Factoring out the Greatest Common Factor (GCF) simplifies the expression, making further manipulation and factoring simpler. It reduces complexity, much like simplifying fractions in arithmetic, and aids in revealing patterns for easier factoring. This step also minimizes calculation errors and assists in proper unit analysis during problem-solving.
Factoring out the Greatest Common Factor (GCF) is a critical step in the process of factoring algebraic expressions. This is important because it simplifies the remaining expression, making it easier to manipulate and factor further if necessary. It is similar to simplifying fractions before performing operations with them; the process becomes cleaner and more straightforward.
For example, when you have an equation with multiple terms, each with a common factor, factoring out this GCF reduces the complexity of the terms, possibly revealing a more obvious pattern or structure that can then be factored more easily. Additionally, removing the GCF early in the process can prevent calculation errors and make other factoring techniques, like the difference of squares or trinomial factoring, more apparent and easier to apply.
In cryptography, algorithms rely on the principle that multiplying large numbers is computationally simple, whereas factoring a large number into its prime factors is difficult. Similarly, in algebra, starting by factoring out the GCF simplifies the entire problem, making the next steps more manageable. In physics equations, where units are involved, ensuring that all factors are in proper form before solving can prevent unit conversion errors, thus factoring out can play a useful role in unit analysis as well.
Use the functions a(x) = 3x + 10 and b(x) = 2x − 8 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (3 points) Part B: Find (a ⋅ b)(x). Show your work. (3 points) Part C: Find a[b(x)]. Show your work. (4 point
There are values of t so that the equation cos t= 5/3
impossible, the maximum value of either cos(t) or sin(t) is 1; look to the unit circle for proof
Find the length of a line segment with endpoints of 19 and –39. A. –58 B. –20 C. 20 D. 58
Answer:
Option D, 58
Step-by-step explanation:
Line segment having end points are 19 and -39
So total length of line segments having end points of 19 and (-39) = distance from origin to one end at (19) + distance of another end from origin
= 19 + 39
= 58
Option D, 58 is the answer.
Help!!!!! how do i slove this equation
How can you prove that a constructed line is parallel to a given line? assume that the transversal line is not perpendicular to the other lines?
To prove that a line is parallel to another, one usually shows that two lines cut by a transversal have either congruent corresponding angles or alternate interior angles. In the lack of perpendicular transversal or angle knowledge, projecting lines onto a new coordinate system can show matching slopes to confirm parallelism.
Explanation:In mathematics, proving that a constructed line is parallel to a given line typically involves showing that the lines do not intersect and have the same slope or use a parallel postulate. The most common method is taking two lines l and m and a transversal t. If the corresponding angles or alternate interior angles created by t are congruent, then l and m are parallel.
For example: If line l and line m are cut by a transversal t and the corresponding angles (∠1 and ∠2) are congruent, then lines l and m are parallel. The same can be said if the alternate interior angles are congruent.
In some cases, if the transversal line is not perpendicular and we do not know about corresponding or alternate interior angles, we can establish a different coordinate system, project the lines onto the x-axis and y-axis, and show that they have the same slope which proves them to be parallel.
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3x-4y=-5 y=4x-2 Is (1,2) a solution of the system?
The pie store is having a 15% percent off sale on all of its pies. If the pie you want regularly costs $11 how much would you save with the discount?
Please help a brother out! Thank you!
they are saying x = 3 so you would use the middle equation
so -4x becomes -4(3)
-4 * 3 =-12
What is the volume of the sphere? Round the answer to the nearest cubic unit. Diameter: 22 cm
1) 507 cm^3
2) 1,394 cm^3
3) 5,575 cm^3
4) 16,725 cm^3
The volume of the Sphere is 5,575 cm^3.
What is the volume of the Sphere ?
The volume of the Sphere is the capacity it has. It is the space occupied by the sphere.
Formula used to find volume of the Sphere is :
V = 4/3 × π × r^3
Given : diameter = 22 cm
r = diameter/2
r = 11 cm
So ,
V = 4/3 × π × 11 ^3
⇒ 4/3 × π × 1331
⇒ 1.34 × 4179.34
V = 5575.28 cm^3
The nearest cubic unit is 5,575 cm^3.
Hence , the volume of the Sphere is 5,575 cm^3 .
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What is 2(x+6)=20 pls I need help
Solve by factoring: 8p2 - 64p = 0
The radius of the earth is approximately 3960 miles find the approximate surface area to volume ratio of the earth
Which of the following is a parent function
Julie is a math tutor. She charges each student $210 for the first 7 hours of tutoring and $20 for each additional hour. When the number of hours (h) that Julie spends tutoring a student is greater than 7 (h > 7), the equation that gives the amount (A) that Julie earns in dollars is . If Julie earns $410 tutoring one student, the total number of hours she spent tutoring the student is .
Answer:
box 1- A=210+20(h-7) box 2- 17
Step-by-step explanation:
I got it right on plato, watch out for positive and negative answers i almost got it wrong
5(2x-8) i dont get how to do distributive prop on this
All I know is it's not B.
Joel is laying pipe for a sprinkler system before he plants his lawn. The lawn is a rectangle, 15 feet long and 8 feet wide. He needs to lay a piece of pipe that will be run along the diagonal of the lawn. It will divide the area of the lawn into two right triangles. What will be the length of that diagonal piece of pipe?
Analyze the diagram below and answer the question that follows.
Which of the following best describes triangle GFH?
A.
isosceles triangle
B.
acute triangle
C.
scalene triangle
D.
right triangle
Help a brother out here! Thank you!!!
7 blue cards
26 total cards
probability = 7/26
Thompson Alberts purchased a pack of 12 pencils for $4.99. What is the unit price per pencil rounded to the nearest tenth of a cent?
divide total coast by number of pieces
4.99/12 = 0.415833
rounded to 0.42
42 cents each
$0.416
This is the correct answer for primavera
$4.99/12=0.4158 Rounded to the nearest tenth of a cent is $0.416
75% of a number is 4.5 cm
Answer: 6 cm
Step-by-step explanation: 4.5 cm is 75/100
75/100=4.5/x
100*4.5=75*x
450=75x
divide both sides by 75
6=x
The number 4.5 is 75 percent of the number 6.
The given number is 4.5 cm.
Let 75% of x is 4.5 cm.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, 75% of x=4.5
[tex]\frac{75}{100} \times x=4.5[/tex]
[tex]\frac{75x}{100}=4.5[/tex]
[tex]75x=4.5\times100[/tex]
[tex]75x=450[/tex]
[tex]x=\frac{450}{75}[/tex]
[tex]x=6[/tex]
Therefore, the number 4.5 is 75 percent of the number 6.
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"Your question is incomplete, probably the complete question/missing part is:"
75% of what number is 4.5 cm.
Assume that y varies inversely with x. If y=7 when x=2/3, find y when x=7/3
The function H(t) = −16t2 + 60t + 95 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 20 + 38.7t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points) (10 points)
We are given the functions:
h(t) = -16t^2 + 60t + 95
g(t) = 20 + 38.7t
Part A. All we have to do is to plug in the value of t = 1 to 4 on the two functions
t h(t) g(t)
1 139 58.7
2 151 97.4
3 131 136.1
4 79 174.8
Looking at
the table, we can say that the time when h(t)=g(t) must be between t=2 and t= 3
seconds
At t=2 seconds h(t) is above g(t), and at t = 3 seconds h(t) is below g(t).
Therefore the two functions must be at the same height in between.
Part B. The solution in Part A gives us the exact time where the two objects have the same height. Further, we can see from the table that h(t) is decreasing meaning the projectile is going down while g(t) is increasing so the other projectile is going up.
The area of a rectangle is 65 m2 , and the length of the rectangle is 3 m less than twice the width. find the dimensions of the rectangle.
The dimensions of the rectangle are 10 meters and 6.5 meters
Let the width of the rectangle be represented by w.
The length of the rectangle will then be:
= 2w - 3
Area of the rectangle = 65m²
Note that length × width = Area
Therefore, w × (2w - 3) = 65
2w² - 3w = 65
2w² - 3w - 65 = 0
2w² - 13w + 10w - 65 = 0
2w(w - 6.5) + 10(w - 6.5) = 0
Therefore, w - 6.5 = 0
w = 0 + 6.5
w = 6.5
Width = 6.5 meters
Length = 2w - 3
Length = 2(6.5) - 3
Length = 13 - 3
Length = 10 meters.
The dimensions of the rectangle is 10 meters and 6.5 meters
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A 100-foot ramp is tilted at a 45° angle. How high is the top of the ramp from the ground?
Quadrilateral ABCD is similiar to quadrilateral EFGH The lengths of the three longest sides in quadrilateral ABCD are 24 feet, 16 feet, and 12 feet long. If the two shortest sides of quadrilateral EFGH are 9 feet long and 18 feet long, how long is the 2nd longest side on quadrilateral EFGH
?
Answer:
A.) 24 feet
Step-by-step explanation:
I got it correct on founders edtell!
If the correlation between two variables is .496, how much of the variance has not been accounted for
If the correlation between two variables is .496, it has 24.6 percent (24.6%) of the variance that has not been accounted for. Hence, correlation is a statistical technique that is used to measure and describe the strength and direction of the relationship between two variables and 24.6% has not been accounted for the two variables which is .496.
Final answer:
About 75.40% of the variance between two variables with a correlation coefficient of .496 is unaccounted for, as it is the complement of the coefficient of determination (24.60%) obtained by squaring the correlation coefficient.
Explanation:
To determine the amount of variance not accounted for by the correlation between two variables with a correlation coefficient of .496, we must use the coefficient of determination. The coefficient of determination is the square of the correlation coefficient (r₂), which represents the proportion of the variance for the dependent variable that's explained by an independent variable in a regression model.
First, we calculate r₂:
.4962 = .246016, or approximately 24.60%. This means that about 24.60% of the variance in the dependent variable is explained by the independent variable.
Next, we find the unexplained variance by subtracting r₂ from 1:
1 - .246016 = .753984, or approximately 75.40%. Therefore, 75.40% of the variance has not been accounted for by the correlation.
two adjacent sides of a rhombus are represented by 5x + 7 and 6x -1. find the value of x
The value of x in equation 5x + 7 = 6x -1 is 8.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
5x + 7 and 6x -1
Now,
The equation is:
5x + 7 = 6x - 1
To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 5x from both sides and adding 1 to both sides. This gives us:
5x + 7 - 5x = 6x - 1 - 5x
7 + 1 = x - 1 + 1
8 = x
Therefore, by the given equations the answer will be x = 8.
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10 POINTS PLEAAAAAASE HELP
Suzie drew the line of best fit on the scatter plot shown. A graph is shown with scale along x axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 15 at increments of 1. The ordered pairs 0, 3 and 1, 3 and 2, 4 and 3, 7 and 4, 6 and 5, 8 and 6, 10 and 7, 10 and 8, 12 and 9, 14 and 10, 15 are shown on the graph. A straight line joins the ordered pairs 0, 3 and 10, 15. What is the approximate equation of this line of best fit in slope-intercept form?
Answer:
y = 1.2 x + 3
Step-by-step explanation:
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