For the function f(x)= x^2+4x-1, what is the range of f (x) for the domain {-2,0,1}?
Answers
The range of the given function is {-5,-1,4} which is the B option.
Given function:-
[tex]f(x) = x^2+4x-1[/tex]
Domain = {-2,0,1}
We have to find the range of the given function for the given domain.
Putting x = -2 in the given function, we get,
[tex]f(-2) = (-2)^2+4(-2)-1[/tex]
f(-2) = 4 - 8 - 1 = -5
Putting x = 0 in the given function, we get,
[tex]f(0) = (0)^2+4(0)-1[/tex]
f(0) = 0 + 0 -1 = -1
Putting x = 1 in the given function, we get,
[tex]f(1) = (1)^2+4(1)-1[/tex]
f(1) = 1 + 4 - 1 = 4
Hence, the range of the given function is {-5,-1,4}.
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Related Questions
the angle of depression of the light to the nearest minute is
Answers
Answer
θ = 37° 30'
Explanation:
The angle of depression has the same measure as the angle of elevation, so a trigonometric function that related the sides of the triangle and the angle of elevation θ is tangent. Then:
[tex]\text{tan }\theta\text{ =}\frac{39.57}{51.56}[/tex]Therefore, the value of θ is:
[tex]\begin{gathered} \tan \text{ }\theta\text{ = 0.7674} \\ \theta=\tan ^{-1}(0.7674) \\ \theta=37.50 \end{gathered}[/tex]So, in grades and minutes, we get:
θ = 37.50 = 37° 30'
Therefore, the angle of depression is 37° 30'
solve the following proportionx 2— = —32 8x=
Answers
We have to solve for x:
Multiply both sides of the proportion by 32:
[tex]\frac{x}{32}(32)=\frac{2}{8}(32)[/tex][tex]x=\frac{64}{8}[/tex]Simplify:
[tex]x=8[/tex]The shaded portion in each glass represents an amount of grape drink Martin's glass of grape drink has a weaker tasting grape flavor than Tia's glass of grape drink.
Answers
The stronger flavor of grape is in Tia's glass.
Given,
Martin's glass of grape drink has weaker tasting grape flavor
Tia's glass of grape drink has stronger tasting grape flavor
3 ounces of water is added to Martin's glass
One table spoon of grape mix is added to Tia's glass
We have to find the glass which contain the stronger grape flavor
Already in Martin's glass flavor is low. When we add water again to his glass, the flavor will again dissolves with water.
In Tia's glass grape flavor is stronger. By adding one tablespoon of grape mix the flavor will become more stronger.
That is,
The stronger flavor of grape is in Tia's glass.
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Write the sum of 7√28x6 + 4√7x6 in simplest form, if x # 0
Answers
The sum equivalent to 7√28x⁶+4√7x⁶ is :
18√7x⁶ .
Solution:Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.Given ,7√28x⁶+4√7x⁶,
To find sum in simplest form ;
7√28x⁶+4√7x⁶
By splitting to factors,
= 7√(7*4)x⁶+4√7x⁶
= 7*2√7x⁶+4√7x⁶
= 14√7x⁶+4√7x⁶
By factoring out like terms,
= 2√7x⁶(7+2)
= 2√7x⁶(9)
= 18√7x⁶
Therefore sum is = 18√7x⁶.
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Lexi and Raymond are hosting events that are catered by the same company. Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582. Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. How much does the caterer charge for each meal?
Every adult's meal costs $
, and every child's meal costs $
.
Answers
The cost for children meal is $16 and the.cost for adult meal is $26.
How to calculate the value?Let cost of adult meal = a
Let cost of child meal = c
Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582.This will be:
63a + 59c = 2582 ...... i
Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. This will be;
63a + 93c = 3126 ...... ii
Collect both equations
63a + 59c = 2582 ...... i
63a + 93c = 3126 ...... ii
Subtract i from ii
34c = 544
Divide
c = 544 / 34
c = 16
The cost of children meal is $16.
From equation i, 63a + 59c = 2582
63a + 59(16) = 2582
63a + 944 = 2582
Collect like terms
63a = 2582 - 944
63a = 1638
a = 1638/63
a = 26
Adult meals is $26.
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Xavier has a bag of 20 marbles. 8 are blue, 7 are red, and 5 are green. Xavier pulls out a marble, records what color it is, and puts it back. He then selects another marble and records its color What is the probability of pulling out a blue marble and then a green marble?
Help please
Answers
Answer:
.1
We have 20 marbles.
Probability of blue marble = 8/20 = .4
Since the blue marble is put back, we still have 20 marbles.
Probability of green marble = 5/20 = .25
Multiplying these probabilities:
.4 × .25 = .1
any given season, a soccer team plays 65 % of their games at home.
When the team plays at home, they win 83 % of their games.
When they play away from home, they win 26 % of their games.
find the probability the team wins with explanation
Answers
Based on the percentage of games played at home by the team, and the percentage win rate, the probability that the team wins is 63.05%
How to find the probability the team wins?First, find the probability that the team wins playing at home:
= Percentage win rate at home x Percentage played at home
= 83% x 65%
= 53.95%
Then find the probability of winning away:
= Percentage win rate away x Percentage played away
= 26% x (1 - 65%)
= 9.1%
The probability the team wins is:
= 53.95 + 9.1
= 63.05%
In conclusion, the probability of the team winning at home and the probability of them winning away, can be summed up to find the probability of the team winning which is 63.05%.
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sat scores have a mean of 500 and standard deviation of 200. act scores have a mean of 20 and a standard deviation of 5. suppose that student a has an sat score of 600, and student b has an act score of 25. using z-scores, which student had a better college entrance exam score?
Answers
‘B’ had a better college entrance exam score due to the higher value of Z-Score.
The Z-score of an observation is the number of standard deviations it falls above or below the mean. Standard deviation is a statistic that is used to measure the dispersion of a dataset relative to its mean and is calculated by doing the square root of the variance.
[tex]Z=\frac{(observation-mean)}{standard deviation}[/tex]
By putting the values as given in the question,We get,
A's score is (600 - 500) / 200 = 0.5 standard deviation i.e. above the mean.
B's score is (25 - 20) / 5 = 1 standard deviations i.e. above the mean.
Thus ‘B’ had a better score.
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Christina is doing an obstacle course in gym class. First, she runs 100 feet and jumps over a hurdle. Then, she crawls through a 20-foot tunnel. Finally, she dribbles a soccer ball 60 feet to the finish line. How many yards long is the obstacle course?
Answers
Answer:
60 yards
Step-by-step explanation:
100 feet + 20 feet + 60 feet = 180 feet
180 feet = 60 yards (there are 3 feet in 1 yard)
Dwayne puts $200.00 into an account to use for school expenses. The account earns 9% interest, compounded quarterly. How much will be in the account after 4 years? nt 1 Use the formula A = P 1 + where A is the balance (final amount), P is the principal (starting n amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
Answers
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
P= 200
r= 0.09
n = 4
t= 4
And solving we got:
[tex]A=200(1+\frac{0.09}{4})^{4\cdot4}=285.52[/tex]Help, I don’t get this
Answers
The total earnings for the week for the same wage per hour is $501.6.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
For 5 of working earnings is $76
Hourly rate = 76 / 5 = $15.2 per hour
Now for 33 hours of working in a week,
Earning = 15.2 * 33 = $501.6
Thus, the total earnings for the week for the same wage per hour is $501.6.
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27. A table and five chairs cost $3500. The cost of three chairs is $1050. What is the cost of a table if all the chairs cost the same price?
Answers
Find the area of the figure. Use 3.14 for pi.
Answers
The area is 144
Ryan Pick 6 1/2 cups of berries from his garden he use 3 3/8 cups of to make fruit salad if he needs 3 cups of berries to make a pie does Ryan have enough very stuff to also make a pie?
Answers
We will simply subtract 3 3/8 from 6 1/2
That is;
6 1/2 - 3 3/8
= 3 4-3/8
=3 1/8
The amount of berry left is more than 3 cups, hence Ryan have enough very stuff to also make a pie
Use integers or fractions for any numbers in the expression.
Answers
Solution:
Consider the following injective function:
[tex]f(x)=\frac{3x+6}{x-5}[/tex]this is equivalent to:
[tex]y=\frac{3x+6}{x-5}[/tex]by cross-multiplication, this is equivalent to:
[tex](x-5)y\text{ = 3x+6}[/tex]now, applying the distributive law, we get:
[tex]xy-5y\text{ = 3x+6}[/tex]this is equivalent to:
[tex]xy\text{ -5y -3x = 6}[/tex]Applying the common factor, we get:
[tex]x(y-3)\text{ -5y = 6}[/tex]this is equivalent to:
[tex]x\text{ (y-3)}=\text{ 6+5y}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{6+5y}{y-3}[/tex]so that, we can conclude that the correct answer is:
[tex]f^{-1}(x)=\frac{6+5x}{x-3}[/tex]A kite is gliding 74 feet above sea level. There is a stingray coasting 7 feet below sea level. What is the vertical distance between the kite and stingray.
Answers
The vertical distance between the kite and stingray is 81 feet.
Given that, a kite is gliding 74 feet above sea level. There is a stingray coasting 7 feet below sea level.
What is the vertical distance?Vertical distance or vertical separation is the distance between two vertical positions. Many vertical coordinates exist for expressing vertical position: depth, height, altitude, elevation, etc.
The vertical distance between the kite and stingray is
74-(-7)
= 74+7
= 81 feet
Therefore, the vertical distance between the kite and stingray is 81 feet.
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8. Find the polynomial function of degree 3 for the given conditions I.f(1) = 32 and x-2, x-3,x+1 are factors of the polynomial II.f(3) = -24 and 5,2,4 are zeros of the polynomial
Answers
Part I
In factored form, [tex]f(x)=a(x-2)(x-3)(x+1)[/tex]. Substituting x=1,
[tex]f(1)=32=a(1-2)(1-3)(1+1)\\\\\implies 32=4a\\\\a=8\\\\\therefore f(x)=8(x-2)(x-3)(x+1)[/tex]
Part II
In factored form, [tex]f(x)=a(x-5)(x-2)(x-4)[/tex]. Substituting x=3,
[tex]f(3)=-24=a(3-5)(3-2)(3-4)\\\\\implies 24=2a\\\\a=12\\\\\therefore f(x)=12(x-5)(x-2)(x-4)[/tex]
Help please i need it for a grade
Answers
Answer:
(3,13 ) & (-1,5)
Step-by-step explanation:
a. 2x + 7 = x^2 + 4
b. move all terms to the left side and set equal to zero. then set each factor equal to zero. which gives you the x values 3, -1
c. substitute x with the x values to get y. 2(3) + 7 = -1^2 + 4
d. the solution is (3,13 ) & (-1,5)
jessica jogs on a path that is 25 meters long to get a park that is south of her location.it takes her 2.5hrs. what is her velocity
Answers
Answer:
10 meters per hour
Step-by-step explanation:
Velocity = Distance / Time
Do the interior angles of a quadrilteral always add up to the same thing? Explain why you think so.
Answers
For the equation, complete the given ordered pairs.Need help solving the last order pair.
Answers
Hello!
First, let's remember:
In an ordered pair, we will have two variables represented as (x, y).
In the first two ordered pairs, the exercise informed the value of x. In the third ordered pair, it informs the value of y. We will solve it in a similar way, look:
[tex]\begin{gathered} 4x-y=7 \\ 4x-7=7 \\ 4x=7+7 \\ 4x=14 \\ x=\frac{14}{4}=\frac{7}{2} \end{gathered}[/tex]Answer:x = 7/2 or also x = 3.5.
What is the absolute value of the number plotted on the number line?.
A. -1.75
B. -1.25
C. 1.25
D. 1.75
Answers
Answer:
D. 1.75
Step-by-step explanation:
Absolute value cannot be negative, so that gets rid of A & B. The point is at -1.75 so it has to be D.
Please help me asapppppp
Answers
Explanation:
To find circumference we need the radius, however in the figure they gave you the diameter and the diameter is two times the radius d=2r, from the figure the diameter equals 20 so we substitute to get 20=2r, dividing both sides by two we get that r=10 ft
Now we substitute in our circumference formula C=2 πr
So C=2*3.14*10
C=62.8 ft
8. Find the area of the kite.
Answers
Answer:
A=16, the formula to find the area of a kite is A=pq/2
Step-by-step explanation:
A=pq/2 = 4×8/2=16
2 varieties of gift wrap paper are to be mixed. The assortment will cost $7. One sells for 50 cents a sheet the other for 25 cents a sheet. the number of 50 cents sheets is 3 times the number of 25 cent sheets. how many of each type of sheet should be included in the package
Answers
Given:
One variety of gift wrappers sells for 50 cents a sheet the other for 25 cents a sheet.
In dollars,
One variety of gift wrappers sells for 0.5 dollars a sheet the other for 0.25 dollars a sheet.
The assortment will cost $7.
Let x be the number of 50 cents sheets.
Let y be the number of 25 cents sheets.
It is also given that,
The number of 50 cents sheets is 3 times the number of 25 cent sheets.
x=3y ........ (1)
0.5x+0.25y=7 ....... (2)
Substitute (1) in (2) we get,
[tex]\begin{gathered} 0.5(3y)+0.25y=7 \\ 1.5y+0.25y=7 \\ 1.75y=7 \\ y=\frac{7}{1.75} \\ y=4 \end{gathered}[/tex]Hence, x=3(4)
x=12
So, the number 50 cents sheets are 12 and the number of 25 cents sheet is 4.
Give two examples of each type of number: real, natural, integers, rational and irrational.
Answers
The following examples are shown below:
Natural numbers: 2, 9Integers: - 3, 0Rational numbers: 5 / 7, - 13 / 8Irrational numbers: √5, πReal numbers: 0, √6What kind of real numbers does exist?In this problem we have to present five types of real numbers, which are defined and shown below:
Natural numbers - Smallest subset of real numbers: N = {1, 2, 3, 4, ...}. Examples: 2, 7, 9Integers - Combination of the subset of real numbers and another subset N' = {0, - 1, - 2, - 3, - 4, ...}. Examples: - 5, - 3, 0, 5, 8Rational numbers - Subset of all real numbers of the form m / n, where m and n are integers and n is a non-zero integer. Natural numbers and integers are also rational numbers. Examples: 5 / 7, - 9 / 11, 19 / 3, - 10 / 7Irrational numbers - Subset of all real numbers that are not rational. This subset is the complement of the subset of rational numbers. Examples: √2, - e, πReal numbers - Set of all rational and irrational numbers. Examples: - 5, 0, 2, 19 / 3, √3To learn more on real numbers: https://brainly.com/question/551408
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overbooking flights is a common practice of most airlines. a particular airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 278 tickets. question 1. what is the expected number of ticket holders that will fail to show for the flight? (use 2 decimal place in your answer.) question 2. what is the probability that the airline will not have enough seats for all the ticket holders who show for the flight? (use 3 decimal places.)
Answers
1. 3.2673 is the expected number of ticket holders that will fail to show for the flight.
2. 0.425 is the probability that the airline will not have enough seats for all the ticket holders who show for the flight.
P(airline will not have enough seats for all the ticket holders who show for the flight) = P(more than 267 people show up for the flight)
p = P(will show for flight) = 1 - 0.04 = 0.96
n = 278
µ = n * p = 278 * 0.96 = 266.88
σ = [tex]\sqrt{ n*p* (1 - p)} = \sqrt{278 * 0.96 * 0.04} = 3.2673[/tex]
P(X > 267) = P(X > 267.5)
p(x- µ) / σ > 267.5- µ /σ
= P(Z> 267.5 – 266.88/ 3.2673 )
= P(Z > 0.19)
= 0.425.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. To understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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If M is between G and T, MG = 2x + 1, MT = 3x + 3, and GT = 19, Then X = ___.MG = ___.MT = __.
Answers
We are given the following information
M is between G and T
MG = 2x + 1
MT = 3x + 3
GT = 19
Let us draw a sketch to better understand the problem
As you can see, the sum of MG and MT must be equal to the GT
Mathematically,
[tex]\begin{gathered} GT=MG+MT \\ 19=(2x+1)+(3x+3) \end{gathered}[/tex]Let us solve the above equation or x
[tex]\begin{gathered} 19=2x+1+3x+3 \\ 19=2x+3x+1+3 \\ 19=5x+4 \\ 19-4=5x \\ 15=5x \\ \frac{15}{5}=x \\ 3=x \\ x=3 \end{gathered}[/tex]So, the value of x is 3
[tex]\begin{gathered} MG=2x+1 \\ MG=2(3)+1 \\ MG=6+1 \\ MG=7 \end{gathered}[/tex][tex]\begin{gathered} MT=3x+3 \\ MT=3(3)+3 \\ MT=9+3 \\ MT=12 \end{gathered}[/tex]Therefore, the required values are
x = 3
MG = 7
MT = 12
a television program director has 14 shows available for monday night but can choose only 5 shows. how many different possible combinations are there?
Answers
There are 240240 possible permutations of choosing 5 shows from 14 available shows. It can be obtained by applying the formula of permutation.
What is permutation?
In mathematics, it is the number of ways in which given number of items can be arranged in different orders.
Here, we need to select 5 iteams from the given 14 iteams.
[tex]P(14,5)=\frac{14!}{(14-5)!}\\=\frac{14!}{(9!)}\\=\frac{(14)(13)(12)(11)(10)(9!)}{(9!)}\\=(14)(13)(12)(11)(10)\\=240240[/tex]
Hence, there are 240240 possible permutations of choosing 5 shows from 14 available shows.
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Cassie baked 24 cookies with 4 scoops of flour. How many scoops of flour does Cassie need in order to bake 42 cookies?
Answers
Answer:
7
Step-by-step explanation:
24 with four scoops is 6 with one scoop and 6 times 7 is 42 so 1 times 7 is 7 so the answer is 7 scoops