Answer: The Answer is (-5,-3)
hope so my answer is correct
Step-by-step explanation:
How many and of which kind of roots does the equation f(x) = x3 – x2 – x + 1 have?
A. 2 real; 1 complex
B. 1 real; 2 complex
C. 3 real
D. 3 complex
The kind of roots does the equation f(x) is option (C) 3 real roots is the correct answer.
What is a polynomial equation?A polynomial equation is a sum of constants and variables. A polynomial is an expression consisting of indeterminate's (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
For the given situation,
The equation [tex]f(x) = x^3 - x^2 - x + 1[/tex]
The roots of the polynomial equation can be found as follows,
Step 1:
Substitute the value of x in which the equation f(x) equals zero.
⇒ Put [tex]x = 1[/tex], the equation becomes
⇒ [tex]f(1) = 1^3 - 1^2 - 1 + 1[/tex]
⇒ [tex]f(1) = 0[/tex]
Thus [tex](x - 1)[/tex] is the one root of the equation.
Step 2:
The other roots can be found by framing the quadratic equation on dividing the equation [tex]f(x) = x^3 - x^2 - x + 1[/tex] by [tex](x - 1)[/tex]
On dividing [tex]f(x) = x^3 - x^2 - x + 1[/tex] by [tex](x - 1)[/tex] we get the quotient,
⇒ [tex](x^{2} -1)[/tex]
Step 3:
Now factorize the quadratic equation, [tex](x^{2} -1)[/tex]
It can be expand using the identity,
⇒ [tex](x^{2} -1^{2} ) = (x+1)(x-1)[/tex] [∵ (a^2 - b^2) = (a+b)(a-b) ]
Thus the factors of the equation are [tex](x-1)(x+1)(x-1)[/tex]. So the roots are [tex]1,-1,1[/tex].
Hence we can conclude that the kind of roots does the equation f(x) is option (C) 3 real roots is the correct answer.
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When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten? It should be written as 8x−15x. It should be written as −2x−5x. It should be written as x−8x. It should be written as −x−7x. I think it should be B but im not quite sure Is the given equation a quadratic equation? x(x−6)=−5 The equation is not a quadratic equation because there is no x2-term. The equation is a quadratic equation because there is an x2-term. The equation is not a quadratic equation because the expression is not equal to zero. The equation is not a quadratic equation because there is a term with degree higher than 2. For this one i think its A but once again im not sure. Which of the following is an example of the difference of two squares? x2−9 x3−9 (x+9)2 (x−9)2 this one i have no clue i would appreciate it if anyone could explain this one.
Answer:
(3x+4)(2x-5)
Step-by-step explanation:
Factor by grouping.
Plz Help I Will Mark Brainliest If Right f(x) = x^2 + 3 A). y > -3 B). All real numbers C). y ≥ 3 D). y ≤ 3
Answer:
C) y ≥ 3
Step-by-step explanation:
The answer choices suggest that you're interested in the range of the function. x^2 cannot be negative, so its value will be 0 or greater. Adding 3 to x^2 ensures that the value of f(x) will be 3 or greater.
y ≥ 3 . . . . matches C
Need help give you a good rating pls.
Answer:
x^(1/2)
Step-by-step explanation:
For this, we need to understand exponent rules. This one is like this, "A power to a power, you multiply the exponents". This is simply, because this expression would be equivalent to 3 base terms:
(x^(1/6))^3 = (x^(1/6)) * (x^(1/6)) * (x^(1/6))
And when you perform this multiplication "Powers of like bases, you add the exponents", you will get the following
(x^(1/6)) * (x^(1/6)) * (x^(1/6)) = x^(1/6 + 1/6 + 1/6) = x^(3/6) = x^(1/2)
Hence, this expression simplifies to x^(1/2).
Cheers.
Answer:
[tex] \boxed{ {x}^{ \frac{1}{2} } }[/tex]Option D is the correct option.
Step-by-step explanation:
[tex] \mathrm{ ({x}^{ \frac{1}{6} } ) ^{3} }[/tex]
[tex] \mathrm{simplify \: the \: expression \: by \: multiplying \: exponents}[/tex]
[tex] \mathrm{ = {(x)}^{ \frac{1}{6} \times 3 } }[/tex]
[tex] \mathrm{ = {x}^{ \frac{1}{2} } }[/tex]
Hope I helped!
Best regards!
Kevin ordered some books online for seven dollars each he paid a total of six dollars for shipping the total cost of the purchase was $97 how many books did he buy?
Answer:
a) 7b+6=97
b)b=13
Step-by-step explanation:
Total cost = $97
Cost of each book = $7
Cost of shipping =$6
Therefore ,
Cost of the total no. of books+ Cost of shipping = Total Cost
=>7b+6= 97 <------- Answer to part(a)
=>7b=97-6
=>7b=91
=>b=13
No. of books = 13 <--------- Part (b)
Ja'Von kicks a soccer ball into the air. The function f(x) = –16(x – 2)2 + 64 represents the height of the ball, in feet, as a function of time, x, in seconds. What is the maximum height the ball reaches?
Answer:
The maximum height the ball reaches is 64 feet
Step-by-step explanation:
The given function is f(x) = -16·(x - 2)² + 64
From the equation, the path described by the ball is an inverted n-shaped parabola
The maximum height is therefore, the tip of the parabola
At the maximum height, the slope = 0 because the tip is momentarily flat
Since the slope (y₂ - y₁)/(x₂ - x₁) = The derivative Δy/Δx, we find the derivative of the function and equate it to zero to find the coordinates at the maximum height
Δy/Δx = dy/dx = d(-16·(x - 2)² + 64)/dx = -32·(x - 2) = -32·x + 64
To check if it is a maximum, we have;
d²y/dx² = d(-32·x + 64)/dx = -32 which is negative, indicating that the slope is reducing and we at the maximum point of the slope
Therefore for the maximum height Δy/Δx = dy/dx = -32·x + 64 = 0
64 = 32·x
x = 64/32 = 2 seconds
We now have the x-value at the slope, the f(x) value, is therefore;
f(2) = -16·(2 - 2)² + 64 = 64 feet
Therefore, the maximum height the ball reaches is 64 feet.
Answer:
D: 6
Step-by-step explanation:
I got it right on the test Edge nuity
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
there is no visible graph
Step-by-step explanation:
Which phrase best describes the relationship indicates by the scatter plotting?
Answer: negative correlation
Step-by-step explanation: If you look at the points in this graph here, I would say that those points are very close to a perfect line.
Notice that the slope of the line is negative.
This means it will be a negative correlation.
So the line is a very good estimate of the points.
Which of the following statements is false? A. A rectangle is an equiangular quadrilateral. B. Opposite sides of a parallelogram are congruent. C. A square is a regular quadrilateral. D. The diagonals of a rectangle are perpendicular.
Answer:
D.
Step-by-step explanation:
Choices A., B., and C. are always true.
Choice D. is true only for rectangles with congruent sides, which are squares.
Answer: D.
6 points are placed on the line a , 4 points are placed on the line b . How many triangles is it possible to form such that their vertices will be the given points, if a ∥ b ?
Answer:
7
Step-by-step explanation:
Given line a with 6 points on it, and line b with 4 points on it. Line a is parallel to line b, such that the two lines do not meet at any point even when extended.
Join the first point on line a to that on b, then back to the second point on a, return back to the second point on b, and continue till the line stops at the 5th point on line a. This forms triangles with vertices at the given points on the lines. The possible number of triangles that can be formed is 7.
WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!
In the following graph, ∆ABC is congruent to ∆A’B’C’. A teacher asks Janine to state the translation rule for this transformation. She focuses on point C’ and states that “the translation rule is
(x,y)→(x-2, y-6).
In other words, to shift from the blue to the red triangle, you must shift each point two units to the left and six units down. Janine made an error.
Explain how to correct her rule by either using transformation notation showing each step or explain using 2-3 sentences.
Answer:
She moved 3 to the left and 5 down.
She could have calculated each point seperately.
A(1,-1) then subtract 2 and subtract 6 from the x and then the y-coordanate, which gets you to A'(-1,-7). Then, do this with every other coordanate and you will get your answer. Hope this helped!
jumbo fancy store wants to place an order for candles , if one box contains 144 candles, how many boxes must the shop order for a stock of 100 080 candles?
Answer: The shop must order 695 boxes
Step-by-step explanation:
To find how many boxes that holds 100,080 candles, first divide the amount of candles that is needed to the measured amount of candles that is in a box.
144 candles= 1 box
100,080= ? Box(es)
So:
100,080 ÷ 144= 695 boxes
I hope this helps! I'm sorry if it's wrong.
Translate the following phrase into an algebraic expression using the variable m. Do not simplify
the cost of renting a car for one day and driving m miles if the rate is $48 per day plus 50 cents per mile
Answer:
y = 0.5X + 48
Answer:
48 + 0.50m
Step-by-step explanation:
m, the variable, equals to the number of miles driven. Since there is a base fare of $48, that will be the constant. It is $0.50 per mile, so it's 0.50m. Substituting for m, the miles driven, will give you the final cost.
2x/9 +x/3 = 13/6, solve for x
Answer:
x = 3 9/10
Step-by-step explanation:
2x/9 +x/3 = 13/6
Get a common denominator on the left side
2x/9 + x/3 *3/3 = 13/6
2x/9 + 3x/9 = 13/6
5x/9 = 13/6
Multiply each side by 9/5 to isolate x
5x/9 *9/5 = 13/6 * 9/5
x = 117/30
Divide the top and bottom by 3
x = 39/10
x = 3 9/10
Answer:
[tex]\bold{\red{\boxed{\blue{ x = 3.9}}}}[/tex]
Step-by-step explanation:
[tex] \frac{2x}{9} + \frac{x}{3} = \frac{13}{6} \\ \frac{2x + 3x}{9} = \frac{13}{6} \\ \frac{5x}{9} = \frac{13}{6} \\ use \: \: cross \: \: multipication \\ 5x \times 6 = 9 \times 13 \\ 30x =11 7 \\ \frac{30x}{30} = \frac{117}{30} \\ x = 3.9[/tex]
Which equation represents a population of 320 animals that decreases at an annual rate of 19% ?
A. p=320(1.19)t
B. p=320(0.81)t
C. p=320(0.19)t
D. p=320(1.81)t
Use the ^ symbol to indicate exponents. So for instance 4^2 = 4 squared.
A decrease of 19% means we have r = -0.19 and 1+r = 1+(-0.19) = 0.81 as the base of the exponent. A decrease of 19% means the population retains 81% each year.
Solve for X in the diagram below
PLS HELP BRAINLIST AND A THANK YOU WILL BE REWARDED :)
The 3 angles need to equal 180
The middle angle is given as 100.
180 -100 = 80
There is an x on each side so you have 2x
2x = 80
X = 80/2
X = 40 degrees
What is the possibility that a red or green marble will be selected from a bag containing 9 red marbles, 6 blue marbles , 7 green marbles and 11 yellow marbles
Answer:
16/33
Step-by-step explanation:
We have a bag of :
9 red marbles
6 blue marbles
7 green marbles
11 yellow marbles
Total number of marbles = 33 marbles.
The possibility that a red or green marble will be selected from a bag
P( Red or Green) = P(Red) + P(Green)
In the question we are not told if it is with replacement or without. We do both
With replacement
P( R or G) = P(Red) + P(Green)
P(Red)= 9/33
P(Green) = 7/33
= 9/33 + 7/33
= 16/33
Therefore, the possibility that a red or green marble will be selected from a bag is 16/33
12 people can paint the orchard in one hour How long would it take five people Give your answer in minutes
Answer:
[tex] \boxed{144 \: \: \: minutes}[/tex]Step-by-step explanation:
Let's solve :
[tex] \mathsf{ \: people \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:time \: ( \: in \: minutes)}[/tex]
[tex] \mathsf{12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 \: hour \: = \: 60 \: minutes }[/tex]
[tex] \mathsf{5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: t }[/tex]
The amount of time needed for completion is inversely proportional to the number of people working on the orchard. Let t be the amount of time ( in minutes ) needed when there are 5 people working.
[tex] \mathsf{ \frac{12}{5} = \frac{t}{60} }[/tex]
Apply cross product property
[tex] \mathsf{5t = 12 \times 60}[/tex]
Multiply the numbers
[tex] \mathsf{5t = 720}[/tex]
Divide both sides of the equation by 5
[tex] \mathsf{ \frac{5t}{5} = \frac{720}{5} }[/tex]
Calculate
[tex] \mathsf{t = 144 \: minutes}[/tex]
Hope I helped!
Best regards!!
It will take five people 144 minutes to paint the orchard.
12 people can paint the orchard in one hour, which is 60 minutes.
If there are five people, it will take them 12 × 60 / 5 = 144 minutes to paint the orchard.
So the answer is 144
Here's the explanation:
We know that the number of people and the time it takes to paint the orchard are inversely proportional. This means that if we increase the number of people, the time it takes to paint the orchard will decrease.
We can also set up a proportion to find the time it takes five people to paint the orchard. The proportion will look like this:
12 people : 5 people :: 60 minutes : x minutes
Cross-multiplying, we get:
12 × x = 5 × 60
x = 5 × 60 / 12
x = 144 minutes
Therefore, it will take five people 144 minutes to paint the orchard.
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A recipe for peanut butter cookies calls for 1 cup of sugar, 1 cup of chunky peanut butter, and 1 medium egg. The recipe yields 18 cookies. If the baker has 12.5 cups of sugar, 15 cups of chunky peanut butter, and 10 eggs. How many full batches of cookies can the baker make
Answer:
10 batches - they only have 10 eggs, so they can't make any more batches without them
Question 2 Multiple Choice Worth 5 points)
(03.01 LC)
The leg of a right triangle is 2 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle?
O2 units
0 6 units
O V12 units
O V20 units
Answer:
√20 units.
Step-by-step explanation:
Please see attached photo for diagram.
The other leg of the triangle is x as shown in the attached photo.
Using the pythagoras theory, we can obtain the the value of x as follow:
x² = 4² + 2²
x² = 16 + 4
x² = 20
Take the square root of both side.
x = √20 units
Therefore, the value of the other leg x of the triangle is √20 units
Answer:
[tex]\sqrt{} 20[/tex] is your answer hope this helps
Step-by-step explanation:
which of the following are exterior angles ? check all that apply
Answer: A, D,E
Step-by-step explanation:
The exterior angles are the angles that are out of the figure.In this case angle, 4,3 and 2 are all exterior angles.
Use the figure shown. Find the slope of the line.
у
4
3
C(-2,2)
B(-4, 2)
2
1
A(-2, 1)
-7-6-5-4-3-2
OY
X
The slope is
Answer:
The slope is [tex] -\frac{1}{2} [/tex]
Step-by-step explanation:
With points A(-2, 1), and B(-4, 2), slope (m) of the line can be calculated using the formula [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex],
Where,
[tex] y_2 = 2 [/tex]
[tex] y_1 = 1 [/tex]
[tex] x_2 = -4 [/tex]
[tex] x_1 = -2 [/tex]
Plug in the values into the slope formula:
[tex] m = \frac{2 - 1}{-4 -(-2)} [/tex]
[tex] m = \frac{2 - 1}{-4 + 2} [/tex]
[tex] m = \frac{1}{-2} [/tex]
[tex] m = -\frac{1}{2} [/tex]
Two mechanics worked on a car. The first mechanic charged $85 per hour, the second mechanic charged $90 per hour. The mechanic worked for a combined total of 25 hours, and together they charged a total of $2200. How lond did each mechanic work?
Answer:
First mechanic worked for = 10 hours
Second mechanic worked for = 15 hours.
Step-by-step explanation:
Let the number of hours the First mechanic worked = X
Let the number of hours the Second mechanic worked = Y
The first mechanic charged = $85 per hour
The second mechanic charged = $90 per hour
We are told in the question that: The mechanic worked for a combined total of 25 hours, and together they charged a total of $2200
Hence, we have the following equations from the above question
85X + 90Y = 2200....... Equation 1
X + Y = 25 ........ Equation 2
X = 25 - Y
Substitute 25 - Y for X in equation 1
85(25 - Y) + 90Y = 2200
2125 - 85Y + 90Y = 2200
Collect like terms
5Y = 2200 - 2125
5Y = 75
Y = 15
Since Y is the number of hours the second mechanic worked, hence, the second mechanic worked for 15 hours.
X + Y = 25 ........ Equation 2
Y = 15
X + 15 = 25
X = 25 - 15
X = 10
Since X represents the number of hours that the first mechanic worked, hence, the first mechanic worked for 10 hours.
Therefore, the first mechanic worked for 10 hours and the second mechanic worked for 15 hours.
Find the volume of the tank below. * PLEASE ANSWER ASAP *
Answer:
63
Step-by-step explanation:
pie multiply 2 sq. 2 multiply with 5
Point P' (1, 5) is the image of P (-3,1) under a translation. Determine the translation. Use non-negative numbers.
Answer:
T: 4 units right, 4 units up
Step-by-step explanation:
From x = -3 to x = 1, you need to add 4 to x, so the translation in x is 4 units right.
From y = 1 to y = 5, you need to add 4, so the translation in y is 4 units up.
T: 4 units right, 4 units up
The translation vector is (4, 4).
Vectorially speaking, a translation between two distinct point on cartesian plane is described by the following formula:
[tex]P'(x,y) = P(x,y) + T(x,y)[/tex] (1)
Where:
[tex]P(x,y)[/tex] - Original point.[tex]P'(x,y)[/tex] - Translated point.[tex]T(x,y)[/tex] - Translation vector.If we know that [tex]P(x,y) = (-3, 1)[/tex] and [tex]P'(x,y) = (1,5)[/tex], then the translation vector is:
[tex]T(x,y) = P'(x,y) - P(x,y)[/tex]
[tex]T(x,y) = (1,5) - (-3, 1)[/tex]
[tex]T(x,y) = (4,4)[/tex]
The translation vector is (4, 4).
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land and sea corporation has just purchased some shoreline property, and according to their calculations it will cost 2.5 times as much to develop the land as much as it did to buy it. If land and sea believe it will end up spending a combined total of $13,457,500 on both the land and its developments, how much must be the land alone have cost?
Answer:
5,383,000 / *improvments cost 8,074,500
Step-by-step explanation:
if 2.5 is by 'times' then,
13,457,500 / 2.5 =
5,383,000
Which means the cost of the land is 5,383,000
To check just multiply:
5,383,000 x 2.5 = 13,457,500
*Extra
13,457,500 - 5,383,000
= the cost of improvements = 8,074,500
Hope this helps, and have a good day :)
Answer:
$3,845,000
Step-by-step explanation:
Land cost = lDevelopment cost = dTotal cost = $13,457,500As per given:
d= 2.5 lThen total is:
l+2.5l= 134575003.5l= 13457500l= 13457500/3.5l= $3845000Cost of the land alone is $3,845,000
What is the average time for the toy car to move 1.0 m on dirt? 20.2 s, 24.4 s, 28.1 s or 60.7 A student collected data about the distance a ball falls over time. Which type of graph should he use to represent the data? circle graph, scatterplot, histogram or bar graph
Answer:
1) Incomplete question
2) Scatterplot
Step-by-step explanation:
1) The question is incomplete. To calculate the average time required for the toy car to move, the formula to be used will be
velocity = distance ÷ time
Hence; time = distance ÷ velocity
2) There are two variables in the question; the distance (it takes the ball to fall) and the time. The type of graph (from the option) that can have two variables represented on it is a scatterplot.
Answer:
answer; A. 20.2 s.
Step-by-step explanation:
i had the same question but i had a graph to help me anyways
20.0 + 19.2 + 21.5 = 60.7 s, but you divide the total by 3, then here is your answer: 20.23333333333333 and you simplify it to 20.2 s,
Write 30+x^2-11 in standard form.
Answer:
x^2+19
Step-by-step explanation:
-10(x+5) with steps canvas
Answer:
[tex]\Large \boxed{-10x-50}[/tex]
Step-by-step explanation:
[tex]-10(x+5)[/tex]
Distribute -10 to the terms in the brackets.
[tex]-10(x)-10(5)[/tex]
[tex]-10x-50[/tex]
Answer: -10x - 50
Step-by-step explanation:
Distribute -10 to both terms.
-10 * x = -10x
-10 * 5 = -50
The equation now looks like this:
-10x - 50
You have nothing to simplify, so you're finished.
Hope this helps!
Please help with 6 and 7
Answer:
6a) i- 2hrs 36mins ii- 3hrs 12mins
b) car A≈ 76.9km/h car B≈ 62.5km/h
c)------
7a) 35km
b) car A=75km car B=60km
c) 30km
d) car A≈36mins car B≈48mins
Step-by-step explanation:
6a) Using the graph follow the lines until they finish then go downwards until you get to the x-axis. The x-axis is going up by 12mins for each square.
b) Using the answer from a, you divide 200km by the time.
For car A 2hrs 36mins becomes 2.6 because 36mins/60mins=0.6
∴ car A: 200/2.6≈ 76.92km/h
For car B 3hrs 12mins becomes 3.2 because 12mins/60mins=0.2
∴ car B: 200/3.2≈ 62.5km/h
7a) Using the graph go down from where the line of car A finished to meet car B. The y-axis is going up by 5km for each square.
b) Starting from the x-axis at 1 hour go upwards to see where you meet the car B line (60km) and car A line(75km). (sorry if that does not really make sense).
c) Difference from car A line to car B:
155km-125km=30km
d) Going across from 50km meet car A line and go down to see it has been travelling for approx. 36mins. Then continue across to car B line, go down to see it reached 50km at approx. 48mins.
Hope this helps.
