The inequality in which involves one or more rational expressions is Rational inequality.
What is inequality?
Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.
An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.
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The answer is d. Rational inequality, which includes fractions with polynomials. Other options involve exponential, linear, or logarithmic functions, without rational expressions as in inequalities.
The right choice is d. Rational inequality. An objective disparity includes at least one sane articulations, which are portions with polynomials in the numerator and denominator. These disparities can be settled by finding the basic places where the normal articulation is indistinct or changes sign.
The arrangement includes deciding the stretches where the disparity turns out as expected in view of the indication of the judicious articulation in those spans. Interestingly, dramatic, direct, and logarithmic disparities include various kinds of numerical capabilities.
Remarkable imbalances contain dramatic terms, direct disparities incorporate straight capabilities, and logarithmic imbalances contain logarithmic capabilities. Each kind of imbalance has its own qualities and strategies for settling, however just objective disparities straightforwardly manage levelheaded articulations including parts of polynomials.
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denmark uses kroner as its currency. Before a trip to denmark. Mia wants to exchange
$1700 for kroner.
bank a
dollars kroner
80 408
100 510
120 612
Denmark uses kroner as its currency. Before a trip to Denmark. Mia will get 8670 Kroner in exchange for $ 1700.
bank A
Dollars ($) Kroner
80 408
100 510
120 612
Since $ 80 = 408 Kroner
=> $ 1 = 408 / 80 = 5.1 Kroner . . . . . . conversion rate of $ to Kroner)
=> $ 1700 = 1700 x 5.1 = 8670 Kroner
Hence Mia will get 8670 Kroner in exchange for $ 1700
The exchange rate of conversion from $ to Kroner is arrived at by applying Unitary System of calculation in arithmetic (mathematics).
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Hello, I need some assistance with this homework question please for precalculusHW Q10
SOLUTION
Recall that a quadratic equation is of the form
[tex]ax^2+bx+c=0[/tex]The possible number of zeros of a quadratic function is 2The zeroes of a quadratic function could be real or complex
Therefore a quadratic function can have zero real roots
or 1 real root or 2 real roots.
Answer Please
F(x)=5x-1
Answer:
-1
Step-by-step explanation:
Correct option is A)
Given,
f(x)=5x−1
To find: f(0)
Put x=0 in the given eqation.
Therefore, we get
f(0)=5(0)−1
=0−1
=−1
Solve the equation.
−3=z−8
z=
The answer is 5
Step-by-step explanation:
-3=z-8
put +8 underneath -8. Then cross it out.
Put +8 underneath -3. -3+8=5
The answer is 5.
I hope this helped you!
Which of the following rational fractions is graphed below?
Help please!
Answer:
[tex]\textsf{A.} \quad f(x)=\dfrac{1}{x-4}[/tex]
Step-by-step explanation:
An asymptote is a line that the curve gets infinitely close to, but never touches.
A vertical asymptote occurs when the denominator of a rational function is zero.
From inspection of the given graph, there is a vertical asymptote at [tex]x=4[/tex] .
Therefore, the denominator of the rational function must equal zero when [tex]x=4[/tex] .
Therefore, the only solution where the denominator is zero when [tex]x=4[/tex] is:
[tex]\boxed{f(x)=\dfrac{1}{x-4}}[/tex]
I need help with the whole question
Given:
[tex]\begin{gathered} f(x)=2x^2-4x-6 \\ g(x)\text{ = 3x-4} \\ h(x)\text{ = }\frac{2}{x} \\ \end{gathered}[/tex]1.1.1 The equation of the reflection of g(x) in the x-axis is of the form:
The rule for the reflection in the x-axis:
[tex](x,y)\rightarrow\text{ (x,-y)}[/tex]Applying the rule:
[tex]\begin{gathered} g^{\prime}(x)\text{ = -g(x)} \\ =-(3x\text{ -4)} \\ =\text{ 4 -3x} \end{gathered}[/tex]Hence, g'(x) = 4-3x
1.1.2 The equation of the reflection of h(x) in the y-axis.
The rule for reflection in the y-axis:
[tex](x,y)\rightarrow\text{ (-x,y)}[/tex]Applying the rule:
[tex]h^{\prime}(x)\text{ = }\frac{2}{-x}[/tex]Hence, h('x) = 2/-x
1.1.3 The values of k for which :
[tex]k=2x^2-4x-6[/tex]Re-arranging:
[tex]\begin{gathered} 2x^2-4x-6-k\text{ =0} \\ 2x^2-4x\text{ -(6+k) = 0} \end{gathered}[/tex]Using the rule that for an equation to have non-real roots, the discriminant (D) must be less than zero.
[tex]\begin{gathered} D=b^2-4ac \\ (-4)^2\text{ -4(2)-(6+k) }<\text{ 0} \end{gathered}[/tex]Simplifying we have:
[tex]\begin{gathered} 16\text{ +48+8k }<\text{ 0} \\ 64\text{ + 8k }<\text{ 0} \\ 8k\text{ }<\text{ -64} \\ \text{Divide both sides by 8} \\ \frac{8k}{8}\text{ }<\frac{-64}{8} \\ k\text{ }<\text{ -8} \end{gathered}[/tex]Hence, the values of k for which the equation has non-real roots is that k must be less than -8
1.1.4 The average gradient of f(x) between x=-4 and x=0:
First, we need to find the value of f(x) at x=-4.
[tex]\begin{gathered} f(-4)=2(-4)^2\text{ -4(-4) -6} \\ =\text{ 32+16 -6} \\ =\text{ 42} \end{gathered}[/tex]Next, we must find the value of f(x) at x=0:
[tex]\begin{gathered} f(0)=2(0)^2-4(0)\text{ -6} \\ =\text{ -6} \end{gathered}[/tex]Using the average gradient formula:
[tex]\begin{gathered} \text{Average gradient = }\frac{y_B-y_A}{x_B-x_A} \\ =\text{ }\frac{-6-42}{0-(-4)} \\ =\frac{-48}{4} \\ =\text{ -12} \end{gathered}[/tex]Hence, the average gradient is -12
Match each unit of measurement on the right with the appropriate measurement system on the left. The answer options on the left will be used more than once.Metric system U. S. Customary SystemCentiliterYardPoundMilligramMileKilometer
Metric system:
Centiliter
Miligram
Kilometer
U.S. Customary System:
Yard
Pound
Mile
(05.03 MC)
Two families visited an amusement park. The first family bought 3 hot dogs and 5 bottles of waters, which totaled $20. The second family bought 6 hot dogs and 3 bottles of
waters, which totaled $33. How much did one hot dog cost?
$3
$4
$5
$6
The cost of one hotdog based on the given situation is $5
The correct answer option is Option C
How to find the cost of one hotdog?let
Cost of hotdogs = hCost of bottle water = wFamily A:
3h + 5w = 20
Family B:
6h + 3w = 33
Solve the two equations simultaneously:
3h + 5w = 20
6h + 3w = 33
Multiply (1) by 2
6h + 10w = 40
6h + 3w = 33
Substract the equations to eliminate h
10w - 3w = 40 - 33
7w = 7
divide both sides by 7
w = 7/7
w = 1
Substitute w = 1 into
3h + 5w = 20
3h + 5(1) = 20
3h + 5 = 20
3h = 20 - 5
3h = 15
divide both sides by 3
h = 15/3
h = 5
So therefore, the cost of one hotdog and one bottle water is $5 and $1 respectively.
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Answer: the answer is 5 dollars
Step-by-step explanation:
||x+4|-7|<5 how to solve this?
Answer: [tex](-16, -6) \cup (-2, 8)[/tex]
Step-by-step explanation:
[tex]||x+4|-7| < 5\\\\-5 < |x+4|-7 < 5\\\\2 < |x+4| < 12\\\\1. -2 < x+4 < 2 \implies -6 < x < -2\\\\2. -12 < x+4 < 12 \implies -16 < x < 8\\\\\therefore (-16, -6) \cup (-2, 8)[/tex]
step by step explanations for the following
g(x)=4x-5
f(x)= -2x-3
find (f•g) (-8)
and problems on the paper numbers 5-8 please
Answer:
5. [tex]\bold{(g \circ f)(-3) = 16}}[/tex]
6. [tex]\bold{h(h(-3x)) = -12x + 15 }}[/tex]
7. [tex]{\bold{f\left(g\left(x-3\right)\right):\quad 3x-21}}[/tex]
8. [tex]\bold{\text \bold g(f(-3x)) = -36x + 15}}[/tex]
Step-by-step explanation:
These are examples of composite functions.
What is a composite function?
A function by definition is a process that takes a collection of inputs and produces a corresponding collection of outputs in such a way that the process produces one and only one output value for any single input value.
Since we consider a function a process it makes sense to think of two functions acting in sequence to produce a single output. The output from one function is fed into the second function.
A composite function can be written as:Note that we can have [tex]f[/tex][tex]g[/tex] as the outer function, in which case the notation will be [tex](g \circ f)(x)[/tex] or [tex]g(f(x))[/tex]
Problem Solution
5. [tex]g(x) = x + 3 \;\text and\; f(x) = 3x + 4[/tex]
Find [tex](g \circ f)(-3) = g(f(-3))[/tex]
6. [tex]h(x) = 2x + 5[/tex]
Find [tex]h(h(-3x))[/tex]
[tex]7.\;\;\;g\left(x\right)\:=\:x-\:3,\:f\left(x\right)\:=\:3x\:-\:3\\\\\text{Find } \:f\left(g\left(x-3\right)\right)[/tex]
[tex]\mathrm{For}\:g=x-3\:\mathrm{substitute}\:x\:\mathrm{with}\:x-3[/tex].[tex]\bold{8.\;\;g(x) = 3x + 3, f(x) = 4x + 4}\\\\\bold{\text{Find } g(f(-3x))}[/tex]
[tex]\text {For}\:f(x) =4x+4\:\mathrm{substitute}\:x\:\mathrm{with}\:-3x}[/tex]What are the order pairs for y=2/5x?(14,35)(30,1250,2010,440,2425, 5/2
Ok
y = 2/5x
ok
a) y = 2/5(14)
y = 28/5
y = 5.6 the first one is not an order pair
b) y = 2(30)/5
y = 60/5
y = 12 the second one is an order pair
c) y = 2/5(50)
y = 100/5
y = 20 the third one is an order pair
d) y = 2/5(10)
y = 20/5
y = 4 the four one is an order pair
e) y = 2/5(40)
y = 80/5
y = 16 the fifth one is not an order pair
f) y = 2/5(25)
y = 50/5
y = 10 the sixth one is not an order pair.
The solutions are (30, 12), (50, 20) and (10, 4)
Calculate the circumference of a circle with a radius of 15 inches .Use 3.14 for pi.Round answer to the nearest tenth ,if necessary
The circumference of a circle whose radius is 15 inches measures 94.2 inches.
How to find the circumference of the circle?For a circle of radius R, the circumference is given by the formula:
C = 2*pi*R
Where pi is 3.14
In this case, we know that the radius is 15 inches, then we can write:
R = 15 in
Replacing that in the circumference formula we get:
C = 2*3.14*15 in = 94.2 inches.
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If f(x) = -x³ + x² + x, find f(-3)
Line segments JK and JL in the xy-coordinate plane both have a common endpoint /(-4, 11) andmidpoints at M, (2,16) and M, (-3, 5), respectively.What is the distance between M, and M.? Round to the nearest tenth
SOLUTION
From the question, since the coordinates of the mid-points JK and JL has been given as M (2,16) and M, (-3, 5), respectively.
To find the distance between these two mid-points, we simply use the distance formula to do that.
The distance formula is given as
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ where\text{ d is the distance } \end{gathered}[/tex]Applying these to the points M (2,16) and M, (-3, 5), we have
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(-3-2)^2+(5-16)^2} \\ d=\sqrt{(-5)^2+(-11)^2} \\ d=\sqrt{25+121} \\ d=\sqrt{146} \\ d=12.083045 \\ d=12.1\text{ units } \end{gathered}[/tex]Hence the answer is 12.1 units
Help! Please!!!!!!!!!?
The estimates for [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{10}{21}[/tex]
The actual answer of [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{30}{63}[/tex]
How to estimate fractions?The estimated answer of the fraction can be done as follows:
[tex]6\frac{1}{9}. 1\frac{5}{7}[/tex]
Hence,
[tex]6\frac{1}{9} = \frac{55}{9}[/tex]
[tex]1\frac{5}{7} = \frac{12}{7}[/tex]
Therefore, the actual answer of the fractions is as follows:
[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = 10\frac{30}{63}[/tex]
Hence, the estimated answer of the fractions can be calculated as follows
[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = \frac{220}{21} = 10\frac{10}{21}[/tex]
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What is −12÷2/3?
Responses
−36
−24
−18
−8
Find the area of a pantry shelf that measures 3 yards by yard. 6.4yd? 6.4 yd 1żyd 1 fyd
Option (c)
Given:
The measure of pantry shelf is 3 yard by 3/7 yrds.
The objective is to find the area of the pantry shelf.
The area of shelf can be calculated as,
[tex]\begin{gathered} A=3\times\frac{3}{7} \\ =\frac{9}{7} \\ =1\frac{2}{7}yd^2 \end{gathered}[/tex]Hence, option (c) is the correct answer.
A 15-gallon gas tank. If you can drive 330 miles on a full tank of gas, what is the unit rate of miles per gallon he gets?
HELP WITH 1 AND 2 PLEASE 20 POINTS AND BRAINLIEST SHOW YOUR WORK!!!!!!
1. The least number of hours that.Kee can work is 7 hours.
2. The maximum number of miles that Julie will drive will be 272 miles.
How to illustrate the information?1. Lee makes $64 per hour and he wants to make no less than $400 each hours for the trip. The number of hours will be:
Let the number of hours = h
64h >= 400
Divide
h >= 400/64
h >= 6.25
The least hour should be 7 hours.
2. The maximum number of miles that Julie will drive will be:
44(3) + 0.25m = 200
m = number of miles
132 + 0.25m = 200
0.25m = 200 - 132
0.25m = 68
m = 68 / 0.25
= 272
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what's the value of k
The sum of complementary angles = 90°
The angle shown is a right angle
Therefore:
k + 54.3 = 90
k = 90 - 54.3
k = 35.7°
Protein bars come in a 4 pack box or a 12 pack box the 4 pack costs 7.68 and the 12 pack costs 22.32 which box is the better
Buying 12 pack is better as it is cheaper than 4 pack.
What is unitary method?A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. The unitary method involves determining the value of a single unit before determining the value of the necessary quantity of units.
Given Data
Protein bars come in a 4 pack box or a 12 pack box
4 pack costs 7.68 and the 12 pack costs 22.32
In 4 pack
4 pack = 7.68
1 pack = 1.92
In 12 pack,
12 pack = 22.32
1 pack = 1.86
4 pack > 12 pack
Buying 12 pack is better as it is cheaper than 4 pack.
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Use the properties of equality to solve each equation r + 18 = 26
To solve this equatio you use the next property:
Subtraction Equal Property: it is used in expressions with adds. State that you can substract the same amount from both sides of the equation and maintain euality.
In this case, to solve r you substract 18 in both sides of the equation:
[tex]r+18-18=26-18[/tex]As 18-18 is 0;
[tex]r=8[/tex]Then, The solution of r+18=26 is r=8LESSON 1 SESSION
Solve.
Numbers with more than three digits have a comma to separate groups
of three digits. Digits in groups of three places are called periods.
Thousands Period
Hundred
Thousands
2
Ten
Thousands
8
Thousands Hundreds
4
Ones Period
3
Tens
7
Ones
1
Write the number shown above in standard form (the way you usually see it).
A method of notation in which digits are divided into groups of three by commas is known as the standard form of a number.
When a number has three digits, these groups are termed periods?
The periods are separated by commas.
Large numbers have three spots between each group of digits. Periods are the names of the groups.
The periods are typically separated by commas.
number follows 100000 and 100001
nonetheless, does not include decimals, negative integers, or fractions. Let's first express the quantity in numerical form, so 100,000 represents 100,000. The next whole number after 100,000 is the one obtained by adding 1 to the previous amount. As a result, 100000 + 1 Equals 100001, the following whole number.
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A and B shares a certain amount of money in the ratio x:y. B then
shares his money with C & D in the ratio of p:q respectively. What
fraction out of the total money does C receive?
So C receives py/(x+y)(p+q) share of money out of the total money
The ratio of money shared between A and B = x:y
Sum of the ratios is x+y
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.
B' share of money = y/(x+y)
The ratio of money between C & D = p:q
Sum of the ratio = p+q
B's share of the money is further divided among C & D in the ratio of p:q therefore:
C's share of money = y/(x+y)*p/(p+q)
= py/(x+y)(p+q)
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Write the equation of the line that passes through the points (0,3) and (2,-1). Put your answer in point-slope form, using fractional form for m and b.
The equation of the line that passes through the points (0, 3) and (2, - 1) in point-slope form is y - 3 = - 2 · x, that is equivalent to y = - 2 · x + 3 (m = - 2, b = 3).
How to determine the equation of a lineAccording to Euclidean geometry, a line can be constructed by knowing the location of two distinct points on a plane. Then, we can determin the slope of the line from the two points. First, determine the slope of the line by using the secant line formula:
m = (- 1 - 3) / (2 - 0)
m = - 4 / 2
m = - 2
Second, substitute all the variables in the equation of the line in point-slope form:
y - 3 = - 2 · x (Point-slope form)
y = - 2 · x + 3 (Slope-intercept form)
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I need to know which is the best estimate for rabbit population after 5 years
Answer:
[tex]\text{ B: 800 rabbits}[/tex]Explanation:
Here, we want to estimate the rabbit population after 5 years
From the question, there was an approximate increase in the rabbit population by 150 (from 150 to 300) in a space of 2 years
Let us have an exponential relationship for this:
[tex]P=I.a^t[/tex]Let us get the value of t
P is the current population at 300
I is the initial
a is ?
t is the number of years which is 2
Mathematically, we have it that:
[tex]\begin{gathered} 300\text{ =150 }\times a^2 \\ a^2\text{ = 2} \\ a\text{ = }\sqrt[]{2} \end{gathered}[/tex]Now, for the 5 years tenor, we substitute 5 for t
We have that as:
[tex]\begin{gathered} P\text{ = 150}\times\text{ (}\sqrt[]{2})^5 \\ P\text{ = 849} \end{gathered}[/tex]From the option, we have an approximate value of 800 rabbits
The boxplot below shows salaries for Construction workers and Teachers.ConstructionTeacher20254530 35 40Salary (thousands of S)50If a person is making the median salary for a construction worker, they are making more than what percentage ofTeachers?They are making more than% of Teachers.Check Answer
It is known that that the median divides the range into half.
And the first and third quartiles are the landmark for 25% and 75% of the data values.
Therefore, a dot plot is divided into 4 parts, each of ehich represents 25% of the population.
In the given dot plot diagram, it is observed that the mean of the construction worker's salary, coincide with the upper quartile of the salary., at $45,000
It means that 50% population of construction workers is getting at most $45,000 while 75% population of teachers is getting at most $45,000.
So if a construction worker is making the median salary i.e. $45,000, so he/she will be making more than 75% of the teachers.
Choose the most convenient method to graph the line y=-1/4x+3
The graph for the function (y = -(1/4)x + 3) is given in the attached image. See the explanation below.
Step 1 Find (x,y) pairs
Step 2: plot the points
Step 3 Draw the line on the graph.
Let's look at Step 1.
Using the graph as an example, our first pair of x,y is (0, 3)
This is obtained by substituting 0 in the equation y = -(1/4)x + 3
⇒ y = -(1/4)0 + 3
y = 0 +3
y = 3, where x = 0
If we repeat this process with x = 1, x = 2, x = 3, we will get the corresponding y for case.
Step 2: Plotting the x,y pairs will give us points on the graph.
Step 3: connecting the dots will give us the same line in the graph that is attached.
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coffee loses 12% of its weight when roasted. How much fresh coffee do you need to obtain 14 2/25 lb of roasted coffee
16 fresh coffee are needed to obtain 14 2/25 lb of roasted coffee.
How to calculate the number of fresh coffee needed ?Coffee loses 12% of it's weight when it is roasted
The number of fresh coffee that is needed to obtain 14 2/25 lb of roasted coffee can be calculated as follows
let y represent the number of fresh coffee needed
100%-12%
= 88%
= 88/100
= 0.88
14 2/25
= 352/25
= 14.08
The number of fresh coffee can be calculated as follows
0.88y= 14.08
y= 14.08/0.88
y= 16
Hence to obtain 14 2/25 lb of roasted coffee, 16 fresh coffee is required.
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Answer:
16 lbs
Step-by-step explanation:
Please help me solve both a and b of this problem.
A. The relationship between number of towers and number of customers is proportional.
B. 12 customers.
What is a Proportional Relationship?A proportional relationship between two variables, x and y, is a relationship whereby the ratio y/x is the same all through the table of values.
Thus, the value of y/x is constant, and is referred to as the unit rate or constant of proportionality, k.
Part A:
Given the table of values, we have:
Constant of proportionality (k) = y/x = 252/5.25 = 300/6.25 = 348/7.25 = 444/9.25 = 48.
Therefore, it is a proportional relationship because it has a constant of proportionality, k = 48.
Part B:
Substitute k = 48 into y = kx (proportional relationship)
y = 48x.
The equation for the relationship is, y = 48x. Substitute y = 576 into the equation to find the value of x, number of customers:
576 = 48x
Divide both sides by 48
576/48 = 48x/48 [division property of equality]
12 = x
x = 12
The number of customers is 12.
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