The width of the piece of metal will be 21 inches while the length will be 26 inches.
What is a rectangle?
A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Main body:
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the width of metal w then the length will be w + 5
Now if we cut 1 inch square from the corner of the metal and then fold then the resultant cuboid will have;
Length = w+5 - 2 -= w + 3
Width = w - 2
Height = 1
So,
Volume = (w+3)(w-2)1
456 = w² - 2w + 3w - 6
w² + w - 462 = 0
By solving this
w = 21 so width will be 21 and length will be 21 + 5 = 26.
Hence "The width of the piece of metal will be 21 inches while the length will be 26 inches".
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b is the midpoint of segment ac. a has coordinates (-3, 4) and b has coordinates (-1 1/2, 1). find the coordinates of c
The coordinates point C of the given line segment AC is C(0, -2) whose midpoint is at B.
How to calculate a midpoint of a line segment?To calculate the midpoint of a line segment, find the average for the coordinates of the endpoints of the line segment. I.e.,
Consider a line segment AC, B is its midpoint.
So, the coordinates of B are (Where we have A(x1, y1) and C(x2, y2))
B(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
Calculation:It is given that, B is the midpoint of a line segment AC.
Where A has coordinates as (-3, 4) and B has coordinates as (-1 1/2, 1).
So, the coordinates of the other end point C of the given line segment are calculated as
B(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
⇒ (-1.5, 1) = [tex](\frac{-3+x2}{2}, \frac{4+y2}{2})[/tex]
⇒ -1.5 = (-3 + x2)/2 and 1 = (4 + y2)/2
⇒ -3 = -3 + x2 and 2 = 4 + y2
⇒ x2 = 0 and y2 = 2 - 4 = -2
Therefore, point C has coordinates as (0, -2).
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Write this ratio as a fraction in simplest form without any units 27 feet to 8 yards
The ratio of 27 feet to 8 yards is 9/8 while converting feet to yards and the ratio is also 9/8 while converting yards to feet.
What are yards and feet?Yards and feet are units use to measure the length of geometrical shapes.
1 foot equal to 0.333 yards and similarly 1 yard equal to 3 feet. There is proportional relationship between them.
what did you get from the above fraction value?We got the same fraction value from the ratio of two units which implies that the two units are proportional.
1 foot =0.333 yard so
27 feet = 9 yards
similarly, 1 yard = 3 feet
so, 8 yard = 24 feet
hence, the ratio is 9/8
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Marta found a website that sells her favorite style of coffee mugs. She writes the function C(m)=4.50 m+7, where C(m) represents the total cost of ordering m mugs, to decide how many mugs to order. Determine whether each statement about the features of the function is true or false in terms of the context.
The range is {y l y ≥ 11.5\}.
The domain is all real numbers.
The y-intercept is 4.5.
There is no x-intercept.
The rate of change is $ 4.5 per mug.
The true or false values of the statements are:
The range is {y l y ≥ 11.5\}: FalseThe domain is all real numbers: FalseThe y-intercept is 4.5: TrueThere is no x-intercept.: TrueThe rate of change is $4.5 per mug: TrueHow to determine the true statements from the scenario?From the question, we have the following parameters that can be used in our computation:
C(m) = 4.50m + 7
The smallest number of mugs she can sell is 0
So, we have the following equation
C(0) = 4.50 * 0 + 7
Evaluate
C(0) = 0
This means that the range is y ≥ 0
Next, the domain cannot be all real numbers
This is because real numbers include negative and decimal numbers
For the y-intercept, we have
C(m) = 4.50m + 7
Set m to 0
y-intercept = 4.5 * 0 + 7
Evaluate
y-intercept = 7
For the y-intercept, we have
C(m) = 4.50m + 7
Set C(m) to 0
4.5 * x-intercept + 7 = 0
Evaluate
x-intercept = -7/4.5 -- this cannot be taken as the x-intercept because it is a negative number
Also, we have the slope to be 4.5
So, the rate of change is $4.5 per mug
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Suppose a simple random sample of 30 students from this district is selected. What is the probability that at least half of them have brown eyes? (Use technology. Round your answer to three decimal places.)
In the simple random sample, the probability that at least half of the students have brown eyes is 0.400
How to calculate probability of an event at a particular time?Probability is defined as the chance of occurrence of an event.
Probability is defined as follows:
P(E)=[tex]\frac{no of required outcome}{total of possible outcomes}[/tex]
The given parameters are:
The sample size= 30 students
Number with brown eye=40%
40% x 30 = [tex]\frac{40}{100} * 30[/tex]
=12
This means that there 12 students out of 30 that have brown eyes.
Applying the probability formula
[tex]\frac{12}{30}[/tex]= 2/5
In conclusion 0.400 of the students have brown eyes.
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determine the sample size needed to construct a 95 % confidence interval to estimate the population proportion is 0.54, and the margin of error is 0.06. use two decimal places for the critical value and round to the nearest integer for your final answer. eg. 48.47
The sample size needed is at least 311.17.
We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2. So:
α = [tex]\frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of 1-α
So it is z with a p-value of , so
1-0.025 = 0.975, so z = 1.96
Now, find the margin of error M as such
[tex]M = z*\frac{sd}{\sqrt{n} }[/tex]
where sd = σ = standard deviation
At least n, in which N is found when M= 0.06 and σ = 0.54. So
[tex]M = z*\frac{sd}{\sqrt{n} } \\0.06 = 1.96 * \frac{0.54}{\sqrt{n}} \\\sqrt{n} = \frac{1.96*0.54}{0.06} \\\sqrt{n} = 17.64\\n = 311.1696\\[/tex]
Rounding off to the nearest integer, we get n = 311.17.
Thus, the sample size needed is at least 311.17.
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Explain the steps in solving 2.14x - 12.18 = -5.76, and write the solution to the equation.
WRITER
Someone please help me with this!!!
Answer:
x = 3
Step-by-step explanation:
You want to solve for x, so you want to get x on one side of the equation. To do this, you can add the -12.18 to both sides of the equation (you add since it's negative).
2.14x - 12.18 = -5.76
2.14x = 6.42
Then you want to get x by itself, without the 2.14 in front of it. To do this, you can divide both sides of the equation by 2.14.
This will give you,
x = 3
Need quick
Foci: (-2, 0) and (2, 0)
Length of major axis: 8
Find equation of ellipse
The equation of the ellipse is x²/8² + y²/(2√15)² = 1.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
Foci: (-2, 0) and (2, 0)
Length of major axis: 8
The equation of an ellipse.
x²/a² + y²/b² = 1
Where a is the major axis and b is the minor axis.
Now,
b² + c² = a²
c = 2
a = 8
b² = a² - c²
b² = 64 - 4
b² = 60
b = √60
b = √(4 x 15)
b = 2√15
Now,
x²/a² + y²/b² = 1
x²/8² + y²/(2√15)² = 1
Thus,
The ellipse equation is x²/8² + y²/(2√15)² = 1.
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a. When the relationship for a regression is positive, an X score above the mean will correspond to a Y score (above/below) the mean.b. When the relationship for a regression is negative, an X score above the mean will correspond to a Y score (above/below) the mean.
(a) For positive Linear Regression , Y score will be above mean .
(b) For negative Linear Regression , Y score will be below the mean .
What is Linear Regression ?
The term Linear regression analysis is used to predict the value of one variable based on the value of another variable.
Part(a)
when the relationship of regression between two variables is positive then if one variable increase the other variable also increases ,
So , if the the x score is above the mean then the Y score will be also above the mean .
Part(b)
when the relationship of regression between two variables is negative then if one variable increase the other variable decreases ,
So , if the the x score is above the mean then the Y score will be below the mean .
Therefore , (a) Y score will be above the mean .
(b) the Y score will be below the mean .
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a) Work out the minimum number of dogs that could have a mass of more than 24 kg
b) Work out the maximum number of dogs that could have a mass of more than 24 kg}.
Mass(kg) Frequency
0≤x<10 2
10≤x<20 7
20≤x<30 12
30≤x<40 6
a) A minimum number of dogs that could have a mass of more than 24 kg is 6.
b) The maximum number of dogs that could have a mass of more than 18 kg is 20.
How to find the minimum and maximum value mean?We will rearrange the function using fundamental algebraic concepts to process the value of x when the derivative equals 0. This response gives us the x-coordinate of the function's vertex, which is the point that the maximum or minimum will occur. To find the minimum or maximum, we will start by rewriting the solution into the original function.
From the given parameters, we can see that the minimum of the values present in the interval 20 to 40 is 6
From the given parameters, we can see that the maximum of the values present in the interval 20 to 40 is;
(12 + 6) = 18
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help!! please! i don’t understand
Answer:
[tex] 2 \sqrt[3] {60}~mm [/tex]
Step-by-step explanation:
The volume of a cube is the side cubed, so each edge is the cubic root of the volume.
V = 480 mm³
[tex] s = \sqrt[3] {V} [/tex]
[tex] s = \sqrt[3] {480~mm^3} [/tex]
[tex] s = \sqrt[3] {2^3 \times 2^2 \times 3 \times 5~mm^3} [/tex]
[tex] s = \sqrt[3] {2^3} \times \sqrt[3] {2^2 \times 3 \times 5~mm^3} [/tex]
[tex] s = 2 \sqrt[3] {60}~mm [/tex]
Write an inequality with x isolated on the left side that is equivalent to the given inequality.
Fx+Wy>R; Assume F > 0.
The equivalent inequality with x isolated on the left side is
Need help asap
The inequality Fx + Wy > R written with x isolated to the left sides is
x > (R - Wy) / FHow to write the inequality with x isolated to the left hand sideInequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.
The signs used in inequality are of 4 types namely
less thangreater thanless than or equal togreater than or equal toThe given inequality in the problem has greater than sign and it is written as Fx + Wy > R
rearranging the inequality gives
Fx + Wy > R
Fx > R - Wy
divide through by F
Fx / F> R/F - Wy/F
x > (R - Wy) / F
isolating x to the left side gives x > (R - Wy) / F
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Question 4
May use your own graph paper for this question. Show all algebraic work for full By graphing, find the coordinates of the vertices of the original triangle H L K, give midsegment triangle MNP are M(-1,3), N(4,0), P(-2,-2).
With the mid segment of the triangle MNP as M (-1, 3), N (4, 0), P (-2, -2) the coordinates of the triangle are
(-7, 1), (5, 5), and (3, -5)How to find the coordinates of the triangle when the mid segment is knownThe coordinates is calculated from the midsegment using the formula
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
Vertex 1 and 2: point M (-1, 3),
X
-1 = (x₂ + x₁)/2
-2 = x₂ + x₁
Y
3 = (y₂ + y₁)/2
6 = y₂ + y₁
Vertex 2 and 3: point N (4, 0)
X
4 = (x₂ + x₃)/2
8 = x₂ + x₃
Y
0 = (y₂ + y₃)/2
0 = y₂ + y₃
Vertex 1 and 3: point P(-2, -2)
X
-2 = (x₃ + x₁)/2
-4 = x₃ + x₁
Y
-2 = (y₃ + y₁)/2
-4 = y₃ + y₁
The equations
X
-2 = x₂ + x₁
8 = x₂ + x₃
-4 = x₃ + x₁
Y
6 = y₂ + y₁
0 = y₂ + y₃
-4 = y₃ + y₁
from -2 = x₂ + x₁, we find x₁ = -2 - x₂
plugging in x₁ = -2 - x₂ to -4 = x₃ + x₁ gives
-4 = x₃ + -2 - x₂
-2 = x₃ - x₂
then we have
8 = x₂ + x₃
-2 = x₃ - x₂
solving simultaneously
x₃ = 3, x₂ = 5 then x₁ = -2 - x₂ = -7
from 0 = y₂ + y₃, we find that y₂ = -y₃
plugging in y₂ = -y₃ into 6 = y₂ + y₁ gives
6 = -y₃ + y₁
then we have
-4 = y₃ + y₁
6 = -y₃ + y₁
solving simultaneously gives
y₁ = 1, y₃ = -5, then y₂ = -y₃ = -(-4) = 5
The vertex of the triangle are
(-7, 1), (5, 5), and (3, -5)
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A football club sells, on average, 23000 tickets per match. In one season they play, on average, 46 matches.How many tickets do they sell, on average, each season?
Answer:
On average, the football club sells 1,058,000 tickets per season.
Step-by-step explanation:
[tex]23000[/tex] × [tex]46 = 1058000[/tex]
A employee must create 140 gallons of slash burn fuel that must have a ratio of 8 parts diesel to 2 parts gas. How much diesel and gas are needed to create this mixture?
The amount of diesel required to create slash burn fuel is = 112 gallons
The amount of gas required to create slash burn fuel = 28 gallons
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
The total amount of slash fuel = 140 gallons
The ratio of diesel to gas in slash fuel is = 8 : 2
Let the amount of diesel required to create slash burn fuel be = 8x
Let the amount of gas required to create slash burn fuel be = 2x
So , the equation of proportion is given by
Total amount of slash fuel = amount of diesel required to create slash burn fuel + amount of gas required to create slash burn fuel
Substituting the values in the equation , we get
Total amount of slash fuel = 8x + 2x
8x + 2x = 140
10x = 140
Divide by 10 on both sides of the equation , we get
x = 14 gallons
Substituting the value of x in the above expressions , we get
Amount of diesel required to create slash burn fuel = 8x
Amount of diesel required to create slash burn fuel = 8 x 14
Amount of diesel required to create slash burn fuel = 112 gallons
And ,
Amount of gas required to create slash burn fuel = 2x
Amount of gas required to create slash burn fuel = 2 x 14
Amount of gas required to create slash burn fuel = 28 gallons
Hence ,
The amount of diesel required to create slash burn fuel is = 112 gallons
The amount of gas required to create slash burn fuel = 28 gallons
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Simplify to create an equivalent expression.
2(-n -3) -7(5+2n)
Answer:
-16n-41
Step-by-step explanation:
213. Sandy has 1 quart and 1 pint of soda.
How many cups can she divide this
amount into?
7. What is the equation of a line that is parallel to -x+3 y=6 and passes through the point (3,5) ?
y=___ x +_____
The equation of a line that is parallel to -x + 3y = 6 and passes through the point (3,5) is y = 1 / 3 x + 5
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of a line that is parallel to -x + 3y = 6 and passes through the point (3,5) can be found as follows:
Parallel lines have the same slope.
-x + 3y = 6
3y = x + 6
y = 1 / 3 x + 2
Therefore, the slope is 1 / 3. Let's find the y-intercept using (3, 5).
y = 1 / 3 x + b
5 = 1 / 3 (3) + b
b = 5
Therefore, the equation is y = 1 / 3 x + 5
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(a) Solve the given inequality 3 (x +2) ≥ 5 (x + 1).
(b) Find the greatest possible value of x, if it is;
1. a rational number
2. an integer
3. a prime number
plssss helpppp right answers only and explaintion.
The equivalent of the expression 2³/2⁷ using the law of indices is (a) 1/2⁴
How to determine the equivalent expression?From the question, we have the following parameters that can be used in our computation:
2³/2⁷
The above expression can be solved using the law of indices
When the law of indices is applied, we have the following representation
2³/2⁷ = 2(³ ⁻ ⁷)
Remove the bracket in the above expression
So, we have the following representation
2³/2⁷ = 2³ ⁻ ⁷
Evaluate the difference
This gives
2³/2⁷ = 2⁻⁴
Rewrite as
2³/2⁷ = 1/2⁴
Hence, the solution is (a) 1/2⁴
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5. Which of the following is true about the solution to the
system of equations?
3x - 2y = 10
2y = 3x - 16
4
A. The x-value of the solution is4/3
B. The y-value of the solution is -1.5.
C. There are infinitely many solutions to this system.
D. There is no solution to this system.
6
i
Answer:
D
Step-by-step explanation:
3x - 2y = 10 → (1)
2y = 3x - 16 → (2)
substitute 2y = 3x - 16 into (1)
3x - (3x - 16) = 10
3x - 3x + 16 = 10
16 = 10 ← not possible
this indicates the system has no solution.
There is no solution to this system. Therefore, option D is the correct answer.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given that the system of linear equations are
3x - 2y = 10 -------(i)
2y = 3x - 16
3x-2y=16 -------(ii)
Subtract equation (ii) from equation (i), we get
3x-2y-(3x-2y)=10-16
0≠4
Therefore, option D is the correct answer.
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20. You buy 4 online games for $0.99 each. You make 2 in-game purchases for
$3.99 each. What is the total you spent on games?
Answer: $11.94
Step-by-step explanation: 4 x 0.99 = $3.96 and then 2 x $3.99 = $7.98 now $7.98 + $3.96 = $11.94
Where does the line f(x) = x-1 cross the parabola g(x) = (x+2)^2-9?
Answer:
The line and the parabola cross at x = -4 and x = 1
Step-by-step explanation:
Set f(x) = g(x)
[tex]x-1 = (x+2)^2-9\\x - 1 = x^2+4x+4-9\\x = x^2 + 4x - 4\\0 = x^2 + 3x - 4\\Factor\\0 = (x - 1) (x + 4)\\x = 1, -4[/tex]
Question 5 id points
Do not round or enter wards, use a decimal answer.
You are playing a carnival game. You will spin the two spinners below.
Rule 1: To win the grand prize, you need to spin an "A" and a "1". What is the probability that you win a bōsic prize?
Answer:
Rule 2: To win you a basic prize, you need to spin an "A" or a "1". What is the probability that you win a basic prize?
Probability of winning a grand prize is 1/10
Probability of winning a basic prize is 11/20
What is the probability of two independent events?
If A and B are two independent events, then P(A and B) = P(A) * P(B).
If Events A and B are independent, the probability that either Event A or Event B occurs is: P(A or B) = P(A) + P(B) - P(A and B).
Solution:
P(A) = no. of A / total possibility
= 4/10
P(B) = no. of 1's/total possibility
= 3/12
= 1/4
Now,
To win a grand prize you need an "A" and "1" .
∴ P(A and B) = P(A) × P(B)
= 4/10 × 1/4
P(A and B) = 1/10
Now ,
To win a basic prize you need to spin an "A" or a "1"
∴ P(A or B) = P(A) + P(B) - P(A and B)
= 4/10 + 1/4 - 1/10
= 3/10 + 1/4
∴ P(A or B)= 11/20
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Probability of winning a grand prize is 1/10
Probability of winning a basic prize is 11/20
What is the probability of two independent events?If A and B are two independent events, then P(A and B) = P(A) * P(B).
If Events A and B are independent, the probability that either Event A or Event B occurs is: P(A or B) = P(A) + P(B) - P(A and B).
Evaluating :P(A) = no. of A / total possibility
= 4/10
P(B) = no. of 1's/total possibility
= 3/12
= 1/4
Now,
To win a grand prize you need an "A" and "1" .
∴ P(A and B) = P(A) × P(B)
= 4/10 × 1/4
P(A and B) = 1/10
Now ,
To win a basic prize you need to spin an "A" or a "1"
∴ P(A or B) = P(A) + P(B) - P(A and B)
= 4/10 + 1/4 - 1/10
= 3/10 + 1/4
∴ P(A or B)= 11/20
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Write an equation for a rational function with:
Vertical asymptotes at x = 6 and x = 3
x intercepts at x = 1 and x = -1
y intercept at 5
Answer:
Making a fraction is the easiest way to do this.
The x-intercepts give solutions to a problem that equals zero.
The vertical asymptotes are values x cannot be, in a fraction the denominator can not be zero.
Horizontal asymptotes are the values y approaches. This can be accomplished by making the leading term have a coefficient of 6
Step-by-step explanation:
There is a fee to enter the county fair, plus a fixed amount to play each game. The
line shows the money spent at the fair, y, when a games are played.
Money Spent at the Fair
Money Spent ($)
y
Write an equation for the line in slope-intercept form.
Drag a number into each box to write the equation.
Y
An equation for the line in slope-intercept form is y=(6/5)x+8
What is a slope?The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.
The steepness, incline, or grade of a line can be approximated by the slope's absolute value. The slope of a line determines how steep it is.
From the graph,
The line passes through the points (0,8) and (5, 14)
Slope m=(14-8)/(5-0)
m=6/5
(0, 8) passes through the line y=mx+c
So, 8=6(0)/5+c
Then, c=8
An equation for the line in slope-intercept form is y=(6/5)x+8.
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Find a polynomial f(x) of degree 4 with real coefficients and the following zeros. 1 (multiplicity 2) , 1+2i
Answer:
Factorization
Step-by-step explanation:
Question
the third term of GP is 4 the product of its first 5 term is
please solve it
Don't Spam
[tex] \huge{ \bold{ \color{purple}{Solution }}}[/tex]
Let a be the first term and r be the common ratio
Now,
[tex] \large{ \sf{T _3 = 4}}[/tex]
[tex] \large{ \sf{ {ar}^{2} = 4}}[/tex]
[tex]\large{ \sf{ \therefore \: product \: of \: first \: 5 \: term \: = a _1 \times a_2 \times a_3 \times a_4 \times \: a _5}}[/tex]
[tex] \large{ \sf{ = a(ar)( {ar}^{2} )( {ar}^{3} )( {ar}^{4} ) = {a}^{5} r {}^{10} }}[/tex]
[tex] \large{ \sf{ \red{(ar {}^{2} ) {}^{5} = {4}^{5} }}}[/tex]
[tex] \rule{150pt}{5pt}[/tex]
Output(y) 8 less than 3 times x
Answer:
y = 3x - 8
Step-by-step explanation:
Consider the expression 40+24 . Find the greatest common factor of the two numbers, and rewrite the expression using the distributive property.
The greatest common factor of 40 and 24 would be; 8.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We can rewrite this expression for distribution using the amount of times 8 goes into both numbers as;
8(5 + 3)
Using the distributive property, we get:
8(5) + 8(3) = 40 + 24.
Threfore,
The greatest common factor of 40 and 24 would be; 8.
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Simplify. (3x² - 2x + 2) - (x² + 5x-5) A. 2x² - 7x+7 B. 2x²-3x - 3 C. 2x² + 3x - 3 D. 4x² + 3x 3
The equivalent expression is 2x² - 7x + 7
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
2x + 6 - 9 is an expression.
3x = 9 is an expression.
We have,
(3x² - 2x + 2) - (x² + 5x - 5)
Remove the parenthesis.
3x² - 2x + 2 - x² - 5x + 5
Add like terms.
2x² - 2x + 2 - 5x + 5
Add like terms
2x² - 7x + 7
Thus,
The final expression is 2x² - 7x + 7
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