PART 2!!
Topic: Addition and Subtraction of polynomials
Directions: Simplify each rational expressions
Answers
Step-by-step explanation:
4.
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{a - b}{a + b} [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{(a - b)(a - b)}{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{ {a}^{2} - 2ab + {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - ( {a}^{2} - 2ab + {b}^{2} ) }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - {a}^{2} + 2ab - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{7ab - {a}^{2} - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] \: [/tex]
5.
[tex] = \frac{5}{n + 5} + \frac{4n}{2n + 6} [/tex]
[tex] = \frac{5}{n + 5} + \frac{4n}{2(n + 3)} [/tex]
[tex] = \frac{5}{n + 5} + \frac{2n}{n + 3} [/tex]
[tex] = \frac{5(n + 3) + 2(n + 5)}{ {n}^{2} + 8n + 15 } [/tex]
[tex] = \frac{5n + 15 + 2n + 10}{ {n}^{2} + 8n + 15} [/tex]
[tex] = \frac{7n + 25}{ {n}^{2} + 8n + 15} [/tex]
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve these problems ~
Problem 1 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ {a}^{2} - {b}^{2} } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ (a + b)(a - b) } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b)(a - b)}{ (a + b)(a - b) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b) {}^{2} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a {}^{2} - 2ab + {b}^{2} ) {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - a {}^{2} + 2ab - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{7ab - a {}^{2} - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
Problem 2 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5}{n + 5} + \dfrac{4n}{2n + 6} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5(2n + 6) + 4n(n + 5)}{(2n + 6)(n + 5)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{10n +30 + 4n {}^{2} + 20n}{2n {}^{2} + 10n + 6n +30} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{4n {}^{2} + 30n + 30}{2n {}^{2} + 16n + 30} [/tex]
[ taking 2 common out ]
[tex]{ \qquad \sf \dashrightarrow \: \dfrac{2n {}^{2} + 15n + 15}{n {}^{2} + 8n + 15}} [/tex]
Related Questions
Find the first five terms of each sequence. an =5 n-3
Answers
The first five terms of the sequence an =5 n-3 are 2, 7, 12, 17 and 22.
According to the question.
We have a formula or a rule for finding the terms of a sequence i.e.
an = 5n -3.
The first term of the sequnence an = 5n - 3 is given by
a(1) = 5(1) -3 = 5 -3 = 2
The second term of the sequence an = 5n - 3 is given by
a(2) = 5(2) - 3 = 10 - 3 = 7
The third term of the sequence an = 5n -3 is given by
a(3) = 5(3) - 3 = 15 - 3 = 12
The fourth term of the sequence an = 5n - 3 is given by
a(4) = 5(4) - 3 = 20 - 3 = 17
The fifth term of the sequence an = 5n - 3 is given by
a(5) = 5(5) - 3 = 25 - 3 = 22
Hence, the first five terms of the sequence an =5 n-3 are 2, 7, 12, 17 and 22.
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A. Solves each equation by extracting square root.
1.) x² = 16
2.) x² = 49
3.) x² = 128
4.) x² = 108
5.) x² = 121
6.) x²-169 = 0
7.) x²-80=0
8.) x²-63=0
9.) 5x2 – 125 = 0
10.) 3x²-132-0
Answers
1,2,5 square root both sides
47simplify into 8 root 2simplify into 6 root 311add 169 to both sides and square root to get 13add 80 to both sides and simplify into 4 root 5add 63 to both sides and simplify into 3 root 7add 125 to both sides, divide both sides by 5, x^2=25, square root, x=5add 132 to both sides, divide by 3, x^2=44, square root simplified is 2 root 11what does x equal
4x+5x+=6+11
Answers
4x+5x+=6+11
9x=17
x=17/9
☞ user58580~ ♥
Answer:
x= 17/9
Step-by-step explanation:
4x+5x=6+11
Combine like terms
9x=17
x=17/9
What is the sum of the solutions of |3|y-4| = 9 and |y-4|=3 ?
Answers
The sum of the solutions are 32/3.
The modulo (or "modulus" or "mod") is the remainder after dividing one number by another.
Example: 100 mod 9 equals 1
Because 100/9 = 11 with a remainder of 1
Another example: 14 mod 12 equals 2
Because 14/12 = 1 with a remainder of 2
12-hour time uses modulo 12 (14 o'clock becomes 2 o'clock)
It is where we end up, not how many times around.
|3y-4|=9
3y-4=9 or 3y-4=-9
3y=13 or 3y=-5
y=13/3 or y-5/3
|y-4|=3
y-4=3 or y-4=-3
y=7 or y=1
The solutions are y=13/3, y=-5/3, y=7, y=1
Hence the sum of the solutions are 32/3.
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y-2=¼(x+5) into slope-intercept form?
Answers
The slope intercept form is y = 1/4x + 13/4
The general expression for slope intercept form is given as follows
y = mx + c
where, m = slope of the line
c = intercept
We have been given the equation that is,
y – 2 = 1/4(x+ 5)
We will solve this step by step to convert it into the general form that is,
y – 2 = 1/4(x+ 5)
y – 2 = 1/4x + 5/4
y = 1/4x + 5/4 + 2
y = 1/4x +13/4
which is in the general form of y= mx + c where m = 1/4 and c = 13/4
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Determine whether the graph represents a function. Explain
Answers
Order from least to greatest
-1.2, 2.7, -3.1, -0.3
Don’t you order it with the highest negative to the lowest negative then the last should be the positive?
Answers
In this scenario, least -> greatest, it would go as following;
-3.1, -1.2, 0.3, 2.7
The higher you get in the negative numbers, the less it is. I apologize if it’s confusing, let me know if you’d like a more in depth response!
Have a great one, take care.
what number is the square root of 78 in between of
Answers
Answer:
the square root rounded up is around 8
Step-by-step explanation:
because if the 5 is not beside the number it rounds down and the number was 3 so its 8
You can find the equation of a line through two points even if one point is not the y -intercept. Find the slope m of the line passing through the two points.Using either point, substitute for x, y , and m into y=m x+b . Solve for b and rewrite y=m x+b for the values of m and b . Write an equation in slope-intercept form for the line passing through each pair of points.
a. (2,5) and (6,7)
Answers
5 = (1/2)2 + 4 is an equation in intercept form for the line passing through the points (2,5) and (6,7)
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope.
We have been asked to write an equation in slope-intercept form for the line passing through (2,5) and (6,7)
First we will find the slope(m)
We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (2,5) and (6,7)
⇒ m = [tex]\frac{7- 5}{6 - 2}[/tex]
⇒ m = [tex]\frac{2}{4 }[/tex]
⇒ m = 1/2
We know that the equation for slope(m) and y - intercept(b) of a line is given by :
y = mx + b
Here lets take equation 5 = (1/2)2 + b .Here x and y is substituted with the first two points.
⇒ 5 = (1/2)2 + b
⇒ 5 = 1 + b
⇒ b = 5 - 1
⇒ b = 4
The equation in the slope intercept is as follows:-
5 = (1/2)2 + 4
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What is the equation of the line that is perpendicular to the line y=3/5x+10 and passes through the point (15,-5)?
y=3/5x-20
y=-3/5x+20
y=5/3x-20
y=-5/3x+20
Answers
Answer: Option (4)
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the line we want to find is -5/3.
Of the options, the only one that satisfies this is choice 4.
If mA = 29° and m/B= 29°, then mZA = m/B represents the property of what?
Answers
The statement, m∠A ≅ m∠B, represents the congruence property.
What is the Congruency Property of Equality?The congruency property of equality states that if two angles have measures that are equal to each other, then both angles are said to be congruent to each other.
Given that:
The measure of angle A = 29 degrees
The measure of angle B = 29 degrees.
Since both angles have the same measure, then both angles are congruent to each other.
Therefore, the statement, m∠A ≅ m∠B, represents the congruence property.
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Help pleaseeeeeeeeee
Answers
Answer: 4.7 gallons
Step-by-step explanation:
The range is the difference in the highest number and the smallest number, so 2.8 - -1.9 = 4.7
I need help with both question pls
Answers
Answer:
0.03x+0.05=1.50
Hopely this can help you
Step-by-step explanation:
What number is represented by
(a) 6 tens 7 ones
Answers
The number is represented by 6 tens 7 ones 67 .
2-digit ranges square measure the amounts that have 2 digits and that they begin from the amount ten and end wise the number ninety nine.They can't begin from zero as a result of therein case it'll be thought of as a single-digit range. The digit on the tens place will be any range from one to nine.Let the unit's place digit be " x " and ten's place digit be " y ".
Two digit number is given by = 10 y + x .....(1)
It is given that 6 tens 7 ones.
Putting x = 6 and y = 7 in equation (1) , we get
10(6) + 7 = 60 + 7
= 67
Hence , the number is 67 .
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Here is a distribution of quiz scores for a statistics course: 87, 91, 74, 73, 80, 84, 68, 75 what is the standard deviation?
Answers
The standard deviation is 7.35.
What is standard deviation?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79
Determine the difference between each value and the mean and then square the result:
(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)² + (84- 79)² + (68 - 79)² +( 75- 79) ²
64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432
Determine the mean of the sum of the squared differences and then find the square root of the mean:
√432 / 8 = 7.35
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Use this activity to explain how the AA criterion for triangle similarity follows from the definition of similarity in terms of dilations. (Hint: Use parallel lines)
Answers
The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.
What is a triangle similarity criterion?
According to the Angle-Angle (AA) criterion, two triangles are considered comparable if "two angles of one triangle are respectively equivalent to two angles of another triangle."
What distinguishes AA similarity from AAA similarity?
The total number of angles in a triangle is 180. Therefore, the third angle of a triangle will automatically become equal if two of its angles are equal. Triangles are related because of the AA resemblance. Three angles should equal the other triangle in AAA.Learn more about Angle-Angle-Side (AAS)
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(02.02 LC)
If f(x) is the total cost, in dollars, of x brownies, which of the following statements best describes the meaning of f(4) = 10?
a
The total cost of 2 brownies is $4.
b
The total cost of 4 brownies is $2.
c
The total cost of 4 brownies is $10.
d
The total cost of 10 brownies is $4.
Answers
The total cost of 10 brownies is $4 is the statement that best describes the meaning of f(4) = 10, if f(x) is the total cost, in dollars, of x brownies.
What is a function?In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are widespread in mathematics and are required for the formulation of physical relationships in the sciences. The present concept of function was initially proposed in 1837 by the German mathematician Peter Dirichlet.
If a variable y is so closely tied to a variable x that whenever a numerical value is assigned to x, there is a rule that determines a unique value of y, then y is said to be a function of the independent variable x.
As we can see it is mentioned that f(x) = total cost = f(4)
So only option d. has 4 as total cost, that why d is the right option and statement as follows The total cost of 10 brownies is $4.
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Complete the square. x² -5 x+ ____
Answers
The full quadratic expression is expressed as follows:
x² - 5x + 6.25
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:
(a - b)² = a² - 2ab + b²
x² - 5x + ?
x² = a²5x = 2abb = ?5x = 2xb
2b =5
b = 5/2
Let's complete the square
x² - 5x + (5/2)²
x² - 5x + 25/4
x² - 5x + 6.25
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Evaluate each expression for the given value of the variable. 5c³ - 6c√-2 c ; c=-5
Answers
The value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] at c = -5 is [tex]5(-125 +6\sqrt{10})[/tex] .
An algebraic expression is an expression having constant and variable joined with algebraic operation(+,-,×,÷).
For Example , 2c+5x+6 is an algebraic expression.
In the given expression
[tex]=5c^{3} -6c\sqrt{-2c}[/tex]
Substituting the value of c = -5 .
We get ;
[tex]=5(-5)^{3} -6(-5)\sqrt{-2(-5)}[/tex]
[tex]=5(-125) +30\sqrt{-2(-5)}\\ \\ =-625 +30\sqrt{10}[/tex]
taking 5 common from both the terms
[tex]=5(-125 +6\sqrt{10})[/tex]
Therefore , the value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] is [tex]5(-125 +6\sqrt{10})[/tex].
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in exercises 1-4, find m 1 and m 2. Tell which theorem you use in each case.
Answers
Answer:
m1 = 122°
m2= 58°
Step-by-step explanation:
M1 is an alternate interior angle, of 122°, which means that that angle is also 122°.
The line with m1 and m2 added together equal 180°, so we can subtract 122 from 180 to find m2.
180-122= 58
−
6
x
−
4
≤
2
(
x
−
10
)
Answers
Answer:
x > 2
Step-by-step explanation:
because , you have to use inverse operation to check your answer .
-6x-4< 2x-20
-6x-4+4<2x-20=4
-6x<2x-16
-6x-2x<2x-16-2x
-8x<-16
(-8x)(-1)>(-16)(-1)
8x>16
8x/8 > 16/8
x>2
Simplify each expression.
-35 / (-5)
Answers
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
The simplified expression of -35 / (-5) is 7.
What is an expression?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.In order to help establish the order of operations and other elements of logical syntax, mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Let the given expression be -35 / (-5) then
-35 / (-5) = -35/-5
simplifying the above equation, we get
= 35/5
= 7
Therefore, the value of -35 / (-5) is 7.
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Find the coordinates of point P on →AB that partitions the segment into the given ratio AP to PB .
a. A(0,0), B(0,6), 2 to 1
Answers
The point P which partitions the line segment AB have coordinates as P(0,3)
Line Segment is a line which joins together two points to form a straight line. It can be extended in either side.
It is given that,
A line segment AB having coordinates such as A(0,0) and B(0,6) respectively
The line segment AB is partitioned by a given point P in two minor line segments AP and PB
We need to find, the coordinates of the partitioning point i.e. P
The given formula will be used,
The coordinates of the point P = ([tex]\frac{x1+x2}{2}[/tex], [tex]\frac{y1 + y2}{2}[/tex])
Now, x1 = 0, x2 = 0, y1 = 0, y2 = 6
Putting values in the formula, we get
([tex]\frac{0+0}{2}[/tex], [tex]\frac{0+6}{2}[/tex])
(0,3)
Hence, the point P which partitions the line segment AB have coordinates as P(0,3)
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Evaluate each finite series for the specified number of terms. 80-40+20- . . . ; n=8
Answers
Answer:
The value of the given series is 49.75
Step-by-step explanation:
This is a problem from geometric progression ,
As we know the formula for geometric progression is aₙ = a₁ r ⁿ⁻¹
Where , a₁ is the first term and r is the ratio , and n is the number of terms.
Ratio is , 40/80 = 1/2
Here , a₄ = 80 . (1/2)⁴ ⁻ ¹ = 80 / 8 = 10
a₅ = 80 . (1/2)⁵ ⁻ ¹ = 80 / 16 = 0.5
a₆ = 80 . (1/2)⁶ ⁻ ¹ = 0.25
a₇ = 80 . (1/2)⁷ - ¹ = 0.125
a₈ = 80 . (1/2) ⁸ ⁻ ¹ = 0.625
Now the series can be written as .
80-40+20- 10 + 0.5 - 0.25 + 0.125 - .625 = 49.75
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the amount Evelyn makes a week she gives x haircuts a $25 each and y perms at $90 each
Answers
the expression representing the total amount earned by Evelyn is $ 25 x + $ 90 y .
We are given that
Evelyn makes x haircuts for $ 25 and y perms for $ 90.
We need to write an expression representing the situation
We will use multiplication for the same.
So, Amount earned from the haircuts = x × $ 25 = $ 25 x
Amount earned from perms = y × $ 90 = $ 90 y
Total amount earned = $ 25 x + $ 90 y
Therefore, we get that, the expression representing the total amount earned by Evelyn is $ 25 x + $ 90 y .
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Two stores are having sales on the same shirt. the sale at store 1 is "2 shirts for $22" and the sale at store 2 is "each $12.99 shirt is 10% off". explain how much will you save by buying at store 1.
Answers
Answer:
22 divided by 2 equals 11, so each shirt at store one, you are getting for $11. Store 2 is having a sale of 10% off 12.99 is 11.69, so each shirt is $11.69. So, Store 1 is a better deal.
Step-by-step explanation:
Answer:
1.38$
Step-by-step explanation:
QUESTION
Two stores are having sales on the same shirt. the sale at store 1 is "2 shirts for $22" and the sale at store 2 is "each $12.99 shirt is 10% off". explain how much will you save by buying at store 1.
EXPLANATION
store one 2 shirts 22$
store 2 1 shirt 12.99/10=1.30 so 12.99-1.30=11.69x2=23.38
23.38-22=1.38
Help please need it for rn
Answers
Check the picture below.
NEED THIS NOW DONE CORRECTLY
The figure shows three quadrilaterals on a coordinate grid:
B and C are similar and also congruent.
A and B are similar but not congruent.
A and B are similar and also congruent.
A and C are similar but not congruent.
Answers
Step-by-step explanation:
A and B are similar but not congruent
similar=same shape
congruent=same shape and same size
In a rectangle, the width is 1 feet shorter than the length. The area of the rectangle is 30 square feet. Find the length of the rectangle.
(ANSWER ASAP EXTRA POINTS)
Answers
A=lw so you take the known factor and run with it. What equals 30 that one number is 1 more than the other number. The only one I can think of it 6x5.
Suppose you turn the water on in an empty bathtub with vertical sides. After 20 s , the water has reached a level of 1.15 in. You then leave the room. You want to turn the water off when the level in the bathtub is 8.5 in. How many minutes later should you return? (Hint: Begin by identifying two terms of an arithmetic sequence.)
Answers
I should return after 7.7 minutes later to bathtub.
What is bathtub?You want to turn the water off when the level in the bathtub is 8.5
66/8.5
7.7 minutes
A bathtub is a long, typically rectangular container that you sit in to bathe your body after filling it with water.
Let's start with the truth: Showers are cleaner than baths. Showers spray polluted water out of sight while distributing water evenly over your body.
Actually, there is nothing that sets one apart from the other. All of them include jets, bubbles, and frequently different colored lights and other decorations. They are all sizable hot water containers. Overall, the terms "whirlpool bath," "Jacuzzi," and "hot tub" all refer to the same thing.
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