Answers
20) 10x-7
15) 10x+2
18) 14x-3
21) 17-2x
16) 30+6x
19) -2x-11
22) 13x-12
Hope it helps!!!
16. 30+6x
17. 7x-12
18. 14x-3
19. -2x-11
20. 10x-7
21. 17-2x
22. 13x-12
Related Questions
What is the formula of remainder theorem?
Answers
The constant f(a) is the result of dividing a polynomial f(x) by xa, and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.
What are polynomials?Algebraic expressions called polynomials include constants and indeterminates.
Polynomials can be thought of as a type of mathematics.
Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
A specific kind of expression is a polynomial.
A mathematical statement without the equals symbol (=) is called an expression. Let's examine the definition and usage of polynomials as they are described below.
An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.
Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.
Hence, The constant f(a) is the result of dividing a polynomial f(x) by xa, and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.
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The remainder theorem helps us find the remainder when dividing a polynomial by a linear expression, using the formula R = f(a), where a is the root of the linear expression. Using this formula, we can easily calculate the remainder without performing long division.
The remainder theorem is a concept in algebra that helps us find the remainder when we divide a polynomial by a linear expression. The formula for the remainder theorem can be stated as follows:
If we have a polynomial f(x) and we divide it by a linear expression x - a, then the remainder R is given by the formula:
R = f(a)
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What is the other name for factorization method Mcq?
Answers
Answer:
Another name for factorization method Mcq is Doolittle's Method
Step-by-step explanation:
Hope it helps!
How do you get A+ in 7th grade?
Answers
In seventh grade, you received an A+:
1. Immediately after class, go through your notes.
2. Spend the most of your time studying throughout the day.
3. Read ahead rather than catching up.
4. Instruct someone else on the material.
5. Establish a study schedule from the start.
What is grading system?Grading in education is the practice of assigning standardized grades to students based on their degree of success in a course. Grades can be assigned in the form of letters, a range, a percentage, or a number out of a potential total. Grades are averaged in certain countries to get a grade point average. A 10-point grading scale is commonly used in Indian institutes (though some use a 4-point scale). Your GPA is derived by dividing the entire amount of your grades by the number of credits you took.
Here,
You get A+ in 7th grade:
1. Review your notes from class immediately after.
2. Do the bulk of your studying during the day.
3. Try to read ahead rather than play catch-up.
4. Teach the material to someone else.
5. Create a study schedule from day one.
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Bus 1 leaves Bulawayo at a constant speed of 80mph headed for Harare, 550 miles away. Bus 2 leaves Harare at 8:30AM traveling at 50mph. At what time will the buses pass each other?
Answers
The buses will pass each other at 12:37:30 PM
Calculation of time two buses pass each other.Bus 1 leaves Bulawayo at a constant speed of 80 mph headed for Harare, 550 miles away, Bus 2 leaves Harare at 8:30 AM traveling at 50 mph.To find the time when the two buses will meet, you need to find the time that Bus 2 will take to travel to the point where the buses will meet, and the time that Bus 1 will take to travel the same distance.
You can find the time that Bus 2 will take to travel to the point where the buses will meet by dividing the distance (550 miles) by the speed of Bus 2 (50 mph), which is 11 hours.
Then you can find the time that Bus 1 will take to travel the same distance by dividing the distance (550 miles) by the speed of Bus 1 (80 mph), which is 6.875 hours (or 6 hours and 52.5 minutes).
Now, you can subtract the time that Bus 2 takes to reach the point of intersection from the time that Bus 1 takes to reach the same point.
6.875 hours (or 6 hours and 52.5 minutes) - 11 hours = -4.125 hours (or -4 hours and 7.5 minutes)
Since Bus 2 leaves Harare at 8:30AM, you can subtract -4.125 hours from 8:30AM to find the time the buses will meet.
8:30AM - -4.125 hours = 12:37:30 PM
So the buses will pass each other at 12:37:30 PM
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Match the notation on the left with the term that best describes it.
1. AB
2.
3.
4.
5.
6.
7.
AB
OC
AC
CD
Point C
Point O
a.
b.
C.
d.
e.
f.
center
chord
diameter
radius
point of tangency
tangent
secant
D
B
You Try
A
Answers
Answer: AB : secant
OC : radius
AC : tangent
CD : chord
Point C : center
Point O : Point of tangency
D B You Try A : Not enough information provided to match the notation.
Step-by-step explanation:
Choose one item of interest to you in the Historical Pricing Chart on the next page.
2. Calculate the percent of change of the item's price each decade, and use your results to determine the average rate of change from 1980-2020.
3. Comment on the trend in your item's percent of increases.
4. Go shopping! Find the average current price of your item online, in the newspaper, or locally by looking at the price when you go to the store in the next day or two. Does the current price match the trend from 1980-2020 that you identified? Explain your thinking.
5. Create a line graph or other visual model to show the pricing trend. Be sure to include the current price in your model.
6. Predict the item's price at a future date. Use your calculations and visual model to justify your prediction.
7. Organize your analysis, prediction, explanations, and visual model in a brief news article. Your completed article will be submitted as your portfolio assessment.
Answers
I decided to use Gallon Of Gas
The rate of change is 19.8 cents annually.
The average cost of a gallon of gas is $3.744 this year (2021).
Does It Match The Trend ?
Gas prices increased significantly in 2021, almost by $2 in some states, due to disease.
Gas prices forecast for the coming year!
Capital price at the average rate of change and economic fixtures: $4 per gallon (Real-Life Problems)
Detailed explanation:
Determine the average rate of change from 1960 to 2000 by computing the percentage change in the item's price for each decade.
A simple reveals the anticipated rise in petrol prices over the coming ten years.
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I made the decision to utilise a gallon of gas. The annual change is 19.8 cents. This year, a gallon of gasoline costs on average $3.744. (2021).
What is the percent of change of the item's price each decade?Disease caused a substantial rise in gas prices in 2021, almost by $2 in some places. Future gas prices, the average rate of change in capital prices, and economic indicators: At $4 per gallon (Real-Life Problems). By calculating the price change percentage for each decade, you can calculate the overall rate of change between 1960 and 2000.
A quick calculation shows how much gasoline prices are expected to climb over the next ten years. Subtract the original price from the new price to determine the percent change, then divide the result by the original price and multiply by 100. We must now calculate the percentage change when 25 is raised to 45. To determine the percentage change, we can easily use the formula.
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You deposit $1000 in a savings account that earns 5% annual interest compounded yearly.
a. Write an exponential equation to determine when the balance of the account will be $1500
b. Solve the equation.
Answers
Answer:
a. 1500 = 1000 × 1.05^x
b. 1500 = 1000 × 1.05^x
Divide both sides by 1000
1500/1000 = 1.05^x
Take the natural log of both sides
ln(1500/1000) = ln(1.05^x)
ln(1.5) = x ln(1.05)
x = ln(1.5) / ln(1.05)
x = 5.12 years
Which of the relations given by the following sets of ordered pairs is a function?
A. ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))
B. ((1,2), (2, 3), (3,4), (2, 1), (1, 0))
C. ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3))
D. ((1,3), (1, 1), (1, 1), (1,3), (1,5)}
Answers
Answer:
[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))
Step-by-step explanation:
Given:
Which of the relations given by the following sets of ordered pairs is a function?
A. ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))
B. ((1,2), (2, 3), (3,4), (2, 1), (1, 0))
C. ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3))
D. ((1,3), (1, 1), (1, 1), (1,3), (1,5)}
Solve:
Knowing that; In order to know if a set of ordered pairs is a function or not we must see that if every x value have one or more than one y value that a function. If there is more than one same x value then it isn't a function.
Summary:
x value can't be duplicate but y can - in a working function
Hence, based on what we see in the answer choices;
[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6)) is a function. Due to none repeat x values.
[B]((1,2), (2, 3), (3,4), (2, 1), (1, 0)) isn't a function. Due to repeat x -values (1 and 2)
[C] ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3)) isn't a function. Due to repeat x-values (2)
[D] ((1,3), (1, 1), (1, 1), (1,3), (1,5)} isn't a function. Due to repeat x-values (1)
RevyBreeze
to translate an expression from words into a mathematical expression, _______________
Answers
Answer: to sum up
Step-by-step explanation:
how will the interval compare to the interval calculated for the same percentage if a normal distribution is assumed and the Empirical Rule is used?
Answers
The 68-95-99.7 rule, also known as the empirical rule, is a shorthand for remembering the percentage of values in a normal distribution that lie within an interval estimate: 68%, 95%, and 99.7% of values lie within one, two, and three standard deviations of the mean, respectively.
What is empirical rule?The empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule, is a statistical rule stating that for a normal distribution, nearly all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
The Empirical Rule states that 99.7% of data from a normal distribution is within 3 standard deviations of the mean.
68% of the data is within one standard deviation of the mean, 95% is within two standard deviations, and 99.7% is within three standard deviations, according to this rule.
Three-sigma limits that follow the empirical rule are used to define the upper and lower control limits in statistical quality control charts and risk analysis such as VaR.
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leirbe the vector with magnitude |vi|l = 89.5 at an angle of 305° from the positive x axis. Find the component form of vector v.
a) v=<-73.3,51.3>
b) v=<73.3,-51.3>
c)v=<-51.3,73.3>
d) v=<51.3,-73.3>
Answers
The required component form of the vector V is given as v=<51.3,-73.3>. Option D is correct.
What is vector?Vector is defined as property of object that describes both magnitude and direction of object when in motion is called vector.
here,
|V| = 89.5
and Ф = 305
now,
x component = |V| cos305°
= 89.5×cos305° = 51.3
y component = |V| sin305°
= 89.5×sin305° = -73.3
Thus, the required component form of the vector is given as v=<51.3,-73.3>. Option D is correct.
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14. Select all the expressions that are
equivalent to 28c-56
A. 7(4c-8)
B. 28(c-2)
C. -2(14c-28)
D. - 7(4c + 8)
E. - 7(8-4c)
Answers
The equivalent expressions are 7(4c - 8), 28(c - 2), - 7(8-4c). Options A, B, E
What are algebraic expressions?
Algebraic expressions are described as expressions that are made up of terms, variables, coefficients, factors and constants.
They are also composed of mathematical operations, such as;
SubtractionMultiplicationDivisionFloor divisionAdditionBracket, etcEquivalent expressions are those with the same solution but different arrangement of values, we have the expression;
28c-56
Let's factor the terms, we get;
7(4c - 8)
Also,
28(c - 2)
Hence, the expressions are 7(4c - 8), 28(c - 2), - 7(8-4c)
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Please help! Trig!!!!!!!l. Look at the image! And answer the question! Thank u!
Answers
Cosθ and secθ are positive when θ is in the third quadrant while other trigonometric ratios are negative.
what is trigonometric ratios ?The values of all trigonometric functions depending on the side ratio of a right-angled triangle are known as trigonometric ratios. The ratios of a right-angled triangle's sides to any acute angle are the angle's trigonometric ratios. Trigonometric ratios can be used to calculate the lengths of one (or both) of the acute angles in a right triangle if you know the lengths of two of its sides.
given
sinθ = - 4 / 5
cosθ = 3/5
tanθ = -4/3
secθ = 5/3
cotθ = -3/4
cosecθ = - 5/4
as Cosθ and secθ are positive when θ is in the third quadrant while other trigonometric ratios are negative.
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The y-intercept of function h(z) = −3(z+13)² - 28 is _____The domain is ________
and the range is______
Answers
The domain and range of the given function are (-∞,∞),{x|x∈R} and (-∞,-28],{y|y≤-28} respectively.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are h(z)=-3(z+13)²-28.
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): None
y-intercept(s): (0,-535)
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (-∞,∞),{x|x∈R}
Range: (-∞,-28],{y|y≤-28}
Therefore, the domain and range of the given function are (-∞,∞),{x|x∈R} and (-∞,-28],{y|y≤-28} respectively.
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What is called XYZ in algebra?
Answers
Therefore , as a result, the x, y, and z axes are the axis that the supplied coordinate plane problem is solved with.
A coordinate plane is defined.The phrase "coordinate plane" describes a two-dimensional area made up of two rational numbers. It appears at the point where the X and Y axes connect, called the origin. A coordinate grid's numbers can be used to find points.
Here,
The x, y, and z axes of the Cartesian coordinate system,
which is used to represent three-dimensional space, are three axes that are mutually perpendicular to one another.
The origin is the location where the three axes converge.
Therefore , as a result, the x, y, and z axes are the axis that the supplied coordinate plane problem is solved with.
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Solve for y
6x+8y=10
Answers
-6x -6x
8y=-6x +10
——————-
8
Y=-6/8x +5/4
What is the golden rule of algebra?
Answers
Answer: To keep both sides of the equation balanced
Step-by-step explanation:
The Golden Rule states that what you do to one side of an equation, that side being what is on one side of the equal sign, you must do to the other side. This is very important.
What are the 10 types of equation?
Answers
The 10 types of equation used in the mathematics are explained.
What are the 10 different types of equations?The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions.
For instance, the equation 3x 5 = 14 consists of the two expressions 3x 5 and 14, which are separated by the 'equal' sign.A linear equation is an algebraic equation. Each term in a linear equation is either a constant or the result of a constant plus one variable.In the case of a linear equation with two variables, the graph is a straight line.Equation with one variableEquation with two variablesMonomial EquationsBinomial EquationTrinomial EquationQuadratic equationTrigonometric equationRadical equationExponential equationRational equationThus, the 10 types of equation are mentioned.
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What is the change of base property?
Answers
The change of base property is a formula that makes it possible to express a logarithm in terms of logs expressed in a different base.
It is possible to express a logarithm in terms of logs stated in a different base using the change of base property formula. This is especially useful when evaluating a log to a base other than 10 or e using a calculator. X, a, and b are all taken to be positive. The base change property can be used to simplify equations with different bases for the logarithmic terms. All the logarithmic terms of an equation with logarithmic functions should have the same base in order to be solved.
Examples given below:
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y less than or equal to 5
Answers
The equation should be rearranged such that "y" is on the left and everything else is on the right.
What does less than or equal to mean in math?Plot the "y=" line, using a solid line for y or y and a dashed line for y or y>. For "more than" or "less than" indications, shade above the line (y> or y), or below the line variable (y or y).
The symbols for less than and less than or equal to are "" and "," respectively. In contrast to less than or equal to, which requires that the variable or quantity be either equal to or less than the specified limit, less than means that the variable or quantity must have a value lower than the specified limit. There must be a difference between a and b's values.
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The complete question is " How do you graph the inequality y≥−5?"
What is a table value?
Answers
When numbers are substituted into an equation, they typically produce a set of ordered pairs called a table of values (relation). Each ordered pair of numbers in the values table's table of values is related to one another according to the equation.
In math, what is a value?
Each digit's value varies based on where it is in the number, and this is referred to as the value. We figure it out by multiplying the digit's place value by its face value.
Value is composed of Place Value and Face Value. Honesty, integrity, benevolence, kindness, courage, and self-assurance are a few examples of values.
What does a table of values example mean?
You can choose two or more points to include in your graph by using a table of data, a graphic organizer or chart. For the equation y= 2x + 1, an example table of values is shown here.
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Willing to give 15 points for help please help me
Answers
Note that the above problems are solved using the knowledge of the sum of angles in a triangle.
10) when computed, x = 13°
11) when computed m∠S = 158°
12) when computed, ∠P = 115.625°; ∠Q = 21.125°; ∠R = 43.25°
13) when computed, angles L, J, K is 52°, 45°, 83° respectively.
14) When computed,
∠b = 108°
∠c = 36°
∠d = 36°
What is the sum of angles in a Triangle?Note that the Triangles Theorem posits that the sum of Angles in a Triangle = 180°
10) To solve for x, we know that:
the triangle is an Equilateralall the angles are equalAll the angles sum up to 180°one of the angles is given as 8x-44°Given the above, we can state:
8x-44 = 180/3
8x-44 = 60
8x = 60 +44
x = 104/8
x = 13°
Thus x = 13°
11) For this problem, the key to solving for x is to note that the triangle is isosceles.
This means that,
15x - 31 = 9x + 11
Thus, collecting like terms, we have:
15x-9x = 11+ 31
24x = 42
x = 42/24
Thus,
x = 1.75
Since we are looking for m∠S, we can arrive at this by removing (15x - 31 ) + (9x + 11) from 180° based on the rule of the Sum of Angles in a triangle.
That is:
180 - (15x - 31 ) + (9x + 11) = m∠S
To do this, we must impute the value of x in to the above equation:
⇒ m∠S = 180 - ((15 * 1.75) - 31 ) + ((9 * 1.75) + 11)
⇒ m∠S = 180 - (-4.75) + 26.75
m∠S = 180 - 22; thus
m∠S = 158°
12) <M, <P, <R, recall that the sum of the interior angles of triangle MPR will add up to 180 degrees
so <M + <P + <R = 180
We have ∠P is 14 less than five times x = 5x-15
∠Q is five less than x = x - 5
∠R is nine less than twice x =2x - 9
Recall the angle sum property of the triangle: The sum of all angles of a triangle is 180°
So, 5x -15 + x - 5 + 2x - 9 = 180°
Collect like terms to get
8x - 29 = 180
8x = 180+29
Thus,
x= 26.125
So,∠P = 5x-15
=5 (26.125) -15
∠P = 115.625°
∠Q =x-5
=26.125 - 5
∠ Q =21.125°
∠R = 2x - 9
=2(26.125)-9
Thus
∠R = 43.25°
To confirm, if the above ∠ sum up to 180°, we say
Check 43.25+21.125+115.625
⇒ 43.25+21.125+115.625 = 180° is TRUE.
13) To solve for ∠J, ∠K and ∠ L, recall that
The sum of the interior angles of triangle JKL will add up to 180 degrees
so <J + <K + <L = 180
L = measure of angle L
J = measure of angle J = L - 7
K = measure of angle K = 2L - 21
Thus, L + L-7 + 2L - 21 = 180; Collect like terms and we have
4L - 28 = 180
4L = 208
L = 52°,
If L is 52 then
J = L - 7 = 52 - 7
= 45°
K = 2L - 21 = 2(52) - 21
= 83
To check that they all sum up to 180° we say:
52+ 45+83
= 180°
14)
The sum of angle in a triangle is 180 degrees
Hence <b + <c + <d = 180
13x-35 + 5x - 19 + 2x + 14 = 180
13x+5x+2x-35-19+14 = 180
20x-40 = 180
20x = 180 + 40
20 x = 220
x = 220/20
x = 11
Get <b
<b = 13x-35
<b = 13(11) - 35
<b = 143-35
<b = 108 degrees
Get <c
c =5x-19
<c = 5(11)-19
<c = 55-19
<c = 36degrees
Get <d
<d = 2x+14
<d = 2(11) + 14
<d = 22+14
<d = 36 degrees
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Full Question for Number 14:
In ΔBCD if bc =bd angle b = 13x-35 angle c =5x-19 and angled d = 2x+14 find x and the measure of each angle
An Isosceles triangle has two congruent sides. the first side is expressed by x+2 and the second side is expressed by 2x-25 what is the value of X
Answers
The value of x is 27
How to determine the value
From the information given, we have that the triangle is an isosceles triangle.
The properties of an isosceles triangle are;
It has two equal sidesTwo equal anglesIt has three edges and three verticesSum of internal angles is 180We have that;
First side = x + 2
Second side = 2x - 25
Equate the two sides, we get;
x+ 2 = 2x - 25
collect like terms
x - 2x = - 25 - 2
subtract like terms
-x= -27
make 'x' the subject
x = 27
Hence, the value is 27
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Is a dilation with a scale factor of 2 A reduction?
Answers
When the scale factor is between 0 and 1, a dilation is considered a reduction.
How To Find The Scale Factor Of A Dilation?The center point of the dilation is located, and the distances between this center point and various points on the preimage and the image are measured in order to determine the scale factor for the dilation. According to Math Bits Notebook, we can determine the scale factor by dividing these distances by two.Given that each angle is congruent, each segment is proportional, the slope of each segment is preserved, and the perimeter of the preimage and image have the same scale factor, using dilation scale factors allows us to enlarge or reduce a figure to the desired size.To Learn more Aboutdilation refer To:
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Can anyone help me to solve this question....
Answers
If Ahmad works at a constant rate, he will take 90 minutes in finishing his exam, and he will finish it at around 1:15 pm.
How long takes Ahmad to answer all the questions?We know that Ahmad answers at a constant rate, and he takes around 1.5 minutes to answer each answer.
The total time that it will take him to answer the 60 questions is equal to the number of questions times the time that it took him to answer each one, then the total time is:
T = (1.5 min)*60 = 90 minutes
So it will take him an hour and a half.
And e know that the exam starts at 11:45 am
After one hour, it will be:
0:45 pm
And after 30 minutes, it will be:
1:15 pm
Ahmad will finish his exam at 1:15 pm.
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What is an exponential function for 0 3?
Answers
The exponential function cannot be found.
To find an exponential function, f(x)=[tex]a^{x}[/tex], containing the point, set f(x) in the function to the y value 3 of the point, and set x to the x value 0 of the point. 3 = [tex]a^{0}[/tex]
Solve the equation for a.
Let's rewrite the equation,
[tex]a^{0}[/tex] = 3
Anything with 0 in power is 1
1 = 3
As, 1 ≠ 3
There are no solution.
Since there is no real solution, the exponential function cannot be found.
Hence, the exponential function cannot be found.
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A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 403 gram setting. Is there sufficient evidence at the 0.01 level that the bags are underfilled? Assume the population is normally distributed.
State the null and alternative hypotheses for the above scenario.
Answers
The null hypothesis is H0: p = 403
The alternative hypothesis is given as: H1: p < 403
What is the alternative hypothesis and the null hypothesis?The null hypothesis is a statement that there is no significant difference or relationship between two groups or variables. It represents the status quo or the default assumption that there is no effect.
The alternative hypothesis is the statement that there is a significant difference or relationship between the groups or variables. It is the opposite of the null hypothesis and represents the research hypothesis or the claim that you are trying to test.
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Add the following interger ing algebra title/counter. Illutrate your olution uing algebra tile/counter red for poitive counter and black for negative counter. Do thi in your notebook
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This problem can be represented with color counters/tiles. In this case, the red counters represent positive numbers and the black ones represent negative numbers.
One technique to introduce the idea of adding and subtracting numbers is through the use of integer tiles. When working on the kind of issue that many students find more challenging—problems like -4 + -5—this paradigm might be helpful.
One positive counter and one negative counter/tile equal zero because 1+(−1)=0. Draw a line through the counters that equals zero.
The remaining counters represent the answer. Therefore, 4+(−2)=2. The answer is the difference between 4 and 2. The answer takes on the sign of the larger number. In this case, the four has a positive value and it is greater than 2.
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Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point (1,70) she made on her graph. After day 4, Lin reaches page 190, which does not match the point (4,160) she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.Sketch a line showing Lin's original plan on the axes. Click on the graph and select edit to complete the graph. Once done, hit save and close to see your completed graph. What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
Answers
No. of pages read on day of planning are represented by vertical intercept.
The difference between vertical intercept of original plan and line drawn by Lin is 10 unit.
What is slope-intercept form of line?The slope intercept form equation for a straight line with a slope, 'm', and 'c' as the y-intercept can be given as:
y = mx + c.
Given,
No. of pages Lin read on day of planning = 30
No. of pages she plans to read everyday = 40
If total pages are y for x days then,
y = 40x + 30
which is the original plan of Lin.
comparing it with slope-intercept form of line
y = mx + c
slope m = 40
vertical intercept of original plan c = 30 unit
slope m represents the no. of pages read everyday.
vertical intercept represents the no. of pages read on day of planning.
vertical intercept c' of line drawn by Lin = 40 unit
Comparing intercept of original plan to line drawn by Lin
= |c - c'|
= |30 - 40|
= 10 unit
Hence, the vertical intercept represents the no. of pages read on day of planning.
There is 10 unit difference between vertical intercept of original plan and line drawn by Lin.
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What is the factored form of the polynomial f (x) = 8x³ - 60x² +150x - 125?
Answers
Answer:
(2x-5)^3
Step-by-step explanation:
(((8 • (x3)) - (22•3•5x2)) + 150x) - 125
((23x3 - (22•3•5x2)) + 150x) - 125
3.1 8x3-60x2+150x-125 is not a perfect cube
Factoring: 8x3-60x2+150x-125
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 150x-125
Group 2: -60x2+8x3
Pull out from each group separately :
Group 1: (6x-5) • (25)
Group 2: (2x-15) • (4x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.