The factors of the expression x² 4x 3 are (x + 3)(x − 3).
What is factor?Factor is a number that can be multiplied to produce another number. Factors are used to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers. Factors are also used in equations to find solutions and in algebra to solve polynomials. Factors are also important in computing, since they are used to identify prime numbers and prime factorisation.
This is determined by using the factoring technique called factoring by grouping.
First, the expression is written in two groups: x2 and 4x 3. Then, each group must be factored. For the first group, the factors are x and x, since any number multiplied by itself results in the number itself. For the second group, the factors are 4 and 3, since 4 multiplied by 3 equals 12.
Next, the two factors of each group must be multiplied together. The product of x and 4 is 4x, and the product of x and 3 is 3x. The product of 4 and 3 is 12.
Finally, the two groups of factors are combined to form the final expression: (x + 3)(x − 3).
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Option A: You are given $100 on the first day and then receive $10 each day for the month of February.
Option B: You are given one cent on the first day and that amount will double each consecutive day for the month of February.
Write a function rule to represent the total amount earned with Option A.
Write a function rule to represent the amount of money you will have earned with Option B.
The function rule to represent the total amount earned with Option A and earned with Option B are f(x) = 100 + 10x and f(x) = (1/100) * 2^x.
What is the function rule?
The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
For Option A, the total amount earned can be represented by the function:
f(x) = 100 + 10x
where x is the number of days in February (x = 28 for a standard non-leap year)
For Option B, the total amount earned can be represented by the function:
f(x) = (1/100) * 2^x
where x is the number of days in February (x = 28 for a standard non-leap year)
the above function will be in cents, to get dollar values divide it by 100.
hence, the function rule to represent the total amount earned with Option A and earned with Option B are f(x) = 100 + 10x and f(x) = (1/100) * 2^x.
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1. True or False: The solution you get from substitution is the same as the solution you would get
from graphing. *
False
True
2. For substitution, we want *
(1 Point)
a. both equations to be in standard form Ax + By = C
b. equations with negative numbers
C. at least one equation to be y= or x=
d. equations with positive numbers
answer:
my answer to the first one would be false
my answer to the second would be a
help me on this one bro I hate math
The initial amount of the investment is $800, the investment grows at the rate of 10% each year, and the value of the investment after 12 years is $1760.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates from the graph.
(0, 800), (1, 880), (2, 968)
x-coordinate is the number of years and the y-coordinate denotes the Value.
Now,
The initial amount of the investment is when x = 0.
= 800
Now,
Rate of change of the value each year.
=(880 - 800) / (1 - 0)
= $80
Rate of percentage.
= 80/800 x 100
= 10%
Now,
The value of the investment after 12 years.
= 800 + 12 x 80
= 800 + 960
= $1760
Thus,
The initial amount of the investment is $800.
The investment grows at the rate of 10% each year.
The value of the investment after 12 years is $1760.
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What kinds of problems are not solved by algorithms?
Answer:
Undecidable Problems
Step-by-step explanation:
a ski area claims that its lifts can move 47000 people per hour. if the average lift carries people about 200m (vertically) higher, estimate the maximum total power needed?
The peak is located at R=1 according to a power curve analysis. To put it another way, the load and source resistance must match.
At what point does maximum total power occur?The ski area's name needs to be changed first. Squaw is not a kind way to refer to a woman. It is an expression that refers to female genitalia. (a decent slang equivalent in English begins with "c" and rhymes with "runt") During my time as a teacher in an Indian school, I learned this in a very embarrassing manner.
If we suppose that each person weighs roughly 70 kilograms (154 lbs) on Earth, then the power required to simply raise the people is P = W/t, and since W = mgh in this situation, P = W/t = mgh/t = (47,000 people)(70 kg/person).
(2 MW) = (1791222.222 W)(9.8 N/kg)(200 m)/(3600 s).
The complete question is:
Squaw Valley ski area in California claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the maximum total power needed.
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If 2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0, find lim x→2 f(x).
The value of [tex]\lim _{x \rightarrow 2}[/tex] f(x) by Sandwich theorem is 2.
As per the given data the function limits are:
2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0
Here we have to determine the value of [tex]\lim _{x \rightarrow 2}[/tex] f(x)
Hence by Sandwich theorem:
The sandwich theorem, also known as the squeeze theorem, asserts that if two functions, g (x) and h (x), are squeezed between one another and their respective limits at a given position are both equal to L, then the limit of f (x) at that point is also equal to L.
We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" [tex]\frac{sin(x)}{x}[/tex] between two nicer functions and using them to find the limit at x = 0.
[tex]& \lim_{x \rightarrow 2}(2 x-2) \leq\lim_{x \rightarrow 2} f(x) \leq \lim_{x \rightarrow 2}\left(x^2-2 x+2\right) \\[/tex]
[tex]& \Rightarrow 2 \leq \lim _{x \rightarrow 2} f(x) \leq 2 \\[/tex]
Hence [tex]\lim _{x \rightarrow 2}[/tex] f(x) = 2
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Is 7th interval perfect?
7th interval is not perfect
7th interval is not perfect
A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤1. The group of numbers such that 0 < x< 1 and the group of all real numbers are other examples of intervals.
the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).
Real intervals are the simplest sets whose "length" (or "measure" or "size") is straightforward to define, making them significant in the theory of integration. The Borel measure and ultimately the Lebesgue measure can subsequently be produced by applying the concept of measure to more intricate sets of real numbers.
Interval arithmetic is a broad numerical computing method that automatically generates assured enclosures for all formulas, even in the presence of errors, approximations in mathematics, and arithmetic roundoff.
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How many one-cup servings of milk are in a two-liter bottle? Round your answer to the nearest tenth.
____________one-cup servings
The number of cups of serving that is possible in a two-liter bottle is 8.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know 1 liter is equal to 4 cups.
Therefore, The number of cups serves possible in a two-liter bottle is,
= (2×4) cups.
= 8 cups.
So, 8 cups of servings are possible from a two-liter bottle.
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What is the difference of the polynomials 5x 3 4x 2 )-( 6x 2 2x 9?
The Solving we get the difference of the given polynomials [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] as [tex]5x^{3} - 2x^{2} + 2x + 9[/tex] .
What is a Polynomial ?
The polynomial is defined as the expression that is composed of variables, constants and exponents, which are combined by using mathematical operations such as addition, subtraction, multiplication and division .
Based on number of terms present in polynomial , they can be classified as monomial, binomial, and trinomial .
For Example : [tex]3x^{2} +4x[/tex] .
The polynomial is given as : [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] ;
On simplifying the above given polynomial ,
we get ,
= [tex]5x^{3} + 4x^{2} - 6x^{2} + 2x + 9[/tex]
On subtracting the like terms together in above equation ,
we get ;
= [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]
Therefore , the difference of the polynomials is (d) [tex]5x^{3} - 2x^{2} + 2x + 9[/tex] .
The given question is incomplete , the complete question is
What is the difference of the polynomials?
[tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex]
A. –x³ + 6x² + 9
B. –x³ + 2x² – 9
C. 5x³ – 2x² – 2x – 9
D. 5x³ – 2x² + 2x + 9
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Put these numbers in order from least to greatest.
-8.52
-8.15
8.25
0.55
Answer:
-8.52, -8.15, 0.55, 8.25
Step-by-step explanation:
The lowest of negatives goes first, and the highest of positives goes last.
Answer:
from the least to the highest which is:
-8.52
-8.15
0.55
8.25
Triangle EFG is dilated by a scale factor of 2/3 to form a triangle E'F'G'. What is the measure of side E'F'?
By using scale factor formula we can evaluate the measure of side EF.
What happens when we dilate a triangle?When a triangle is dilated by scale factors.The base and height change by the scale factor s while the area changes by a factor of s^2. While the scale distances between points dilations do not change angles.Dilation is used to make the objects larger or smaller.
How do you find scale factor?The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
From the question ΔE'F'G' is the image formed by the dilation of preimage ΔEFG.
Therefore,
2/3 =[tex]E_{1}[/tex][tex]F_{1}[/tex]/EF
EF=3/2[tex]E_{1}[/tex][tex]F_{1}[/tex]
By substituting any value of F'G' given in the equation we can evaluate the measure of side FG.
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50 Points!
Which linear equation shows a proportional relationship?
Answer: y=3/ 4x
Step-by-step explanation: in the linear equations y= Kx shows the proportionality relations . Where k is the proportionality constant which can be any number . x an y are the variables, so according to this answer will be y=3/
Answer:
y=3/4x
Step-by-step explanation:
Let's first define some words;
Proportional: If a line or a ray through the origin it proportional
Non proportional: If a line or ray that does not pass through the origin
Origin: Initial point or the starting point
Now we have define the words now let's graph these points by using Desmos.
Graphs are shown below.
Base on the graphs below we can see that;
y=3/4x pass through the origin which means the that this linear equation is proportional.
RevyBreeze
If we remove 11 books from my shelf and multiply the remaining number of books by 12, we will get the same result as of we remove 10 books from the shelf and multiply the remaining number of books by 11. How many books are on my shelf before any are removed?
Answer:
22
Step-by-step explanation:
I timesed 11 by 12 which is 132 and then timesed 10 with 11 which then gave me 110. I then subtracted 132 with 110 which gave me the answer 22. if we remove 11 from the 22 books we then end up with 11. then times it by 12 = 132. then if you subtract 10 of the 22 books then we end up with 12. then times it by 11 which is 132 as well.
What is 1 mole equal to grams?
Therefore, one mole of any substance is equal to its molar mass in grams.
Define molar mass.Mass per mole is a definition of molar mass. In other terms, molar mass is the total mass of all the atoms in a material that makes up a mole. It is measured in gram-per-mole units.
What are atoms?A chemical element is uniquely defined by its atoms, which are tiny pieces of substance. An atom is made up of a core nucleus and one or more negatively charged electrons that orbit it. The positively charged, comparatively hefty protons and neutrons that make up the nucleus may be present.
The molar mass of a substance is the mass of one mole of that substance and is usually expressed in grams per mole (g/mol).
For example, the molar mass of carbon is 12.01 g/mol, so one mole of carbon weighs 12.01 grams.
Therefore, one mole of any substance equals its molar mass in grams.
It is essential to mention that the molar mass is the weight of one mole of a substance and is determined by the atomic or molecular weight of the substance.
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Given triangle ABC, which equation could be used to find the measure of ∠C?
a
tan m∠C = one half
b
sin m∠C = square root of 5 over 5
c
sin m∠C= square root of 5 over 2
d
tan m∠C = 2
The measure of the angle ∠C in the triangle ABC can be gotten using tan m∠C = 2
What is an equation?An equation shows how two or more numbers and variables are related to each other.
On the other hand, trigonometric ratios are used to show the relationship between the sides and angles of a right angled triangle.
The basic equations of the trigonometry ratios are
sinФ = opposite/hypotenuse; cosФ = adjacent/hypotenusetanФ = opposite/adjacentUsing the above as a guide, and the given triangle:
We have:
tan m∠C = opposite/adjacent
Substitute the known values in the above equation, so, we have the following representation
tan m∠C = 6/3
Evaluate
tan m∠C = 2
Hence, the true equation is (d) tan m∠C = 2
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This is mad confusing
Answer: 112 degrees
Explanation:
By the alternate interior angles theorem, m<CAD=40 and m<ACD=28. The quadrilateral is divided into two triangles. The sum of the angles of a triangle is equal to 180 degrees. Now that you know the measurements of two out of the three angles, you can add them up and subtract them from 180.
180-(40+29)=112
Triangle BAC was rotated 90° clockwise and dilated at a scale factor of 2 from the origin to create triangle XYZ. Based on these transformations, which statement is true?
<Z=<A
<B=<Y
<A=<X
<C=<Z
We know that a 90-degree clockwise rotation is the same as a 270-degree counterclockwise rotation, which means that the coordinates of each point in the original triangle BAC will be flipped across the x-axis, and then rotate 270 degrees.
We also know that a dilation at a scale factor of 2 means that the coordinates of each point are multiplied by 2.
Based on these transformations, the statement that is true is <C=<Z
In triangle BAC, point C has the same coordinates as point Z in triangle XYZ.
This because, the original point C is transformed by rotating 90 degrees counterclockwise and scaling by a factor of 2, This result in point C moving to the position of point Z.
The rest of the statements are not true based on this rotation and dilation because the coordinates of points A, B, and Y will be different from the original triangle BAC.
(Simplify: 7a + 6 - 3 - 2
Jeremy made nine out of twelve basketball shots in P.E. class. What decimal and percent represents the number of shots he made?
is two displacement vectors add to give a total displace,ment of 0 what do you know about the two diplacemenst
The two vectors are equal in magnitude and opposite in direction. This means that they cancel each other out, resulting in a net displacement of 0.
If the total displacement of two vectors is 0, it means that the final position of an object after being displaced by the two vectors is the same as its initial position. This can happen in a few ways:
The two vectors are equal in magnitude and opposite in direction. This means that they cancel each other out, resulting in a net displacement of 0.
The two vectors are parallel but pointing in opposite directions. This means that the object is displaced in one direction and then back again, resulting in a net displacement of 0.
The two vectors are perpendicular and the magnitude of each vector is the same. This means that the object is displaced in one direction and then back again in the perpendicular direction, resulting in a net displacement of 0.
Therefore, In all cases, it can be inferred that the two vectors are in some way related to each other in terms of direction and magnitude.
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Felix hasa bucket of golf bals, The table shows the number of golf balls of each color in the bucket. Golf Balls in a Bucket Color Pnk White Orange Green Number 11 8 18 (A)e Felix selects a golf ball at random. Based on the Information in the table, which statement is true? A The golf ball is more likely to be green than all other colors combined. B The golf ball is equally likely to be pink, white, orange, or green. C The golf ball is 2 times as likely to be orange as it is to be pink. D The golf ball is 7 times as likely to be green as it is to be white.
The correct statement regarding the probabilities from the table is given as follows:
C The golf ball is 2 times as likely to be orange as it is to be pink.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of balls for this problem is given as follows:
4 + 11 + 8 + 18 = 41.
Hence the probability of selecting each ball is obtained as follows:
Pink: 4/41.White: 11/41.Orange: 8/41.Green: 18/41.Hence statement C is correct, as:
2 x 4/41 = 8/41.
(which is the probability of orange, obtained multiplying the probability of pink by two).
Missing InformationThe number of pink balls is of 4.
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Find m (angle) 1 . Then classify the triangle by its angles.
M (angle) 1 =
Answer:
60 degrees and an equilateral triangle
Step-by-step explanation:
every triangle adds to 180 degrees
add 60+60=120
180-120=60 to find remaining angle
all angles are the same which makes all sides the same: equilateral
Answer:
1 =60
Step-by-step explanation:
a+b+c=180
60+60+c=180
120+c=180
-120. -120
c=60
The scatter plot shows the number of strawbernes that have been picked on the farm during the month of February.
Part A Using computer software, a correlation coefficient of 0. 01 was calculated Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B. Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for strawberries picked on the farm (5 points)
There is a relationship between the numbers of strawberries gathered and the amount of rainfall that can be found in a model (function).
What is a Scatter Plot?A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.
Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.
Part A:
The correlation coefficient of r = 0.1 is valid based on the provided scatter plot.
Part B:
The independent variable (the explanatory variable) is the cause of the dependent variable in a causal connection.
As a result, you need to identify a plausible factor that can influence the number of strawberries collected.
The week before harvest, I could picture how much it would rain.
Hence, There is a relationship between the number of strawberries gathered and the amount of rainfall that can be found in a model (function).
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:
Step-by-step explanation:
The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:
f(–10) = (–10)^2 – 5(–10) + 12 = 100 – (–50) + 12 = 162
The statement "The graph of the function is a parabola" is true. Because the equation of the function is of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0, the graph of the function is a parabola.
The statement "The graph of the function opens down." is true. The coefficient of x^2 is a positive value, which means the parabola opens down.
So, the true statements are
The graph of the function is a parabola.
The graph of the function opens down.
The graph does not contain the point (20, –8)
You have 50 coin that worth $8. 25. You have dime, quarter and nickel. The number of quarter i 5 more than twice the number of nickel. How many dime, quarter and nickel do you have individually
4 12. DISCUSS MATHEMATICAL THINKING Recall that a perfect square is a number with integers as its
square roots. Is the product of two perfect squares always a perfect square? Is the quotient of two
perfect squares always a perfect square? Explain your reasoning.
Please help will give Brain liest
Yes the product of two perfect squares is always a perfect square, But the quotient of two perfect squares is not always a perfect square.
What is perfect square?A perfect square is a number that can be expressed as the product of an integer multiplied by itself.
Examples of perfect squares include 4 (2*2), 9 (3*3), and 25 (5*5).
What is quotient of a number?The quotient is the result obtained after performing division of one number by another. It is the number of times that the divisor can be subtracted from the dividend until the remainder is smaller than the divisor.
The product of two perfect squares is always a perfect square because the root of the products is equal to the product of roots as shown below,
let us take the two perfect squares 4 and 9, so the square root of 4*9 is,
[tex]\sqrt{4*9} =\sqrt{4} *\sqrt{9} \ =2*3=6[/tex]
But , the quotient of two perfect squares is a perfect square,
When we divide two perfect squares we are not always going to get a quotient that can be represented as the square of an integer. For example, (36/16) = 9/4 which is not a perfect square.
However, if the numerator and denominator in the quotient are the same perfect square then the quotient will be 1 which is a perfect square.
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What does ln () do in Excel?
ln() is a function in Excel that calculates the natural logarithm of a number. The natural logarithm is the logarithm to the base e, where e is an irrational number approximately equal to 2.718281828.
1. Enter the number for which you want to calculate the natural logarithm in a cell.
2. Click on the cell and enter "=ln()" function (without the quotation marks) in the formula bar.
3. Within the parentheses, enter the cell reference or the number for which you want to calculate the natural logarithm.
4. Press the Enter key and the natural logarithm of the number will be calculated and displayed in the cell.
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10. Find the solution set for the following
y=x²-3x-4
y-x=-4
Answer:
I have no idea tbh I need help with this too
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!
The coordinate of A i -9 and the coordinate of C i 12. The ditance between A and B i 1/3 of AC. What i the coordinate of B?
The cordinate of point B is -2.
To find the coordinate of point B, we need to determine its distance from point A and then add that distance to the coordinate of point A. We are given that point B lies on a number line between points A and C, and that the distance between A and B is 1/3 of the distance between A and C.
First, we'll find the distance between points A and C. We know that the coordinate of A is -9 and the coordinate of C is 12. To find the distance between these two points, we simply subtract the coordinate of A from the coordinate of C. So, 12 - (-9) = 21. This tells us that the distance between points A and C is 21 units.
Next, we'll use this information to find the distance between points A and B. We know that this distance is 1/3 of the distance between A and C, so we'll multiply 21 (the distance between A and C) by 1/3. 21 * 1/3 = 7. This tells us that the distance between points A and B is 7 units.
Finally, we'll add this distance to the coordinate of point A to find the coordinate of point B. Since A is at -9, B is at -9 + 7 = -2. Therefore, the coordinate of B is -2.
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If Marvin has 47 pencils and Mark has a total number of pencils is 4 tens
and 3 ones, who would have a greater total? Draw a math drawing to explain
how you know.
Number of pens x=10.
Number of pencils y=30.
How many pencils are there?The Five Principles are: freedom, efficiency, mutuality, responsibility, and quality. Victoria that she always incorporates The Five Principles into her conversations with other businesses, government officials, and other partners and leaders. The writing core is tougher and leaves a lighter trace on the paper as the number increases.
Let number of pens =x
And number of pencils =y
⇒ x+y=40
⇒(5+y)+(x−5)=4x
⇒3x=y
Substituting in above equations ;
⇒x+3x=40
⇒x=10
⇒y=30
∴number of pens =x=10
⇒number of pencils =y=30
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