2x^3-x^2+x-2 factorize
Answers
Answer:
\((x-1)(2x^2+x+2)\)
Step-by-step explanation:
Factorize:
\(f(x)=2x^3-x^2+x-2\)
Factor Theorem
If f(a) = 0 for a polynomial then (x - a) is a factor of the polynomial f(x).
Substitute x = 1 into the function:
\(\implies f(1)=2(1)^3-1^2+1-2=0\)
Therefore, (x - 1) is a factor.
As the polynomial is cubic:
\(\implies f(x)=(x-1)(ax^2+bx+c)\)
Expanding the brackets:
\(\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c\)
\(\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c\)
Comparing coefficients with the original polynomial:
\(\implies ax^3=2x^3 \implies a=2\)
\(\implies (b-a)x^2=-x^2 \implies b-2=-1 \implies b=1\)
\(\implies -c=-2 \implies c=2\)
Therefore:
\(\implies f(x)=(x-1)(2x^2+x+2)\)
Cannot be factored any further.
put x = 1,
2•(1³) - 1² + 1 - 22 - 1 + 1 - 20it's value is 0.
hence, it's a solution
divide 2x³ - x² + x - 2 by (x - 1)
2x² + x + 2it can be written as :
(x - 1)(2x² + x + 2)Related Questions
The scatterplot below shows the ages of some children in the amount of time each been playing outside last week. Which equation could represent the line of best fit for the number of hours a child spends playing outside based on the age of the child? Is the correct answer A, B, C, or D?
Answers
Answer:
y = 0.75x + 45
Explanation:
The line of best fit is a line that describes in a better way the distribution of the points. Therefore, the best fit will be like
Then, the equation of this line can calculate using two points in the line, for example (x1, y1) = (2, 6) and (x2, y2) = (6, 9). So, the slope of the line is
\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{9-6}{6-2}=\frac{3}{4}=0.75\)Finally, the equation of the line is
\(\begin{gathered} y-y_1=m(x-x_1) \\ y-6=0.75(x-2) \\ y-6=0.75x-0.75(2) \\ y-6=0.75x-1.5 \\ y=0.75x-1.5+6 \\ y=0.75x+4.5 \end{gathered}\)Therefore, the answer is
y = 0.75x + 45
Jamal needs to plot at least 1 point from each set of numbers in the chart. If he graphs -5 and 5, which sets of numbers can he cross first? choose all that apply
A Rational numbers
B Integers
C whole numbers
D Natural numbers
Answers
Answer:
A Rational numbers
B Integers
Without using a calculator, determine the number of real zeros of the function
fox) = x2 + 4x + x - 6.
Answers
Answer:
1, -6
Step-by-step explanation:
Since there are alike numbers, add them together.
4x+x= 5x
Now the function is: f(x)= \(x^{2}\)+5x-6
The function is in \(a^{2}\)+bx+c form.
So find the factors of a x c = b.
Factors of -6(a) that fits (b)5 is (-1,6).
Then you just factor it:
f(x)= \(x^{2}\)+5x-6
(x-1)(x+6)
x-1= 0 x+6=0
+1 +1 -6 -6
x=1 x=-6
Those are the real zeroes: 1, -6
Membership at the YMCA costs $15 per month plus $80 to sign-up. Blink costs $29 per month but is free
to sign-up. After how many months will the two gyms cost the same amount?
Answers
Let months be x
\(\\ \sf\longmapsto 80+15x=29x\)
\(\\ \sf\longmapsto 29x-15x=80\)
\(\\ \sf\longmapsto 14x=80\)
\(\\ \sf\longmapsto x\approx 6months\)
Answer:
43 months in ymca including the $80 sign up fee is equal to 25 months in blink
Step-by-step explanation:
$725 divided by $29 =25 months
$ 725 - $80 sign up = $645 .
Now we divide this by $15.
$645 divided by 15= 43 months
an outdoor pavilion has 30 rows with 20 seats in the first row each row thereafter has 6 more seats using a formula find the total of seats at the pavilion
Answers
A burrito was cut into 6 equal pieces. If Carmen ate 2/6of the burrito, and Chris ate 1/6of the burrito,
how many whole pieces of the burrito are left?
Answers
Answer:
3/6 peices are left
Step-by-step explanation:
Find the slope between (3,5) (0, -4)
The slope is:?
Answers
Answer:
Slope=3
Step-by-step explanation:
Slope formula y2-y1/x2-x1
This makes -4-5/0-3= -9/-3=3.
The slope is 3
Find the median of the data in the dot plot below.
Answers
Answer: 3 4 4 5 5 5 5 7 7
Step-by-step explanation:
your answer is 5 because 5 is the number in the middle
What function is shown by the graph
Answers
Answer:
B
Step-by-step explanation:
Y=3x. The slope is 3 6-(-6)/2-(-2) and the y intercept is 0.
What is the y-intercept of y=3-4xy=3−4xy, equals, 3, minus, 4, x?
Answers
Answer:
y = 3 - 4x
To find the y intercept let x = 0
y = 3 - 4(0)
y = 3 or ( 0 ,3)
Hope this helps.
15. A train is running at a speed of 72 km/hr, how far will it go in 7 seconds?
(3 Points)
Enter your answer
I
Answers
Answer:
140
Step-by-step explanation:
72/3.6*7
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The product of two numbers is 1536.
If the HCF of the two numbers is 16.
find the LCM of these two numbers.
Answers
Work Shown:
LCM = (product of two numbers)/(HCF of the two numbers)
LCM = 1536/16
LCM = 96
34
James was participating in a school readathon and his parents agreed to donate $ 2
plus an extra dollar for every book read. The dot plot below shows this:
Searned
10
3
20
340
If James reads more books, the next point marked on the plot will be:
5
Answers
Answer:
the next point will be 4, 6
Step-by-step explanation:
if you follow the dots in the line that they make, the next on will be 4, 6
Pls help me I will mark the brainliest
Answers
The most specific correct name for this figure is a trapezoid.
A trapezoid is a quadrilateral with only one pair of parallel sides. >>>This figure is a trapezoid.
An isosceles trapezoid is a trapezoid in which the top and bottom sides are parallel, while the remaining two non-parallel sides have the same length. >>> this figure is not an isosceles trapezoid.
A parallelogram has opposite sides parallel. >>> This figure is not a parallelogram.
A quadrilateral is a four-sided polygon, having four edges and four corners. >>>This figure is a quadrilateral.
Two numbers are in the ratio of 3:7.one of the numbers is 42 there are two possible values for the other number.what are the possible values
Answers
Answer:
98
Step-by-step explanation:
Please help on question asap if you are correct with answer I'll give brainlie st, a thanks and five stars.
When we have a trapezium and w e are finding out the area , would it be possible to have a radius\diameter in the trapezium or is that just for 3D shapes
Answers
Is not possible to define a radius nor a diameter in a trapezium.
Is it possible to have a radius/diameter in the trapezium?Radius and diameter are two measures defined for circles.
Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).
At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.
To get the area use the formula:
Area = (base1 + base2)*height / 2
Learn more about trapeziums:
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Solve (3x+7)=4x for x
Answers
Answer:
x=7
Step-by-step explanation:
(3x+7)=4x
Subtract 3x from each side
(3x+7) -3x=4x-3x
7 = x
Growth or decay? And percentage rate
Determine if the exponential function shows exponential growth or decay and find the rate at which is growing/decaying as a percent.
Answers
The exponential functions are interpreted below
exponential function growth / decay rate
y =3,500(1,12)^t growth 12%
y = 10000(0.9)^t decay 10%
y = 5(1.025)^t growth 2.5%
y = 160(0.79)^t decay 21%
y = 1,950(0.875)^t decay 12.5%
for the function plotted in graph
f(x) = 2(1.5)^x growth 50%
f(x) = 2(0.8)^x decay 20%
How to interpret the given exponential functionsExponential functions are functions of the form
f(x) = a(b)ˣ
the initial = a
the base = b
the exponents = x
The base is used as described
0 < b < 1 decay function b > 1 growth functionrate
for growth function rate, r = b - 1
for decay function rate, r = 1 - b
y =3,500(1,12)^ t
b = 1.12 (growth)
r = 1.12 - 1 = 12%
y = 10000(0.9)^t
b = 0.9 (decay)
r = 1 - 0.9 = 0.1 = 10%
y = 5(1.025)^t
b = 1.025
r = 1.025 - 1 = 0.025 = 2.5%
y = 160(0.79)^t
b = 0.79
r = 1 - 0.79 = 0.21 = 21%
y = 1950(0.875)^ t
b = 0.875
r = 1 - 0.875 = 12.5%
The plotted functions
f(x) = 2(1.5)ˣ
b = 1.5 (growth)
r = 1.5 - 1 = 0.5 = 50%
f(x) = 2(0.8)^x
b = 0.8 (decay)
r = 1 - 0.8 = 0.2 = 20%
Learn more about exponential function here:
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7(4p+2q+3r) apply the distributive property to create an equivalent expression
Answers
Answer:
28p + 14q + 21r
Step-by-step explanation:
7(4p + 2q + 3r) ← multiply each term in the parenthesis by the 7 outside
= 28p + 14q + 21r
You can sand 4/9 square yard of wood in 1/2 hour. How many square yards can you sand in 3.2 hours? Justify your answer.
Answers
Answer:
4/9 = 1/2 x
Step-by-step explanation: 2.84 sands
209.106 in expender form
Answers
Answer:
209.106 = (2 x 100) + (0 x 10) + (9 x 1) + (1/10) + (0/100) + (6/1000)
Answer:
200+9+0.1+0.006.
Step-by-step explanation:
The revenue function R in terms of the number of units sold, x, is given as R = 290x-0.52x^2where R is the total revenue in dollars. Find the number of units sold x that produces a maximum revenue?Your answer is x=What is the maximum revenue?$
Answers
Solution
Step 1:
The function reaches a maximum where the derivative is equal to 0.
Find the first derivative of the function.
Step 2:
Write the function
\(R(x)\text{ = 290x - 0.52x}^2\)Step 3
Find the first derivative
\(\begin{gathered} R(x)=\text{ 290x -0.52x}^2 \\ R^{\prime}(x)\text{ = 290 - 1.04x} \end{gathered}\)Step 4:
The function reaches a maximum where the derivative is equal to 0.
\(\begin{gathered} 290\text{ - 1.04x = 0} \\ 1.04x\text{ = 290} \\ \text{x = }\frac{290}{1.04} \\ \text{x = 278.8 }\approx\text{ 279} \end{gathered}\)So the number of units which produce the maximum revenue = 279
Step 5:
Substituting this value in the original equation gives the revenue:
\(\begin{gathered} R\text{ = 290x - 0.52x}^2 \\ R\text{ = 290}\times279\text{ - 0.52 }\times\text{ 279}^2 \\ R\text{ = 80910 - 42034.14} \\ R\text{ = \$38875.86} \end{gathered}\)Maximum revenue = $38875.86
Vertical lines have a /an ______ slope
Answers
Answer:
N/A
Step-by-step explanation:
Vertical lines do not have a slope, unlike horizontal lines, which have a slope of 0
Explanation
Vertical lines have an “undefined slope”because the horizontal change on the x axis is 0 — and slope is y/x - you cannot divide a number by 0.
Find the lengths of the missing side. Round your answer to the nearest tenth
Answers
Answer:
13.2
Step-by-step explanation:
using the Pythagorean theorem:
L² = 20² - 5²
L² = 400 - 225 = 175
L = 13.23
a^2 + b^2 = c^2
a^2 + 15^2 = 20^2
a^2 + 225 = 400
a^2 = 175
a = 13.23
Help anyone?? Not that hardd
no links ! :(
Answers
Answer:
1.2
Step-by-step explanation:
First, you cancel out \(\frac{6}{20}\) to become \(\frac{3}{10}\)
Then that becomes \(-\frac{3}{10}+1.5\)
Now, you convert the element to a decimal form to be \(-0.3+1.5\)
Finally, you subtract them (because a negative plus a positive is subtraction) to get the final answer of 1.2
Hope this helps!
27 deliveries in 3 hours = ___ deliveries per hour
Answers
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
27÷3=9
(hope this helps can i plz have brainlist :D hehe)
Can somebody help ill give you brainliest!!! and 20 points
Answers
Answer:
Genotype: 100% rr
phenotype: 100% white
Step-by-step explanation:
since there are no dominant genes the cross will definitely be a rr genotype
can someone please help me
50 points
Answers
Answer:.
Step-by-step explanation im not sure
Answer:
Step-by-step explanation:
47.) sin20 = 6/b
b = 6(sin20) = 17.5
c = √6²+17.5² = 18.5
48.) tan61 = y/18
y = 18(tan61) = 32.5
z = √18²+32.5² = 37.1
49.) r = √25²+23² = 34
50). d = √30²+7² = 30.8
51.) sin71 = j/19
j = 19(sin71) = 18
k = √19²-18² = 6.2
52.) y = √4²-1² = √7 = 2.6
53.) sin49 = f/26
f = 26(sin49) = 19.6
h = √26²-19.6² = 17
54.) t = √7²+4² = 8.1
kinds of numeric number
Answers
OMG I NEED HELP BADLY RN
What are the coordinates of the point at H?
A.
(-3 , -3)
B.
(-3 , 3)
C.
(3 , 3)
D.
(3 , -3)
Answers
Answer:
B (-3,3)
Step-by-step explanation:
coordinates are x,y and h has -3x and 3y