The least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is (x-6)(x+1)(x-6).
In the given question
[tex]=\frac{1}{x^{2} -5x-6} , \frac{1}{x^{2} -12x+36}[/tex] ...(i)
First we will factor each denominator
So,
x²-5x-6
On splitting the factors of the above expression , we get
(x+1)(x-6) ....(ii)
x²-12x+36
On splitting the factors of the above expression , we get
(x-6)(x-6) ...(iii)
Substituting the value of (ii) and (iii) in (i) ,we get ;
[tex]=\frac{1}{(x+1)(x-6)} , \frac{1}{(x-6)(x-6)}[/tex]
As the LCM of denominator is the Least common denominator , we have
LCM of (x+1)(x-6) and (x-6)(x-6)
LCM=(x-6)(x+1)(x-6)
Hence the LCD is (x-6)(x+1)(x-6).
Therefore , the least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is (x-6)(x+1)(x-6).
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Dexter's family buys tickets every year for a concert. Last year they were in seats C3, C4, C5 , and C6 . This year, they will be in seats D16, D17, D18 , and D19 . Write a translation in words and using vector notation that can be used to describe the change in their seating.
A translation in words and using vector notation that can be used to describe the change in their seating as-
In words: Dexter's family move 13 seats to the right and one row back.In vector notation: < 13, -10>.What is meant by translation?In geometry, translation refers to a function which moves an object a specified distance. The object isn't otherwise altered. It has not been rotated, mirrored, or resized.
Each point of a object must be relocated in the same direction and at the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, and also the object after the translation is referred to as the image.Now, as per the stated question.
In the previous year the seats given to Dexter's family were C3, C4, C5 , and C6.
Now, for current year, seats are at D16, D17, D18 , and D19.
Choose a seat from the new row & compare it to the seat with the previous row. Seat D16 is 13 seats to the right and 1 row back from C3.
As a result, the translation vector could be written as < 13, -10>.
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If f(x) and its inverse function, f superscript negative 1 baseline (x), are both plotted on the same coordinate plane, where is their point of intersection? (0, 6) (1, 4) (2, 2) (3, 0)
The point of intersection for the function is (2, 2)
Considering to the line passing through the points (0,6) and (3,0) to be f(x).Therefore the slope intercept of the function is
m = 0-6/3-0 = -2
So, the functions F(x) in the slope-intercept form f(x)= -2x+6 ......1
interchanging the variable x to y and y to x
=> x =-2y + 6
=> 2y = -x + 6
=> y= -0.5x + 3
let f⁻¹(x)= y
f⁻¹(x) =-0.5x+3 ......2
Solving the equation 1 and 2, we get
=> -0.5x + 3 = -2x + 6
=> 2x - 0.5x = 6 - 3
=> 1.5x = 3
=> x = 2
Substituting the values of x in the function we get,
f( x) = -2(2) + 6 = 2
Thus, the outcome is (2,2)
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Sally receives the following scores on her math tests: 78, 92, 83, 99. What score does she need on the next test in order to have an average of 90 on her math tests?
Answer:
they would need a 98 on the next math test.
PLEASEEE HELP!!!!! I’m desperate!
Solve each system.
-6 = 3x - 6y , 4x = 4 + 5y
After solving each system, -6 = 3x - 6y, 4x = 4 + 5y, the values of x and y are calculated to be 6 and 4 respectively.
The two equations, -6 = 3x - 6y, and 4x = 4 + 5y can be considered as linear equations as the highest power of the variables in these equations is one.
By rearranging the first equation, the value of x can be found to be,
-6 = 3x - 6y
3x = 6y - 6
x = 6y - 6 / 3
Putting the calculated value of x in the second equation,
4x = 4 + 5y
4(6y - 6 / 3) = 4 + 5y
24y - 24 / 3 = 4 + 5y
24y - 24 = 3 ( 4 + 5y)
24y - 24 = 12 + 15y
Rearranging,
24y - 15y = 12 + 24
9y = 36
y = 36 / 9
y = 4
To solve for x, put y = 4 in the first equation as follows,
-6 = 3x - 6y
-6 = 3x - 6(4)
-6 = 3x - 24
Rearranging,
24 - 6 = 3x
18 = 3x
x = 18/3
x = 6
Thus the value of x and y in these systems are calculated to be 6 and 4 respectively.
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Which fraction is an improper fraction?
• 11/12
• 8/9
•11/11
•9/15
Answer:
11/11 is an improper fraction.
Step-by-step explanation:
In order for a fraction to be considered "Proper" a < b, when a/b. Meaning that the numetator must be less than the denominator.
In the case for 11/11, it does not follow these qualifications.
Hope this helps!
Evaluate each expression for the given value of the variable. y²+3 ; y= √7
The result of the expression [tex]y^{2}+3[/tex] for the variable y= [tex]\sqrt{7}[/tex] is 10
Given,
The algebraic expression = [tex]y^{2}+3[/tex]
The value of y = [tex]\sqrt{7}[/tex]
Substitute the values in the expression
[tex]y^{2}+3=(\sqrt{7} )^{2}+3[/tex]
=7+3
=10
Hence, the result of the expression [tex]y^{2}+3[/tex] for the variable y= [tex]\sqrt{7}[/tex] is 10
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Find the measures of the sides of ΔX Y Z and classify
triangle by its sides.
x(7,6), y(5,1), Z(9,1)
The triangle is an isosceles triangle with sides XY and XZ equal to [tex]\sqrt{29}[/tex] units and side YZ as 4 units.
Given that:-
Coordinates of X = (7,6)
Coordinates of Y = (5,1)
Coordinates of Z = (9,1)
We have to find the measures of the sides of ΔXYZ and classify the triangle by its sides.
Using distance formula, we can find the measure of the sides of the triangle.
Distance formula for the line segment with points (a,b) and (c,d):-
[tex]\sqrt{(d-b)^2+(c-a)^2}[/tex]
Hence,
XY = [tex]\sqrt{(1-6)^2+(5-7)^2} =\sqrt{25+4} =\sqrt{29}[/tex] units.
YZ = [tex]\sqrt{(1-1)^2+(9-5)^2} =\sqrt{0+16} =\sqrt{16}[/tex] = 4 units.
XZ = [tex]\sqrt{(1-6)^2+(9-7)^2} =\sqrt{25+4} =\sqrt{29}[/tex] units.
Here,
XY = XZ, hence it is an isosceles triangle.
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Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠4 and ∠5
The relationship between the ∠4 and ∠5 is that both are consecutive interior angles
Given,
The angles =∠4 and ∠5
Here, ∠4 and ∠5 are interior angles.
Both are lies on the opposite sides of the transversal.
So, ∠4 and ∠5 are consecutive interior angles
Hence, The relationship between the ∠4 and ∠5 is that both are consecutive interior angles
The complete question is :
Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠4 and ∠5
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-9 - (x + 1) = -2-(3x - 5)
Answer: The answer is x = 6.5
Somerville has a population of 38,400 people. The town has been seeing its population decline by 3% every year. If this trend continues, what will the population be in 3 years?
The population of Somerville is approximately 35047 after a depreciation of of 3% every year .
Depreciation is economics refers to two different aspects of the same idea: first, the actual decline in an asset's fair value as it is used and worn, such as the annual decline in value of factory equipment; and second, the allocation in accounting statements of the asset's original cost to the periods during which it is used.
Here depreciation is the gradual decline in population each year in the town.
The rate of depreciation or decline is the percentage amount of population that decreases every year.
The formula used to calculate depreciation is given by:
[tex]A=P(1-r)^t[/tex]
Given the rate of depreciation as 3%.
Population at present = 38400
Population after 3 years:
= 38400 (1 - 0.03 )³
= 38400 ( 0.97 )³
= 35046.6432
≈ 35047
Hence the population after 3 years will be approximately 35047.
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Answer: =35047
Step-by-step explanation:
If f(x)=7-3 x and g(x)=3 x-7 , what is the value of f(1)+g(1) ?
If f(x)=7-3 x and g(x)=3 x-7 , the value of f(1)+g(1) is 0
What is function composition?A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
f(x)=7-3 x and g(x)=3 x-7
For, f(1) = 7 - 3(1)
= 7 - 3
= 4
For, g(1) = 3x - 7
= 3(1) - 7
= -4
f(1) + g(1) = 4 - 4
= 0
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PLEASEE HELPP. Im rlly struggling please help if you can. with steps
Answer:
lol
Step-by-step explanation:
L O LDJDDHDHDHDHFFHFVDVDVDBSSBDBDBDBD
Find the surface area of water tower that is 40 feet tall and has a diameter of 30 feet. DO NOT ROUND YOUR ANSWER!
================================================
Work Shown:
[tex]SA = 2\pi r^2 + 2\pi r h\\\\SA \approx 2*3.14*15^2 + 2*3.14*15*40\\\\SA \approx 5181\\\\[/tex]
The cylinder has a surface area of about 5181 square feet.
Side notes:
The diameter of d = 30 leads to a radius of r = d/2 = 30/2 = 15.The picture is misleading. The conical top is ignored and we only are finding the surface area of the cylinder.Answer:
Step-by-step explanation:
3768 feet. Is this right?
I dont understand this at all so here is 100 points
Answer:
Step-by-step explanation: First row, first column 500 * 7 = 3500
1st row , second column 7 * 60 = 420
1st row, third column 7 * 3 = 21
Do similary for the others
2nd row, 40,000 4800 240
3rd row , 100000 12000 6000
Answer:
[tex]\large\text{ \quad \quad \quad \quad 500 \quad \quad\;\;\;60 \quad \quad \;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{3500} &\boxed{420} & \boxed{21}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{40000} & \boxed{4800} & \boxed{240}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{100000} & \boxed{12000} & \boxed{600}\\\cline{2-4} \end{array}[/tex]
Step-by-step explanation:
For each box, multiply the number of the row by the number of the column:
[tex]\large\text{ \quad \quad \quad \quad \quad 500 \quad \quad \quad\;\;60 \quad \quad \quad \;\;\;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{7 \times 500} &\boxed{7 \times 60} & \boxed{ 7 \times 3}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{80 \times 500} & \boxed{80 \times 60} & \boxed{80 \times 3}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{200 \times 500} & \boxed{200 \times 60} & \boxed{200 \times 3}\\\cline{2-4} \end{array}[/tex]
When multiplying numbers ending in zeros (multiples of 10, 100, etc.), first multiply the numbers as if they didn't have zeros, then add all the zeros to the final answer.
For example:
200 × 500 has a total of 4 zeros.
Multiply 2 × 5 = 10
Then add 4 zeros: 10 0000
Therefore, 200 × 500 = 100000
Final Solution
[tex]\large\text{ \quad \quad \quad \quad 500 \quad \quad\;\;\;60 \quad \quad \;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{3500} &\boxed{420} & \boxed{21}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{40000} & \boxed{4800} & \boxed{240}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{100000} & \boxed{12000} & \boxed{600}\\\cline{2-4} \end{array}[/tex]
Look at the Example. The area of Rhode Island is about 43.07 billion square feet. About how many times as many times as great is the area of Colorado than the area of Rhode Island? Show your work.
According to the given statement
The area of Colorado is 67.43 times greater than the area of Rhode Island
Define Area?Area is typically thought of as a specific instance of volume for two-dimensional regions. By applying axioms, one can define area as the relationship between a set of real numbers and a collection of particular plane figures.
Area is a mathematical concept that describes the size of a region on a planar or curved surface. The area of an open surface or the border of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
According to the given values;
The area of Rhode Island = 43.07 billion square feet.
The area of Colorado = 2.9045 trillion square feet.
43.07 billion =43,070,000,000
2.945 trillion =2,9045,000,000,00
Now we have to find how many times as great is the area of Colorado than the area of Rhode Island.
For this ,we divide area of Colorado by area of Rhode Island.
=2,9045,000,000,00/43,070,000,000
=67.43
So, the area of Colorado is 67.43 times greater than the area of Rhode Island.
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Evaluate the functions
F(-2)
F(3)
F(5)
F(e+4)
Answer:
F(5)
Step-by-step explanation:
its right very sorry if its late
FH bisects ZEFG. Find the indicated angle measures.
m/EFG = 119 °. Find m/EFH and m/GFH.
m/EFH =
m/GFH =
The measures of the indicated angles are
m ∠EFH = 59.5°
m ∠GFH = 59.5°
Calculating anglesFrom the question, we are to determine measures of the indicated angles
The angles are ∠EFH and ∠GFH
From the given information,
FH bisects ∠EFG
Since FH bisects ∠EFG,
Then,
m ∠EFH = m ∠GFH
and
m ∠EFH + m ∠GFH = m ∠EFG
Then,
We can write that
m ∠EFH + m ∠EFH = m ∠EFG
2 × m ∠EFH = m ∠EFG
2 × m ∠EFH = 119°
m ∠EFH = 119°/2
m ∠EFH = 59.5°
Thus,
m ∠GFH = 59.5°
Hence, the measures of the indicated angles are
m ∠EFH = 59.5°
m ∠GFH = 59.5°
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Find the geometric mean between pair of numbers.
a. 5 and 45
For numbers 5 and 45 the value of the geometric mean of these numbers is
Gm (5, 45) = 15
What is the geometric mean?The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:
Gm (a,b) = √ab
Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b
a = 5b = 45We substitute and solve for the square root
Gm (5, 45) = √5×45
Gm (5, 45) = √225 ; In this case the square root is direct-
Gm (5, 45) = 15
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What do we mean by decimal writing or writing in base 10?
Answer:
decimal is the number system of 10base .
Write an explicit formula for each sequence. 2,5,10,17, . . . .
The explicit formula for give sequence an = n² + 1:
What is an explicit formula?An arithmetic sequence has the explicit formula a = a + (n - 1)d, and each term of the series may be calculated without knowing the values of the previous terms. The nth term in an arithmetic, geometric, or harmonic series is usually the explicit formula.
a1 = (1) + 1 = 2
a2 = 2.2 + 1 = 5
a3 = 3.3 + 1 = 10
a4 = 4.4 + 1 = 17
a5 = 5.5 + 1 = 26
and so on.
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whatis the answer to 4.5x=18
[tex] \large \bf \implies{x = 4}[/tex]
Step-by-step explanation:Let's solve your equation step-by-step[tex] \bf \longrightarrow{4.5x = 18}[/tex]
Divide both sides by 4.5[tex] \bf \frac{ \cancel{4.5}x}{ \cancel{4.5}} = \frac{18 }{4 \cancel{.}5} = \frac{18 \times 10}{45} = \frac{180 \div 3}{45 \div 3} = \frac{60 \div 3}{15 \div 3} = \frac{20 \div 5}{5 \div 5} = \frac{4}{1} = 4 \\ [/tex]
[tex] \large \bf \implies \boxed{x = 4} \: ans.[/tex]
Use the given information to write an equation of a circle.
center at (0,0) , radius 6
The equation of the circle with radius 6 and center at (0 , 0) is x^2 + y^2 = 36.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = 6
(x - 0)^2 + (y - 0)^2 = 6^2
x^2 + y^2 = 36
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help asp show ur work you’ll get BRAINILEST
Answer:
x = -14
Step-by-step explanation:
Solve:
7x - 28 = 2(4x - 7)
7x - 28 = 8x - 14
Substrate 8x from both sides.
7x - 28 - 8x = 8x - 14 - 8x
-x - 28 = -14
Add 28 to both sides.
-x - 28 + 28 = -14 + 28
-x = 14
Divide both sides by -1.
-x/-1 = 14/-1
x = -14
Therefore x = -14
Meals with a Purpose are selling to-go charcuterie boards. You can purchase a small board or a medium board. On Thursday, Meals with a Purpose sold 10 small charcuterie boards and 12 medium charcuterie boards for a total of $144. On Thursday, Meals with a Purpose sold 5 sold charcuterie boards and 9 medium charcuterie boards for a total of $93.
What is the cost of each small charcuterie boards and one medium charcuterie boards?
The cost of each small charcuterie boards is $6 and one medium charcuterie boards is $7.
How to illustrate the information?A mathematical statement known as an equation is made up of two expressions joined together by an equal sign. It is a formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Let small charcuterie boards = c
Let medium charcuterie boards = m
Therefore, the equation will be:
10c + 12m = 144
5c + 9m = 93
Multiply equation i by 5
Multiply equation ii by 10
50c + 60m = 720
50c + 90m = 930
Subtract
30m = 210
m = 210/30
m = 7
Therefore, 5c + 9m = 93
5c + 9(7) = 93
5c + 63 =93
5c = 93 - 63
5c = 30
Divide both sides by 5
c = 30 / 5
c = 6
Therefore, based on the information the cost of each small charcuterie boards is $6 and one medium charcuterie board is $7.
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You can choose between two tennis courts at two university campuses to learn how to play tennis. One campus charges 25 per hour. The other campus charges 20 per hour plus a one-time registration fee of 10 .
c. If you want to practice for a total of 10 hours, which university campus should you choose? Explain.
I should choose second or other campus, as it is cost effective.
We will begin with forming the equation according to the information provided in question. Let us represent the number of hours with t.
Cost on choosing first or one campus to play tennis-
Cost = 25 × t
Cost on choosing second or other campus to play tennis -
Cost = 10 + 20 × t
Now finding cost on each campus for duration of ten hours.
First campus -
Cost = 25 × 10
Cost = 250
Second campus -
Cost = 10 + 20 × t
Cost = 10 + 20 × 10
Cost = 10 + 200
Cost = 210
Therefore, to practice for a total of 10 hours, I should choose second or other campus, as it is cost effective.
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1. 2ײ + 5× - 11 + 3ײ - 11 × + 2
please solve this thankyou!!!
I believe it's 3ײ - 6x - 7.56
Sorry if this isn't helpful!
The other option would be -6x + 3ײ-7.56 (but this is the problem in a simplified form and not when it is evaluated).
In order to scuba dive safely, divers must be aware that the water
pressure in the ocean is a function of depth. The water pressure increases by
0.445 pounds per square inch (psi) for each foot of depth. The pressure at the
surface is 14.7 psi. Write a function to represent water pressure. What is the
value of the function for an input of 50, and what does it represent?
The value of the function at an input of 50 will be 36.95.
How to calculate the value?Since the pressure at the surface is 14.7 psi, a function to represent water pressure will be:
= 14.7 + (0.445 × p)
where p is the increase in pressure for each foot
= 14.7 + 0.445p
Therefore when the input is 50, the amount will be:
= 14.7 + 0.445p
= 14.7 + 0.445(50)
= 14.7 + 22.25
= 36.95
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The operator *= is called a(n) _____ operator.
a) increment
b) multiple assignment
c) double compound
The operator *= is called multiple assignment operator.
How to determine the name of the operator?The operator is given as
*=
Take for instance, we have the following statement in Python
a *= b
The meaning of the above statement is
a = a * b
Assume the following values for the variables
a = 6 and b = 3
The value of the operation a *= b would be
a *= b --- given expression
a = a * b --- expanded expression
a = 6 * 3 ---- when the values are substituted
a = 18 --- the result
This implies that the operator represents an assignment and a multiply operator
Hence, the operator *= is called multiple assignment operator.
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Kudi and Ladi share 20 oranges in the ratio 2 is to 3 how many oranges has Ladi
Answer:
12 oranges
Step-by-step explanation:
The ratio is K/L where K = Kudi's oranges and L = Ludi's oranges
K/L = 2/3
To find the number of oranges that Kudi has, divide the numerator by the sum of numerator and denominator.Then multiply by total number of oranges
For Ladi, divide the denominator by the sum of numerator and denominator. Then multiply by total number of oranges
[tex]K = 20\cdot \dfrac{2}{2+3} = 20 \cdot \dfrac{2}{5} = 8 \; \mathrm {oranges}\\\\L = 20\cdot \dfrac{3}{2+3} = 20 \cdot \dfrac{3}{5} = 12 \; \mathrm {oranges}[/tex]
So answer is Ladi has 12 oranges
