If x + 1 and x-1 ghe factors of f (x) = x ^ 3 + 2ax + b calculate the valves of a and b. using theses values of and by factorise f(x) completely.
Since both x + 1 and x - 1 are factors of f(x), we have the factorization
x³ + 2ax + b = (x + 1) (x - 1) (x - b)
where the last root must be x = b in order that b is the constant term in the cubic.
Expanding the right side and equating coefficients gives
x³ + 2ax + b = x³ - bx² - x + b
which tells us
-b = 0 ⇒ b = 0
2a = -1 ⇒ a = -1/2
Then we have
f(x) = x³ + 2 (-1/2) x + b = x³ - x
or
f(x) = x (x + 1) (x - 1)
Where does the energy stored in coal originally come from?
A. The Earth's Core
B. Minerals
C. The Sun
D. Radioactive material in the crust
Answer: The Sun
Step-by-step explanation:
Energy has existed from the beginning of time. The sun was the initial source of energy, providing heat and light during the day. People used light to wake up and sleep, depended on wood and dung for heat, and water power to run primitive mills.
Find the missing angle
Answer:
36 degrees
Step-by-step explanation:
We do bottom triangle first:
33+90=123. 180-123=57
Go to upper tri: 90-57=33
111+33=144. 180-144=36.
?=36 degrees
Hope it helps
Find the slope easy giving brainlest
Answer:
Problem 20: [tex]m[/tex] = [tex]2[/tex]
Problem 21: [tex]m[/tex] = [tex]-2[/tex]
Problem 22: [tex]m[/tex] = [tex]1[/tex]
Problem 23: [tex]m[/tex] = [tex]3[/tex]
Step-by-step explanation:
The formula to find the slope of a line: [tex]m = \frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex].
Problem 20:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{3-7}{2-4}[/tex]
[tex]m[/tex] = [tex]\frac{-4}{-2}[/tex]
[tex]m[/tex] = [tex]2[/tex]
Problem 21:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{-5-1}{2--1}[/tex]
[tex]m[/tex] = [tex]\frac{-6}{3}[/tex]
[tex]m[/tex] = [tex]-2[/tex]
Problem 22:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{3-7}{-6--2}[/tex]
[tex]m[/tex] = [tex]\frac{-4}{-4}[/tex]
[tex]m[/tex] = [tex]1[/tex]
Problem 23:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{-4-2}{-4--2}[/tex]
[tex]m[/tex] = [tex]\frac{-6}{-2}[/tex]
[tex]m[/tex] = [tex]3[/tex]
*Extra*: The equation of a line is written in this form: [tex]y = mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is [tex]y[/tex]-intercept
Find the surface area and volume of the figure.
Step-by-step explanation:
this is again a combined object.
at the bottom there is a cylinder.
and on top there is half of a sphere (I assume it is a sphere, because there is no additional information about its height, and we could therefore not solve this otherwise).
for the total volume we need to calculate both volumes and add these results.
for the total surface area we need to calculate both surface areas, but remove the top surface area of the cylinder, because the half-sphere is covering it.
so, let's start with the volume :
the volume is a cylinder is
ground area × height = pi×r² × height
the radius is half of the diameter, so, r = 18/2 = 9 ft.
in our case that gives us
pi×9² × 10 = pi×81 × 10 = 810×pi = 2,544.690049... ft³ ≈
≈ 2,544.7 ft³
the volume of a sphere is
pi×r³ × 4/3
and of a half-sphere therefore
pi×r³ × 4/3 / 2 = pi×r³ × 2/3 = pi×9³ × 2/3 = pi×9² × 2 =
= pi×81 × 2 = 162×pi = 508.9380099... ft³
≈ 508.9 ft³
the total volume is then
3,053.628059... ft³ ≈ 3,053.6 ft³
the surface area :
the surface area of a cylinder is
the areas of the circles on the top and the bottom (but here we need only the bottom) plus the area of the lateral side area, the "mantle", which is the circumference of the basic circle times height.
so, in our case we get
pi×r² + 2×pi×r×height
pi×9² + 2×pi×9×10 = 81pi + 180pi = 261pi =
= 819.9556826... ft² ≈ 820 ft²
the surface area of a sphere is
4×pi×r²
and therefore if a half-sphere
4×pi×r² / 2 = 2×pi×r²
in our case
2×pi×9² = 2×pi×81 = 162pi = 508.9380099... ft²
≈ 508.9 ft²
the total surface area is then
1,328.893692... ft² ≈ 1,328.9 ft²
Which of the triangles shown are obtuse triangles?
A group of triangles. Triangle A has three equal angles. Triangle B has two acute angles and one obtuse angle. Triangle C has two acute angles and one ninety degree angle. Triangle d has two acute angles and one obtuse angle.
Group of answer choices
Triangle A and Triangle B
Triangle B and Triangle D
Answer:
BD
Step-by-step explanation:
Hello Please Find The Answer To This Question (easy)
Answer:
y=-2x-4
Step-by-step explanation:
by using this website
its a graphing calculator
desmos. com/calculator
In a random sample of 2500 sports fans, 61% prefer basketball over soccer.
What is the Margin of error in this survey?
Margin of error = [m]%
The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The Margin of error in this survey is 1%.
What is the margin of error?The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.
The random sample of 2500 sports fans, out of which 61% prefer basketball over soccer, therefore, we can write n=2500 and p=0.61. Thus, the margin of error can be written as,
[tex]MOE=\sqrt{\dfrac{\hat p(1-\hat p)}{n}} = \sqrt{\dfrac{0.61(1-0.61)}{2500}} = 0.00975 = 0.975\% \approx 1\%[/tex]
Hence, the Margin of error in this survey is 1%.
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Surface area of cubes and rectangular prisms
Answer:
130 square yards
Step-by-step explanation:
5 x 4 = 20
5 x 5 = 25
20 x 4 = 80
25 x 2 = 50
80 + 50 = 130
The surface area for this cube and rectangular prisms is 75 cubic square inches.
How do you find the surface area of a square and rectangular prism
Surface area of a prism is the sum of the area of the 2 polygonal bases and the area of the lateral faces. The surface area of a prism is measured in terms of square units. The Surface Area of a Prism Formula is given as, Surface Area Of A Rectangular Prism is A = 2 (wl + lh + hw)
B x W x HSo [tex]5[/tex] · [tex]4[/tex] · [tex]5=75[/tex] [tex]cubic[/tex] [tex]inches[/tex]
Therefore, The surface area for this cube and rectangular prisms is 75 cubic square inches.
b) f(x) = 3 |x – 41| + 5
Domain:
Range:
write the decimal equivalent for this fraction 7/100
Answer:
0.07
Step-by-step explanation:
To convert from fractions into decimals, you have to divide the numerator by the denominator. The numerator is the number on top of the fraction, and the denominator is the number on the bottom of the fraction.
7/100 = 0.07
Please mark brainliest!
write a event that has a probability of 1
A probability of 1 means that the event will happen. If the probability of a road traffic accident was 1 there would be nothing you could do to stop it.
that's my answer
which graph represents y=3x-5
Answer:
(it won't let me paste a graph here)
(but it a / line on the graph.)
Step-by-step explanation:
Use Desmos Graphic Calculator, plot this equation in and it should show up a graph of that. : )
how many solutions does the following have? 3 (2x-4) = 2 (3x-6)
Answer: There are infinite solutions.
Step-by-step explanation:
3(2x-4) = 2(3x-6)
6x - 12 = 6x - 12
-12 = -12
0 = 0
Marcus is rolling a number cube will show 10 is?
Answer:
no
Step-by-step explanation:
The cube has only 6 sides,
so it has only 6 numbers : 1, 2, 3, 4, 5 & 6.
The histogram below represents the high tempatures recorded each day over a one month period. How many days had a tempature below 60
Answer: 22
Step-by-step explanation:
Please help so lost, it is not making any sense
????????
Step-by-step explanation:
1,1,1
could i have some quick quick help?
Turn over into vertex form
y=-30t²+450t-790y=-30(t²-15x+79/3)Solving
y=-30[(t-15/2)²-359/12]Open brackets
y=-30(t-15/2)²+1795/2Accurating
y=-30(t-7.5)²+897..5Compare to Vertex form y=a(x-h)²+k
Vertex
(h,k)=7.5,897.5Max profit is $897.5
ticket price should be $7.5Answer:
$7.50
Step-by-step explanation:
Completing the square formula
[tex]\begin{aligned}y & =ax^2+bx+c\\& =a\left(x^2+\dfrac{b}{a}x\right)+c\\\\& =a\left(x^2+\dfrac{b}{a}x+\left(\dfrac{b}{2a}\right)^2\right)+c-a\left(\dfrac{b}{2a}\right)^2\\\\& =a\left(x-\left(-\dfrac{b}{2a}\right)\right)^2+c-\dfrac{b^2}{4a}\end{aligned}[/tex]
[tex]\begin{aligned}P & =-30t^2+450t-790\\& =-30\left(t^2+\dfrac{450}{-30}t\right)-790\\\\& =-30\left(t^2+\dfrac{450}{-30}t+\left(\dfrac{450}{2(-30)}\right)^2\right)-790-(-30)\left(\dfrac{450}{2(-30)}\right)^2\\\\& =-30\left(t-\left(-\dfrac{450}{2(-30)}\right)\right)^2-790-\dfrac{450^2}{4(-30)}\\\\& =-30(t-7.5)^2+897.5\end{aligned}[/tex]
Therefore, the vertex is (7.5, 897.5)
So the ticket price that maximizes daily profit is the x-value of the vertex: $7.50
A car's speed is 80 2/3 miles in one hour. Going at the same speed, how far (in miles) will it travel in 2 1/4 hours?
Answer:
181.5 miles
Step-by-step explanation:
80 2/3 m/hr * 2 1/4 hr = 181. 5 miles
I need some help with this question.
Answer:
I believe it would be C
Step-by-step explanation:
71+36=107
180-107=73
it don't make sense for it to be right because none of the angles are 90°
In how many ways can a teacher arrange 5 students in the front row of a classroom if there are 20 students in the class
Answer:
4 times
Step-by-step explanation:
because there's only enough space for that many in each row.
3. Seth uses a bowl to fill a container with soil. The
bowl holds 3/4 cup of soil. How many cups of soil
does the container hold if it takes 13 full bowls of soil
to fill it?
I need help with this
Answer:
Step-by-step explanation:
Remark
The longer the line, the larger the arc is. So
How to put in order.
It can be shown that the angle opposite the chord is related to the arc length by α = arc length / r Since r never changes, you are left with
α = k * chord length.
So what you conclude is that the larger the angle, the larger the arc length.
The largest angle is Q so the length of the arc opposite Q is the largest. The other two lines are handled the same way.
Answer:
Arc length PR is the largest.Arc Length PQ is the second largest.Arc Length RQ is the Smallest.Which sport is required to have both male and female competitors ?
A. Hockey
B. Water polo
C. Mixed doubles tennis
D. Swimming
Answer:
Mixed Doubles Tennis
Step-by-step explanation:
The key word is "mixed." In this case it means a male and female competitor
answer these questions and show working out.
(extra points for all)
Answer:
See below
Step-by-step explanation:
We can find the Highest Common Factor (HCF) by the prime factorization of the terms.
===============================================================
a) 4 and 5
⇒ 4 = 4 x 1
⇒ 5 = 5 x 1
⇒ HCF (4, 5) = 1
=============================================================
b) 8 and 13
⇒ 8 = 2 x 2 x 2 x 1
⇒ 13 = 13 x 1
⇒ HCF (8, 13) = 1
=============================================================
i) 80 and 120
⇒ 80 = 40 x 2
⇒ 120 = 40 x 3
⇒ HCF (80, 120) = 40
Select all the correct answers.
Which four inequalities can be used to find the solution to this absolute value inequality?
Answer:Which four inequalities can be used to find the solution to this absolute value inequality?3+2|x-11 <9
2(x - 1) <-3
x-1 <9
X-1 >-9
-2(x - 1) > 3
x-1-3
X-1 <3
Step-by-step explanation:
There is no document, so nobody could answer.
The graph of Fx), shown below, resembles the graph of G(x) = x, but it has
been changed somewhat. Which of the following could be the equation of
Fx)?
5
GO) = x2
5
FOO = ?
+
O A. F(x) = -x2 - 4
O B. FX) = x2 - 4
O C. Fx) = -(x - 4)2
O D. Fx) = -(x+4)2
Using translation concepts, it is found that the equation of F(x) could be given by:
A. F(x) = -x² - 4.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function g(x) = x² was reflected over the x-axis and shifted 4 units down, hence f(x) is given by:
A. F(x) = -x² - 4.
More can be learned about translation concepts at https://brainly.com/question/4521517
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Juan has 22 balloons and each balloon can hold up to 8.23 ounces of water. How much water would he use if he filled all the balloons completely?
Answer:
181.06
Step-by-step explanation:
Which scale you would use on the coordinate plane to plot each set of points? A Select . (1.-6).(-7,-8), (-3, 7), (0.9) • (-20, -30).(-40, 10), (20, -10), 5. -20) Select] Select) •,( (-3,-1), (§. -13), 3, 3), (1,0
Answer:qjs
Step-by-step explanation:
A
X= -7 to 1
Y= -8 to 9
B
X= -40 to 20
Y= -30 to 10
Sarah makes home-made jewelry sets. Each jewelry set includes a necklace, a bracelet and two earrings. Given below are the number of beads Sarah adds to each type of jewelry.
Necklace: 48
Bracelet: 19
Earrings: 6 (both earrings combined)
What is the largest number of jewelry sets she can make with 7100 beads?
Based on the number of beads that are needed to make a jewelry set, the largest number of jewelry sets that Sarah can make with 7,100 beads is 97 jewelry sets.
What amount of jewelry sets can Sarah make?First find the total number of beads used per jewelry set:
= Necklace + Bracelet + Earrings
= 48 + 19 + 6
= 73 beads
If she had 7,100 beads, the sets she could make would be:
= Total number of beads / Beads per set
= 7,100 / 73
= 97 jewelry sets
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