The range of the function, f(x)=4x+2 for the domain {–2, –1, 1, 4} includes (-6, -2, 6, 18).
What is the range of a function?The range of the function, f(x)=4x+2, includes all the possible output values of the function.
What is the domain of a function?The domain of a function, f(x)=4x+2, is the set of all possible input values (domain {–2, –1, 1, 4}) of the function.
Remember that a function is a mathematical expression that equates an independent variable with a dependent variable.
Data and Calculations:f(x)=4x+2
Domain = {–2, –1, 1, 4}
The range for -2:
f(x)=4x+2 = 4(–2) + 2 = -6
Range for -1:
f(x)=4x+2 = 4(–1) + 2 = -2
Range for 1:
f(x)=4x+2 = 4(1) + 2 = 6
The range for 4:
f(x)=4x+2 = 4(4) + 2 = 18
Thus, the range of the function, f(x)=4x+2 for the domain {–2, –1, 1, 4} includes (-6, -2, 6, 18).
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Find the equation of the graph
Find the average rate of change from x = 5 to x = 7
Answer: y=-(x-6)(x-8)
Average rate of change: 2
Step-by-step explanation:
Graph facing downward, so equation is negative
Since the equation is quadratic, the degree is 2.
When you look at the graph, you see the values of x when y=0
x=6 ==> y=0
x=8 ==> y=0
Equation: y=-(x-6)(x-8) ==> add the negative sign to show the equation is going down.
x=5 ==> y=-3 ==> (5, -3)
x=7 ==> y=1 ==> (7, 1)
Slope formula: m=(y2-y1)/(x2-x1)
m=(1-(-3))/(7-5)
m=(1+3)/(2)
m=4/2
m=2 ==> average rate of change
A bicycle is traveling at 18 miles per hour. How many feet will it cover in 40 seconds? Round your answer to the nearest tenth of a foot.
Answer:
720 miles
Step-by-step explanation:
18×40=70 is all you need to do
What is the area of?
6- sqaureroot 11 and 6+ sqaureroot 11
I really need help please
Answer:
see attached
Step-by-step explanation:
Given a partially-filled circle pattern, you want to place the remaining numbers so the sum in each circle is 21.
ApproachThere are seven (7) circles, and nine (9) unknown values. This means there are a couple of "free choice" values that cannot be found directly. Our approach is to limit the number of possibilities we must examine.
EquationsWe note that if we multiply the sum (21) by the number of circles, that product includes the "single cover" circle shapes once, and each of the overlapping "double cover" areas twice. There are three unknown "single cover" values, and six unknown "double cover" values. If we represent the sums of these by "s" and "d" respectively then we have ...
(10 +11 +6 +4 +s) +2(d +5) = 7×21
41 +d +2s = 147 . . . simplify
d +2s = 106 . . . . . . subtract 41
The total of all of the unplaced numbers is ...
(2 +12 +7 +14 +1 +8 +9 +3 +13) = s +d
69 = s +d
Now, we have two equations in s and d:
d +2s = 106d +s = 69Subtracting the second from the first gives ...
(d +2s) -(d +s) = (106) -(69)
s = 32
The sum s is the sum of 'a', 'b', and 'c' as marked in the attachment. There is only one set of unplaced numbers that has a total of 32: {7, 12, 13}.
Using these numbers means that the set of allowed values for the "double cover" areas is {1, 2, 3, 8, 9, 14}.
Trial and errorWorking clockwise from the space marked 'c' in the attachment, the "double cover" oblong spaces must have the values ...
16 -cc -515 -c6 -(a -c)9 +(a -c)8 -(a -c)As we noted above, {a, b, c} is some permutation of {7, 12, 13}. This means the value (a-c) will be one of ±1, ±5, ±6.
If (a-c) = ±6, then 6 -(a-c) = {0, 12}. Neither value is allowed: 0 is not on the list, and 12 is already used.
If (a-c) = ±5, then we would have ...
for (a-c) = -5, 6 -(a-c) = 11, not an allowed value (already used).
for (a-c) = 5, all of the values 6-5=1, 9+5=14, and 8-5=3 are allowed. This case corresponds to {a, b, c} = {12, 13, 7}.
If (a-c) = ±1, then we would have 6 -(±1) = {5, 7}. Neither value is allowed.
ConclusionThe only allowed choice for {a, b. c} is {12, 13, 7}. Using c=7 and (a-c)=5, the "double cover" values clockwise from 'c' are ...
16-7 = 97 -5 = 215 -7 = 86 -5 = 19 +5 = 148 -5 = 3When all of the values are filled in the diagram it looks like the attachment.
__
Additional comment
As you might imagine, there was a bit of thrashing around before this method of solution presented itself. The system of 7 equations in 9 unknowns cannot be solved directly, and we know of no way to include the requirement that the solution set must include each number of the given set, used only once.
Fortunately, the method we tried here proved to find a solution in fairly straightforward fashion.
What is the answer to 8.118 divided by 0.615
Answer:
13.2
Hope this helps :)
Step-by-step explanation:
8.118 ÷ 0.615 = 13.2
You can also solve it by using long division.
Check:
13.2 × 0.615 = 8.118 ✓
If a 2-liter bottle holds 67 3/5 ounces, about how many 8-ounce cans will it take to fill the 2-liter bottle?
A. 13
B. 22
C. 8
D. 4
By taking the quotient between the two volumes in ounces, we conclude that you will need about 8 cans to fill the bottle. So the correct option is C.
How many 8-ounce cans will take to fill the 2-liter bottle?We know that the 2-liter bottle holds (67 + 3/5) ounces of water, and each one of the cans holds a volume of 8 ounces.
To see how many cans we need to fill the bottle, we need to take the quotient between the two volumes (using ounces in both cases, obviously), we will get:
Q = (67 + 3/5)/8 = 8.45
So you need 8.45 cans to completely fill the 2 liter bottle, then we can see that the correct option will be C, 8 cans, as that is the best estimation.
We conclude that you need about 8 cans to fill the bottle.
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y=5x−3
Find the output, yyy, when the input, xxx, is 555.
y = 5x-3
The solution of an equation refers to the values of the variables involved in that given equation. The value of output y is 22.
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
The Solution to an equation is finding values of the variable included in the considered equation for which the equation considered evaluates to be true.
For a solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point
The expression is y = 5x-3
We need to determine the output y, when the value of input is x is 5 so
That is, substituting in , we get the following;
y = 5x-3
y = 5(5)-3
Multiplying the value within the bracket, we have;
y = 25-3
Then Subtracting the terms, we get,
y = 22
Therefore, the value of output y is 22.
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The complete question is
Find the output, y, when the input, x, is 5. The equation is y = 5x-3
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A naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet.
If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet then 145 is the position of the submarine relative to the surface of the ocean now.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet. we need to find the position of the submarine relative to the surface of the ocean now.
The submarine initial position= 310 feet.
To pass above an underwater mountain, or seamount, it rose = 165 feet.
The position of submarine is
310-165
=145 feet.
Therefore the position of the submarine relative to the surface of the ocean now is 145 feet.
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the prime factorization for 2020 is 2^2 x5^1 x 101^1. How many different whole numbers are factors of 2020?
There are three different whole numbers are factors of 2020.
What is Prime factorization ?
Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors. As we know, a composite number has more than two factors, therefore, this method is applicable only for composite numbers and not for prime numbers.
Prime factors of 2020 = 2,2,5,101
different whole numbers are = 2,5,101
As these three numbers are prime numbers, these are the different whole numbers for 2020.
Therefore, there are three different whole numbers are factors of 2020.
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Find n(A) for the set A
Answer:
This is the answer for the sequence
Maria works for a salary of $2,750 per month. She has federal income tax withheld at the rate of 15 percent, Social Security tax withheld at the rate of 7.2 percent, Medicare tax withheld at the rate of 1.37 percent, and health insurance premiums of $76 per month. Maria’s net pay is $____________.
Maria’s net pay is $2,025.82.
What is the net pay?The net pay is the gross pay minus mandatory and voluntary deductions, like taxes, insurance, and other expenses.
The net pay represents the amount of money the income earner receives.
The net pay is also known as the take-home.
Data and Calculations:Monthly salary = $2,750
FICA withholding = 15%
Social security tax withholding = 7.2%
Medicate tax withholding = 1.37%
Health Insurance Premium = $76 per month
Total withholding = 23.57%
= $648.18 (2,750 x 23.57%)
Total deductions and withholding = $724.18 ($76 + $648.18)
Net pay = $2,025.82 ($2,750 - $724.18)
Thus, Maria's net pay after the withholdings and deductions is $2,025.82.
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The product of 9 and Jenny's age is 135
The product of 9 and Jenny's age 15 is 135.
What is a mathematical operation?Similar to the principle of superposition denotes a mathematical operation (e.g., differentiation, multiplication by a constant) in which the action on the sum of two functions is the sum of the action of the operation on each function.So, let the missing value be 'x'.
Then,
9 × x = 1359x = 135x = 135/9x = 15Therefore, the product of 9 and 15 is 135.
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an accountant needs to withhold 21% of income for taxes if the income is below $40,000 and 26% of income if the income is $40,000 or more. The income amount is in cell A1 Write a spreadsheet expression that would calculate the amount withhold.
A spreadsheet expression=IF(A1<40000,(21%*I21),(26%*A1))
The "IF" function should be used in the spreadsheet expression. The "IF" function returns a value based on the criteria specified in the spreadsheet formula. This, like other spreadsheet functions, begins with =.In response to the question,
Cell A1 contains the value to be inspected. If A1 is smaller than $40000 (written as A140000), the spreadsheet performs the following function: (21%*I21). otherwise (which may be understood as A1 higher than or equal to $40000 in this example), calculate the following command as indicated above; (26%*A1).
The command is finished with the last parenthesis.
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Question 3 !!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 0.6
:) hope this helps you
Answer:
0.6
Step-by-step explanation:
[tex]{ \tt{ \frac{3}{5} }} \\ [/tex]
Multiply the numerator and denominator by 2;
[tex] = { \tt{ \frac{3 \times 2}{5 \times 2} }} \\ \\ = { \tt{ \frac{6}{10} }} \\ \\ = 0.6[/tex]
The diagram below represents the rate of making copies on a copy machine. Which table represents this rate? Copies : 15 Seconds : 5
Answer:
The answer would be A.
Step-by-step explanation:
You can eliminate b because 15/5=3 copies but 5/5 would be 1 not 15. You can eliminate d because 15/3=5 copies but 5/3 would not equal 1. You can eliminate c because 15/15=1 but 5/15 does not equal 3.
Find f(- 3), f(0) and f(3) for the following function.
f(x) = 3x
f(- 3) = ?
For f(x)= 3x required values of the function are f(-3)=-9, f(0)=0, f(3)=9
What is the value of a function?
A function gives exactly one output to each input . f(2) means that we should find the value of our function when x equals 2. f(x) is the value of the function
Given function is f(x)= 3x
Then f(-3) = 3(-3) =-9
f(0) = 3(0) =0
f(3) = 3(3) =9
Therefore, values of the function at x = -3,0,3 are -9,0,9 respectively
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A bookstore sells a textbook for $35.10. If the bookstore makes a profit of 30% on each sale, what does the bookstore pay the publisher for each book?
The bookstore pays the publisher $27 for each book thus making a profit of 30%.
The profit is defined as the difference between the sell price and the cost price.
The sell price is defined as the price at which an object is sold.
The cost price is defined as the price at which an object is bought.
When the sell price is greater than the cost price profit is made by the seller.
Let the cost price (price paid to publisher) be x dollars.
Therefore when sold at a profit of 30% then
profit= 30%of x=0.3x dollars
Now the sell price = cost price +profit
∴Sell price= x+0.3x=1.3x
But the sell price is given as $35.10
So we can equate the two terms to get a linear equation in x.
∴1.3x=35.10
or, x=35.10÷1.3
or, x=27
Therefore the cost price is $27.
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If f(x) = square root of x, which equation describes the graphed function
The equation that describes the graphed function is [y = f(-x + 4)].
As per the question statement, we are provided with the information about a function f(x) which is equal to square root of "x", and a reference graph diagram.
We are supposed to determine the equation from the given four options that describes the graphed function.
To solve this question, we will use the trial and error method, using the options to determine out correct answer.
First of all, from the graph, we can see that the graph cuts the x-axis at
(4, 0) and y-axis at (0, 2). Now, since [y = f(x)], our equation must be equal to 0 when (x = 4) is substituted, and 2 when (x = 0).
Considering option (A), [tex]y=f[(-x)+4]=\sqrt{[(-x)+4]}[/tex], and substituting
(x = 4), we get,
[tex]y=\sqrt{[(-4)+4]}\\or, y=\sqrt{(4-4)}\\ or,y=\sqrt{0}\\ or,y=0[/tex]
While substituting (x = 0), we get,
[tex]y=\sqrt{[(-0)+4]}\\or, y=\sqrt{(4-0)}\\ or,y=\sqrt{4}\\ or,y=2[/tex]
Hence, option (A) satisfies at the points of (4, 0) and (0, 2).
Similarly, if we substitute and check on the other three options, we will see that for (x = 4), (y ≠ 0) and for (x = 0), (y ≠ 2).
Therefore, if [f(x) = (√x)], then the equation that describes the graphed function is [y = f(-x + 4)].
Function: In mathematics, a function is an operator which when provided with an input, will perform a specified set of operations on the input and then produce a specified output.To learn more about Functions, click on the link below.
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Fourteen increased by the number d is the same as 6 times the number d
Answer: d = 14/5
Step-by-step explanation:
14 + d = 6d
14 = 5d
14/5 = d
Check Work:
14 + (14/5) = 6(14/5)
16.8 = 16.8
A hospital received a shipment of 11 mg doses of medicine. Each 11 mg package was repackaged into two smaller doses of unequal size and labeled packet A an B. The hospital then used 4 doses of packet A and 11 doses of packet B in one week. The hospital used a total of 148mg oh medicine. How many mg of medicine are contained in each A packet and B packet
In linear equation, A = - 27/7 and B = 140/7 are mg of medicine are contained.
What in mathematics is a linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Let one dose be x.
Other does will be 11 - x ............ y
4x + 11 ( 11 - x) = 148
4x + 121 - 11x = 148
-7x = 148 - 121 = 27
x = - 27/7
y = 140/7
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<(1,000)
5. 1 × 1 + 9 × (1) + 8 ×(₁0) + 1 ×
Answer:
3
Step-by-step explanation:
Syop doing homework and gdt a life
Eduardo, Martin, & Becky each saved $150 from
their summer jobs. They have decided to donate
a portion of their savings to a charity. Eduardo
donated 2/7 of his savings, Martin gave 2/9, &
Becky donated 2/5. To the nearest penny, how
much should the charity expect?
A. $33.33
B. $42.86
C. $60.00
D. $136.19
E. $180.00
Step-by-step explanation:
much should the charity expect?
A. $33.33
B. $42.86
C. $60.00
D. $136.19
E.
The charity expects a donation of D. 136.19 dollars from Eduardo, Becky, and Martin.
What is a fraction?Fractions describe how many parts of something is there to the total part.
To obtain how much each individual donated we have to multiply the fraction of donation to the amount of money they saved and take the sum.
Eduardo donated 2/7 of his savings which is (2/7)×150 dollars.
= 42.85 dollars.
Martin donated 2/9 of his savings which is (2/9)×150 dollars.
= 33.33 dollars.
Becky donated 2/5 of his savings which is (2/5)×150 dollars.
= 60 dollars.
∴ The total money they donated is ( 42.85 + 33.33 + 60 ) dollars.
= 136.18 dollars.
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At the beginning of the month, you have $1500 in your bank account. Each time you visit the ATM you take $60 out of your account. Last month you lent your friend $50.
What is the rate at which your balance is changing each time you visit the ATM?
The required expression of the rate at which the balance is changing each time is 1450 - 60x, where x is the number of visits to the ATM.
Here,
At the beginning of the month, you have $1500 in your bank account.
Each time you visit the ATM you take $60 out of your account.
Rate of money out = 60x, where x is the number of times atm visit.
Last month you lent your friend $50.
Money left = 1500 - 50 - 60x = 1450 - 60x
Thus, the required expression of the rate at which the balance is changing each time is 1450 - 60x, where x is the number of visits to the ATM.
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The perimeter of a square must be greater than 102
102
inches but less than 112
112
inches. Find the range of possible side lengths that satisfy these conditions.
The possible range for side lengths of the square is (25.25 to 28) both values not included.
What is defined as the square?A square is made up of four sides and four vertices. A square's sides are all the same length. The perimeter of the a square would be the total length of each of its sides. As a result, we can calculate the perimeter of such a square by adding its four sides. The given square's perimeter is a + a + a + a. We just need one side of a square to obtain its perimeter because all of its sides are equal.For the given question;
Let the side length of the square be 'a'.
The, the perimeter of the square is 4a.
The perimeter must be less than 112.
Thus, 4a < 112.
The perimeter also must be greater than the 102.
4a > 102.
So, the combined inequality will be.
102 < 4a < 112
Divide the inequality by 4
25.25 < a < 28.
Thus, the side length of the square must be greater than 25.25 inches and less than 28.
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Write a short essay of the given topic "The Fibonacci sequence and its uses in understanding real-life problems".( I need answer ASAP)
Answer:
The Fibonacci sequence is a series of numbers in which each number is the sum of the two that precede it. Starting at 0 and 1, the sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on forever. The Fibonacci sequence can be described using a mathematical equation: Xn+2= Xn+1 + Xn.
Step-by-step explanation:
250.12+16.8÷1.2 please tell me
Answer:
hello the asnwer is 264.12hello the asnwer is 264.12Step-by-step explanation:hello the asnwer is 264.12Step-by-step explanation:first we will put 16.18÷1.2 in brackets so it will be 250.12+( 16.8/1.2). we will work out the brackets so : 250.12+14hello the asnwer is 264.12Step-by-step explanation:first we will put 16.18÷1.2 in brackets so it will be 250.12+( 16.8/1.2). we will work out the brackets so : 250.12+14then simply add the two numbers and the answer is 264.12. hope it helps!!Complete the inequality below to describe the
domain of the graph shown.
Domain:
DONE
Complete the inequality below to describe the
range of the graph shown.
Range:
≤y <5
DONE
Intro
-5
5
y
5
X
Answer:
[tex]Domain: \;\boxed{-4 } < x \le 4\\\\Ramge: \boxed{-2} \le y < 5[/tex]
Step-by-step explanation:
Domain
Domain is the set of all valid x values for the function
Looking at the graph we see that the function x values go from x- 4 to x = +4.
Note the unfilled circle at x = -4, y = 5. This means that this point is not included in any set of values that we intend tp find. It will represent a < or > inequality.
A filled circle means that value is included
So the domain of the function is -4 < x ≤ 4 (note that -4 is not included in the domain
Range
The range is the set of all y values for the entire domain. Basically it is defined using the min and max values that y can take
The minimum y value occurs at x = 4 and y is -2 (this is included because of the filled circle)
The max value occurs at x = -4 and the value of y here is 5 (5 is not included)
Therefore the range is -2 ≤ y < 5
Question 6
Find m/IJP if mZIJP = x + 117,
m/IJK 150°, and m/PJK = x + 47.
If the linear equation [(x + 117) = 150°], then the value of (x + 47) will be 80.
As per question statement, we are provided with a linear equation, as
[(x + 117) = 150°].
We are required to calculate the value of (x + 47) using the above mentioned equation.
To solve this question, we will find out the value of "x" from the equation
[(x + 117) = 150°] and then, add 47 to the value of x to obtain our desired answer, i.e.,
[tex][(x + 117) = 150]\\or, x=(150-117)\\or,x=33\\or, (x + 47)=(33+47)\\or, (x + 47)=80[/tex]
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-3x-p>0 solve the inequality for x
Work Shown:
-3x-p > 0
-p > 3x
3x < -p
x < -p/3
