Answer:
[tex]P(x)=x^3-5x^2+2x+8[/tex]
Step-by-step explanation:
If the polynomial has the following zeros: x= 4, x=2, and x=-1, then it must have the following factors which guarantee the polynomial will render zero at the given points:
[tex]P(x)=C (x-4)\, (x-2) \,(x+1)[/tex]
where C is any multiplicative constant. Since there is no other condition imposed on the polynomial, we can adopt a simple constant C = 1 to facilitate our final calculation of writing the polynomial in standard form:
[tex]P(x)=(x-4)\, (x-2) \,(x+1)\\P(x)=(x^2-2x-4x+8)\,(x+1)\\P(x)= (x^2-6x+8)\,(x+1)\\P(x)=x^3+x^2-6x^2-6x+8x+8\\P(x)=x^3-5x^2+2x+8[/tex]
f(x) = x + 2 g(x) = x – 4
(f g)(x) =
2x – 2
x2 – 8
x2 – 2x – 8
x2 + 2x – 8
Answer:
x² - 2x - 8
Step-by-step explanation:
The notation (f·g)(x) means to multiply the two functions. Use the distributive property to simplify.
(f·g)(x) = (x+2)(x-4) = x² + 2x - 4x - 8 = x² - 2x - 8
Give me brainliest please
Answer:
x² - 2x - 8
Step-by-step explanation:
multiply (x+2)(x-4) to get x² - 2x - 8
Write each statement as an algebraic expression. The quotient of the number that is 1 greater than a number b and the number that is twice as large as b. RMS NEED BY 3:58 today 6/20/2020
Answer:
Quotient = (1 + b)/2b
Step-by-step explanation:
The term quotient implies the result after dividing a number or expression by another number or expression.
In other words,
Quotient = Dividend/Divisor
From the question, we understand that
Dividend = Number that is 1 greater than a number b
So,
Dividend = 1 + b
And
Divisor = Number that is twice as large as b...
So, Divisor = 2 * b
Divisor = 2b
Recall that:
Quotient = Dividend / Divisor
Quotient = (1 + b)/2b
It is 3:00pm here, and Australia is 13 hours ahead of us. What time is it in Australia?
2:00 am
3:00 pm
4:00 am
5:00 am
Answer:
4 am
Step-by-step explanation:
Answer:
4:00 AM
Step-by-step explanation:
15:00 + 13:00
28:00
24:00+4:00
00:00+4:00
4:00 AM
The M virus has a diameter of 5 x 10^-7meters, while the P virus measures about 2 x 10^-8meters in diameter. A) is the M virus or P virus larger in diameter? B) how many times as larger is the larger virus than the smaller virus?
Answer:
(A) The M virus is larger than the P virus in diameter
(B) Diameter of virus M is 25 times the diameter of virus P
Step-by-step explanation:
Notice that the values given are in the so called "scientific notation", and which involves in this case negative exponents for the multiplier 10.
So we can write these values in decimal form for easier comparison of which one is he largest one:
Diameter of M virus = [tex]5\,*\,10^{-7}\,m = 0.0000005\,\,m[/tex]
Diameter of P virus = [tex]2\,*\,10^{-8}\,m = 0.00000002\,\,m[/tex]
Which clearly shows that virus M is larger than virus P in diameter
The quotient between diameters will give us the answer to how many times larger virus' M diameter is:
[tex]\frac{M}{P} =\frac{0.0000005}{0.00000002} \\\frac{M}{P} =25[/tex]
There are five more blue blocks than green blocks. Three times the number of green blocks, increased by double the number of blue, equals 95. How many of each colour are there?
Answer:
22 blue blocks
17 green blocks
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
There are five more blue blocks than green blocks.
So, the number of blue blocks (b) is equal to the number of green blocks (g) plus 5.
b = g+5Three times the number of green blocks (3g), increased by double the (+2b) number of blue, equals 95.
3g+2b =95The system is
b = g+5
3g+2b =95
Replacing b=g+5 in the second equation:
3g + 2 (g+5)=95
Solving for g:
3g +2g+10 =95
5g = 95-10
5g=85
g= 85/5
g= 17
Replacing g=17 in the first equation:
b = g+5
b = 17 +5
b=22
Trapezoid DEFG is dilated according to the rule
DO,4(x,y) to form the image trapezoid D'E'F'G', which is shown on the graph.
On a coordinate plane, trapezoid D prime E prime F prime G prime has points (negative 8, 8), (negative 3, 8), (negative 5, 4), and (negative 8, 4).
What are the coordinates of point G of the pre-image?
Answer: A. (-2,1)
Step-by-step explanation:
Just took the test! Hope this helps!
Answer:
It's A
Step-by-step explanation:
ABC is reflected over the y-axis. What are the vertices of
A' B' C' ?
A (0-2), B'(-2,-4). C'(-5, -1)
A(-2,0), B(-4, 2), C (-1, 5)
A' (0.2). B (-2,4), C'(-5,1)
A'(0, 2). B' (2, 4). C'(5.1)
Answer:
The answer is the first option.
Step-by-step explanation:
When you flip it over the y axis. A would still be the same. ANd the first one matches A.
Sharyn needs yards of fabric to make a dress for herself and yards of the same fabric to make a matching dress for her daughter. If she buys yards of fabric, how much will she have left over?
A.
yards
B.
yards
C.
yards
D.
of a yard
Answer: The answer is C 5/8 yards
Step-by-step explanation:
Which expression is equivalent to 10√5
Answer: square root of 500
Step-by-step explanation:
10 squared is 100
100 * the square root of 5 = the square root of 500.
What is the y-intercept of this quadratic function?
fin = -x^2 + 10x- 22
Answer:
- 22
Step-by-step explanation:
To find the y- intercept let x = 0 , that is
y = 0² + 10(0) - 22 = 0 + 0 - 22 = - 22 ← y- intercept
hi can anybody help me please i will mark them as a brainlest
Answer:
area 4.5
Step-by-step explanation:
C has the largest Area. It's area is 4.5
hope this helps
Answer:
C has the largest area.
Step-by-step explanation:
3x3=9, 9/2=4.5
What is the volume of the cone to the nearest tenth? A) 401.2 yd3 B) 421.4 yd3 C) 484.3 yd3 D) 536.2 yd3
Answer:
Option (D). 536.2 yd³
Step-by-step explanation:
Radius of the circular base of the cone = 8 yd
Height of the given cone = 8 yd
Formula for the volume of the cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here r = radius of the circular base of the cone
h = height of the cone
By substituting the values of r and h in the formula,
V = [tex]\frac{1}{3}\pi (8)^2\times (8)[/tex]
= [tex]\frac{1}{3}(512\pi )[/tex]
= 526.165
≈ 526.2 yd³
Therefore, volume of the given cone is 526.2 yd³.
Option (D) will be the answer.
Answer:
D
Step-by-step explanation:
Stephan has a piece of wood that measures 18 inches long and 12 inches wide. He wants to make a tray with sides 2 inches high. Maurice says that he can make a tray that has a base measuring 101/2 inches by 101/2 inches. Is he correct? Use the drop-down menus to explain your answer.
Answer:
He is wrong, because for 2 inches of height, the peice of wood for base has smaller width than the width required for the base Maurice wants to make.
Step-by-step explanation:
Length of wood = 18 inches
Width of wood = 12 inches
If height of the table is needed = 2 inches
2 inches are reduced from each side of the piece of wood.
The new measurement become:
Length of wood = 18 - 2 - 2 inches
Length of wood = 14 inches
Width of wood = 12 - 2 - 2
Width of wood = 8 inches
Maurice wants to make a table with following dimensions:
Base = [tex]10\frac{1}{2}\cdot10\frac{1}{2}[/tex]
which means
Length required = [tex]10\frac{1}{2} = \frac{21}{2}=10.5 inches[/tex]
Width required = [tex]10\frac{1}{2} = \frac{21}{2}=10.5 inches[/tex]
As width is greater than the width of the piece of wood , he cannot make a table of such dimension from it.
Combine the like terms to create an equivalent expression: -2k-(-5)+1
Answer:
-2k + 6
Step-by-step explanation:
-2k -(-5) + 1 -(-5) is also +5
-2k + 5 + 1 Combine like terms
-2k + 6
Answer:
-2k+6
Step-by-step explanation:
-2k-(-5)+1
-(-5)+1=6
-2k+6
Each question on a multiple-choice exam has four choices. One of the choices is the correct answer, worth 5 points, another choice is wrong but still carries partial credit of 1 point, and the other two choices are worth 0 points.
If a student picks answers at random, what is the expected value of his or her score for a problem?
_____points
If the exam has 30 questions, what is his or her expected score?
_____points
Answer:
1.5
45
Step-by-step explanation:
The probability for each answer is 1/4
(5+1+0+0)/4 = 6/4= 1.5Each question has an expected value of 1.5 points.
The expected score of the test is 30*1.5= 45 points
Question 4
A book sold 31,300 copies in its first month of release. Suppose this represents 9.9% of the number of copies sold to date. How many copies have been sold to date?
Answer:
313131 total books
Step By Step Explanation: We can use the equation 9.9%x=31000 and x represents the total number of books.
We could also convert this percent to a decimal by moving it two places to the left (0.99).
Nevertheless, we can divide both sides by 9.9% to find that the total number of books is 313131 books.
Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).
Answer:
three functions are
f(x) = 3(x + 4)^2 + 1
g(x) = 2x^2 - 16x + 15
h(x) = a(x - 1) - 3
Axis of symmetry for f(x) is x=-4 For g(x)
by taking the derivative
g'(x) = 4x - 16
= 4(x - 4)
The Axis of symmetry for g(x) is x=4
The Axis of symmetry for h(x) is x=1
hope it helps
pls answer i will mark as brainliest
If f(x) = 5x – 2 and g(x) = 2x + 1, find (f+g)(x).
O A. 3x-1
O B. 4x-3
O c. 7x-1
O D. 7x-3
SHUB
Help plzzz
Answer:
C
Step-by-step explanation:
(f + g)(x) = f(x) + g(x), thus
f(x) + g(x)
= 5x - 2 + 2x + 1 ← collect like terms
= 7x - 1 → C
Answer:
it is C.
Step-by-step explanation:
How do I do this?
Calculate the number of protons and the number of neutrons for each of the below
Answer:
to calculate the number of protons and neutrons, you can look at the element on the periodic table. the number of protons is equal to the atomic number of the element (for example, hydrogen is the first element on the periodic table, so it has 1 proton).
The number of neutrons is the mass number (listed on the periodic table as well) - the number of protons, aka the atomic number.
for example, for the element krypton, we take the mass number, 83.80, and round it up to 84. Then we subtract it's atomic number, 36, from it, to get 48, which is the number of neutrons in the atom
Homework Help please!
Answer:
7x4
28
Step-by-step explanation:
Answer:
The correct answer is D. 28 miles
Step-by-step explanation:
Because 7 miles in 2 hrs so in 8 hrs it will be 28 miles.
Hope it helps you !!!!What is the opposite of the number -2.5? How does the position of -2.5 compare to its opposite on the number line?
Answer:
-2.5 and 2.5 compare to eachother on the number line because they are the exact same distance away from 0.
Step-by-step explanation:
0 is in the very middle and to get -2.5 you go to the left 2.5 paces but to get to +2.5 you go to the right 2.5 paces. Either way you have to move Exactly 2.5 paces either to the left or right depending on if you want a positive or negative.
Four statistics professors and six chemistry professors are available to be advisors to a student organization. The student organization needs two of the professors to be advisors. If each professor has an equal chance of being selected, what is the probability that both professors are chemistry professors?
Step-by-step explanation:
Total professors = 10
Probability of chemistry professors = 2/6 = 1/3
If F(x) = log 5 2x, find F^-1(x). a. 5^y=2x b. 5^2y=x c. y = (5^x)/2
Answer:
y = [tex]\frac{5^{x} }{2}[/tex]
Step-by-step explanation:
y = log 5 2x
inverse ------> y=x
x = log 5 2y
[tex]5^{x} = 2y[/tex]
y = [tex]\frac{5^{x} }{2}[/tex]
Answer:
y = ([tex]5^{x}[/tex] )/2
Step-by-step explanation:
Hope This Helps!!
Use the values in the table to verify the relationship
between the functions representing the investments.
Which conclusion can be made?
O The functions are inverses because the domain of Table
A is the same as the range of Table B.
The functions are inverses because the range of Table A
is different from the domain of Table B.
the functions are not inverses because for each
ordered pair (x, y) for one function, there is no
corresponding ordered pair (x, y) for the other function.
O The functions are not inverses because for each
ordered pair (x, y) for one function, there is no
corresponding ordered pair (y, x) for the other function.
Answer:
The functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function.
Step-by-step explanation:
In the figure attached, the tables are shown.
For example, in table A the pair (1, 1051.21) is present, but the pair (1051.21, 1) is not present in Table B. Therefore, the functions are not inverses.
Answer:
The answer is D
Step-by-step explanation:
Happy Paws charges $19.00 plus $3.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $4.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours. help???????????//
Answer: 6.4 hours
Step-by-step explanation:
Hi, to answer this question we have to write an equation for each case:
Happy paws: the cost is equal to the fixed charge (19) plus the product of the charge per hour (3.50) and the number of hours (h).
Happy Paws Cost = 19+3.50h
Woof Watchers: the cost is equal to the fixed charge (11) plus the product of the charge per hour (4.75) and the number of hours (h).
Woof Watcher Cost = 11+ 4.75h
Since both costs must be equal:
Happy Paws Cost =Woof Watcher Cost
So:
19+3.50h = 11+ 4.75h
Solving for h:
19-11 = 4.75h-3.50h
8 = 1.25h
8/1.25 =h
h = 6.4 hours
Two distinct number cubes, one red and one blue, are rolled together. Each number cube has sides numbered 1 through 6.
What is the probability that the outcome of the roll is an odd sum or a sum that is a multiple of 5?
Enter your answer, in simplest fraction form, in the box.
Answer:
[tex]P(E_1 or E_2) = \frac{7}{12}[/tex]
Step-by-step explanation:
Given
Two cubes of side 1 - 6
Required
Probability that the outcome of the roll is an odd sum or a sum that is a multiple of 5
First, the sample space needs to be listed;
Let [tex]C_r[/tex] represent the Red cube
[tex]C_b[/tex] represent the Blue cube
S represent the sample space
[tex]C_r = (1,2,3,4,5,6)\\C_b = (1,2,3,4,5,6)\\S = (2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12)[/tex]S is gotten by getting the sum of [tex]C_r[/tex] and [tex]C_b[/tex]
[tex]n(S) = 36[/tex]
Calculating the Probability
Let [tex]E_1[/tex] represent the event that an outcome is an odd sum
[tex]E_1 = (3,5,7,3,5,7,5,7,9,5,7,9,7,9,11,7,9,11)[/tex]
[tex]n(E_1) = 18[/tex]
[tex]P(E_1) = \frac{n(E_1)}{n(S)}[/tex]
[tex]P(E_1) = \frac{18}{36}[/tex]
Let [tex]E_2[/tex] represent the event that an outcome is a multiple of 5
[tex]E_2 = (5,5,5,5,10,10,10)[/tex]
[tex]n(E_2) = 7[/tex]
[tex]P(E_2) = \frac{n(E_2)}{n(S)}[/tex]
[tex]P(E_2) = \frac{7}{36}[/tex]
Let [tex]E_3[/tex] represent the event that an outcome is an odd sum and a multiple of 5
[tex]E_3 = E_1 and E_2[/tex]
[tex]E_3 = (5,5,5,5)[/tex]
[tex]n(E_3) = 4[/tex]
[tex]P(E_3) = \frac{n(E_3)}{n(S)}[/tex]
[tex]P(E_3) = \frac{4}{36}[/tex]
Calculating [tex]P(E_1 or E_2)[/tex]
[tex]P(E_1 or E_2) = P(E_1) + P(E_2) - P(E_1 and E_2)[/tex]
[tex]P(E_1 or E_2) = P(E_1) + P(E_2) - P(E_3)[/tex]
[tex]P(E_1 or E_2) = \frac{18}{36} + \frac{7}{36} - \frac{4}{36}[/tex]
[tex]P(E_1 or E_2) = \frac{18 + 7 - 4}{36}[/tex]
[tex]P(E_1 or E_2) = \frac{21}{36}[/tex]
[tex]P(E_1 or E_2) = \frac{7}{12}[/tex]
Hence, the probability that the outcome of the roll is an odd sum or a sum that is a multiple of 5 is [tex]\frac{7}{12}[/tex]
Answer:
P=(E1 or E2) 7/12
Step-by-step explanation:
Find the midpoint of the line segment.
Answer:
(9,-5)
Step-by-step explanation:
Find the middle of each of the x and y coordinates. Then put that together.
Answer:
The correct answer is
(9, -5)
Find the middle of each of the x and y coordinates. Then you can plug in each x/y into a coordinate. This will get you the midpoint.
Hope I could help
- Quinn :)
If 1/x + 1/y = 1/4 and 1/x − 1/y = 3/4 , then x = ? PLEASE ANSWER ASAP!!! Thank you!!!!
Answer:
2
Step-by-step explanation:
1/x + 1/y = 1/4
1/x − 1/y = 3/4
add up side-by-side
2/x=4/4
2/x=1
x=2
somebody please help me
Answer:
382.5 square inches
Step-by-step explanation:
The surface area of a 3D object is the sum of the area of all of the surfaces. Therefore, the surface area of this prism is:
[tex]9\cdot 13.5 + 2(\dfrac{1}{2} \cdot 10\cdot 9)+ 9\cdot 9 + 10\cdot 9= 382.5[/tex] square inches.
Hope this helps!