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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Anyone ?? Know the answers to these both? Due tmr morning
Answer:
Just use m a t h w a y for the answer
Step-by-step explanation:
Thank me later,or dont thank me at all
If the functions f(x) and g(x) are
increasing on an interval, is the
interval? how about f(x) – g(x)?
Answer:
The difference will be increasing too
Step-by-step explanation:
If f(x) and g(x) is increasing in nature then
f(b) < f(a) and g(b) < g(a) for any a and b in the interval.
Subtracting these 2 equations, we get
f(b) - g(b) < f(a) - g(a) for any a and b in the interval.
Which means f-g is increasing in the interval (a, b) but as a and b were random real numbers we took, f(x) - g(x) will be increasing for an interval
Help me please Will give brainlist
Answer:
Step-by-step explanation:
These are geometric means problems. In the top one, a is the geometric mean as the height for both the smaller triangles inside the big one. Therefore,
[tex]\frac{4}{a} =\frac{a}{25\\}\\a^2=100\\a=10[/tex]
The next one has the geometric mean of b, being a part of the smaller triangle on the left and the big triangle as a whole:
[tex]\frac{4}{b} =\frac{b}{29}\\b^2=116\\b=10.77[/tex]
Find the value of z. A. 141 B. 110 C. 80 D. 100
Answer:
B. 110
Step-by-step explanation:
z is supplemental to 70°, so the add up to 180°
z+70°=180°
z=180°-70°
z=110°
Option B is correct. The required value of z is 110 degrees
Supplementary angles are angles summing up to 180 degrees. According to the circle geometry, we can see that z and 70 degrees lie on the same line, this shows that both angles are supplementary.
Since supplementary angles sum up to 180degrees, hence;
[tex]z + 70 = 180\\[/tex]
Subtract 70 from both sides
[tex]z+70-70=180-70\\z=110^0[/tex]
Hence the value of z is 70 degrees
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100÷50000 it's has to be step by step aka show work
100÷50000 can be written as 100/50000, then cancel out 2 of the zeroes, and you will get 1/500 or 0.002 as your final answer.
Someone please help me ASAP
Answer:
the percentage share for BBC2 remained almost the same at about 11 % each year
if you look at the chart the BBC2 almost remains stable between 10 and 12 %
1980 ( between 39 and 51)
1985 ( between 37 and 49 ) and so on
( these numbers are not exactly the same , it is about or approximately)
How would you write 7 is subtracted from the cube of a number
Answer:
n³ - 7
Step-by-step explanation:
n³ - 7
The required expression for the 7 subtracted from the cube of a number is x³- 7.
Given that,
A string of statements is given,
Here, we have to transform the statement, 7 is subtracted from the cube of a number into a mathematical inscription.
Arithmetic, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is an expression?A mathmetical expression is formulated structure of a statement using variables.
Let the number be x,
Now 7 subtracted from the cube of number x
= x³ - 7
Thus, the required expression for the 7 subtracted from the cube of a number is x³- 7.
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Please help me I promise I will mark you brainliest if you are correct!!!!!!!!!!!!!!!!!!!!!!!!!! Use the graph of f to estimate the local maximum and local minimum. A quadratic graph is shown. The graph intercepts the x axis at approximately -2.8 and 1.2. A). No local maximum; local minimum: approx. (1,-7.67) B). Local maximum: (-2,8); local minima: (-3,0) and (3,3) C). Local maximum: approx. (1,8.08); local minima: approx. (-2,-7.67) and (3,2.75) D). Local maximum: ∞ local minima: (-3,0) and (3,3)
Answer:
Local Maximum Approx.: (1,8.08)
Local Minima Approx.: (-2,-7.67) and (3,2.75)
Step-by-step explanation:
Local maximums and minima there the highest and lowest points, respectively, on a graph in a specific region. (This is different from absolute maximum and minimum, which are the highest and lowest points overall.)
These are pretty clear to see on a curve, as they are the "turns" or the points where the curve switches direction from up to down or down to up.
On your graph, we have two local minima and one local maximum. The local minima are at x= -2 and x=3. The local maximum is at x=8. Because of the way the graph is, we have to approximate the y-values of each point.
The answer option which best describes this is the third option, so that is your answer.
plz help asap i have limited time i will give brainliest
Answer:
358
Step-by-step explanation:
In 1995, the boys were 50 %
Take the number of people at the convention in 1995 ( 716)
and multiply by 50%
716 * 50%
716 * .50
358
Answer:
b. 358
Step-by-step explanation:
First, find what percentage of attendees were boys in 1995:
By reading the graph, we can see 50% were boys.
In the table, we can see that there were 716 attendees in 1995.
To find how many boys attended in 1995, find 50% of 716.
716(0.5) = 358
Write in word form.
4. 572
5. 2.897
6. $325.10
Answer:
heyyy thereee
4) 572 = five hundred seventy two
5) 2.897 = two and eight hundred ninety seven thousandths
6) three hundred twenty five and 10 hundredths or three hundred twenty five and 1 tenth
glad if brainliest ig ?
Someone help pleasee
Answer:
-80
Step-by-step explanation:
We can write the quadratic as
ax^2 + bx+c
4x^2 +8x+9
a=4 b = 8 c=9
The discriminant is
b^2 -4ac
8^2 - 4(4)(9)
64 - 144
-80
Answer:
-80
Step-by-step explanation:
The discriminant is the value under the radical in the quadratic formula. The part of the quadratic formula that is under the radical is [tex]\sqrt{b^2-4ac}[/tex]. So, plug in the needed values and solve for what is under the radical. The b-value is 8; this squared is 64. Then, plug in a and c, 4 and 9. Then multiply these by 4, 4*4*9=144. Finally subtract, 64-144=-80.
3
4
x
+
6
=
1
+
1
3
x
Answer:
[tex]\boxed{x = -5/21}[/tex]
Step-by-step explanation:
Hey there!
To simplify we need to combine like terms and use the communicative property,
34x + 6 = 1 + 13x
-13x to both sides
21x + 6 = 1
-6 to both sides
21x = -5
Divide both sides by 21
x = -5/21
Hope this helps :)
Answer: I'm guessing you need me to solve this for you.
I interpreted the equation this way: 34x + 6 = 1 + 13x
The solution is -5/21.
Step-by-step explanation:
34x + 6 = 1 + 13x
Step 1: Simplify both sides of the equation.
34x + 6 = 13x + 1
Step 2: Subtract 13x from both sides.
34x + 6 − 13x = 13x + 1 − 13x
21x + 6 = 1
Step 3: Subtract 6 from both sides.
21x + 6 − 6 = 1 − 6
21x = − 5
Step 4: Divide both sides by 21.
21x/21 = -5/21
x = -5/21
Hope this helped you!
Yael used to have a square garage with 254 ft2 of floor space. She recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
Answer:
120
Step-by-step explanation:
What is the slope of the graph?
points are
(0,3)(1,0)[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{0-3}{1-0}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-3}{1}[/tex]
[tex]\\ \sf\longmapsto m=-3[/tex]
if R=[2 3 4] what is the number of element in
2 4 5
the matrix R?
Answer:
5
Step-by-step explanation:
May be correct than follow me please
PLS HELP I WILL GIVE YOU A BRAINLIST AND A THANK YOU!!!!
Answer:
75
Step-by-step explanation:
We have a 90 degree angle and a 15 degree angle that add up to 105. The angle that is missing can be found by doing 180 - 105 = 75 (since it's a straight line). X is vertical from the 75 degree angle, so 75 is your answer.
Answer:
x= 75°
Step-by-step explanation:
i have added a sketch of it
Please help I’ll mark as brainlist
Answer:
Ekta and Preyal
Step-by-step explanation:
Write in point-slope form an equation of the line that passes through the point (8, 9) with slope 7.
Answer:
y=7x-47Step-by-step explanation:
[tex](8,9)=(x1,y1) \\ m=7 \\ y−y1=m(x−x1) \\ y−9=7(x−8)
[/tex]
[tex]y - 9 = 7x - 56 \\ y = 7x - 56 + 9 \\ y = 7x - 47[/tex]
For what value of k does the equation (2k+1)x^2+2x=10x-6 have two real and equal roots?
Answer:
[tex]\displaystyle k = \frac{5}{6}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle (2k+1)x^2 + 2x = 10x - 6[/tex]
And we want to find the value of k such that the equation has two real and equivalent roots.
Since the equation is a quadartic, we can find its discriminant (symbolized by Δ). Recall that:
If Δ < 0, we have no real roots (two complex roots). If Δ > 0, we have two real roots. And if Δ = 0, we have one real root, or two equivalent ones.First, rewrite our equation:
[tex](2k+1)x^2 -8x + 6 =0[/tex]
The discriminant is given by:
[tex]\displaystyle \Delta = b^2 -4ac[/tex]
In this case, b = -8, a = (2k + 1), and c = 6.
Therefore, the discriminant is given by:
[tex]\displaystyle \Delta = (-8)^2 - 4(2k+1)(6)[/tex]
For it to have two equal roots, the discriminant must be zero. Hence:
[tex]\displaystyle 0 = (-8)^2 - 4(2k+1)(6)[/tex]
Solve for k:
[tex]\displaystyle \begin{aligned} \displaystyle 0 &= (-8)^2 - 4(2k+1)(6) \\ 0 &= 64 - 48k - 24 \\ 0 &= 40 - 48k \\ -40 &= -48k \\ \\ k &= \frac{5}{6} \end{aligned}[/tex]
Hence, the value of k is 5/6.
A certain composite number has 4 factors and the sum of them is 96. Find the number(hint the number is divisible by 7). Just don't give me the answer by guessing. show me how you arrived at the solution elaborately i.e. show me your working in detail
Answer:
[tex]\huge\boxed{77}[/tex]
Step-by-step explanation:
The number can be divisible by 7.
The multiples of 7 are 7,14,21,28,35,42,49,56,63,70,77,84 and so on
Finding the factors for all of the multiples of 7:
7 => 1,7 [Not 4 factors]
14 => 1,2,7,14 [4 factors but Sum = 24]
21 => 1,3,7,21 [4 factors but Sum = 32]
28 => 1, 2, 4, 7, 14, 28 [Not 4]
35 => 1,5,7,35 [4 factors but Sum = 48]
42 => 1, 2, 3, 6, 7, 14, 21, 42 [Not 4]
49 => 1,7,49 [Not 4]
56 => 1, 2, 4, 7, 8, 14, 28, 56 [Not 4]
63 => 1, 3, 7, 9, 21, 63 [Not 4]
70 => 1, 2, 5, 7, 10, 14, 35, 70 [Not 4]
77 => 1, 7, 11, 77 [4 factors and Sum = 96]
Answer:
77
Step-by-step explanation:
The first factor is 1
Since it is divisible by 7, 7 will also be one of its factors.
Therefore the four factors are
1, 7, x, y
When x and y are integers
Using the following law...
The product of factors of a number in the same position (left or right) (increasing or decreasing order) is equal to the number
Counting from left
y is the first factor
x is the second factor
Counting from the right
1 is the first factor
7 is the second factor
Applying the last
y×1=x×7
y = 7x
the sum of the factors is 96
1+7+x+7x = 96
8x+8=96
8x = 88
x= 11
Hence the number is
7x = 7(11)
=77
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Outliers can cause the _________ to be misleading when summarizing a data set.
A. mean
B. interquartile range
C. all of these
D. median
Answer:
A. Mean
Step-by-step explanation:
Mean, because it's the average of the numbers and if one number's way off, it would throw the average off by a lot! I honestly forgot a bit about interquartile ranges, but it doesn't affect the median at all/have a very little effect so that's why it's not all of these. But mean is for sure!
I hope this helped! :D
is 1+isqrt3 a complex number
Answer:
Step-by-step explanation:
Yes, due to the presence of that operator " i "
n/2-3n/4+5n/6=21 please tell the answer
Answer:
n= 36
Step-by-step explanation:
36/2-3 x 36/4+5 x 36/6=21
please give me brainliest if i got this right
Answer:
n=36
Step-by-step explanation:
By simplifying both sides of the equation, then isolating the variable.
n=36
I did this quickly so sorry if it's no help
Complete the transformations below. Then enter the final coordinates of the figure.
Consider the equation: 12x=13-x^212x=13−x 2 12, x, equals, 13, minus, x, squared 1) Rewrite the equation by completing the square. Your equation should look like (x+c)^2=d(x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or (x-c)^2=d(x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation
Answer:
[tex](x + 6)^2 = 49[/tex]
[tex]x = 1[/tex] or [tex]x = -13[/tex]
Step-by-step explanation:
Given
[tex]12x = 13 - x^2[/tex]
Using Completing the Square
[tex]12x = 13 - x^2[/tex] ---- Add [tex]x^2[/tex] to both sides
[tex]x^2 + 12x = 13 - x^2 + x^2[/tex]
[tex]x^2 + 12x = 13[/tex]
Divide the coefficient of x by 2; then add the square to both sides
[tex]x^2 + 12x + 6^2 = 13 + 6^2[/tex]
[tex]x^2 + 12x + 36 = 13 + 36[/tex]
[tex]x^2 + 12x + 36 = 49[/tex]
Factorize
[tex]x^2 + 6x + 6x + 36 = 49[/tex]
[tex]x(x + 6) + 6(x + 6) = 49[/tex]
[tex](x + 6)(x + 6) = 49[/tex]
[tex](x + 6)^2 = 49[/tex]
Hence, the equation is [tex](x + 6)^2 = 49[/tex]
Solving further
Take square root of both sides
[tex](x + 6) = \sqrt{49}[/tex]
[tex]x + 6 = \±7[/tex]
[tex]x = \±7- 6[/tex]
This implies that
[tex]x = 7 - 6[/tex] or [tex]x = -7 -6[/tex]
[tex]x = 1[/tex] or [tex]x = -13[/tex]
HEnce, the solutions are [tex]x = 1[/tex] or [tex]x = -13[/tex]
Answer:
(x+6)^2=49 and x=−6±7
Step-by-step explanation:
factorize, x(x +2)3x+6
x(x+2)+3x+6
x^2+2x+3x+6
x (x+2)+3(x+2)
(x+3) (x+2)
Determine the value of x.
Answer:
x = 4.59
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 74 = 16/ x
x tan 74 = 16
x = 16/ tan 74
x=4.58792
[tex]\huge\text{Hey there!}[/tex]
[tex]\boxed{\boxed{\huge\text{Formula: \boxed{\text{tan } \theta = \mathsf{\dfrac{Opposite}{Adjacent}}}}}}[/tex]
[tex]\boxed{\huge\text{\boxed{\mathsf{\bold{tan\ 74} = \dfrac{16}{x}}}}}[/tex]
[tex]\boxed{\boxed{\huge\textsf{x tan 74 equals \bf 16}}}[/tex]
[tex]\boxed{\huge\text{x = }\boxed{\mathsf{\dfrac{16}{tan \ 74}}}}[/tex]
[tex]\boxed{\boxed{\huge\text{x = \bf x=4.58792}}}\boxed{\boxed{\huge\text{\bf (ORIGINALLY)}}}[/tex]
[tex]\boxed{\boxed{\huge\text{x = \boxed{\bf 4.58792\ or \ 4.58 \ is \approx \underline{\underline{4.59}}}}}}\huge\checkmark[/tex]
[tex]\boxed{\boxed{\huge\text{Therefore, your answer is: \boxed{\textsf{Option C. \bf 4.59}}}}}\huge\checkmark[/tex]
[tex]\huge\text{\huge\text{Good luck on your assignment \& enjoy your day!}}[/tex]
~[tex]\boxed{\huge\text{\boxed{\frak{Amphitrite1040:)}}}}[/tex]
Sandra spotted the sailboat from the shore and measured the angle from the waterline to the top of the boats mast to be 7° if the top of the mask is 23 feet above the water how far is the middle of the sailboat from the shore? Estimate your answer to the nearest tenth.
Answer:
The middle of the sailboat is approximately 268.8 feet from the shore.
Step-by-step explanation:
Let the distance from shore to the middle of the boat be represented by x, the angle of elevation of Sandra from the shore to the top of the boat mast is 7°. Applying the required trigonometric function to this question, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 7° = [tex]\frac{23}{x}[/tex]
⇒ x = [tex]\frac{23}{Tan 7^{0} }[/tex]
= [tex]\frac{23}{0.12279}[/tex]
= 268.7515
∴ x = 268.8 feet
The middle of the sailboat is approximately 268.8 feet from the shore.
The number of dollars in Teo's bank
account on Tuesday was 3 times as
much as the amount on Friday. How
many dollars were in the account on
Friday?
Answer:
y = $ x/3
Step-by-step explanation:
Let the amount of dollars in Teo's bank on Tuesday be $x and the amount in his bank on Friday be $y.
If the number of dollars in Teo's bank account on Tuesday was 3 times as
much as the amount on Friday, this can be represented mathematically as;
x = 3y where y is the amount in his bank on Friday.
The amount of dollars in his account on friday will be gotten by dividing both sides of the equation by 3
3y = x
3y/3 = x/3
y = x/3
Hence the amount of dollars in his account on Friday is y = $ x/3
Enter the repeating digit.
Answer:
Does the answer help you?
Answer:
6
Step-by-step explanation:
Dividing 2 by 3 gives you a repeating decimal of 0.6666...