Option A is the correct option. The polynomial correctly combines the like terms and expresses the given polynomial in standard form is,
f(m,n) = n⁶+7mn⁵+14m²n⁴-5m³n³-6m⁶-2m⁶
What is the polynomial equation?A polynomial equation is an equation in which the unknown variable is one and the highest power of the unknown variable is n. Here n can be any real number.
Given information-
The polynomial equation given in the problem is,
8mn⁵-2m⁶+5m²n⁴-m³n³+n⁶-4m⁶+9m²n⁴-mn⁵-4m³n³
Let the above polynomial is. Thus,
f(m,n) = 8mn⁵-2m⁶+5m²n⁴-m³n³+n⁶-4m⁶+9m²n⁴-mn⁵-4m³n³
The terms with the same base and exponents can be added or subtracted from each other. Thus solve the equation further as,
f(m,n) = ( 8mn⁵ - mn⁵ ) -2m⁶ + ( 5m²n⁴+9m²n⁴ ) - ( m³n³-4m³n³) + n⁶-4m⁶
f(m,n) = 7mn⁵ - 2m⁶ + 14 m²n⁴ - 5 m³n³ + n⁶- 6m⁶
Arrange it as,
f(m,n) = n⁶+7mn⁵+14m²n⁴-5m³n³-6m⁶-2m⁶
Thus the polynomial correctly combines the like terms and expresses the given polynomial in standard form is,
f(m,n) = n⁶+7mn⁵+14m²n⁴-5m³n³-6m⁶-2m⁶
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It is estimated that 75% of all young adults between the ages of 18 and 35 do not have a landline in their homes and only use a cell phone at home. What is the probability that everyone in a simple random sample of 100 young adults owns a landline
Using it's concept, it is found that the probability that everyone in a simple random sample of 100 young adults owns a landline is given by:
[tex]p = (0.25)^{100}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 25% of the adults own a landline, and the probabilities for each adult are independent, hence the probability that everyone in a simple random sample of 100 young adults owns a landline is given by:
[tex]p = (0.25)^{100}[/tex]
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Twelve toy turtles run a race. Each turtle is numbered from 1 to 13. A turtle can move forward one step whenever their number is rolled from the sum of two six- sided number cubes. Who do you think is most likely to win the race? Make an argument to justify your answer.
The turtle that would most likely win the race is the turtle 7
How to determine the turtle with the most chance?The turtles are given as:
Turtle = 1 to 13
When two dice are rolled and the sum of the outcomes are taken, the sample space is:
Outcome Frequency
2 1
3 2
4 3
5 4
6 5
7 6
8 5
9 4
10 3
11 2
12 1
The outcome 7 has the highest frequency of 6
This means that the turtle 7 has the highest chance of winning the race
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Elijah henson sold $1,576 worth of merchandise. his commission rate is 7 1/2%. what was his commission on the sales?
The commission on the sales will be $118.2.
What is the percentage?
The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
Elijah Henson sold $1,576 worth of merchandise. his commission rate is 7 1/2%
The commission amount will be:-
7.5 % of $1576 will be calculated as:-
Commission = 1576 x 0.075
Commission = $118.2
Therefore the commission on the sales will be $118.2.
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The distance from the top of the cone to the edge is 15 feet. The height of the cone is 6 feet. What is the radius of the cone? Round to the nearest tenth.
Answer: 13.7 ft
Step-by-step explanation:
Use Pythagorean theory to find radius
C^2 - B^2 = A^2
We know the hypotenuse (cone to edge) is 15
We will call that C
We know the height is 6
We will call that B
We are looking for A or radius
15^2 - 6^2 = A^2
225 - 36 = A^2
189 = A^2
Take square root of both sides
13.7 = A (radius)
I need help please I’m just trying to pass
Answer:
a
Step-by-step explanation:
Q5. An earthquake causes a sea wave. This sea wave travels 26 400 m in two minutes. Calculate the speed of the wave. Use the equation Q6. wave speed distance time speed =
Answer:
13.2 Kilometers an Minute, or 220 Kilometers an Hour
Step-by-step explanation:
26,400 divided by 2 = 13.2 (Minutes) Divided by 60 = 220 (Hours).
Which of the following could not be the value of sin(0)
The ratio of any side and hypotenuse is always less than 1.
The question seems incomplete
The options are not given the options are
a. 1
b. 0.5
c. 2
What is the sin ratio?[tex]sin\theta=\frac{Opposite side}{hypotenuse}[/tex]
Therefore, the ratio of any side and hypotenuse is always less than 1. Now, in the case of 0 or 90 degrees, the figure is no longer a triangle because one of the sides ceases to exist while the other side coincides with the hypotenuse.
This is the reason that in these extreme cases, sin and cosine take values 0 or 1.
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Choose the best description of an irregular polygon.
A. a polygon with unequal angles
B. a polygon with equal sides
C. a polygon with unequal sides and unequal angles
D. a polygon with unequal sides
Answer:
The answer is C
Step-by-step explanation:
Irregular polygons are polygons with unequal sides and angles.
Question 4 multiple choice answer for me
Answer:
B
Step-by-step explanation:
the symbol in the x < 0 has a line under it meaning it is a closed circle, and the other equation does not, so it is an open circle. And since the question has (or) in it, it means that the arrows should be facing away from eachother.
(b) Evan also has a bag of apples that weighs 3.545 pounds. The value of the digit 5 in the tenths place of 3.545 is how many times the value of the digit 5 in the thousandths place? Explain.
The value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
Evan has a bag of apples that weighs 3.545 pounds.
The value of the digit 5 in the tenths place of 3.545 is 0.500
The value of the digit 5 in the thousandths place of 3.545 is 0.005
Take the ratio of both values:
tenths place value/thousandths place value = 0.500/0.005
tenths place value/thousandths place value = 100
tenths place value = 100(thousandths place value)
Thus, the value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.
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Bill is also planning to buy a condo and he needs to finance $115,000. At which mortgage lender will Bill get the better deal? How much less will Bill pay with this lender?
The better deal based on the information is mortgage A as it's cheaper.
How to calculate the better deal?From the information given, the loan amount for mortgage A will be:
= 3% × $4500
= $135
The loan amount for mortgage B will be:
= 6% × $7500
= $450
From the information, the better deal is mortgage A.
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What is the quotient? startfraction 3 y 2 over 3 y endfraction divided by startfraction 6 y squared 4 y over 3 y 2 endfraction
The quotient of the expression [tex]\frac{3y+2}{3y} divided \frac{6y^{2} + 4y}{3y + 2}[/tex] is 3y + 2 / 6y
How to find quotient of an expression?
The quotient of the expression can be found as follows:
3y + 2 / 3y ÷ 6y² + 4y / 3y + 2
Therefore,
3y + 2 / 3y × 3y + 2 / 6y² + 4y
Hence,
3y + 2 / 3y × 3y + 2 / 2y(3y + 2)
Therefore,
1 / 3y × 3y + 2 / 2
Hence,
3y + 2 / 2(3y)
3y + 2 / 6y
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PLEASE HELP I'LL GIVE YOU 50 POINTS Explain how you would find the area of the shape below. HELP PLEASEE
Answer:
You count the cat's ears as the area of a right triangle, the middle as the area of a rectangle, and the cat's chin as the area of a semi-ellipse.
Sally won 40 super bouncy balls playing horseshoes at her school's game night. Later, she gave two to each of her friends. She only has 8 remaining. How many friends does she have?
Answer: Sally has 16 friends
Step-by-step explanation:
she has 40 balls
subtract by how many she gave away
40-8=32
she gave 2 to each friend
divide the balls left by 2
32/2=16
Sally has 16 friends
Write down the reciprocal of 2
If f (x) = 3x²-x, find f (-2).
Answer:
f(-2) = 14
Step-by-step explanation:
put -2 where x is
f(x) = 3x²-x
f(-2) = 3(-2)²-(-2)
f(-2) = 3(4)+2
f(-2) = 12+2
f(-2) = 14
Find the slope of the line through the given points: (-19, 5), (19, 15)
Answer:
Step-by-step explanation:
(15 - 5)/(19 + 19)= 10/38= 5/19 is the slope
y - 5 = 5/19(x + 19)
y - 5 = 5/19x + 5
y = 5/19x + 10
4. What are the coefficients in the polynomial 7x² - 4x + 6? (1 poin
O-7,4
07, 4, -6
07,-4, 6
07,-4
Add or subtract.
Answer:
D.) 7 and -4
Step-by-step explanation:
Coefficients are numbers placed directly before a variable.
(7) is a coefficient because it is placed before x².
(-4) is a coefficient because it is placed before x. The negative is included.
(6) is not a coefficient because it is not altering any variable through multiplication/division.
**URGENT PLEASE HELP SOON** Each brick in the wall has the dimensions shown below. A rectangular prism with a length of 8 inches, width of 4 inches, and height of 2.25 inches. What is the volume of each brick?
Options:
56 in^3
72 in^3
118 in^3
144 in^3
The volume of each individual brick is 72 cubic inches.
How to get the volume of each brick?
The volume of a rectangular prism of height H, width W, and length L is given by:
V = L*H*W
In this case we have:
L = 8inW = 4inH = 2.25 inThen, replacing these in the volume equation, we get:
V = (8 in)*(4 in)*(2.25 in) = 72in³
So the correct option is the second one.
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Answer:
The volume of each individual brick is 72 cubic inches.
Step-by-step explanation:
How to get the volume of each brick?
The volume of a rectangular prism of height H, width W, and length L is given by:
V = L*H*W
In this case we have:
L = 8in
W = 4in
H = 2.25 in
Then, replacing these in the volume equation, we get:
V = (8 in)*(4 in)*(2.25 in) = 72in³
So the correct option is the second one.
what is the slope of the line graphed
Answer: undefined
Step-by-step explanation:
The slope of a vertical line is undefined because there is no rise/run and the slope formula would give you something over 0, which is undefined
Answer:
undefined
Step-by-step explanation:
the slope of the line graphed (a vertical line) is undefined.
No matter how large we set out slope, we will never reach a vertical slope. As we approach infinity, we will get closer, and closer, but we can never fully have a slope of a vertical line.
A slope of 1 means that we move up 1, over 1. A slope of 2 means that we move up 2, over 1. Even if we move up 5000, we still move over at least slightly (with a slope).
It is undefined because it does not run horizontally.
Question 18
A wholesale grocery supplier shipped x2-pound blocks of cheese and y3-pound blocks of cheese to a caterer. The total weight of the cheese in the shipment was 44 pounds, and
the shipment consisted of 18 blocks of cheese. Which of the following systems of linear equations best represents this situation?
z+y=18
A
3z +2y=44
z+y=18
2x + 3y = 44
z+y=44
3z + 2y = 18
z+y=44
2z+3y=18
B
C
D
Imported (1)
The G
The system of linear equations that best represents the situation are:
z+y=18
3z +2y=44
What are the linear equations?In order to determine the values of the two types of cheese, two set of linear equations can be formed from the question. The equations have to be solved together using either the elimination , substitution or graphical methods.
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Solve the following system of equations. Show all work and solutions.
y = 2x^2 + 6x + 1
y = −4x^2 + 1
Answer: (0, 1), (-1, -3)
Given two equation's:
y = 2x² + 6x + 1y = −4x² + 1Solve them simultaneously:
[tex]\sf 2x^2 + 6x + 1 = -4x^2 + 1[/tex]
[tex]\sf 2x^2 + 4x^2 = 1 - 1[/tex]
[tex]\sf 6x^2 + 6x = 0[/tex]
[tex]\sf 6x(x + 1) = 0[/tex]
[tex]\sf 6x = 0, \ x + 1 = 0[/tex]
[tex]\sf x = 0, \ x = -1[/tex]
(a) When x = 0, y = −4(0)² + 1 = 1
(b) When x = -1, y = -4(-1)² + 1 = -3
Solution: (x, y) → (0, 1), (-1, -3)
Answer:
System of equations
[tex]\large \begin{cases}y=2x^2+6x+1\\y = -4x^2+1\end{cases}[/tex]
To solve the given system of equations, use the substitution method:
[tex]\large\begin{aligned}2x^2+6x+1 & = -4x^2+1\\2x^2+6x+1+4x^2-1 & = 0\\6x^2+6x & = 0 \\6x(x+1) & = 0\\\implies x+1 & = 0 \implies x=-1\\\implies 6x & = 0 \implies x=0\end{aligned}[/tex]
Therefore the x-values of the solutions are:
[tex]\large \begin{aligned}x & =-1\\x & =0\end{aligned}[/tex]
Substitute the found values of x into the second equation to find the y-values:
[tex]\large \begin{aligned}x & =-1 & \implies &-4(-1)^2+1 =-3 & \implies & (-1,-3)\\x & =0 & \implies & -4(0)^2+1 =1 & \implies & (0,1)\end{aligned}[/tex]
Therefore, the solutions of the system of equations are:
(-1, -3) and (0, 1)
2. Mikaela counted 2 more turtle nests
on a North Carolina beach than
Diego. If Mikaela counted 38 turtle
nests, which equation could you use
to find the number of turtle nests
Diego counted?
A 2x = 38
B x÷2=38
C x - 2 = 38
D x + 2 = 38
Find the value of x so the line that passes through the pair of points has the given slope.
(x, 4) (-3, 8), m = undefined
Answer:
x = - 3
Step-by-step explanation:
using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (x, 4 ) and (x₂, y₂ ) = (- 3, 8 )
m = [tex]\frac{8-4}{-3-x}[/tex]
since m is undefined, then the denominator must be zero, since division by zero is undefined , then equating the denominator to zero
- 3 - x = 0 ( add 3 to both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
What is the volume of a cone with base diameter 14 and height 16?
Answer:
Your answer is 3282.34
Step-by-step explanation:
1/3 x 3.14 x 14 ^2 x 16
this is all you have to do really.
find the distance between the points (-5.4,-9.5) and (-5.4, -5.5)
Answer:
4 units
Step-by-step explanation:
formula
d = √(x2-x1)^2 + (y2-y1)^2
then fill in the spots
d = √(-5.4+5.4)^2 + (-5.5+9.5)^2
the subtraction sign became an addition sign due to it being a double negative
Hope this helped
If a shape has four sides, then it is a quadrilateral. A square has four sides. (It is asking What is a logical conclusion from the given statements)
A. Therefor, a square is a polygon
B. Therefor, a square is a quadrilateral
C. Therefor, a square has four sides
D. Therefor, a square is a parallelogram
Answer:
B: A square is a quadrilateral
Step-by-step explanation:
What is the slope of the line with this equation y = 7x - 3 ? Explain.
Answer:
7
Step-by-step explanation:
y=mx+bm=pendiente
por lo tanto:
pendiente=7
Hii!
__________________________________________________________
Answer:
Slope = 7! ^^
Step-by-step explanation:
Note that the equation is given to us in slope intercept form.
The slope intercept formula is y=mx+c.
m denotes the slope
c denotes the y intercept.
/--------------\
The slope of the line that we are working with is 7.
Remember how I said that the slope of the line y=mx+c is m?
Similarly, the slope of the line y=7x-3 is 7! ^^
--
Hope that this helped! Best wishes.
--
what is the length of AB?
choices:
6 units
14 units
10 units
12 units
Answer:
[tex]\huge\boxed{\sf |AB|=10 \ units}[/tex]
Step-by-step explanation:
Coordinate of A = [tex](x_1,y_1)[/tex] = (-7,-6)
Coordinate of B = [tex](x_2,y_2)[/tex] = (1,0)
We will use distance formula to find the length of AB.
Length of AB:[tex]|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\|AB|=\sqrt{(1-(-7))^2+(0-(-6))^2} \\\\|AB|=\sqrt{(1+7)^2+(6)^2} \\\\|AB|=\sqrt{(8)^2+36} \\\\|AB|=\sqrt{64+36} \\\\|AB|=\sqrt{100} \\\\\boxed{|AB|=10 \ units}\\\\\rule[225]{225}{2}[/tex]
use your graphing calculator to find the equation of the trend line for the scatterplot below. x y 1 18 2 20 3 24 4 30 5 28 6 33
The equation for the scatter plot will be,y=3x+15. Scatter plots are essential for determining relationships, if any, between the values of observable quantities or occurrences.
What is a scatter plot?A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they may demonstrate the degree of connection,
if any, between the values of observed quantities or events, scatter plots are crucial in statistics.
The equation of the trend line for the scatterplot below will be y=3x+15.
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