To find the greatest common factor of a polynomial, find a number that all of its coefficients are divisible by, for example, the GCF of an 8x 2 + 4x + 2 is 2 because all of the coefficients (8, 4, 2) are divisible by 2 and the expression simplifies to 2(4x2 + 2x + 1).
What is the Greatest Common Factor?A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. The GCF of 12, 20, and 24 is 4 because it is the largest.
To find the greatest common factor of a polynomial, find a number that all the coefficients of the polynomial are divisible by i.e. the GCF of a 8x^2 + 4x + 2 is 2 because all the coefficients (8, 4, 2) are divisible by 2 and the expression simplifies to 2(4x^2 + 2x + 1).
The GCF can be smaller than the smallest coefficient, for example 20x^2 + 15x + 10 (GCF is 5, smallest coefficient is 10) and 5 < 10. However it cannot be larger than the smallest coefficient.
Therefore the smallest coefficient should be larger than or equal to the GCF in order to be divisible.
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Here is a linear equation: y = 1/4x + 2. What is the x-intercept of the graph of the equation? Submit and Explain
pls help
f(x) = 6 - 1/(x-4)
Determine the value that the function f approaches as the magnitude of x increases. (If you need to use or –, enter INFINITY or –INFINITY, respectively.)
The value of the function as x increases comes closer to 6 and at limit x→∝ the value is 6.
In mathematics, a limit is the value that such a function (or sequence) gains as the input (or index) gets closer to a particular value.
Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.The concept of a limit of a series is further generalized to encompass the concept of such a limit of a topological net, in addition to being strongly related to limit and indirect limit in category theory.Several different converging ideas can be defined on function spaces. This sometimes relies on how frequently the area is set up. Two well-known examples of function spaces having a notion of convergence are Lp spaces and Sobolev space.Given the function is [tex]f(x) = 6-\frac{1}{x-4}[/tex]
Now we put the limit to the function as [tex]lim_{x\rightarrow \infty} f(x)[/tex]
Therefore :
[tex]lim_{x\rightarrow \infty} (6-\frac{1}{x-4})\\=lim_{x\rightarrow \infty} 6 - lim_{x\rightarrow \infty}\frac{1}{x-4}\\=6 - 0\\=6[/tex]
Hence the value of the function is 6.
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pls help will mark brainliest
The simplest form of the graph is 3x + 0y = 0
And the values of A and B are 3 and 0 respectively.
The point which is plotted in the graph : (3, 0)
What is the general form of linear equation?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). Additionally, when resolving systems of two linear equations, this form is highly helpful.
The given general form of equation is Ax+By+C= 0
So as in this graph it is clearly visible that:
A= 3 and B= 0
Thus we can write it as 3x + 0y = 0
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And the question below
Answer:
(a) 2nd Choice: The amount of time he has walked (in hours) when he is x kilometers from Glen City
(b) [tex]D^{-1}(x) = \dfrac{11.6 - x }{4}[/tex]
(c) [tex]D^{-1}(6.4) = 1.3 \;\text{hours}[/tex]
Step-by-step explanation:
(a)
Since D is distance in km from Glen City after t hours of walking, the inverse D⁻¹ would be the time taken in hours to walk x kilometers from the city. So the second choice
(b)
[tex]D^{-1}(x) = \dfrac{11.6 - x }{4}[/tex]
To find the inverse of a function y = f(x), interchange y and x and solve
y = 11.6 - 4x (using x instead of t)
Interchange y and x ==> x = 11.6 - 4y
Add 4y to both sides ==> 4y + x = 11.6 - 4y + 4y = 11.6
Subtract x from both sides ==> 4y = 11.6 - x
Divide both sides by 4 ==> y = (11.6 - x)/4
(c) [tex]D^{-1}(6.4) = \dfrac{11.6 - 6.4 }{4} = \dfrac{5.2}{4} = 1.3 \;\text{hours}[/tex]
(a) An angle measures 60°. What is the measure of its supplement?
measure of the complement:
(b) An angle measures 31°. What is the measure of its complement?
Answer:
(a) 120°
(b) 149°
Step-by-step explanation:
Supplementary angles add up to 180°
So to find the supplement of a given angle just subtract its measure from 180
(a) 180 - 60 = 120°
(b) 180- 31 = 149°
a) the supplementary angle of 60 degree is 120 degrees.
b) the complimentary angle of 31 degree is 59 degrees.
Supplementary angles are those angles whose sum comes out to be 180 degrees. to find a supplement of an angle we need to subtract the given angle from 180 degree.
supplement of 60 degree (here given angle is 60 degree)
= 180 - given angle = 180 - 60 = 120 degree
Complimentary angles are those angles whose sum comes out to be 90 degrees. To find a compliment of an angle we need to subtract the given angle from 90 degree.
compliment of 31 degree (here given angle is 31 degree)
= 90 - given angle = 90 - 31 = 59 degree
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find the sum or difference 6 3/5 - (-2 1/5)
A. -4 2/5
B. 8 4/5
C. -8 2/5
D. 4 2/5
Answer:
B
Step-by-step explanation:
Fraction subtraction:
[tex]\sf 6 \dfrac{3}{5}-(-2\dfrac{1}{5})=6\dfrac{3}{5}+2\dfrac{1}{5}[/tex]
Convert mixed fraction to improper fraction,
[tex]\sf = \dfrac{33}{5}+\dfrac{11}{5}[/tex]
Now, add.
[tex]\sf = \dfrac{33+11}{5}\\\\=\dfrac{44}{5}[/tex]
Covert improper fraction to mixed fraction.
[tex]\sf = 8\dfrac{4}{5}[/tex]
1 Order the following rational numbers from least to greatest.
-%, 1,-1,-1%, 6,-4
Answer is
-4 < -1 < -1% < 1 < 6
The sales tax rate is 5%. If Abdul buys a wheelbarrow priced at $79, how much tax will he
pay?
Answer:
$3.95Step-by-step explanation:
GivenPrice = $79,Sales tax = 5%.SolutionFind 5% of $79:
79 * 5/100 = 395/100 = 3.95Answer:
Abdul must pay $ 3.95.
Step-by-step explanation:
Now we have to,
→ find the amount of tax he must pay.
Then the amount will be,
→ (79/100) × 5
→ 0.79 × 5 = $ 3.95
Hence, he must pay $ 3.95.
You make a game where people try to throw a ball in a hole. The backboard is 34 by 30 inches. If the diameter of the hole
is 16 inches, what is the probability of getting the ball in the hole? Assume the ball either goes in the hole or hits the
board. Give your answer as a DECIMAL.
Assuming the ball either goes in the hole or hits the board, the probability of getting the ball in the hole is 0.197.
What is the probability?Probability is the chance of an expected event happening out of many other possible events.
Probability can be 1 or zero when there is 100% certainty or uncertainty. Otherwise, probability is always between 0 and 1 as a fractional value.
Dimensions of the backboard:Length = 34 inches
Width = 30 inches
Area = 1,020 in² (34 x 30)
Diameter of the hole = 16 inches
Radius of the hole = 8 inches (16/2)
Area of the hole = πR² or π(d/2)²
= ²²/₇ x 8 x 8
= ²²/₇ x 64
= 201 in²
The probability of getting the ball in the hole = the area of the hole divided by the area of the board.
= 0.197 (201/1,020).
Thus, if a person tries to throw a ball in the hole, the probability of achieving intended objective is 0.197.
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A pastry chef baked 462 cookies. 8 cookies can be packed in one box. How many boxes are needed to pack all the cookies?
Answer:
58 boxes.
Step-by-step explanation:
First, we divide 462 by 8.
462 ÷ 8 = 57.75
Because you cannot have 0.75 of a box, you must have another box.
57 + 1 = 58.
The answer is 58 boxes.
Hope this helps!
Btw, could I get Brainliest? Thanks!
Caleb lost 32 of his marbles when playing against his brother. if he began the game with 56 marbles, what fraction of his original marbles does he have left as a fraction?
Answer:
3/7
Step-by-step explanation:
Hey there!
To find this out, we have to put the numerator of the fraction as the number of marbles he has left, and the denominator as the number of marbles he had in total before he played
# of marbles in total - 56
# of marbles he has left - (56 - 32) 24
Fraction - 24/56
Simplify - 24/56 --> 3/7
So, the fraction of his original marbles he has left as a fraction is 3/7
Having trouble on this one need help
Unknown numbers m represents rational numbers and integer and n represent irrational number for the following case:
d. m = -7, n = √2 is the correct option .
As given is the question,
For given unknown numbers m and n ,
Check whether m is rational numbers and integer and n is irrational or not:
a. m = √3, n= -5
√3 is irrational number.
-5 is an integer and rational number.
b. m=√16 , n = 3 1/5
√16 = 4 is an integer and rational number
3 1/5 = 16/5 is a rational number.
c. m=√4 , n=√9
√4= 2 is an integer and rational number
√9=3 is an integer and rational number
d. m = -7, n = √2
Where,
m = - 7 is an integer and a rational number.
n = √2 is an irrational number.
These numbers can be put in the given diagram in question.
Therefore, unknown numbers m represents rational and integer and n represent irrational number for the following case:
d. m = -7, n = √2 is the correct option .
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Question
The manufacturer of pencils spends $0.05 to make each pencil and sells them for 0.25. The manufacturer also has fixed
costs each month of $2000.
Find the revenue function R when x pencils are manufactured.
Answer:C(x) = 2000+ 0.05 x
Step-by-step explanation: Cost (C) = fixed cost + (cost per pencil x number of pencils)
Since:
Fixed cost: $2000
Cost per pencil : $0.05
Replacing with the values given:
C(x) = 2000+ 0.05 x
Where x is the number of pencils manufactured.
Feel free to ask for more if needed or if you did not understand something.
Find the value of x.
1)
45°
5x
Which point is a point where the graph of y= (x + 2)(x2 + 4x + 3) crosses the x-axis?O A. (-3,0)OB. (2,0)O C. (1,0)OD.(3,0)
Given:
[tex]y=x+2\mleft(x^2+4x+3\mright)[/tex]The point where the graph crosses the x-axis is the x-intercept. At x-intercept, the y-coordinate is always zero.
Set y = 0 and solve for x, to find the x-intercept.
Therefore, the x-intercept of the graph is the following:
[tex]0=(x+2)(x^2+4x+3)[/tex][tex]\begin{gathered} 0=x+2 \\ x\text{ = -2} \\ (-2,\text{ 0)} \end{gathered}[/tex][tex]\begin{gathered} 0=x^2+4x+3 \\ \text{Factorize:} \\ 0\text{ = }x^2+x+3x+3 \\ 0\text{ = (x+1)(x+3)} \\ \\ 0\text{ = x+1} \\ x\text{ = -1} \\ (-1,\text{ 0)} \\ \\ 0\text{ = x + 3} \\ x\text{ = -3} \\ (-3,\text{ 0)} \end{gathered}[/tex]The x-intercepts are:
(-2, 0), (-1, 0), and (-3, 0)
The option that corresponds here is choice A.
ANSWER:
a. (-3, 0)
CAN YALL HELP ME
MY BRAIN HAS COMMITED sucidePLUS I FORGOT EVERYTHING
Answer:
Problem 1. n=28
Problem 2. a=10
Step-by-step explanation:
I'm not completely sure what you are really trying to accomplish but I think you are trying to do linear equations for these shapes.
Problem 1.
n+4n+40=180
add like terms
5n+40=180
subtract 40 from both sides
5n=140
divide by 5 on both sides
n=28
Problem 2.
7a+10a+12a+7a=360
add like terms
36a=360
divide both sides by 36
a=10
Hope this helps you remember how to do linear equations!
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Ray and Jon play a game of chance with two dice. If the sum of thedice is seven, Ray pays Jon $15. But if the sum is anything else,Jon pays Ray $10. What is the expected value of the game for Jon?Answer:-5.83
Given:
Two dice are rolled. n(S)=36
Let A be an event of getting a sum of 7.
[tex]A=\mleft\lbrace(1,6\mright),(2,5),(3,4),(4,3),(5,2),(6,1)\}[/tex][tex]n(A)=6[/tex][tex]P(A)=\frac{n(A)}{n(S)}[/tex][tex]P(A)=\frac{6}{36}[/tex][tex]P(A)=0.1667[/tex][tex]\text{The expected value of the game for Jon =}\frac{6}{36}\times10[/tex][tex]\text{The expected value of the game for Jon = \$}1.667[/tex]Hudson bought snacks for his team's practice. he bought a bag of apples for $1.59 and a 10-pack of juice bottles. the total cost before tax was $7.39. write and solve an equation which can be used to determine xx, how much each bottle of juice cost
The cost of each bottle of juice will be $0.58.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Hudson bought snacks for his team's practice. he bought a bag of apples for $1.59 and a 10-pack of juice bottles. the total cost before tax was $7.39.
The expression will be formed as below:-
10x + 1.59 = 7.39
Here x is the cost of the juice bottle.
10x + 1.59 = 7.39
10x = 7.39 - 1.59
10x =5.8
x = 5.8/10 = $0.58
Therefore, the cost of each bottle of juice will be $0.58.
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Find the slope of the line graphed below
Answer:
Go up 8 and right 2
8/2
Step-by-step explanation:
Simplify (4x −3+2x²) + (2x + 1)
Answer: 2x^2 + 6x - 2
Step-by-step explanation:
4x - 3 - 2x^2 + 2x + 1 =
2x^2 + 6x - 2
Fill in the blank------
Answer:
79.
Domain: (all real numbers)
Range: [1 to infinity)
x-int: none
y int: (0,1)
Function Value: 2 and 4
80.
Domain: (0 to infinity)
Range: [-1 to infinity)
x-int: none
y int: (0,1)
Function Value: 1
6
Mr. Werner works at a computer store. He receives a 20% discount off all merchandise as an employee benefit. Which
proportion can be used to find the amount a of the discount Mr. Werner will receive on a $1,650 computer system?
A
1,650
20
100
a
20
1.650 100
1,650 20
100
-
20
1,650 100
The proportion in (B) a/1650 = 20/100 can be used to find the amount of discount Mr. Werner will receive on purchase of a $1650 computer system.
What is percentage and how can its value be calculated?
A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The word "%" stands in for it. The dimension of percentages is zero. Thus, a dimensionless number is what it is called. By dividing the value by the entire value and multiplying the resulting number by 100, we can calculate the percentage.
Mathematically, Percentage = (Value/Total Value) × 100
Given, the percentage that Mr. Werner will get = 20%
The value of the discount = a
Total value of the computer = $ 1650
Therefore, using the formula established in the literature above, we have,
20 = (a/1650) × 100 ⇒ a/1650 = 20/100
Thus, the proportion in (B) a/1650 = 20/100 can be used to find the amount of discount Mr. Werner will receive on purchase of a $1650 computer system.
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Helppppp please!!! Immediately
Barbara, Mark, and Carlos participated in the third heat of “The Big Race.” Barbara thought she could win with a 3 meter head start even though she only pedaled 3 meters every 2 seconds. Mark began at the starting line and finished the 20 meter race in 5 seconds. Meanwhile, Carlos rode his tricycle so that his distance (y) from the starting line in meters could be represented by the equation y= 5/2x+1 where x represents time in seconds.
1)What is the dependent variable?
2)What is the independent variable?
3)Write an equation that discribes Barbara's motion. HINT: Write the equation in y=mx+by=mx+b form, where mm is the rate of change and bb is the starting point.
4)Write an equation that discribes Mark's motion. HINT: Write the equation in y=mx+by=mx+b form, where mm is the rate of change and bb is the starting point.
5)How fast did Carlos pedal? Write your answer as a unit rate
6)When did Carlos pass Barbara?
PLEASE HELP ASAP
The math counts club had a party at school. There were cookies and 40 slices pizza with nothing left pizza to be shared equally. Each students had the same number of whole cookies and the name number of slices of pizza with nothing left over. How many students How many students could have been at the party? (There is more than one answer. List as many as you can)
Answer:
There could have been 5, 10, or 20 students at the party.If there were 5, each student got 4 cookies and 8 slices of pizza if there were 10, each student got 2 cookies and 4 slices of pizza if there were 20, each student got 1 cookie and 2 slices of pizza
The monthly sale (in thousands of units) for the t^th month after the introduction of a product in the market is given by S = 135t/(t^2 + 50). In which earliest month would the sale (S) have been 9?
Given the following equation:
[tex]\text{ S = }\frac{135t}{t^2\text{ + 50}}[/tex]Let's determine t at S = 9.
We get,
[tex]\text{ 9 = }\frac{135t}{t^2\text{ + 50}}[/tex][tex]\frac{9(t^2+50\rparen}{9}\text{= }\frac{135t}{9}[/tex][tex]\text{ t}^2\text{ + 50 = 15t}[/tex][tex]\text{ t}^2\text{ -15t + 50}[/tex]a = 1, b = -15 and c = 50
Apply the quadratic formula:
[tex]\text{ t = x = }\frac{-\text{b }\pm\text{ }\sqrt{\text{b}^2\text{ - 4ac}}}{\text{ 2a}}[/tex][tex]\text{ = }\frac{\text{ -\lparen-15\rparen }\pm\text{ }\sqrt{(-15)^2\text{ - 4\lparen1\rparen\lparen50\rparen }}}{\text{ 2\lparen1\rparen}}[/tex][tex]=\text{ }\frac{\text{ 15 }\pm\text{ }\sqrt{\text{ 225 - 200}}}{\text{ 2}}[/tex][tex]\text{ = }\frac{\text{ 15 }\pm\text{ }\sqrt{\text{25}}}{\text{ 2}}[/tex][tex]\text{ = }\frac{\text{ 15 }\pm\text{ 5}}{\text{ 2}}[/tex][tex]\text{ x}_1\text{ = }\frac{\text{ 15 + 5}}{\text{ 2}}\text{ = }\frac{20}{2}\text{ = 10th month}[/tex][tex]\text{ x}_2\text{ = }\frac{\text{ 15 - 5}}{\text{ 2}}\text{ = }\frac{\text{ 10}}{\text{ 2}}\text{ = 5th month}[/tex]Therefore, the earliest month will be either the 5th or 10th month.
Among the given choices, only the 10th month is in the choices.
Therefore, the answer is CHOICE B : 10th
92 fewer than the product of 173 and r is equal to the quotient of 247 and r
The solution of the equation is as follows:
[tex]r = \frac{46+3\sqrt{4983} }{173}[/tex] and [tex]r = \frac{46-3\sqrt{4983} }{173}[/tex]
How to represent equation?The expression can be represented in equation as follows:
173 × r - 92 = 247 / r
Note: Quotient, in mathematics, can be defined as the result of the division of a number by any divisor.
Therefore,
173 × r - 92 = 247 / r
173r - 92 = 247 / r
let's solve for the variable r in the equation
add 92 to both sides of the equation
173r - 92 = 247 / r
173r - 92 + 92 = 247 / r + 92
173r = 247 / r + 92
Therefore,
173r - 247 / r = 92
173r² - 247 / r = 92
cross multiply
173r² - 247 = 92r
173r² - 92r - 247 = 0
Therefore,
[tex]r = \frac{46+3\sqrt{4983} }{173}[/tex] and [tex]r = \frac{46-3\sqrt{4983} }{173}[/tex]
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The measure of a supplement of an angle is 35 more than twice the complement of the angle. Find the measures of the angle, its supplement, and its complement.
The measure of the angle is 35°. The complement is 55° and the supplement is 145°.
How to calculate the angle?Let's measure of the angle = x
Supplementary angle of x = 180° - x
Complementary angle of x = 90° - x
By the given condition
180° - x = 2(90° - x) + 35°
Find the measure of the angle
180° - x = 2(90° - x) + 35°
⇒ 180° - x = 180° - 2x + 35°
⇒ - x = - 2x + 35°
⇒ - x + 2x = 35°
⇒ x = 35°
The measure of the angle = 35
The complement will be:
= 90° - 35° = 55°
The supplement will be:
= 180° - 35° = 155°
The concept illustrates how angles are calculated.
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Find the non-extraneous solutions of the square root of the quantity x plus 7 minus 4 equals quantity x plus 3
The non-extraneous solutions of the square root of the quantity x plus 7 minus 4 equal quantity x plus 3 is: x = -7 and x =-6.
How do we find the non-extraneous solutions?
The non-extraneous solution can be found with this calculation:
[tex]\sqrt{x} + 7 - 4 = x + 3\\\\\sqrt{x} + 7 = x + 7\\\\[/tex]
Now, we will square both sides:
[tex](x + 7) = (x + 7)^{2} \\\\(x + 7) = (x+7) (x+7)\\\\x + 7 = x^{2} + 14x + 49\\\\x = x^{2} + 13x + 42\\\\0 = (x + 7) (x+6)\\[/tex]
Thus, we have; x = -7 and x = -6
Note that we collected like terms from the figures on the left-hand-side to the figures on the right-hand side. When the lowest common multiple betwen 14 and 42 was checked, figures 7 and 6 were gotten.
When we plug figure x into both equations, we get the same figures and this confirms the solution.
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What is 2 1/2 ÷ 2 5/8
Answer: THE ANSWER IS 20/21
Step-by-step explanaTion:
Answer:
[tex]5\frac{1}{8}[/tex]
Step-by-step explanation:
[tex]=\frac{5}{2} +\frac{21}{8}[/tex]
[tex]=\frac{40+42}{16}[/tex]
[tex]=\frac{82}{16}[/tex]
[tex]=\frac{41}{8}[/tex]
[tex]=5\frac{1}{8}[/tex]
Hope this helps
elrond is organizing a council in rivendell. he has invited two men, two dwarves, and two elves, and plans to seat them along with himself in a circle with seven seats. he knows that dwarves and elves do not get along, so he plans to seat them so that no dwarf is sitting next to an elf. the circle has a head chair. if elrond (himself an elf) must sit at the head of the circle, in how many ways can he seat the other six guests? all beings are distinguishable from one another, and the head chair is distinguishable from the other chairs.
Elrond can sit his guest in 15 ways around the circle such that all conditions are fulfilled.
A cycle is a shape made up of all the points in a rectangle that are a certain distance from the center. It is the curve drawn by a moving location in a rectangle so that the radius from a given stage remains constant.
The radius of a circle is the distance between any two locations on the circle and the canter.
In most cases, the radius must be positive. A circle with r=0 is a degenerate instance. This section is about rounds in Euclidean geometry, primarily the Euclidean plane, unless otherwise noted.
Now we have to consider the conditions:
Elrond is holding a council at Rivendell. He's invited two men, two dwarves, and two elves, and plans to seat them all in a circle with seven seats, including himself. so 5+6=11
He understands that dwarves and elves do not get along, therefore he plans to arrange them so that no dwarf seats next to an elf. In the center of the circle is a chair. Hence 2=2 = 4
Number of ways = 11+4 = 15
Therefore Elrond can sit his guest in 15 ways around the circle such that all conditions are fulfilled.
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