The domain is:
D: {-4, 5, 6, 8}
The range is:
R: {-4, 3, 5}
And yes, the relation is a function.
How to determine the domain and range?
For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).
Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}
The domain is the set of the first values of each pair, so we have:
D: {-4, 5, 6, 8}
The range is the set of the second values of each pair:
R: {-4, 3, 5}
Now, is this a function?
Yes, it is a function, because each input is mapped into only one output.
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Which equation best represents the graph shown below? Explain in detail how you arrived at your answer by stating each of the mathematical transformations necessary to produce the graph.
please I need help
In the graph we have a parabola, and its equation is y = (x - 2)^2 - 3
How to find the equation of the graphed function?
In the graph, we can see a parabola.
We only need to identify 3 parts, which are the two x-intercepts (if it has) and the y-intercept.
Remember that if the vertex and the y-intercept. Remember that if the vertex is (h, k) and the leading coefficient is a, then we can write the equation as:
y = a*(x - h)^2 + k
In the image we can see that the vertex is (2, -3), then:
y = a*(x - 2)^2 - 3
And the y-intercept is y = 1, then if we evaluate in x = 0 we should get y = 1, replacing that we get:
1 = a*(0 - 2)^2 - 3
1 = a*4 - 3
1 + 3 = a*4
4/4 = a = 1
Then the quadratic equation is y = (x - 2)^2 - 3
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Using the alternate form of the definition of the derivative, Compute f'(c) for f(x) = x+4/x, c=4
The value of the f(x) = (x + 4) / x at x = 4 is equal to - 1 / 4.
What is the value of the derivative of a function?
In this problem we have the following rational equation, which is equivalent to the following sum of functions:
f(x) = (x + 4) / x = 1 + 4 / x = g(x) + h(x)
Then, we must find both the derivatives of the functions g(x) and h(x) by using the definition of derivative:
g(x):
g'(x) = [1 - 1] / h
g'(x) = 0 / h
g'(x) = 0
h(x):
h'(x) = [4 / (x + h) - 4 / x] / h
h'(x) = [4 · x - 4 · (x + h)] / [h · (x + h) · x]
h'(x) = - 4 · h / [h · (x + h) · x]
h'(x) = - 4 /[(x + h) · x]
If h = 0, then:
h'(x) = - 4 / x²
Then, the first derivative of the function is f(x) = - 4 / x². Now we evaluate the function at x = 4:
f(4) = - 4 / 4²
f(4) = - 1 / 4
The value of the f(x) = (x + 4) / x at x = 4 is equal to - 1 / 4.
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What is the standard deviation of this data set ?Reporting 2 more decimal places than the original data. 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61
Answer:6.986
Step-by-step explanation:
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.
Answer: Standard deviation is 6.986.
Step-by-step explanation:
Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.
Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.
In this case standard deviation is 6.986.
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what does the 9 represent in the number 53.89
Find the least numbers which must be subtracted from the following number to make them perfect square
42029
Step-by-step explanation:
[tex] 3\sqrt{8} + \sqrt{114} [/tex]
Mitch drew lines , k, and t so that and k were parallel. He labeled a pair of alternate interior angles 1 and 2. Which diagram did Mitch create?
Considering the concepts of parallel lines and alternate interior angles, it is found that Mitch created diagram C.
What are parallel lines?Parallel lines are lines that never intersect. For this problem, lines l and k are parallel, that is, they are the horizontal lines.
What are alternate interior angles?When two parallel lines are crossed by a transversal, the alternate interior angles are between the two parallel lines, one in each side.
Since 1 and 2 are alternate interior angles, Mitch created diagram C.
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Translate this phrase into an algebraic expression.
67 decreased by twice a number
Use the variable n to represent the unknown number.
Answer:
2n-67
Step-by-step explanation:
Twice a number means 'multiply by 2' so we can write 2 x n. We can also write this in a simpler form- 2n
'67 decreased' means minus 67 off your answer so therefore the answer must be:
2n-67
Love answering your questions by the way :)
A rectangular solar panel has a length that is 12 inches shorter than 3 times its width. If the perimeter of the panel is 132 inches what are the dimensions of the panel?
Answer: 46.5 by 19.5
Step-by-step explanation:
P=perimeter of panel. L=length. W=width
L=3W-12
P=2L+2W
132=2(3W-12)+2W
132=6W-24+2W
132=6W+2W-24
132=8W-24
156=8W
W=19.5
P=2L+2W
132=2L+2(19.5)
132=2L+39
2L=93
L=46.5
46.5 by 19.5
two times the quantity of seven less than twice x
i need put this in algebraic expression
For each of the right triangles, determine the measure of the missing side. Leave the measures in
exact form if irrational.
(if u can please show the work so i can get a better understanding)
Using the Pythagorean theorem, the missing sides are:
1. 5
2. 13
3. √15
4. 3
How to Apply the Pythagorean Theorem?The Pythagorean theorem is given as: c² = a² + b², where c is the longest side and a and b are the other two legs.
1. Missing side = √(3² + 4²) [Pythagorean theorem]
Missing side = 5
2. Missing side = √(12² + 5²) [Pythagorean theorem]
Missing side = 13
3. Missing side = √(4² - 1²) [Pythagorean theorem]
Missing side = √15
4. Missing side = √((√10)² - 1²) [Pythagorean theorem]
Missing side = √(10 - 1) = √9
Missing side = 3
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5000 nails in five boxes. the first and second boxes have 2700 nails all together. the second and the third boxes have 2000 nails all together. the third and fourth boxes have 1800 nails all together. the fourth and the fifth boxes have 1700 nails all together. how many nails are in each box
The number of nails in each box is: 1300, 1400, 600, 1200, and 500
Given 5000 nails in five boxes.
Let X denote the universal set.
Then n(X) = 5000.
Let A denote the first box,
B denote the second box,
C denote the third box,
D denote the fourth box, and
E denotes the fifth box.
The first and second boxes have 2700 nails altogether.
⇒n(A ∪ B) = 2700
The second and third boxes have 2000 nails altogether.
⇒n(B ∪ C) = 2000
The third and fourth boxes have 1800 nails altogether.
⇒n(C ∪ D) = 1800
The fourth and fifth boxes have 1700 nails altogether.
⇒n(D ∪ E) = 1700
We need to find out how many nails are there in each box.
That is to find out: n(A), n(B), n(C), n(D), and n(E).
Note that all these five sets are disjoint. This means that the intersection is empty.
n(A ∪ B ∪ C ∪ D) = n(A ∪ B) + n(C ∪ D) = 2700 + 1800 = 4500
n(E) = n(X) - n(A ∪ B ∪ C ∪ D) = 5000 - 4500 = 500
n(D) = n(D ∪ E) - n(E) = 1700 - 500 = 1200
n(C) = n(C ∪ D) - n(D) = 1800 - 1200 = 600
n(B) = n(B U C) - n(C) = 2000 - 600 = 1400
n(A) = n(A U B) - n(B) = 2700 - 1400 = 1300
Therefore, the number of nails in each box is 1300, 1400, 600, 1200, and 500.
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Fill in the blank set of stamps below with the value that would make the sets equal.
The number in each of the set of blank boxes is 10
How to find the number set equivalent?
From the first number set of stamps, we see that the sum of each row is;
5 + 5 + 5 + 5 = 20
There are four rows. Thus;
Total sum of set of stamps = 20 + 20 + 20 + 20
Total sum of set of stamps = 80
Now, for the blank set of stamps, we see that there are 8 boxes which are al equal. Now, for this 8 boxes t have same sum as that of the initial set of stamps, it means they must sum up to 80.
If the number in each box is x, then;
8x = 80
x = 80/8
x = 10
Thus, the number in each of the set of blank boxes is 10
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Simplifiy the expression 1/2 cubed - 6 divide √64
Answer:
[tex]-\frac{47}{64}[/tex] or [tex]\frac{1}{2}^{3} -6/\sqrt{64}[/tex]
Step-by-step explanation:
A canoe and a paddler have a combined mass of 100.0 kg. The canoe is dropped into a river flowing from east to west. The flowing water exerts a force of 18.0 N on the canoe. The paddler exerts a force of 36.0 N [E 37.0° N]. Determine the net force on the canoe at this instant.
At this point, the canoe will be under a net force of 51.52 N.
What is the force?The total mass of a canoe and a paddler is 100.0 kg. A river that runs from east to west is where the canoe is thrown in. The power of the water current on the canoe is 18.0 N. The paddler exerts a force of 36.0 N [E 37.0° N].
The Free Body Diagram is then displayed below.
The canoe's net force would then be indicated as follows:
F = (18 + 36 cos 37°) i + (36 sin 37°) j
F = 46.75 i + 21.67 j
Therefore the force's strength will be
|F| = √(46.75² + 21.67²)
|F| = √2655.15
|F| = 51.52 N
Thus, at this point, the canoe will be under a net force of 51.52 N.
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What is the next term in each of the sequences below?
a) 16, 25, 36,49,
b) 8,27, 64, 125,
Answer:
a). 16, 25, 36, 49, 64
b). ???
Step-by-step explanation:
16 + 9 = 25
25 + 11 = 36
36 + 13 = 49
49 + 15 = 64
I don't think b is possible
Jaylan makes limeade using 3/4 cup of water for every 1/5 cup of lime juice. Rene's limeade recipe is different. He uses 2/3 cup of water for every 1/6 cup of lime juice.
whose limeade has a weaker flavor
Rene's limeade has a weaker flavor as calculated by division of fractions.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction.On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers. It's not necessary for this number to be an integer.When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with remainder or Euclidean division of two natural numbers yields an integer quotient,Which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.Concentration of Jaylan's limeade [tex]=\frac{3}{4} \div\frac{1}{5} = \frac{15}{4} =3.75[/tex]
Therefore as calculated by division of fractions, concentration of Jaylan's limeade is 3.75 cups of water for 1 cup of lime juice.
Concentration of Rene's Limeade[tex]=\frac{2}{3} \div\frac{1}{6} = \frac{12}{3} =4[/tex]
Therefore as calculated by division of fractions, concentration of Rene's limeade is 4 cups of water for 1 cup of lime juice.
Hence Rene's limeade has a weaker flavor as calculated by division of fractions.
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When the admission price for a baseball game was $4 per ticket, 50,000 tickets were sold. When the price was raised to $5, only 45,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $75,000 respectively.
The profit function is P(x) = ( - x² / 5000 ) + 13.9x - 75000.
50,000 baseball game tickets were sold at $4 per ticket.
When the price is raised to $5, then 45,000 tickets were sold.
The variable and fixed costs for the ballpark owners are $0.10 and $75,000 respectively.
Let's say x is the number of tickets sold, and P is the profit.
Then,
P = ax + b
At P = 4,
4 = (50000)a + b ---------(1)
At P = 5,
5 = (45000)a + b --------(2)
Subtracting (2) from (1),
4 - 5 = (50000)a + b - (45000)a - b
- 1 = 5000(a)
a = ( - 1/5000)
So if a = ( - 1/5000),
Then,
4 = (50000)a + b
4 = (50000)( - 1 / 5000 ) + b
4 = -10 + b
b = 14
Therefore,
p(x) = ( - x /5000) + 14
Now, the profit function is:
Profit = Revenue - Costs
P(x) = R(x) - C(x)
Now, R(x) = xp(x)
R(x) = x[ ( - x/5000) + 14]
R(x) = ( - x² / 5000 ) + 14x
The fixed cost is F(x) = $75000
Hence, the costs will be:
C(x) = 75000 + (0.10)x
Therefore the profit function is:
P(x) = R(x) - C(x)
P(x) = ( - x² / 5000 ) + 14x - 75000 - (0.10)x
P(x) = ( - x² / 5000 ) + 13.9x - 75000
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The complete question is mentioned below:
When the admission price for a baseball game was $4 per ticket, 50,000 tickets were sold. When the price was raised to $5, only 45,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ballpark owners are $0.10 and $75,000 respectively.
Find the profit P as a function of x, the number of tickets sold
3. Clearcut Lumber sells its dimensional lumber with a markup of 60%
What rate of margin do they use?
A batch of plywood sells for $500 what was the cost?
Fence posts with a cost of $10 would sell for how much?
The gross profit on the sale of some 4 by 4's was $50 what was the selling price?
The rate of margin used is 37.5% . The cost price of the batch of plywood is $312.5. Fence post sell for $16. The selling price was $133.33
Margin is the difference between the Selling price and the cost price. The price at which a item is sold is called the selling price and the price at which an item is bought is called the cost price.
The given markup is 60%.
We know that margin=markup÷(1+markup)
markup=60%
Substituting the values we get the rate of margin:
[tex]=\frac{\frac{60}{100} }{1+\frac{60}{100} } \\=\frac{60}{160}\\ =37.5[/tex]
Hence the rate of margin is 37.5 %.
Selling price for the plywood=$500
We know that selling price=cost price ÷(1-margin)
Let the cost price be x
[tex]x=500(1-\frac{37.5}{100} )\\x=312.50[/tex]
The cost price is $ 312.50 .
Now cost of fence = $10
Selling price of fence=cost price÷(1-margin)
substituting the values we get:
Selling price =10÷0.625
or, selling price= $16
Therefore the selling price is $16 .
Now we know that Markup percentage= profit÷ cost price
Substituting the values we get:
[tex]60\% = \frac{50}{CP}\\or,\frac{60}{10}=\frac{50}{CP}\\or,CP=83.33[/tex]
Therefore sell price=cost price+ profit
or, sell price=83.33+50
or, sell price =133.33
The sell price is $133.33
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On average, Carmen can drive 33 miles on every gallon of gasoline. If she fills up her tank for $2.29 per gallon, how much will it cost her to drive 429 miles?
Answer:
$29.77
Step-by-step explanation:
First, divide 429 by 33 to find how many gallons that she's paying for, then multiply that by $2.29 to find the answer.
The cost for Carmen to drive 429 miles is $29.77.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Given that,
Distance car travels per gallon = 33 miles per gallon
Cost of gasoline per gallon = $2.29 per gallon.
33 miles can be travelled with 1 gallon of gasoline.
1 mile can be travelled with 1/33 gallon of gasoline.
429 miles can be travelled with 429/33 = 13 gallon of gasoline.
Amount of gasoline needed for 429 miles = 13 gallon.
Cost of gasoline for 1 gallon = $2.29
Cost of gasoline for 13 gallon = 13 × $2.29 = $29.77
Hence it will cost $29.77 for her to drive 429 miles.
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The lateral surface area of cone A is exactly 1/2 the lateral surface area of
cylinder B.
OA. True
OB. False
Answer:
B. False
Step-by-step explanation:
You want to compare the lateral surface areas of a cone and cylinder, where the slant height of the cone is twice the height of the cylinder. Your proposition is that the cone's lateral area is half that of the cylinder.
Cone lateral areaEffectively, the lateral area of a cone is the area of a triangle whose base is the circumference of the cone, and whose height is the cone's slant height. The formula for the lateral area of a cone of radius r and slant-height s is ...
A = πrs
For the given dimensions (s=2h), the lateral area is ...
A = πr(2h) = 2πrh
Cylinder lateral areaThe lateral area of a cylinder is the area of a rectangle whose base is the circumference of the cylinder, and whose height is the cylinder's height. The formula for the lateral area of a cylinder of radius r and height h is ...
A = 2πrh
ComparisonThe lateral areas of the given figures are both 2πrh, so one is not half the other.
The proposition is False.
Use the definition of complementary angles to solve for x.
Answer:
x = 4 and x = 7
Step-by-step explanation:
→ Find the sum of both the angles
3x + x + 74 = 4x + 74
6x + x + 13 = 7x + 13
→ Equate both equations to 90
4x + 74 = 90
7x + 13 = 90
→ Minus 74 and 13
4x = 16
7x = 77
→ Divide by 4 and 7 respectively
x = 4 and x = 7
Question 13 (1 point)
Saved
Given the following definitions:
U= (a, b, c, d, e, f, g)
A = {a, c, e, g)
B = (a, b, c, d]
Find A U B'
Answer:
{a, c, e, f, g}
Step-by-step explanation:
[tex]B'=\{a,b,c,d,e,f,g\}-\{a,b,c,d\}=\{e,f,g\} \\ \\ A \cup B=\{a,c,e,f,g\}[/tex]
Nina can swim 4 laps in 2 1/3 minutes. At this rate, how many laps can she swim in one minute
lap(s) in one minute
nina can swim 8/7 laps in one minute
given that
nina can swim 4 laps in 7/2 minutes
we have to calculate that how many laps can nina swim in 1 minute
then 4 laps= 7/2 minutes
then 4*2 /7 =1 minute
8/7=1 minute
thus nina can swim 8/7 laps in one minute
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Solve for F: C=5/9(F-32)
Answer:
F=9/5c+32
Step-by-step explanation:
Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:
9/5C = F-32
C=F−32
Then add 32 to both sides, giving you:
9/5C + 32 = F
C+32=F
Thus, you have:
F= 9/5C + 32F=
5
9
C+32
Answer:
[tex]F= \frac{9}{5}C + 32[/tex]
Step-by-step explanation:
Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:
[tex]\frac{9}{5}C = F-32[/tex]
Then add 32 to both sides, giving you:
[tex]\frac{9}{5}C + 32 = F[/tex]
Thus, you have:
[tex]F= \frac{9}{5}C + 32[/tex]
There are 20 flowers in a bouquet, and 2 of them are roses. What percent of the flowers are roses?
Answer:
10%
Step-by-step explanation:
firstly express as a fraction then multiply the fraction by 100% , that is
[tex]\frac{2}{20}[/tex] × 100% = 2 × 5 = 10% of the flowers are roses
(2,−3) and (0,−8) answer
Answer:
y2-y1/x2-x1
-8--3/0-2
Step-by-step explanation:
-8+3/-2=-5/-2=5/2
What is the graetest comon factor on 18 12
Answer: 6
Step-by-step explanation:
Answer:
GCF = 2
Step-by-step explanation:
is 5/10 equivalent to 12/24
The equation will be,
→ 5/10 = 12/24
Is 5/10 equivalent to 12/24?
→ 5/10 = 12/24
→ 24 × 5 = 12 × 10
→ 120 = 120
→ [ LHS = RHS ]
Hence, they are equivalent.
How many 134 minutes is equal to a hour
Error Analysis You and a friend are doing math homework together. You have to solve the equation 5x + 4x - 68 = 34 - 8x. Your friend arrives at the incorrect answer x = -2. Find the correct value of x. Then find the error your friend possibly made. X x=0 What possible error could your friend have made to get x = -2? OA. Your friend should have added 68 to each side of the equation, but instead subtracted 68 from the right side. OB. Your friend should have added 8x to each side of the equation, but instead subtracted 8x from the left side. OC. Your friend should have added 5x and 4x to get a sum of 9x, but instead got a sum of 8x.
This is probably what steps your friend took, or something similar.
5x+4x-68 = 34-8x
9x = 34-8x-68
9x = -8x-34
9x+8x = -34
17x = -34
x = -34/17
x = -2
However, the error is when they subtracted 68 from both sides (line 2).
Instead, they should have added 68 to each side to undo the -68 on the left hand side.
----------------------------
Here's what the steps should look like (one variation of it anyway)
5x+4x-68 = 34-8x
9x = 34-8x+68
9x = -8x+102
9x+8x = 102
17x = 102
x = 102/17
x = 6 is the correct value of x
--------------------------
Check:
5x+4x-68 = 34-8x
5*6+4*6-68 = 34-8*6
30+24-68 = 34-48
54-68 = 34-48
-14 = -14
We get the same thing on both sides after replacing each x with 6, so it confirms x = 6 is the solution.
If you were to try x = -2, then you would end up with -86 = 50 which is a false statement. So that rules out x = -2 as a solution.