find the difference by subtracting the polynomial 4a³+6a²-11a-3 from the polynomial 2a³-4a²-6a+1.
The difference after the subtraction is: 2a³ + 10a² - 5a - 4
What is a polynomial equation?A polynomial is an expression which has one or more of its variables with a power of at least 2 degrees. It can be expressed in form of a term.
Therefore, a polynomial equation is a means of expressing an expression with terms and on variable with a degree of 2 or more.
To find the difference by subtracting the polynomials, we have:
4a³ + 6a² - 11a - 3 - (2a³ - 4a² - 6a + 1) = 4a³ + 6a² - 11a - 3 - 2a³ + 4a² + 6a - 1
collecting like terms,
4a³ - 2a³ + 6a² + 4a² - 11a + 6a - 3 - 1 = 2a³ + 10a² - 5a - 4
Therefore, the difference by subtracting the two polynomials is:
2a³ + 10a² - 5a - 4
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Parker bought 4 times as many marbles as Molly. Cole bought 5 fewer marbles than Parker. If Molly bought p marbles, how many marbles did cole buy. Wouldn’t be 4p-5? If so, why? , and how do you solve it?
Answer:
Kinda Hard to explain hope this helps
Step-by-step explanation:
Lets say molly is 6 and parker bought 4 times as many then he bought 24 marbles.Then cole bought 5 fewer then parker so 24-5=19
the equation is 4(6)m=p(24) Cole p(24)-5=Cole
M=6
what is the surface area formula for half cylinder
Step-by-step explanation:
the surface area of a half-cylinder is, surprise, surprise, half of the surface area of a whole cylinder ...
the surface area of a cylinder is
A=2×pi×r×h + 2×pi×r²
r being the radius, h being the height of the cylinder.
the formula simply adds
the sidewall area (which is a rectangle of
circle circumference × height)
+
the top and base circle areas
half of this area calculation for a half-cylinder is
A/2 = pi×r×h + pi×r²
Each of 36 students at a school play bought either a cup of orange juice or a sandwich. A cup of orange juice costs $1 and a sandwich costs $3. The total amount collected was $76. How many students bought orange juice, and how many bought a sandwich?
Let x represent the number of students who bought a cup of orange juice and y represents the number of students who bought a sandwich. Then the problem can be represented by this system of equations:
x + 3y = 76
x + y = 36
Answer the questions to solve the problem.
1. Explain what you should do with the two equations to eliminate one of the variables. (2 points)
4. Interpret the solution and check the values in the system. (3 points)
1). To eliminate variable x,
we subtract the equation 2 to equation 1
And 2). The solution of the system is x = 16 and y = 20.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Each of 36 students at a school play bought either a cup of orange juice or a sandwich.
A cup of orange juice costs $1 and a sandwich costs $3.
The total amount collected was $76.
Let x represent the number of students who bought a cup of orange juice and y represents the number of students who bought a sandwich.
Then the problem can be represented by this system of equations:
x + 3y = 76 {equation 1}
x + y = 36 {equation 2}
1). To eliminate variable x,
we subtract the equation 2 to equation 1,
2y = 40
y = 20.
And x = 16.
2). The solution of the system is x = 16 and y = 20.
To check the solution, substituting the values to the equation 2,
16 + 20 = 36
36 = 36
Therefore, all the required values are given above.
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1/5 x -2 = 4 help pls
Answer:6/5 or 1 1/5
Step-by-step explanation:
1. Add 2 on each side
2. Then divide 1/5 and 6
Answer:
X = 30
Step-by-step explanation:
Add 2 on both sides, cancelling the -2. Divide 1/5 by 6 (4+2) and you'll get 30
9511961
4. Analyze and Persevere What is the
measurement of the longest line segment
in a right rectangular prism that is
4.8 inches long, 1.4 inches wide, and
8 inches tall? Round to the nearest tenth of
an inch.
9.43 inches is the measure of the longest segment
How to solve for the longest segment
We are aware that the diagonal connecting the two opposing corners at the top and bottom will be the longest segment.
We know how to find the diagonal of a right triangular prism using the following formula:
d = [tex]\sqrt{w^2 + l^2+h^2} \\\\[/tex]
where w = width = 1.4
l = length = 4.8
h = height = 8
We would put these values in the formula above
[tex]d = \sqrt{1.4^2 + 4.8^2+8^2} \\\\[/tex]
d = [tex]\sqrt{1.96+23.04+64}[/tex]
d = 9.43
The measure of the longest line segment is given as 9.43 inches
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SEND HELP PLS IM BEGGING YIU
Answer:
B
Step-by-step explanation:
Because all four packages of baseball cards added up together makes 76 cards, and since 6 is over 5 that makes it closer to 80.
Answer: 1st Package: 17 = 20
2nd Package: 21 = 20
3rd Package: 22 = 20
4th Package: 16 = 20
Total Amount of Cards: 20 + 20 + 20 + 20 = 80
I hope this helps! :)
Step-by-step explanation:
Triangle ABC is being enlarged using a scale factor of 2 and the origin as the centre to give triangle A'B'C'. Work out the coordinates of A' and B'. -10-9-8-7-6-5- 3- RE 2+ ¹C B .... 0 1-2-3-4-5-6-7-8 11 21 -3- 4 +5+ 6- -7- -8- -9- -10+
Answer:
Triangle ABC is being enlarged using a scale factor of 2 and the origin as the center to give triangle A'B'C'. To find the coordinates of A' and B', we will have to multiply each of the x and y coordinates of A and B by the scale factor of 2.
The coordinates of A are (-5, -6) and the coordinates of B are (2, 3)
The coordinates of A' will be (-52, -62) = (-10, -12)
The coordinates of B' will be (22, 32) = (4, 6)
So the coordinates of A' are (-10, -12) and the coordinates of B' are (4, 6).
Identify the linear function I’ll give brainliest
Answer:
A
Step-by-step explanation:
Any equation with a single independant variable (often an 'X') that is not ( x2,x3 ) is linear.
A
Which of the following is equivalent to
3^sqrt32x³y^6/ 3^ sqrt 2x^9 y^2
If the expression be [tex]$\frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}$[/tex] then the equivalent expression exists [tex]$\frac{\sqrt[3]{16 y^4}}{\sqrt[3]{x^6}}$$[/tex].
What is meant by expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.
Expression is a term used in mathematics to describe a grouping of numbers, variables, and operators that illustrates the value of something. A mathematical statement that has two expressions that are equal is known as an equation. A phrase fragment can be used as an expression to represent a single numerical value.
An expression in mathematics is a sentence made up of terms and operations. Terms may be variables with coefficients or constant (numeric) values. Addition, subtraction, multiplication, and division are all possible operations.
Let the given expression be [tex]$\frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}$$[/tex]
Apply radical rule: [tex]$\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}, \quad$[/tex] assuming [tex]$a \geq 0, b \geq 0$[/tex]
[tex]$$\begin{aligned}& \frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}=\sqrt[3]{\frac{32 x^3 y^6}{2 x^9 y^2}} \\& =\sqrt[3]{\frac{32 x^3 y^6}{2 x^9 y^2}}\end{aligned}$$[/tex]
simplifying the above equation, we get
[tex]$\frac{32 x^3 y^6}{2 x^9 y^2}: \frac{16 y^4}{x^6}$[/tex]
[tex]$=\sqrt[3]{\frac{16 y^4}{x^6}}$$[/tex]
Apply radical rule: [tex]$\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}, \quad$[/tex] assuming [tex]$a \geq 0, b \geq 0$[/tex]
[tex]$=\frac{\sqrt[3]{16 y^4}}{\sqrt[3]{x^6}}$$[/tex]
Therefore, the correct answer is option c.
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Answer:
option c
Step-by-step explanation:
edge 2023
The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 2974 employees at the company and wants to
conduct a systematic sample of size 30.
what is k?
Answer:ugy8f67
Step-by-step explanation: yessss
Write the area for the figure below by using distributive property.
The area for the given figure by using distributive property is 5y+35.
What is Area of rectangle?
Area of rectangle can be defined as the product of length and breadth .
From the Given figure,
We have to find the area of rectangle
so,
There is one small rectangle inside that,
So,
total area = area of small rectangle + area of larger rectangle
area = 5*y + 7*5
So by summing up the area of two rectangles
we get,
Total area = 5y+ 35
Therefore, The area for the given figure by using distributive property is 5y+35.
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ten slips of paper, numbered 1 through 10, are placed in a bag. if three slips are chosen at random from the bag without replacement and one of the slips chosen is numbered 7, what is the sum of numbers on the three chosen slips of paper? (1) the sum of two of the numbers chosen is 16. (2) the sum of two of the numbers chosen is 14.
The sum of the numbers on the three chosen slips of paper is either 21 or 23 in both the given cases.
We are given that one of the slips chosen is numbered 7, so the only possible sums of the remaining two slips are:
16 = 7 + 9
14 = 7 + 7
In the statement (1), the sum of two of the numbers chosen is 16, which means that the remaining two slips are 7 and 9. So the sum of the numbers on the three chosen slips of paper is 7 + 9 + 7 = 23.
In the statement (2), the sum of two of the numbers chosen is 14, which means that the remaining two slips are 7 and 7. So the sum of the numbers on the three chosen slips of paper is 7 + 7 + 7 = 21.
Hence, we get that in both cases, the sum of the numbers on the three chosen slips of paper is either 21 or 23.
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John sells cupcakes. He has been offered a salary position at two different companies to make and sell his cupcakes. The first company offered him a weekly salary of $ 800.00 $800.00 plus a commission of $ 0.30 $0.30 for each cupcake he sells. The second company offered him a weekly salary of $ 350.00 $350.00 plus a commission of $ 1.30 $1.30 for each cupcake he sells. How many cupcakes must John sell each week for the total pay from each company to be the same?
PLEASE ANSWER FAST WORTH 92 POINTS
Answer:
450 cupcakes
Step-by-step explanation:
Let x be the number of cupcakes sold for John's total pay to be the same for both companies
For the first company
Salary = $800/week
Commission is $0.30 per cupcake
For sales of x cupcakes, total commission = 0.30x
Total pay = Weekly salary + Total commission from sales
Total Pay = 800+ 0.3x
For the second company
Salary = 350 /week
Commission: $1.30 per cupcake
For sales of x cupcakes, total commission = 1.30x
Total Pay = Weekly salary + Total commission from sales
Total Pay = 350 + 1.3x
If both pay must be he same,
800 + 0.3x = 350 + 1.3x
800-350 = 1.3x - 0.3x
450 = 1x
x = 450 cupcakes ANSWER
Answer: 450
Step-by-step explanation:
If we let x and y represent the number of cupcakes John sells and his total weekly income, respectively, we get the following system of equations.
=0.35x+845
=1.4x+372.5
Since both equations are solved for y, any substitution for y will result in the following
211.4 x+372.5&=0.35
x+845
1.4x+372.5
=0.35x+845
Solving for x will give us the number of cupcakes John needs to sell weekly for each paycheck to be the same. Doing so, we get
1.4 x+372.5&=0.35 x+845
1.05 x&=472.5x=450
1.4x+372.5
1.05x
x
=0.35x+845
=472.5
=450
Therefore, John needs to sell 450450 cupcakes each week for both salaries to be the same.
Construct ∠Y so that ∠Y ≅ ∠Z.
The angle ∠Y so that ∠Y ≅ ∠Z is added as an attachment
How to construct the angleFrom the question, we have the following parameters that can be used in our computation:
Construct ∠Y so that ∠Y ≅ ∠Z.
There are several ways to do this, some of them are:
Construct an isosceles triangle and name the base angles Y and ZConstruct a rectangle or a square and name any of the vertices Y and ZThe above statements are true because the base angles of an isosceles triangle are congruent and all angles in a rectangle/square are congruent
See attachment
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Donna Wagner is a self-employed musician. She pays 100 percent of the PPO insurance premium of 5,824 annually. She also has a dental plan that costs 600 annually and a vision plan that costs 365 annually. What is her total monthly premium for all her insurance
The total monthly premium for all her insurance is 6249 .
What is percentage ?
Percentage can be defined as the product of ratio of given value , total value and hundred.
Given ,
Donna Wagner is a self-employed musician. She pays 100 percent of the PPO insurance premium of 5,824 annually.
She also has a dental plan that costs 600 annually and a vision plan that costs 365 annually.
The total monthly premium for all her insurance = 5284+600+365
= 6249.
So, The total total monthly premium for all her insurance is 6249 .
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Elmhurst School organized an ice cream social for the incoming sixth graders. At the social, 7 students chose vanilla ice cream for every 5 that chose chocolate ice cream.
Pick the diagram that models the ratio in the story.
If 84 students chose vanilla ice cream, how many students chose chocolate ice cream?
students
60 students chose chocolate ice cream If 84 students chose vanilla ice cream.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, Elmhurst School organized an ice cream social for the incoming sixth graders. At the social, 7 students chose vanilla ice cream for every 5 that chose chocolate ice cream.
Since,
The ratio of students who choose vanilla ice cream to chocolate ice cream is: 7/5
Thus,
for every students choose chocolate ice cream = 5/7 student who chooses vanilla ice cream
If 84 students chose vanilla ice cream
Thus, students choose chocolate ice cream = 5/7 * 84
students choose chocolate ice cream = 12* 5
students choose chocolate ice cream = 60
Therefore, If 84 students chose vanilla ice cream, 60 students chose chocolate ice cream.
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Eddie is getting balloons for his mothers birthday party. He wants each ballon string to be 6 feet long. At the party store, string is sold by the yard. If Eddie wants to get 77 balloons, how many yards of string will he need
Answer:
462
Step-by-step explanation:
do 6x77 which is 462. alternative forms: 4.62 x 10^2
sorry for the side view if any one could do this step by step you would be a life saver
Answer:
pls see attached
Step-by-step explanation:
multiply the two polynomials (x+6)(x^2-3x-4)
The simplified form of the polynomial ( x + 6 )( x² - 3x - 4 ) is x³ + 3x² - 22x - 24
What is the simplified form of the given polynomial?Given the polynomial in the question;
( x + 6 )( x² - 3x - 4 )
Apply distributive property.
x( x² - 3x - 4 ) + 6( x² - 3x - 4 )
x³ - 3x² - 4x + 6x² - 18x - 24
Collect like terms
x³ - 3x² + 6x² - 18x - 4x - 24
Add like terms
x³ - 3x² + 6x² - 18x - 4x - 24
Add -3x² and 6x²
x³ + 3x² - 18x - 4x - 24
Add -18x and -4x
x³ + 3x² - 22x - 24
Therefore, the simplified form is x³ + 3x² - 22x - 24.
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*PLEASE HELP SOON* Simplify each part of the expression using the laws of exponents.
What laws or properties did you use to simplify each part? What is the value of the expression?
Using the laws of exponents to simplify the expression, we have; 5 1/3
What is an exponential expression?When the power of one or more terms of an expression is greater than 1, then the expression is in an exponential form. Thus some laws can be require to simplify an exponential expression.
In the given question,
2^7/ 2^5 + (4^5)^0 + 3^-1
Thus applying the division law of indices to the first term, we have;
2^7/ 2^5 = 2^(7 - 5)
= 2^2
In the second term, anything to the power of zero is 1. So that;
(4^5)^0 = (1024)^0
= 1
In the third term, applying the inverse law of indices. We have;
3^-1 = 1/ 3
Therefore,
2^7/ 2^5 + (4^5)^0 + 3^-1 = 2^2 + 1 + 1/3
= 4 + 1 + 1/3
= 5 + 1/3
= 16/ 3
= 5 1/3
The value of the expression is 5 1/3.
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Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply
Answer:
Step-by-step explanation:
x=4
x=-3/2
hope this helps !! :)
Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change?
The rate of change for the Carol with respect to time is 3/16 miles per minute.
What is the rate of change?The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" (ROC) is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line.
Given The table shows the distance Carol traveled after various numbers of minutes,
Input Output
2 1/6
3 17/48
4 13/24
5 35/48
6 11/12
Here, the output values from 1/6 to 11/12 indicate the distance in miles whereas the input values from 2 to 6 describe the time in minutes.
by utilizing the first two sets of input-output numbers, calculating the rate of change
Relative change = change in distance/change in time
(17/48 - 1/6)/(3-2) = (17/48 - 8/48) /1 = 9/48 = 3/16 miles per minute
Hence the rate of change is 3/16 miles per minute.
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Ruby invested $6,200 in an account paying an interest rate of 4. 3% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 12 years?
Total amount in Ruby's account after doing one time investment of $6200 for 12 years with rate of interest 4.3% is equal to $10,300 ( nearest hundreds dollars )
Principal 'P' amount in Ruby's account is equal to $6200
Rate of interest 'r' compounded continuously is 4.3%
Time 'N' = 12 years
Let 'A' be the final amount in Ruby's account after 12 years
Amount 'A' = P × ( 1 + (r/100) )ⁿ
Substitute the value in the formula we get,
⇒ A = 6200 × [ 1 + ( 4.3/100) ]¹²
⇒ A = 6200 × [ 1 + 0.043 ]¹²
⇒ A = 6200 × [ 1.043 ]¹²
⇒ A = $10,275.5
⇒ A = $10,300 ( nearest hundreds dollars )
Therefore , the total money in Ruby's account after depositing $6200 with rate of interest 4.3% compounded continuously for 12 years is equal to
$10,300 ( nearest hundreds dollars ).
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height is an example of a variable that uses the _____ scale.
Height is an example of a variable that uses the ratio scale.
Hence, option (a) is the correct choice.
Weight, height, and distance are all ratio variables. The ratio scale allows you to add, subtract, divide, and multiply data. Ratio scales are further distinguished from interval scales by the presence of a 'true zero'.
Height is an excellent example of a measuring scale based on a ratio. It is not nominal or ordinal since each change in the height unit (inches, metres, feet, etc.) has a standard distance between them, and it is not interval because height has a genuine zero.
Height, for example, is ratio data. There is no such thing as negative height. If the height of an item is 0, there is no object. This is not the same as talking about temperature.
The complete question should be:
Height is an example of a variable that uses the scale.
a. ratio b. interval c. nominal d. ordinal
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A ball freely falling at 20 m/s will in the next second have a speed of ______. 30 m/s. What two units of measurement are necessary for describing speed?
Meters and seconds are the two units of measurement required to describe speed.
A ball freely falling at 20 m/s will in the next second have a speed of 30 m/s.This is because the speed of a freely falling item rises by 9.8 m/s per second owing to gravity's acceleration. The ball begins at a speed of 20 m/s and adds 9.8 m/s to its initial speed after one second, ending in a final speed of 20 + 9.8 = 29.8 m/s (approx. 30 m/s).
Meters and seconds are the two units of measurement required to describe speed. These units are used to calculate the distance travelled by an item as well as the time it takes to traverse that distance. In this scenario, the ball's speed is measured in metres per second (m/s), which is the distance the ball travels in one second.
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What is the equation of a line that passes through the points (3, 6) and (8,4)?
y-2/x-2/2
y-2/x-27
y=-x-24
y=-x+36
Answer:
4th option
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (8, 4 )
m = [tex]\frac{4-6}{8-3}[/tex] = [tex]\frac{-2}{5}[/tex] = - [tex]\frac{2}{5}[/tex] , then
y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (8, 4 ) , then
4 = - [tex]\frac{2}{5}[/tex] (8) + c = - [tex]\frac{16}{5}[/tex] + c ( add [tex]\frac{16}{5}[/tex] to both sides )
[tex]\frac{20}{5}[/tex] + [tex]\frac{16}{5}[/tex] = c , that is
c = [tex]\frac{36}{5}[/tex]
y = - [tex]\frac{2}{5}[/tex] x + [tex]\frac{36}{5}[/tex] ← equation of line
Whay is the y intercept of these two points: (-1,-5) and (6,0)?
The y-intercept of a line is the point at which the line crosses the y-axis. This means that the x-coordinate of the point is 0.
To find the equation of a line passing through two points, we use the slope-intercept form of the equation of a line: y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the y-intercept of a line passing through two points, we can use the slope-intercept form of the equation of a line and the coordinates of the two points:
(y1, y2) = m(x1, x2) + b
m = (y2-y1)/(x2-x1)
In this case, the two points are (-1,-5) and (6,0)
m = (0-(-5))/(6-(-1)) = 5/7
We can substitute the slope in the slope-intercept form of the equation of a line:
y = mx + b
so we can substitute point (-1,-5) in the equation and solve for b
-5 = (5/7)*(-1) + b
b= -5 + (5/7) = -5 + 0.7142857142857143
So, the y-intercept of the line passing through the two points (-1,-5) and (6,0) is -4.2857142857142865
52 students are going on a skiing trip. 28 have skied before, 30 have snowboarded before while 12 have done neither. How many have done both sports before?use a Venn diagram.
Answer:
18
Step-by-step explanation:
see attached
Find the Area of the figure below, composed of a square and four semicircles. Rounded to the nearest tenths place
12
Answer:
370.1 [tex]units^{2}[/tex]
Step-by-step explanation:
Square
a = [tex]s^{2}[/tex]
a = [tex]12^{2}[/tex] = 144
Semi - Circle:
a = 1/2([tex]\pi r^{2}[/tex])
a = 1/2(3.14)(36) The radius is 1/2 the diameter of 12 (6) [tex]6^{2}[/tex] = 36
a = 1/2(113.04)
a = 56.52
144 + 4(56.52)
144 + 226.08
370.08 rounded to the nearest tenths place 370.1