tex]The total area is the sum of all areas:
[tex]A=1910+45+125=2080[/tex]The total surface area is equal to 2080 square inches.
what is the the measure of each base angle of an isosceles triangle if it’s vertex angle measure is 44°?
Answers
An isoceles triangle has one vertex angle and two congruent base angles, that is,
In a recent year, 24.8% of all registered doctors were female. If there were 54,100 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.
Answers
To solve for total number of registered doctors:
Explanation:
The questions says, "24.8% of all registered doctors are females"
(Consider, total number of registered doctors as x)
that's,
[tex]\begin{gathered} 24.8\text{ \% of the x are female registered doctor} \\ 24.8\text{ \% of x = 54,100} \end{gathered}[/tex]Mathematically,
[tex]\begin{gathered} \frac{24.8}{100}.x=54,100 \\ \text{cross multiply} \\ 24.8x=54,100\text{ x 100} \\ 24.8x=5410000 \\ \frac{24.8x}{24.8}=\frac{5410000}{24.8} \\ x=218145.16 \\ x\approx218,145\text{ (nearest whole number)} \end{gathered}[/tex]Therefore the total number of registered doctors ≈ 218,145
How many ounces of a 5% alcohol solution must be mixed with 17 ounces of a 10% alcohol solution to make a 6% alcohol solution?
Answers
Let x be number or ounces of a 5% alcohol solution, then:
[tex]x(0.05)+17(0.10)=(x+17)(0.06)[/tex]Solving the above equation for x, we get:
[tex]\begin{gathered} 0.05x+1.7=0.06x+1.02 \\ 0.01x=1.7-1.02 \\ 0.01x=0.68 \\ x=68 \end{gathered}[/tex]Therefore, you must add 68 ounces of the 5% alcohol solution.
The area of a parallelogram is 22, and the lengths of its sides are 9.2 and 2.6. Determine, to the nearest tenth of a degree, the measure of the obtuse angle of the parallelogram.
Answers
The measure of obtuse angle of the parallelogram is 113.12° .
The Area of Parallelogram with sides a and b and the angle between them as x° is given by the formula .
Area of Parallelogram = a×b×Sin(x)°.
In the question ,
it is given that
the area of the parallelogram is = 22
length of one side of parallelogram = 9.2
length of other side of parallelogram = 2.6 .
Substituting the values in the Area formula , we get
22 = (9.2)×(2.6)×Sin(x)°
22 = 23.92×Sin(x)°
Sin(x)° = 22/23.92
Sin(x)° = 0.9197
x = 66.88°
Since this is an acute angle , we will subtract it from 180° to find the obtuse angle .
So , obtuse angle = 180-66.88 = 113.12°
Therefore , the measure of obtuse angle of the parallelogram is 113.12° .
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Find the equation of the line that is perpendicular to y= -1 over 5x-3 and contains the point (1,2)
Answers
STEP - BY - STEP EXPLANATION
What to find?
Equation of a line.
Given:
Perpendicular equation; y=-1/5 x - 3
Point(1,2)
Step 1
Find the slope of the perpendicular line.
Comparing the line with y=mx + c
[tex]slope(m)=-\frac{1}{5}[/tex]Step 2
Determine thee slope of the new equation.
Slope of perpendicular lines have the following characteristic;
[tex]m_1m_2=-1[/tex]where m2 is the slope of the new equation.
[tex]\begin{gathered} -\frac{1}{5}m_2=-1 \\ \\ m_2=-1\times-\frac{5}{1} \\ \\ =5 \end{gathered}[/tex]Step 3
Find the intercept(c) using the formula below:
[tex]y=mx+c[/tex]Substitute x=1 y=2 and m=5
[tex]\begin{gathered} 2=5(1)+c \\ \\ c=2-5 \\ \\ =-3 \end{gathered}[/tex]Step 4
Form the equation of the line by substituting m=5 and c=-3 into the general equation.
[tex]y=5x+(-3)[/tex]ANSWER
y= 5x + (-3)
If 10 g of a radioactive substance are present initially and 9 yr later only 5 g remain, how much of the substance will be present after 18 yr?After 18 yr there will be g of a radioactive substance.(Round the final answer to three decimal places as needed. Round all intermediate values to seven decimal places as needed.)
Answers
Given:
The initial amount of substance, No=10 g.
The amount of substance left after 9 years, N=5 g.
Since 10 g of substance is present initially, and it became 5 g(half of the initial amount) in 9 years, the half life of the substance is, t =9 years.
Hence, the expression for the amount remaining after T years is,
[tex]N(t)=N_0(\frac{1}{2})^{\frac{T}{t_{}}}[/tex]To find the amount of substance remaining after 18 years, put T=18, N0=10 and t=9 in the above equation.
[tex]\begin{gathered} N(18)=10\times(\frac{1}{2})^{\frac{18}{9}} \\ N(18)=10(\frac{1}{2})^2 \\ =\frac{10}{4} \\ =2.5\text{ g} \end{gathered}[/tex]Therefore, after 18 years 2.5 g of the radioactive substance will remain.
Evaluate the rational expression for the given x value. Express the answer as a fraction in simplest form.
Answers
Given the expression:
[tex]\frac{x-3}{2x+3}[/tex]We need to find the value of the expression when x = 7
So, we will substitute with x = 7 into the expression as follows:
[tex]\frac{7-3}{2\cdot7+3}=\frac{7-3}{14+3}=\frac{4}{17}[/tex]so, the answer will be 4/17
2 ABC Company has a large piece of equipmentthat cost $85,600 when it was first purchased 6years ago. The current value of the equipment is$30,400. What is the average depreciation of theequipment per year?F. $ 5,800G. $ 9,200H. $15,200J. $27,600K. $42,800
Answers
The intial cost of the equipment is C, which is given as 85,600.
The present value is PV, which is given as 30,400.
This simply means the total depreciation over the last 6 years can be derived as;
Depreciation = C - PV
Depreciation = 85600 - 30400
Depreciation = 55200
However, the method of depreciation is not given/specified, and hence the question requires that you calculate the average depreciation per year. That is, the total depreciation would be evenly spread over the 6 year period (which assumes that the depreciation per year is the same figure)
Average depreciation = Total depreciation/6
Average Depreciation = 55200/6
Average Depreciation = 9200
The correct option is option G: $ 9,200
what does this mean i dont get it pls help :)
Answers
Answer:
Left circle: 6x + 2y
Bottom middle circle: 5x
Bottom right rectangle: 3x + y
Step-by-step explanation:
According to the question, the expression in each circle is the result of the sum of the two rectangles connected to it.
The expression in the left circle is the sum of the expressions in the rectangles above and below it:
⇒ (4x + 3y) + (2x - y)
⇒ 4x + 3y + 2x - y
⇒ 4x + 2x + 3y - y
⇒ 6x + 2y
Therefore, the expression in the left circle is 6x + 2y.
The expression in the right circle is the sum of the expressions in the rectangles above and below it, however the expression in the rectangle below this circle is missing.
To find the missing expression, subtract the expression in the rectangle above the circle from the expression in the circle:
⇒ (4x + 5y) - (x + 4y)
⇒ 4x + 5y - x - 4y
⇒ 4x - x + 5y - 4y
⇒ 3x + y
Therefore, the expression in the lower right rectangle is 3x + y.
The expression in the bottom middle circle is is the sum of the expressions in the rectangles to its left and right:
⇒ (2x - y) + (3x + y)
⇒ 2x - y + 3x + y
⇒ 2x + 3x - y + y
⇒ 5x
Therefore, the expression in the bottom middle circle is 5x.
Approximate the measure in degrees of angle in a right triangle given that the side adjacent to angle is 5 and the hypotenuse of the triangle is 9 units. (Round your answer to one decimal place.)
Answers
Measure of perpendicular side for the given right triangle with adjacent side 5units and hypotenuse 9 unit is equal to 7.5 units(Upto one decimal place).
As given in the question,
In a right triangle,
Measure of a adjacent side = 5units
Measure of a hypotenuse = 9units
Let x be the measure of the perpendicular side
Using Pythagoras theorem we get,
(Hypotenuse)² = (Adjacent side)² +(perpendicular side)²
⇒ (9)² = (5)² + (x)²
⇒ (x)² = (9)² - (5)²
⇒x² = 81 -25
⇒ x = √56
⇒ x= 7.4833..
⇒x = 7.5 units(round upto one decimal)
Therefore, measure of perpendicular side for the given right triangle with adjacent side 5units and hypotenuse 9 unit is equal to 7.5 units(Upto one decimal place).
The complete question is :
Approximate the measure in degrees of angle in a right triangle given that the side adjacent to angle is 5 and the hypotenuse of the triangle is 9 units. Find the measure of perpendicular side.(Round your answer to one decimal place.)
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answer this question that stumbles tons of people around the world!!
Answers
The values of x and y in the angles formed by the straight lines are:
x = 18.5
y = 37
What are Angles on a Straight Line?If two or more angles lie on a straight line, they will have a sum of 180 degrees when added together. Therefore, all angles on a straight line have a sum of 180 degree.
Therefore:
16 + 90 + 2y = 180 [straight line angle]
Combine like terms
106 + 2y = 180
Subtract both sides by 106
106 - 106 + 2y = 180 - 106 [subtraction property of equality]
2y = 74
2y/2 = 74/2
y = 37
Also,
16 + 90 + 4x = 180
106 + 4x = 180
4x = 180 - 106 [subtraction property of equality]
4x = 74
4x/4 = 74/4
x = 18.5
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The point (2, 4) is reflected over the x-axis. What are its new coordinates?Use the blank grid below it it helps.-6-54-321-6ch-4-3-2.-1O3N56-1-2-3--4--5-6O (2,-4)O (-2,-4)O (4,2)O (-2,4)
Answers
Let:
[tex]\begin{gathered} A=(x1,y1)=(2,4) \\ A^{\prime}=(x1^{\prime},y1^{\prime}) \end{gathered}[/tex]After a reflection over the x-axis:
[tex]A\to(x,-y)\to A^{\prime}=(2,-4)[/tex]Answer:
(2,-4)
A crowbar 28 in. Long is pivoted 6 in. From the end. What force must be applied at the end in order to lift a 400-lb object at the short end?
Answers
What you are trying to do is balance the “moments" about the fulcrum (pivot).
We will calculate moment at the pivot (M1) due to weight (W):
• L1 = length of the bar = 6in
[tex]M1=W\times L1=400\cdot6=2400in\cdot lb_f[/tex]The moment (M2) at the pivot due to your applied force (Fa) on the other end of the bar must equal M1.
• LT = total lenght = 28in
,• L2 = LT - L1 = 28 - 6 = 22in
,• M2 = M1 = 2400in lbf
[tex]\begin{gathered} M2=Fa\times L2 \\ Fa=\frac{M2}{L2}=\frac{2400inlb_f}{22in}=109.09lb_f \end{gathered}[/tex]Answer: 109.09lbf
A force of 109.091 pounds would have to be applied to move the load.
What is the area of the real object that the scale drawing models?Scale factor: 1:3Area =6 square cmScale drawingOA. 54 square cmOB. 2 square cmO C. 18 square cmD. 6 square cmReal object
Answers
We have a drawing object with an area of 6 square centimeters. Since we have a scale factor of 1 : 3, it means that the real object is 3 times greater than the drawing object.
Therefore, if the drawing object has an area of 6 square centimeters, then the real object will have:
[tex]6cm^2*3=18cm^2[/tex]The real object will be 3 times greater than the one in the drawing.
Therefore, in summary, the real object will have 18 square centimeters (.
For the point P (-12,22) and Q (-7, 27), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ. What is the distance?
Answers
The distance d(P,Q) is equal to 7.1 units and the coordinates of the midpoint M of the segment PQ are (-9.5, 24.5).
How to determine the distance between points P and Q?Mathematically, the distance between two (2) points that are located on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substituting the given parameters into the formula, we have;
Distance, d(P, Q) = √[(-7 + 12)² + (27 - 22)²]
Distance, d(P, Q) = √[5² + 5²]
Distance, d(P, Q) = √[25 + 25]
Distance, d(P, Q) = √50
Distance, d(P, Q) = 7.1 units.
Midpoint on x-coordinate is given by:
xm = (x₁ + x₂)/2
xm = (-7 - 12)/2
xm = -19/2
xm = -9.5
Midpoint on y-coordinate is given by:
ym = (y₁ + y₂)/2
ym = (27 + 22)/2
ym = 49/2
ym = 24.5
Therefore, the coordinates of the midpoint M are equal to (-9.5, 24.5).
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Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total. Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs $8. Let R represent the number of additional rolls that Sofia orders.Which inequality described this scenario?What is the least amount of additional money sofia can spend to get the sushi they need?
Answers
Answer:
the least amount Sofia can spend is $608
Can you please help me out with a question
Answers
right. the lateral area of a hemisfere is the curved area, wich is half the area of a complete sphere
area of a sphere:
4πr²
So, half the area is 1/2(4πr²)= 2πr²
Now, the total surface is the lateral area plus the area of the base. the base is a circle, so the area is equal to πr²
And the volume of a hemisfere is equal to half the volume of a sphere:
[tex](\frac{4}{3}\pi r^3)\cdot\frac{1}{2}\text{ =}\frac{2}{3}\pi r^3[/tex]So, the anwsers are:
[tex]2\pi r^{2}\text{ = }2\pi(24ft)^{2}\text{ = 1152}\pi ft^2[/tex][tex]\pi r^{2}\text{ = }\pi(24ft)^2\text{ = 576}\pi ft^2[/tex][tex]\frac{2}{3}\pi r^3\text{ = }\frac{2}{3}\pi(24ft)^3\text{ = 9216}\pi ft^3[/tex]The answers are in order
how do I write down the values of each letters without measuring it?
Answers
Given the graph of parallel lines and a transversal
There is an angle = 90
This means the transversal is perpendicular to the parallel lines
So, All the angles are right angles
So, the measure of all angles = 90
So,
[tex]\begin{gathered} m\angle g=90\degree \\ m\angle h=90\degree \\ m\angle i=90\degree \end{gathered}[/tex]I have to find cars a speed in miles per hour
Answers
The graph in the picture shows the relationship between the distance traveled (y-axis) and the time (x-axis) that car A traveled.
The slope of the line represents the speed at which the car traveled. To determine the said speed you have to calculate the slope of the line.
-The first step is to determine two points of the line:
(x₁,y₁) → (2,80)
(x₂,y₂) → (0,30)
-The second step is to calculate the slope using the following formula:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]Where
(x₁,y₁) represent the coordinates of one point of the line
(x₂,y₂) represents the coordinates of a second point of the line
Replace the formula with the coordinates of the points and calculate the slope:
[tex]\begin{gathered} m=\frac{(80-30)mi}{(2-0)hr} \\ m=\frac{50mi}{2hr} \\ m=25\frac{mi}{hr} \end{gathered}[/tex]The slope of the line, which represents the speed of the car, is 25 miles per hour
does (51, 58) make the equation y =x -7 true?
Answers
The objective is to verify whether the point (51,58) maes the equation y=x-7.
Substitute the values of x and y coordinate in the given equation.
[tex]\begin{gathered} y=x-7 \\ y-x=-7 \\ 58-51=-7 \\ 7=-7 \end{gathered}[/tex]Since, LHS is not equal to RHS.
Thus, the coordinate (51,58) does not make the equation y=x-7.
Hence the answer is NO.
what is the area of the following Circle R equals 7
Answers
Answer: Area is 153.94
Step-by-step explanation:
Area = π r 2
2. (02.01 LC)While researching the industry she is interested in, Charlize sees that the average employment rate is 97.3%. How many people, out of every 250, are employed? (1point)24.33O 234.66Ο Ο243.25O 256.93
Answers
EXPLANATION
We can compute the average by multiplying the average by 0.973, as shown follows:
[tex]\text{Amount of people}=250\cdot0.973=243.25[/tex]In conclusion, the amount of people is equal to 243.25
Please help me step by step
Answers
Answer:
f(0) = -1
Step-by-step explanation:
to find this out we must first plug in 0 to the equation
f(0) = -0^2 + 4(0) - 1
now solve it
f(0) = 0 + 0 - 1
f(0)= - 1
that is your answer
recommend using graph paper bcuz u can see ur answer that way w/o solving :)
Which of the following polygons has reflective symmetry but not rotational symmetry?
a) square
b) regular decagon
c) kite
d) equilateral triangle
Answers
A kite has reflective symmetry but not rotational symmetry.
Define symmetry.In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more exact meaning of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. When something is identical on all sides, it is said to be symmetrical. If a center dividing line (also known as a mirror line) can be drawn on a shape to demonstrate that both of its sides are identical, then the shape is said to be symmetrical.
Given,
A kite has reflective symmetry but not rotational symmetry.
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8. A certain virus infects one in every 700 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. (a) Find the probability that a person has the virus given that they have tested positive. (b) Find the probability that a person does not have the virus given that they have tested negative.
Answers
Part a
Find the probability that a person has the virus given that they have tested positive
Probability in fraction form
p=(1/700)*(90/100)=90/70,000
simplify
P=9/7,000Part b
Find the probability that a person does not have the virus given that they have tested negative
Probability in fraction form
P=(699/700)*(10/100)
P=6,990/70,000
simplify
P=699/7,000Which point is on the circle centered at the origin with a radius of 5 units?Distance formula: Vx2 - xy)2 + (V2 - y2)?(2, 721)(2, 23)(2, 1)O (2,3)
Answers
To know if the point is on the circle, we mus calculate the distance between the point and the origin.
For the first option, we have:
- (2, √21)
and the origin
- (0, 0)
Then, we must replace the two points in the distance formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(0-2)^2+(0-\sqrt[]{21})^2} \\ d=\sqrt[]{4+21}=\sqrt[]{25}=5 \end{gathered}[/tex]Knowing that the distancie is 5 we can affirm that the point is on the circle because the radius is 5.
Finally, the answer is
[tex](2,\text{ }\sqrt[]{21})[/tex]√64= A. 16 B. 8 C. 7 D. 9
Answers
Answer:
B. 8
Explanation:
[tex]64=8\times8[/tex]We can write this in index form as:
[tex]64=8^2[/tex]Therefore:
[tex]\sqrt[]{64}=\sqrt[]{8^2}[/tex]On the right-hand side, the square root sign cancels the square, so we have:
[tex]\sqrt[]{64}=8[/tex]The correct choice is B.
My answer is correct or no please check
Answers
Answer:
D) 5 minus a number M
hope this helps!
Answer:
Yep. You got it right. Good job!
Step-by-step explanation: