Answers
Answer:
[tex]\frac{k+5}{k-2}[/tex]
Step-by-step explanation:
[tex]\frac{1-\frac{25}{k^2} }{1-\frac{7}{k}+\frac{10}{k^2} }[/tex]
multiply numerator and denominator by k² to eliminate fractions
= [tex]\frac{k^2-25}{k^2-7k+10}[/tex] ← factor numerator and denominator
------------------------------
k² - 25 ← is a difference of squares
= (k - 5)(k + 5)
k² - 7k + 10
= (k - 5)(k - 2)
------------------------------
= [tex]\frac{(k-5)(k+5)}{(k-5)(k-2)}[/tex] ← cancel (x - 5) on numerator / denominator
= [tex]\frac{k+5}{k-2}[/tex]
Related Questions
Someone please help with this !!!!!
Answers
Answer:
[tex]5^{\circ}[/tex]
Step-by-step explanation:
[tex]~~~~~~~\tan \theta = \cot 85^{\circ}\\\\\implies \tan \theta = \tan\left(90^{\circ} - 85^{\circ} \right)\\\\\implies \tan \theta = \tan 5^{\circ}\\\\\implies \theta = 5^{\circ}[/tex]
find the value of x
Answers
Answer:
x=5
\
Step-by-step explanation:
Answer:
x = 0
Step-by-step explanation:
Line segment UV and line segment VW together form line segment UW.
UV + VW = UW
(5 + x) + (6) = (2x + 11)
5 + x + 6 = 2x + 11
x + 11 = 2x + 11
x + 11 - 11 = 2x + 11 - 11
x = 2x
x - x = 2x - x
0 = x
You can also verify the result by substituting x with our result 0.
5 + x + 6 = 2x + 11
5 + (0) + 6 = 2(0) + 11
11 + 0 = 0 + 11
11 = 11
Left side of the equation is the same as the right side of the equation, therefore the result x = 0 is correct.
Does this graph represent a function? Why or why not?
10.
8
6
4
2
-10 8 6 4 2
88
-8
10
2468 10
A. No, because it fails the vertical line test.
O B. No, because it is not a straight line.
OC. Yes, because it passes the horizontal line test.
OD. Yes, because it passes the vertical line test.
Answers
Answer:
D.) Yes, because it passes the vertical line test.
Step-by-step explanation:
For a function to be a function, there must be one output for every input. IN other words, there must be one "y" value for every "x" value. One can see if a graph passes this test by performing the vertical line test.
In this case, the line on the graph passes the test and represents a function. Again, this is because each "x" value has only one "y" value.
Yes, The graph is function because it passes the vertical line test.
We have to given that,
A graph of function is shown in image.
Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
And, The vertical line test is used to determine if a graph of a relationship is a function or not. if you can draw any vertical line that intersects more than one point on the relationship, then it is not a function.
Hence, By given graph,
it passes the vertical line test.
So, Graph shown is a function.
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1. What is the binomial expansion of (x + 3)5?
Answers
Answer:
5x + 15
Step-by-step explanation:
To expand the binomial, you need to multiply each term inside the parentheses by 5.
(x + 3)5
= (x * 5) + (3 * 5)
= 5x + 15
4x² + 6x = 12
Solve by completing square
Answers
4x² + 6x = 12
We move all the terms to the left:
a = 4; b = 6; c = -12;Δ = b² - 4acΔ = 6² - 4 · 4 · ( -12 )Δ = 228The value of Δ is greater than zero, so the equation has two solutions
We use the following formulas to compute our solutions:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a }| \ x_{2}=\dfrac{-b+\sqrt{\Delta} }{2a } } \end{gathered}$}[/tex]
The end solution:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a}=\dfrac{-(6)-2\sqrt{57} }{2*4}=\dfrac{-6-2\sqrt{57} }{8} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b+\sqrt{\Delta} }{2a}=\dfrac{-(6)+2\sqrt{57} }{2*4}=\dfrac{-6+2\sqrt{57} }{8} } \end{gathered}$}[/tex]
{ Pisces04 }The Law of Sines states that sin A/b = sin B/c = sin C/a
True
False
Answers
Law of signs is
SinA = SinB = SinC
——- ——- ———
a. b. c.
A= angle A
a= length of side A
B= angle B
b= length of side B
C= angle C
c= length of side C
Step-by-step explanation:
hope you can understand
Item 18
What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
The figure contains a right rectangular prism. The length of the prism is labeled 6 and one half centimeters, the width is labeled 2 and one half centimeters, and the height is labeled 2 and one half centimeters.
Answers
A mixed number in simplest form, in the box is 40 5/8 cm^3.
We have given that,
The figure contains a right rectangular prism. The length of the prism is labeled 6 and one-half centimeters, the width is labeled 2 and one-half centimeters, and the height is labeled 2 and one-half centimeters.
What is the volume of the prism?The figure is a rectangular prism, so the formula would be Volume = length x width x height.
length = 6 .5cm
width = 2.5cm
height = 2.5cm
If you plug everything you have in the problem into the volume equation, you would get
volume = 6.5cm x 2.5cm x 2.5 cm.
Without a calculator first, turn the mixed numbers into improper fractions.
6 .5=13/2
2.5 = 5/2
Volume = 13/2 x 5/2 x 5/2
When you multiply everything together you should get.
As a mixed number, that would be 40 5/8.
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Dose this tablet represent a function? Why or why not? {(2,1), (2,4), (3,4), (4,2), (5,5)}
Answers
Answer:
This mapping isn't a function.
Step-by-step explanation:
A mapping specifies a relation between two sets of items (input and output). For example, a mapping of the form [tex]\lbrace (x_{0},\, y_{0}),\, (x_{1},\, y_{1})\rbrace[/tex] would map the input [tex]x_{0}[/tex] to output [tex]y_{0}[/tex] and map the input [tex]x_{1}[/tex] to output [tex]y_{1}[/tex].
A function is a mapping where each input is associated with exactly one output.
Note that both [tex](2,\, 1)[/tex] and [tex](2,\, 4)[/tex] are in the mapping given in this question. The input [tex]2[/tex] is mapped to more than one outputs. Thus, this mapping isn't a function.
Pedro's dining room is 5 metres wide and 6 metres long. pedro wants to install a new wood floor. it will cost $2.18 per square metre. how much will pedro's new floor cost?
Answers
Answer:
65.4
Step-by-step explanation:
5 × 6 = 30 square meter
30 × 2.18 = 65.4
Write the algebraic expression for the following statement.
A number plus 15.
Answers
Answer:
the algebraic expression is; x+15
Chloe would like to join a club for dancing entrance fee is $20.00 and will be charged $35.00 per month. Chloe would like to know cost for each month. Write and equation indicating the total cost of dancing lessons
Answers
C is total cost
X is the months
A store selling school supplies advertises a bundle deal. The consumer can
pick a backpack, a binder, a pack of pencils, and notebook paper for a set
price. There are 6 types of backpacks, 4 types of binders, 5 types of pencils,
and 2 types of notebook paper. How many outcomes are possible in this
bundle?
Answers
Answer:
D. 240
Step-by-step explanation:
6 types of backpacks = 6
4 types of binders = 4
5 types of pencils = 5
2 types of notebook paper= 2
6×4×5×2=
24×10=
240
The number of possible outcomes will be 240. The correct option is D.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that there are 6 types of backpacks, 4 types of binders, 5 types of pencils, and 2 types of notebook paper.
6 types of backpacks = 6
4 types of binders = 4
5 types of pencils = 5
2 types of notebook paper= 2
The number of possible outcomes will be calculated as:-
N = 6×4×5×2
N = 24×10
N = 240
Therefore, there will be 240 possible outcomes. The correct answer is D.
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Use the drawing tools to sketch the graph of a rational function with a domain of { x | x ∈ R , x ≠ - 5 , 4 } . Include one removable discontinuity and one nonremovable discontinuity. Label each discontinuity using the text tool.
Answers
If [tex]f(x)[/tex] has a removable discontinuity at [tex]x=a[/tex], then the limit
[tex]\displaystyle \lim_{x\to a} \frac{f(x)}{x-a}[/tex]
exists and is finite.
A non-removable discontinuity at [tex]x=b[/tex] would entail a non-finite limit,
[tex]\displaystyle \lim_{x\to b} \frac{f(x)}{x-b} = \pm\infty[/tex]
or the limit does not exist (which could be due to the limits from either side of [tex]x=b[/tex] not matching or existing).
For a rational function, we want
[tex]f(x) = \dfrac{p(x)}{q(x)}[/tex]
where [tex]p[/tex] and [tex]q[/tex] are polynomials in [tex]x[/tex]. To get a removable discontinuity at [tex]x=a[/tex], both [tex]p[/tex] and [tex]q[/tex] must be divisible by [tex]x-a[/tex], and the limit of their quotient after removing these factors still exists. That is,
[tex]\displaystyle \lim_{x\to a} f(x) = \lim_{x\to a} \frac{p(x)}{q(x)} = \lim_{x\to a} \frac{(x-a)p^*(x)}{(x-a)q^*(x)} = \lim_{x\to a} \frac{p^*(x)}{q^*(x)} = \frac{p^*(a)}{q^*(a)}[/tex]
On the flip side, we get a non-removable discontinuity [tex]x=b[/tex] if [tex]p[/tex] is not divisible by [tex]x-b[/tex], in which case
[tex]\displaystyle \lim_{x\to b} f(x) = \lim_{x\to b} \frac{p(x)}{q(x)} = \lim_{x\to b} \frac{p(x)}{(x-b)q^*(x)} = \frac{p(b)}{0\times q^*(b)}[/tex]
and this is undefined.
Suppose [tex]f(x)[/tex] has a non-removable discontinuity at [tex]x=-5[/tex] and a removable one at [tex]x=4[/tex]. Then one such function could be
[tex]f(x) = \dfrac{x-4}{(x-4)(x+5)} = \dfrac{x-4}{x^2+x-20}[/tex]
Solve for k in g=k-a.
Answers
Answer:
k = g + a
Step-by-step explanation:
g = k - a ( add a to both sides )
g + a = k , that is
k = g + a
find [-4/5]×3/7×15/16×[-14/9]
Answers
The given expression is [tex]\frac{-4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{-14}{9})[/tex].
We need to simplify the given expression.
What is a rational number?In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Now group the rational numbers [tex](\frac{-4}{5}\times \frac{15}{16} ) \times (\frac{3}{7}\times (\frac{-14}{9}))[/tex]
[tex]=(\frac{-4}{16}\times \frac{15}{5} ) \times (\frac{3}{9}\times (\frac{-14}{7}))[/tex]
[tex]=(\frac{-1}{4}\times \frac{3}{1} ) \times (\frac{1}{3}\times (\frac{-2}{1}))[/tex]
[tex]=(\frac{-3}{4} ) \times (\frac{-2}{3})=\frac{1}{2}[/tex]
Therefore, the simplified value of the given expression is [tex]\frac{1}{2}[/tex].
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What are the solution(s) to the quadratic equation 9x² = 4?
0 x =
and x =
0 x =
I
69
4
and x = -
2
0 x = ² and x = -²
2
Ono real solution
Answers
Answer:
x= 2/3, -2/3
Step-by-step explanation:
9x² = 4
To solve this quadratic, divide each side by 9
x^2 = 4/9
Take the square root of each side
sqrt(x^2) = sqrt(4/9)
x = ±2/3
Answer:
x = ± [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
9x² = 4 ( divide both sides by 9 )
x² = [tex]\frac{4}{9}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{4}{9} }[/tex] = ± [tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex] = ± [tex]\frac{2}{3}[/tex]
x = - [tex]\frac{2}{3}[/tex] , x = [tex]\frac{2}{3}[/tex]
A number written in scientific notation has a ________ that indicates the digits used in the number and is always written with 1 digit to the left of the decimal place.
Answers
A number written in scientific notation has a Negative Exponent that indicates the digits used in the number and is always written with 1 digit to the left of the decimal place.
The coefficient is always a number larger than or equal to one and less than ten in scientific notation. There is an integer exponent. When using scientific notation to write integers bigger than ten
The exponent is positive and equals the number of spaces to the left of the original decimal point. When expressed in scientific notation, a negative exponent. The exponent's value is equal to how many places to the right the decimal has been pushed.As a result, when a number is smaller than 1, it will have a negative exponent in scientific notation.
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if the ratio to cats to dogs at the city pound is 92 to 144. which statement describes this relationship?
Answers
Answer:
For every 92 cats in the city pound, there are 144 dogs.
OR
For every 144 dogs in the city pound, there are 92 cats
Step-by-step explanation:
You didn't provide the options, so that was my best shot at it.
Use the graphs below to answer the following questions: a. g(f(2) b. f(f(1)) c. f(g(2))
Answers
Answer:
19-73 19-73 and a very nice little
Step-by-step explanation:
19-73 19-73 and he changed
According to the table below, which of these is a possible taxable income for
a taxpayer filing with the Single filing status in the 33% federal income tax
bracket?
Answers
Based on the table, a possible taxable income for a taxpayer that's filing with the Single filing status in the 33% federal income tax bracket is $300,000.
What is taxation?Taxation is the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.
In this scenario, we can infer and logically deduce that a possible taxable income for a taxpayer that is filing with the Single filing status in the 33% federal income tax bracket is $300,000.
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Order these fractions from smallest to lowest
1[tex]\frac{1}{2} \frac{7}{12} \frac{2}{17}[/tex]
Answers
Answer: [tex]\frac{1}{2} \frac{2}{17} \frac{7}{12}[/tex]
Step-by-step explanation:
Write the sentence as an equation.
253 equals the product of 232 and k
Type a slash ( / ) if you want to use a division sign.
Answers
The solution to a given word problem by writing it as an equation is k = 253/232
Expressing word problems in mathematical forms:The process of expressing word problems in mathematical forms takes a logical and chronological approach while taking the variables and arithmetic operations given into consideration.
From the given information, to express the word problem in mathematical form, we have:
253 = 232 × k253 = 232kMaking k the subject of the equation, we have:
k = 253/232
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the atomic mass unit is presently based on assigning an exact integral mass (in amu) to an isotope of an hydrogen oxygen sodium carbon helium
a. hydrogen
b. oxygen
c. sodium
d. carbon
e. helium
Answers
Answer:
The reference atomic mass is carbon-12 when calculating atomic masses.
Step-by-step explanation:
The one-twelfth mass of an atom of carbon-12 is known as an atomic mass unit.
Because no other nuclide has a mass that is exactly a whole number in this scale except for carbon-12.
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What multiples to 42 but adds to -13
Answers
Find the slope of the line that passes
through these two points.
Point 1
(4,0)
Point 2
(6,2)
Answers
Answer:
1
Step-by-step explanation:
(2-0) / (6-4)
2/2
xxxxxxxx
Answer:
1
Step-by-step explanation:
my father is 4 times old as me. after 5 years my father will be 3 times old how old is my father now
Answers
Answer:
Step-by-step explanation:
Which is a rational function?
A. Y=5
B. Y=√x-3
C. Y=x²-3x+5
D.Y = x-5/x
Answers
The distance on a map between a student’s house and her job is 6 cm. On the same map, the distance between her house and her school 8 cm. The actual distance from her house to school is 12 km. If d represents the approximate distance in km between her house and her job, what is d? A. 4 km B. 9 km C. 48 km D. 16 k
Answers
The approximate distance in km between her house and her job is 9 km.
What is the approximate distance?The map is a scale drawing of the places mentioned. A scale drawing is a smaller image of a larger place or diagram.
The scale of the map = 8cm : 12km
Distance between the house and the job = (12 x 6) / 8 = 9m
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What is the inverse of this function?
8v, for x > 0
Answers
Answer:
f(x) = (x/8)^2 for x ≥ 0
Step-by-step explanation:
y = 8 sqrt x switch x and y
x = 8 sqrt y now solve for y
(x/8)^2 = y
Which is a perfect square?
61
62
63
65
Answers
Answer:
So none of these would be a perfect square but the closet one to it would be 65
Step-by-step explanation: