find the range of the function y = 1/2x + 2 if the domain is {-4, -2, 0}
The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.
The given function is,
y = 1/2 x + 2.
Also, the domain of the function is {-4, -2, 0}.
Since, the domain of the functions defines the values of x,
And range defines the value of y in function.
The value of y at x = -4
y = 1/2(-4) + 2 = -2 + 2 = 0
At x = -2,
y = 1/2(-2) + 2 = -1 + 2 = 1
At x= 0,
y = 1/2 (0) + 2 = 2
The values of y are 0, 1 and 2.
Hence, the range of the function is {0, 1, 2}.
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Sketch a graph of f(x)={- 5 if x < -2 2x-1 if-2 < x≤ 2 0 if x>2. (piecewise)
A graph of the given piecewise-defined function is shown in the image below.
What is a piecewise-defined function?In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.
In conclusion, this piecewise-defined function has a removable discontinuity.
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Ms. Wall will roll a dice. What is
the probability that she will roll an even number?
Answer:
50%
Step-by-step explanation:
half of the numbers on dice are even
Ajar has 20 marvels three green 12 blue five real what is the probability of randomly choosing a red and then a green marble
The answer is 3 I work it out
Fill in the following blank so that the resulting statement is true.
Points: 0 of 1
In order to construct a Venn diagram for a survey, first enter the cardinality of the
to obtain subsequent cardinalities.
Save
region. Then use
In order to construct a Venn diagram for a survey, first enter the cardinality of the universal set to obtain subsequent cardinalities.
How to explain the informationThe universal set is the set of all possible outcomes, and the cardinality of a set is the number of elements in the set. Once you have the cardinality of the universal set, you can use it to calculate the cardinality of any other set in the survey.
For example, if the universal set has a cardinality of 100, and the survey asks people whether they like dogs or cats, you can calculate the number of people who like dogs by subtracting the number of people who like cats from the total number of people surveyed.
In order to construct a Venn diagram, you will need to draw two or more circles, each representing a set in the survey. The circles should be overlapping to represent the sets that have members in common.
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In order to construct a Venn diagram for a survey, first enter the cardinality of the to obtain subsequent cardinalities region. Then use
calculate 5/10÷9 please
Answer:
1/2 times 1/9
which equals 1/18
Step-by-step explanation:
5/10 equals 1/2 and /9 equals *1/9
Answer: i think its 1/9
6x ( 2/3 divided by 2)+ 0.5
Answer:
2.5
Step-by-step explanation:
Given expression:
\(6 \times \left(\dfrac{2}{3} \div 2\right)+0.5\)
Following the order of operations (PEDMAS), carry out the calculation inside the parentheses first.
When dividing a fraction by a whole number, first covert the whole number into a fraction:
\(\implies 6 \times \left(\dfrac{2}{3} \div \dfrac{2}{1}\right)+0.5\)
When dividing fractions, flip the second fraction (swap the numerator and denominator), then multiply:
\(\implies 6 \times \left(\dfrac{2}{3} \times \dfrac{1}{2}\right)+0.5\)
\(\implies 6 \times \left(\dfrac{2 \times 1}{3\times2}\right)+0.5\)
\(\implies 6 \times \left(\dfrac{2}{6}\right)+0.5\)
\(\implies 6 \times \dfrac{2}{6}+0.5\)
Now carry out the multiplication:
\(\implies \dfrac{6 \times2}{6}+0.5\)
\(\implies \dfrac{\diagup\!\!\!\!6 \times2}{\diagup\!\!\!\!6}+0.5\)
\(\implies 2+0.5\)
Finally carry out the addition:
\(\implies 2.5\)
2.5
6*(2/3)/2 + 0.5
6*1/3 + 0.5
2 + 0.5
=2.5
the graph of a certain quadratic function has no x-intercepts. Which of the following are possible values or the disriminant?
The possible values for the discriminant include the following:
A. -1
D. -18
What is the x-intercept?In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.
Discriminant, D = b² - 4ac
In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.
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Complete Question:
The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.
A. -1
B. 3
C. 0
D. -18
There are a total of 58 reindeer and elves helping Santa get ready for Christmas. Each reindeer has 4 legs and each elf has 2 legs. Frosty the Snowman, who doesn’t have any legs, counted 158 legs when all the reindeer and elves were in Santa’s workshop helping Santa. How many elves are helping Santa? Enter your answer as a number only.
Solving a system of equations, we will see that there are 37 elves helping Santa, and 21 reindeer.
How many elves are helping Santa?
Let's define the variables:
x = number of elves.y = number of reindeer.We know that there are 58 of them, then we can write:
x + y = 58
We also know that between all of them they have 158 legs, so we can write the equation:
x*2 + y*4 = 158
Then the system of equations is:
x + y = 58
x*2 + y*4 = 158
To solve this system of equations, we can isolate x on the first equation to get:
x = 58 - y
Replacing that in the other equation we will get:
(58 - y)*2 + y*4 = 158
Now we can solve this equation for y.
(58 - y)*2 + y*4 = 158
116 - 2y + 4y = 158
116 + 2y = 158
2y = 158 - 116
2y = 42
y = 42/2
y = 21
Then the value of x is:
x = 58 - y
x = 58 - 21
x = 37
there are 37 elves.
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Jana can spend, at most, $200 on school clothes.
Which inequality represents the amount that Jana can spend on clothes?
A
x < 200
B
x > 200
с
x 200
D
x 2200
Answer:
x <= 200
Step-by-step explanation:
Your answer choices are unclear so I cannot specify a letter. The answer is
x<=200.
Answer:
x>=200
Step-by-step explanation:
Bean Seed Growth Temp 25 20 15 10 Days S 7 9 If the trend continues, how many days will it take at 10 degrees?
The needed number of days at 10 degrees is given as follows:
11 days.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:
m = -2/5
m = -0.4.
Hence the time needed for a temperature of 10 degrees is given as follows:
9 + 2 = 11 days.
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1. At Tyler College, 1/10 of the students are enrolled in an art class. Of the students enrolled in an art class, 35 are enrolled in a painting class. What fractions of the students at Hope College are enrolled in a painting class? 2. Solve this problem: i. 987(-8.20) - IUI.... 1 - 7 - - i Support | Schoology Blog | PRIVACY POLICY IT
Answer:
The fraction of students enrolled in a painting class is of 35/x
Step-by-step explanation:
The school has x students.
1/10 of the students are enrolled in an art class:
This means that the fraction of students enrolled in an art class is:
(1/10)*x = x/10
Of the students enrolled in an art class, 35 are enrolled in a painting class. What fractions of the students at Hope College are enrolled in a painting class?
35 students enrolled in a painting class.
x total students.
The fraction of students enrolled in a painting class is of 35/x
Adante begins to evaluate the expression 3 1/3x5 1/4using the steps below.
3 1/3 x5 1/4
(3 1/3x(5+1/4)
(3 1/(3+1/3)(1/4)
Step-by-step explanation:
Here you are the answer.
Find f(-2) for f(x) = 2(4)^x
O A.1/16
O B.1/8
O C. -16
OD. - 32
Answer:
B. 1/8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
\(\displaystyle f(x) = 2(4)^x\\f(-2) \ is \ x = -2\)
Step 2: Evaluate
Substitute in x: \(\displaystyle f(-2) = 2(4)^{-2}\)Exponents: \(\displaystyle f(-2) = 2(\frac{1}{16})\)Multiply: \(\displaystyle f(-2) = \frac{1}{8}\)3.5 divided by 85
answers:
at least 500/ at least 50/ at least 20/ at least 200
Ive looked up answers to this question in iready but everyone says the answer is 24?
The value of 3.5 divided by 85 will be 0.4118.
What is division?Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.
Division's opposite is multiplication. Dividend Divisor = Quotient + Remainder is a formula for calculating the division of two numbers.
The dividend in this situation refers to the number that is being divided. The divisor is the number that divides the number (dividend) into equal parts.
In this case, 3.5 ÷ 85 = 0.4118. This can be computed through the use of a calculator.
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Use synthetic division and the Remainder Theorem to evaluate P(c), where p(x)=x^4+7x^3+2x^2+20x+50 c=-7
Answer:
p(c) = 8
Step-by-step explanation:
Given polynomial:
\(p(x)=x^4+7x^3+2x^2+20x+50\)
Remainder Theorem
When we divide a polynomial f(x) by (x − c) the remainder is f(c).
Therefore, if c = -7, then the divisor is:
\(\implies (x - (-7)) = (x + 7)\)
Perform Synthetic Division
Place "c" in the division box.
Write the coefficients of the dividend in descending order.
(Note: As no terms are missing, we do not need to use any zeros to fill in missing terms).
\(\begin{array}{c|ccccc}-7 & 1 & 7 & 2 & 20 & 50\\\cline{1-1}\end{array}\)
Bring the leading coefficient straight down:
\(\begin{array}{c|ccccc}-7 & 1 & 7 & 2 & 20 & 50\\\cline{1-1}&\downarrow &&&&\\\cline{2-6}&1\end{array}\)
Multiply the number you brought down with the number in the division box and put the result in the next column (under the 7):
\(\begin{array}{c|ccccc}-7 & 1 & 7 & 2 & 20 & 50\\\cline{1-1}&\downarrow &-7&&&\\\cline{2-6}&1\end{array}\)
Add the two numbers together and put the result in the bottom row:
\(\begin{array}{c|ccccc}-7 & 1 & 7 & 2 & 20 & 50\\\cline{1-1}&\downarrow &-7&&&\\\cline{2-6}&1&0\end{array}\)
Repeat:
\(\begin{array}{c|ccccc}-7 & 1 & 7 & 2 & 20 & 50\\\cline{1-1}&\downarrow &-7&0&&\\\cline{2-6}&1&0&2\end{array}\)
\(\begin{array}{c|ccccc}-7 & 1 & 7 & 2 & 20 & 50\\\cline{1-1}&\downarrow &-7&0&-14&\\\cline{2-6}&1&0&2&6\end{array}\)
\(\begin{array}{c|ccccc}-7 & 1 & 7 & 2 & 20 & 50\\\cline{1-1}&\downarrow &-7&0&-14&-42\\\cline{2-6}&1&0&2&6&8\end{array}\)
The bottom row (except the last number) gives the coefficients of the quotient. The degree of the quotient is one less than that of the dividend.
The last number in the bottom row is the remainder.
\(\textsf{Quotient}: \quad x^3+2x+6\)
\(\textsf{Remainder}: \quad 8\)
Therefore, as the remainder is p(c) then:
\(p(c)=8\)
Check by evaluating p(-7):
\(\begin{aligned}\implies p(-7)&=(-7)^4+7(-7)^3+2(-7)^2+20(-7)+50\\&=2401-2401+98-140+50\\&=0+98-140+50\\&=98-140+50\\&=-42+50\\&=8 \end{aligned}\)
Can anybody help me out on this? Thanks.
Answer:
\(x = 3\)
Step-by-step explanation:
Given
\(y = -2x^2 + 12x +7\)
Required
The x coordinate of the vertex
Using the general form:
\(y = ax^2 +bx +c\)
The x coordinate is:
\(x = -\frac{b}{2a}\)
In \(y = -2x^2 + 12x +7\)
\(a = -2\)
\(b = 12\)
\(c = 7\)
So, we have:
\(x = -\frac{b}{2a}\)
\(x = -\frac{12}{2*-2}\)
\(x = -\frac{12}{-4}\)
\(x = \frac{12}{4}\)
\(x = 3\)
What is the place value of the number 7 in the number 38764
Answer:
The place value of 7 is Hundredth .
10. Beth has a wooden box. The inside of the box is 5 inches wide, 8.25 inches
long, and 4.5 inches tall. The box has not top. Beth wants to line the box with fest
to protect the items she puts in the box. How many square inches of felt will she
need?
Answer:
the answer is 41.25
Step-by-step explanation: You multiply 5 x 8.25 at least thats
what I think
There were 160 cats rescued in a
community the first year. The next year,
there were 220 cats rescued. What is the
percent increase?
Percent Gain = [? ]%
=
Do NOT round your answer.
New – Original
Hint :
Original
Answer:
the answer is 37.5%
El área de un triángulo es de 18 pies cuadrados y la base mide 6 pies. ¿Cuál es la altura del
triángulo en pulgadas?
Answer:
h = 6 feet
Step-by-step explanation:
It is given that,
Area of a triangle, A = 18 sq feet
Base of the triangle, b = 6 feet
We need to find the height of the triangle. The area of a triangle can be given by the formula as follows :
\(A=\dfrac{1}{2}\times b\times h\)
h is height
\(h=\dfrac{2A}{b}\\\\h=\dfrac{2\times 18}{6}\\\\h=6\ \text{feet}\)
So, the height of the triangle is 6 feet.
Dewan’s bank account balance is -$16.75. He deposits checks totaling $23.59. What is his new balance? -$1.08
Answer:
$6.84
Step-by-step explanation:
This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.
Original balance: -$16.75Deposit: $23.59New balance: -$16.75 + $23.59 = $6.84Graph the line x=2 please help
Answer:
Step-by-step explanation:
Since x=2 is a vertical line, there is no y-intercept
Gail ran 4610 miles on Saturday and 6810 miles on Sunday. How many miles did Gail run over the weekend?
Answer:
He ran 11,420 miles on the weekend.
Step-by-step explanation:
It's simple: add 4610 and 6810 to get 11,420
hope this helped!
Decide if it is more convenient to solve the system of equations using substitution or elimination. 8x-15y= -32
6x+3y = -5
Substitution
Elimination
In this case, either method is straightforward, so the choice between substitution and elimination is a matter of personal preference.
The most convenient method for solving the system of equations depends on the particular equations and what makes the most sense for you. However, in this case, either method could be used.
Using substitution, you can solve for one variable in one of the equations and then substitute that expression into the other equation. This results in a single equation in one variable, which can then be solved. After finding one of the variables, you can then substitute it back into either equation to find the other variable.
Using elimination, you can add or subtract the equations to eliminate one of the variables. This also results in a single equation in one variable, which can then be solved. After finding one of the variables, you can then substitute it back into either equation to find the other.
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It takes 20 days using 12 machines to produce a batch of pens.
due to a fault only 3 machines were used for the first 8 days, all 12 machines were used from day 9 onwards.
how many days in total to produce the batch of pens
It would take a total of 20 days to produce the batch of pens.
Let's calculate the work done by the 3 machines for the first 8 days:
Work done by 3 machines in 8 days = (3/12) * 8 = 2 days' worth of work
The remaining work that needs to be done by all 12 machines is:
Remaining work = 1 - (2/20) = 0.9
Now, we can use the work formula to find the total number of days needed to complete the remaining work with 12 machines:
Total work = 0.9
Work done by 12 machines in one day = 12/20 = 0.6
Total number of days needed = 0.9/0.6 = 1.5
Therefore, the total number of days needed to produce the batch of pens is:
8 (days with 3 machines) + 1.5 (days with 12 machines) = 9.5 days
However, we also need to add the 10.5 days it would take for all 12 machines to complete the batch from the beginning:
10.5 + 9.5 = 20 days
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Shane's bill for lunch at a restaurant was $19 he left a 20% tip what was the amount of the tip
Can somebody please help this is honestly due tomorrow
Answer:
I am almost completely sure its 4.
Step-by-step explanation:
I dont mind brainiests by the way
y= 2x + 7 y= -4x - 5 What is the solution for the system of equations?
Answer:
x = -2, y = 3.
as an ordered pair it is (-2, 3).
Step-by-step explanation:
y= 2x + 7
y= -4x - 5
As both right hand expression are = y we have:
2x + 7 = -4x - 5
6x = -12
x = -2
Substitute for x in equation 1:
y = 2(-2) + 7 = 3.
Which mathematical symbol would best fill in the blank to compare the two real numbers?√7_14/5
Answer:
√7 is less than 14/5
Step-by-step explanation:
√7 equals about 2.6
14/5 equals 2.8