Suppose that the function fis defined, for all real numbers, as follows.
f(x)
-2 if x #2
4 if x=2
Find f(-1), f(2), and f(5).
f (-1)
f(2)
f(5)
Answers
The value of the functions f(-1), f(2), and f(5) are -2, 4, -2 respectively.
What is the function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). The number of dependent variables for a function is 1 and the number of independent variable for a function is 1.
Given function is:
[tex]f(x)=\left\{\begin{matrix}-2 & \text{if } x \ne2 \\ 4 & \text{if } x=2\end{matrix}\right.[/tex]
The meaning of the above function is when x is not equal 2, then the value of f(x) is -2 and when x is equal 2, then the value of f(x) is 4.
The dependent variable is f(x). The independent variable is x.
So the value of f(-1) is -2 since x = - 1 ≠ 2.
So the value of f(2) is 4 since x = 2.
So the value of f(5) is -2 since x = 5 ≠ 2.
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Related Questions
In a lottery, the top cash prize was $620 million, going to three lucky winners. Players pick four different numbers from 1 to 59 and one number from 1 to 47. A player wins a minimum award of $225 by correctly matching three numbers drawn from the white balls (1 through 59) and matching the number on the gold ball (1 through 47). What is the probability of winning the minimum award?
Answers
The probability of winning the minimum award is [tex]\frac{^4C_3 . ^{53}C_1}{^{57}C_4} \times \frac{1}{47}[/tex].
The Player chooses 4 numbers from white balls numbered 1 to 59 and
1 number from gold ball numbered 1 to 47
He has to choose 3 correct numbers out of 4 numbers in the white ball
and 1 number from the gold balls.
He can do in [tex]^4C_3 . ^{53}C_1[/tex] and 1 way respectively.
So, the probability can be given by;
Probability = probability of choosing white ball * probability of choosing red ball
Probability = [tex]\frac{^4C_3 . ^{53}C_1}{^{57}C_4} \times \frac{1}{47}[/tex]
Thus, the probability of winning the minimum award when players pick four different numbers from 1 to 59 and one number from 1 to 47 and a player wins a minimum award of $225 by correctly matching three numbers drawn from the white balls (1 through 59) and matching the number on the gold ball (1 through 47) is [tex]\frac{^4C_3 . ^{53}C_1}{^{57}C_4} \times \frac{1}{47}[/tex].
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Find the equation for the line parallel to the given line and passing through the given point.
3y = -12x + 4; (1,1)
Answers
The equation for the line parallel to the given line and passing through the given point is y = -4x + 5.
Given:
3y = -12x + 4 and point (1,1)
3y = -12x+4
divide by 3 on both sides
3y/3 = -12x/3 + 4/3
y = -4x + 4/3.
m = -4.
y = mx + c
substitute m and (1,1)
1 = -4*1 + c
1 = -4 + c
c = 1 + 4
c =5
substitute c and m value in y = mx+c
y = mx + c
y = -4x + 5.
Therefore the equation for the line parallel to the given line and passing through the given point is y = -4x + 5.
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Sara's mother bought 8 large oranges for $12.00. Sara said there was a ratio of 12 to 8, so the unit rate was $1.50 per orange. Sara's friend Daniel said he thought the ratio would be 8:12, so the unit rate would be of an orange per dollar.
Explain how both Sara and Daniel might have found their unit rates and how both could be correct.
Answers
The unit rate of orange could be found by Sara and Daniel by ratio to be $1.50
Further explanation on how they could be correctIf Sara's mother bought 8 large oranges for $12.00
Sara may have thought of it like if $12 is for 8 oranges the how much is for 1
12 : 8 then X : 1
12/8 then x/1
12/8 = x/1
x = $1.50
Daniel would have taken this method, if 8 oranges costs $12 then 1 orange would cost ?
8 oranges : $12 then 1 orange : ?
8 : 12 = 1 : ?
8/12 = 1/?
8 * ? = 1 * 12
? = 12/8
? = $1.5
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Write a function for the line with a slope of 5 that passes through the point (2, 1).
HINT:Substitute the coordinates of the given point and the slope into y=mx+b to find the y-intercept.
HINT:The slope is m in the equation y=mx+b.
Answers
Step-by-step explanation:
y = mx+ b
m is the slope = 5
you can get x,y from point (x,y); x=2, y=1
substitute all information we have to find b
1 = 5(2) + b
1 = 10 + b
1 - 10 = b
-9 = b
the function for line:
y = 5x - 9
4(x-b) = x solve for x
Answers
[tex]4(x)+4(-b)=x\\4x-4b=x\\4x-x=4b\\3x=4b\\\frac{3x}{3} =\frac{4b}{3} \\x=\frac{4b}{3}[/tex]
⇒They simply wanted you to simplify and make x the subject of the equation.
Measures of center (mean, median) are affected by addition, multiplication, or both?
Answers
Answer:
Measures of center generally tell us about the middle , or center of a distribution. They are the mean , the Mexican , and the mode. Each plays a useful role in statistics. The mean or arithmetic average , is calculated by adding all the data values and dividing by the number of values.
Towns A and B are 400 miles apart. If a train leaves A in the direction of B at 50 miles per
hour, how long will it take before that train meets another train, going from B to A, at a speed
of 30 miles per hour?
(A) 4 hours
(B) 4 hours
(C) 5 hours
(D) 5 hours
(E) 6 hours
Answers
Answer: C or D(they appear the same, the answer is 5 hours)
Step-by-step explanation:
after 5 hours, train a has gone 5*50 miles, or 250 miles
after 5 hours, train b has gone 5*30 miles, or 150 miles
250miles + 150miles = 400 miles
Calculate the volume.
30 cm
60 cm
Volume
85 cm
Not to scale.
Answers
The volume of the cuboid is 153000 [tex]cm^{3}[/tex];
What is the volume of the cuboid?
In general, the volume of a cuboid is equal to the area that it takes up in space. It is dependent upon the cuboid's three dimensions, or its length, breadth, and height. Due to the fact that all of a cuboid's faces are rectangular, the term "Solid Rectangle" is also referred to as a cuboid. All of the angles and the opposite faces of a cuboid in a rectangular cuboid are at right angles. A cuboid's volume is determined by the product of its length, breadth, and height. Cubic units are used to measure cuboids' volume.
The product of a cuboid's base area and height determines its volume. We can therefore write;
Cuboid volume equals base area times height [in cubic units].
The cuboid's base is shaped like a rectangle. As a result, a cuboid's base area is determined by multiplying its length by its breadth. Hence,
A cuboid's volume is equal to its length, width, and height in cubic units, or
A cuboid's volume is equal to l b h [in cubic units].
l = length, b = width, and h = height.
In the given question, we have;
Length = 30 cm;
Breadth = 60 cm;
Height = 85 cm;
And,
we know that:
The volume of the cuboid = lbh
The volume of the cuboid = 30×60×85 [tex]cm^{3}[/tex]
The volume of the cuboid = 1800 ×85 [tex]cm^{3}[/tex];
The volume of the cuboid = 153000 [tex]cm^{3}[/tex];
Hence,
The volume of the cuboid = 153000 [tex]cm^{3}[/tex];
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complete the table below with the needed data
help please help me because this is due tomorrow
Answers
The factors are mentioned in the table given below.
Number Number of factors prime or composite
12 6 composite
20 6 composite
21 4 composite
31 2 prime
43 2 prime
Factors are those numbers which when divide the given number leaves zero as a remainder.
Factor of 12 = 1, 2 ,3, 4, 6 , 12
Factor of 20 = 1, 2 , 4,5,10 , 20
Factor of 21 = 1 ,3, 7, 21
Factor of 31 = 1, 31
Factor of 43 = 1, 43.
Prime number is a number which has only 2 factors that is number one(1) and the number itself.
Composite numbers which has more than 2 factors.
Therefore, the number of factors are mentioned in the table.
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PLEASE HELP ASAP PLEASE HELP ASAP
Answers
The materials travel faster on Belt One, considering the constants of the proportional relationships.
What is a proportional relationship?A proportional relationship is a linear function with intercept zero in which the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, according to the equation presented as follows:
y = kx
For each belt in this problem, the constant gives the velocity that the materials travel.
For Belt One, the relation is:
y = 157.1x.
Hence the velocity is of 157.1 inches per minute.
For Belt Two, the velocity is obtained as follows:
k = 125.6/2 = 62.8 inches per minute.
157.1 > 62.8, hence it travels faster on Belt One.
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there are 17 cookies that will be divided equally among 5 goody bags. How many cookies go in each goody bag.
Answers
For each goody bag we need 3.4 cookies
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
We are given that there are 17 cookies that will be divided equally among 5 goody bags.
17 cookies = 5 goody bags.
For each goody bag.
Thus,
17/5 = 3.4 cookies.
Therefore, 3.4 cookies needed.
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Karen, Pete, Rose, and David are comparing their solutions to a hornework problem below. Select the student who correctly subtracted the rational expressions.
Answers
Answer:
Step-by-step explanation:
we cant see the problem or there answers
Find the area of the circle in terms of Pi
Answers
Area of circle = 1764 pi in² in terms of pi .
What is mensuration ? Measurement is a branch of mathematics that studies the calculation of geometric figures and parameters such as area, length, volume, lateral area, and surface area. She outlines the principles of computation and explains all the important equations and properties of various geometric shapes and numbers. A measurement is a geometry object. Measurements examine the size, area, and density of various shapes in 2D and 3D. Now, as an introduction to measurement, let's look at the differences between 2D and 3D shapes and their differences. A 2D graph is a shape defined by three or more straight lines or closed segments on a plane. Such a shape has neither width nor height. It is called a 2D shape or figure because it has two dimensions, length and width. For 2D shapes, the area (A) and perimeter (P) must be determined. A 3D shape is a structure surrounded by various surfaces or planes. Unlike 2D shapes, these shapes have height and depth. It is called a 3D shape because its length, width and height/depth are three dimensions.Calculationarea of circle = pi r²
= 42 * 42 pi²
= 1764 pi in²
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PLEASE HELP ASAP! I DON'T UNDERSTAND THE QUESTION
2(x-1)^2-4
Use the order of operations to turn the expression back into standard form. Explain your work using complete sentences.
Answers
Step-by-step explanation:
among other details this is the main thing about the standard form :
a polynomial in standard form is the sum of one or more terms; each term must be a monomial in standard form. also, the degrees of the terms should be decreasing as much as possible from left to right.
a monomial is the product of one or more factors: a constant coefficient and one factor for each variable in the expression. via exponent (e.g. 0) we control which variable is actually "showing", as any x⁰ = 1 and can therefore be omitted when writing as factor.
in other words :
e.g.
4x³ + 2x² + 5x + 1
2x + 3y + 7xy
are examples of the standard form.
in our case we have only x a variable. but we need to do all the squaring and multiplications and summing up to get the standard form.
that means
2(x - 1)² - 2 = ...
remember the priorities :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
2(x - 1)² - 2 = 2(x² - 2x + 1) - 2 =
= 2x² - 4x + 2 - 2 = 2x² - 4x
A nonagon has 9 sides. One angle of a regular nonagon measures (3w + 15)°. Determine the value of w. Round to the nearest whole number.
w = 118
w = 72
w = 55
w = 42
Answers
If a nonagon has 9 sides. One angle of a regular nonagon measures (3w + 15)°. The value of w is: D. w = 42.
How to find the value of w?Given data:
Nonagon= 9 sides
Angle of a regular nonagon =(3w + 15)°
Value of w =?
Hence let find the value of w
Value of w = 3w + 15°
Value of w = 3(9) + 15°
Value of w = 27 + 15
Value of w = 42
Therefore the correct option is D.
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Answer: the answer is D. W=42
Step-by-step explanation:
f(x)=x^4 -3x³ + x² + 2x + 1435
use long division to determine whether x + 7 is a factor of f(x).
Answers
x-7 is not a factor of [tex]x^{4}-3x^{3}+x^{2} +2x+1435[/tex].
In long division method, we divide [tex]x^{4}-3x^{3}+x^{2} +2x+1435[/tex] by x-7
x-7 ) [tex]x^{4}-3x^{3}+x^{2} +2x+1435[/tex] ( [tex]x^{3}-10x^{2} +71x-495[/tex]
[tex]x^{4}+7x^{3}[/tex]
-----------------------------
[tex]-10x^{3}+x^{2} +2x+1435[/tex]
[tex]-10x^{3}-70x^{2}[/tex]
--------------------------
[tex]71x^{2} +2x+1435[/tex]
[tex]71x^{2} +497x[/tex]
----------------------------
[tex]-495x+1435[/tex]
[tex]-495x-3465[/tex]
----------------------------
[tex]4900[/tex]
As 4900 is a remainder, x-7 is not a factor.
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GPAS at CCCOnline are normally distributed with a mean of 2.05 and a standard deviation of 0.58.
Find the z-score for a GPA of 2.98
Answers
The Z-score for a GPA of 2.98 is 1.60345
Calculating Z - score:A Z-score is a numerical value or measurement that explains the relationship between a value of data and the mean of a group of values. It will be calculated in terms of standard deviations from the mean.
The formula to calculate the Z -score is given by
Z - score = [tex]\frac{( \bar{x} -\mu) }{\sigma}[/tex]
Where [tex]\bar {x}[/tex] = test value
μ = mean and σ = standard deviation
Here we have
GPAS at CCCOnline are normally distributed with a mean of 2.05 and a standard deviation of 0.58
⇒ mean μ = 2.05
⇒ Standard deviation σ = 0.58
And we need to find the z-score for a GPA of 2.98
⇒ [tex]\bar {x}[/tex] = 2.98
From above observations
Z - score = [tex]\frac{( 2.98 -2.05) }{0.58}[/tex]
= [tex]\frac{( 0.93) }{0.58}[/tex]
= 1.60345
Therefore,
The Z-score for a GPA of 2.98 is 1.60345
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I need some help on this question. I sent a screenshot on this.
Answers
Answer: 1/2
Step-by-step explanation:
I'm assuming this is rise over run. The rise is 1 and the run is 2.
Remember, [tex]\frac{rise}{run}[/tex]
what is 12 x 6 because area = L x w a = 12 x 6 a= ?
Answers
Answer: _______________________________
72
a pair of fair dice are rolled together once and the numbers that come up on the two dice are added. what is the probability that the sum of the numbers on the two dice is 10?
Answers
Answer:
The probability is 1/12Step-by-step explanation:
The are 6 possibilities for each dice, so the number of outcomes is:
6*6 = 36Outcomes with the sum of 10:
4+6, 5+5, 6+4 - three favorable outcomesProbability of getting 10 is 3 out of 36:
P(10) = 3/36 = 1/12If MLDEF = 119, then what are m/FEG and m ZHEG? The diagram is
not to scale.
Answers
The measure of <FEG= 61 and <HEG = 119.
What is Vertical Opposite Angle?The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.
when two lines in a plane intersect, one of the angles that are directly across from one another.
Given:
m< DEF= 119
Now, <DEF + <FEG= 180 (Linear Pair)
119+ <FEG = 180
<FEG = 180- 119
<FEG = 61
and, <DEF= <HEG = 119 (Vertical opposite angle)
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A small van can hold 50 crates and boxes. For every 7 crates the van can hold, there is
room for 3 boxes. How many crates and boxes are in the van when it is completely full?
Answers
There are 15 crates and 35 boxes in the van when it is completely full.
Given,
Total number of crates and boxes=50
For every 7 crates the van can hold, there is room of 3 boxes.
let,
Number of crates =x
Number of boxes =y
As given,
Equation for total number of crates and boxes can be written as
[tex]x+y=50....i[/tex]
Space for 7 crates is equal to space for 3 boxes in van, it's equation can be written as
[tex]7x=3y\\\\x=\frac{3y}{7}[/tex].
Substituting 'x' in eq.[tex]i[/tex]
[tex]\frac{3y}{7}+y=50\\\\ \frac{3y+7y}{7}=50 \\\\10y=7*50\\\\10y=350\\\\y=\frac{350}{10}\\ \\y=35[/tex]
Substituting 'y' in eq.[tex]i[/tex]
[tex]x+35=50\\\\x=50-35\\\\x=15[/tex]
Thus, there are 15 crates and 35 boxes in the van when it is completely full.
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see the picture attached log3 a/3
Answers
Answer: -1.631
Step-by-step explanation:
[tex]\log_{3} \frac{a}{3}=\log_{3} a-\log_{3} 3=-0.631-1=-1.631[/tex]
The perimiter of a square is 60 cm how long is one side of the square
Answers
Answer: 15 cm
Step-by-step explanation:
just divide 60 by 4 and because a squar has 4 sides and that is it
Find m<1 then classify the angle.
Answers
Answer:
81 degrees
This is an acute angle since it’s less then 90 degrees
Step-by-step explanation:
All three angles of a triangle always equal 180 degrees
180-(78+31)
180-109
81 degrees
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the table represents a function.
x
-6
-2
0
3
f(x)
3
1
4
-2
Answers
The value of the function f(x) at x = -2 is , f(-2) = 1 , the correct option is (c) .
Function is defined as an expression that defines a relationship between one variable and another variable .
In the question ,
it is given that ,
the value of the function f(x) at different values of x is given ,
we have to find the value of the f(-2) , that is the value of the function f(x) at x = -2 .
from the table , we see that when x [tex]=[/tex] -2 , the value of f(x) is [tex]=[/tex] 1 ,
that means f(-2) [tex]=[/tex] 1 .
Therefore , The value of the function f(x) at x = -2 is , f(-2) = 1 , the correct option is (c) .
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1. You begin working at Tasty Tacos with the payment schedule listed in the table below:
Write an equation that describes the relationship between the years (x) and the earnings per hour (y).
2. If this pattern continues, what would the earnings per hour be after working for 15 years?
3. If this pattern continues, after how many years of service would you earn $9.65 per hour?
Answers
The earnings per hour be after working for 15 years is $11.4.
From the given table (2, 6.85), (4, 7.55), (6, 8.25).
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)
1) Now, put (x1, y1)=(2, 6.85) and (x2, y2)=(4, 7.55) in slope formula, we get
m=(7.55-6.85)/(4-2)
= 0.7/2
= 0.35
Substitute m=0.35 and (x, y)=(2, 6.85) in y=mx+c, we get
6.85=0.35(2)+c
⇒ 6.85=0.7+c
⇒ c=6.85-0.7
⇒ c=6.15
Now, equation is y=0.35x+6.15
2). Put x=15 in the obtained equation, we get
y=0.35×15+6.15
⇒y=$11.4
3). Put y=9.65 in the obtained equation, we get
9.65=0.35x+6.15
⇒0.35x=9.65-6.15
⇒0.35x=3.5
⇒x=3.5/0.35
⇒x=10 years
Therefore, the earnings per hour be after working for 15 years is $11.4.
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NEED HELP ASAP plsssssssssssssssssssssssssssss
Answers
How is the graph of g(x)=(x-3)³ related to the graph of f(x) = x²?
Answers
The graph of the function f(x) = x³ and g(x) = (x - 3)³ are related to each other that the function g(x) is shifted right to 3 points.
Function
Basically, function is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Given,
Here we need to find how the graph of g(x)=(x-3)³ related to the graph of f(x) = x³.
Here we have the two equations of the function that are,
f(x) = x³
g(x) = (x - 3)³
By looking at the given functions, we have identified that f(x) be the parent function:
And it can be written as,
=> f(x) = x³
And the first transformation is applied as,
f(x) → f(x) - 3
Now, the function f(x) will shift right side by 3 units
Therefore, the function f(x) = x³ and g(x) = (x - 3)³ are related to each other that the function g(x) is shifted right to 3 points.
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Someone j need help with this pls
Answers
Answer:
27/256
Step-by-step explanation:
=(27)(1/4)(1)/(64)
=27/256