y = 7x² is the set of ordered pairs that represent a function.
One clue that the relation is quadratic is found in the second difference:
The first differences are .
7 -0 = 7
28 -7 = 21
63 -28 = 35
112 -63 = 49
The second differences are .
21 -7 = 14
35 -21 = 14
49 -35 = 14
These are constant, indicating the function is 2nd-degree, or quadratic. The coefficient of the x² term is half the value of these second differences, so it will be 7.
When we compare y = 7x² with the given relation values, we find that no additional adjustment is needed in this rule.
for x=0, y = 7·0² = 0
for x=1, y = 7·1² = 7
for x=2, y = 7·2² = 28
for x=3, y = 7·3² = 63
for x=4, y = 7·4² = 112
A rule that represents the function is y = 7x².
What is a function?In mathematics, the function X to Y assigns exactly one element of Y to each element of X. The set X is called the range of the function and the set Y is called the code interval of the function.
Types of operations can be classified into four types.
one-to-one function multiple functions, act one-to-one and function action.In mathematics, a basis function is an element of a certain basis of function space. Every function in a function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.
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Find the error(s) and solve the problem correctly.
Draw a diagram to show the given information.
Given:
AE is the perpendicular bisector of DF.
X is the midpoint of AE.
X is the midpoint of BC
Answer:
It is to be noted that the two inaccuracies were that angle 90 was not shown to be produced at the intersection points of the bisector and that congruent segments were incorrectly indicated. See the corrected diagrams below.
What is the explanation of the above assertion?Take notice of the following to better comprehend the flaws in the diagram: A perpendicular bisector cuts a line segment in half and produces a right angle at the point of intersection.
Congruent segments have an equal number of strokes. Specifically, little straight lines to demonstrate congruency.
Whenever it becomes pertinent to show that two bisected lines are equal, marks resembling an equal sign (=) must be used to cross the line on both sides of the bisector. The equals sign is vertical if the line is horizontal, and vice versa. See a sample of the same with the bisection of DF in the original image.
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Yoko says that when you divide 75 by 5, the answer is 15. How can you check her answer? is she correct?
Two methods...
1How can we divide easily by 5?
We know
[tex]5=\frac{10}{2}[/tex]Then
[tex]\frac{75}{5}=\frac{75}{\frac{10}{2}}=\frac{75\cdot2}{10}=\frac{150}{10}=15[/tex]2The common method
What describes the graph of y = - |x + 1| - 5?
The graph of y = - |x + 1| - 5 will be like an inverted "V" letter, such that the vertex is on the point (-1, -5).
What describes the graph of the given function?
The general absolute value function can be written as:
y = |x - a| + b
This function looks like a "V", such that the vertex of the graph is located at the point (a, b).
Particularly, if we have a negative sign before the absolute value part, like in:
y = -|x - a| + b
The "V" will open downwards.
In this case, the function is:
y = - |x + 1| - 5
In this case, the vertex will be at (-1, 5).
And we can see a negative sign before the absolute value part, so the graph opens downwards.
That is the description of the graph.
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Sara has twice as many records as Jenny. Together they have 78 records. How many records does each have?
Answer:
Sara has 39 and Jenny has 19.5
Step-by-step explanation:
At Marilyn's candy shop, she mixes gummy bears worth 50¢ a pound with chocolate kisses worth 30¢ a pound to create a 97 pound mixture worth 35€. To the nearest pound, how much of each type of candy is in the mixture?
Data:
Gummy bears: G
Chocolate kisses: C
G=50 ¢ a pound
C=30 ¢ a pound
97 pound mixture:
[tex]G+C=97[/tex]mixture worth € 35 (3500 ¢ ):
[tex]50G+30C=3500[/tex]To find how much of each type of candy is in the mixture you use the next system of equations:
[tex]\begin{gathered} G+C=97 \\ 50G+30C=3500 \end{gathered}[/tex]1. Solve one of the variables in one of the equations:
Solve G in the first equation:
[tex]G=97-C[/tex]2. Use the value you find in the fisr part in the other equation:
[tex]50(97-C)+30C=3500[/tex]3. Solve the variable:
- Distributive property to remove the parenthesis:
[tex]4850-50C+30C=3500[/tex]-Combine like terms:
[tex]4850-20C=3500[/tex]-Substract 4850 in both sides of the equation:
[tex]\begin{gathered} 4850-4850-20C=3500-4850 \\ \\ -20C=-1350 \end{gathered}[/tex]-Divide into -20 both sides of the equation:
[tex]\begin{gathered} \frac{-20}{-20}C=\frac{-1350}{-20} \\ \\ C=67.5 \end{gathered}[/tex]4. Use the value in part 3 to find the value of the other variable:
[tex]\begin{gathered} G=97-C \\ G=97-67.5 \\ \\ G=29.5 \end{gathered}[/tex]Then, the mixture has 29.5 pounds of gummy bears and 67.5 pounds of chocolate kissesFor which inequality would x = 5.8 not be a solution?
x-9<0
5 x-14>3
x+6 ≤ 10
6-x≤1
Answer:
137995357864688756864687_57
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 24 cards, which was 4% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
The most appropriate choice for percentage will be given by
Number of cards sold on mother's day = 600
What is percentage?
Percentage is any number which is expressed as a fraction of 100
In percentage,the denominator is 100
For example, 2% means [tex]\frac{2}{100}[/tex]
Here,
Let the number of cards sold for mother's day be x
A salesman sold 4% of the card sold for mother's day
Number of cards sold by the salesman = [tex]\frac{4}{100} \times x[/tex]
= [tex]\frac{x}{25}[/tex]
By the problem,
[tex]\frac{x}{25} = 24[/tex]
[tex]x = 24 \times 25\\[/tex]
[tex]x = 600[/tex]
Number of cards sold on mother's day = 600
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which expression is not equivalent too 24 + 12
1. 2 (12+ 6 )
2. 6 (4+2)
3. 4 (6+ 4)
4. 3 ( 8+ 4 )
Answer:
3
Step-by-step explanation:
Because Math is math and math
49 A numbered cube is rolled once. The cube is numbered from 1 through 6.
What is the probability that a 1 or 6 will be facing upward? Mark all that apply.
06
D
P
0
Answer:
Step-by-step explanation:
the answer would be A because it can be 1 or 6 so if 1/6 means just one number then 2 numbers would 2/6
URGENT!! Help me find the value of Measure 3. I’m super confused
Answer:
68 degrees
Step-by-step explanation:
15x-23= 11x+13
4x= 36
x=9
9 on both sides, so plugin 9 to put in degrees form
180-112=68
So 68 degrees is the answer for angle 3
Is my friend correct or incorrect
Answer:
incorrect
Step-by-step explanation:
Answer: No, he's incorrect
Step-by-step explanation:
Generally you only move the symbol to face the other side when in the case of multiplying both sides by (-1). The correct solution hence would be, x > -27
work out the circumference of the circle below, Give your answer to 1 d.p 7.6m
The circumference of given circle with the radius of 7.6m is 119.43
What is circumference?A circle's circumference is its perimeter. It is the total length of the circle's circumference. The circumference of a circle is equal to the product of the constant and the circle's diameter. This metric of the circumference of a circle is required for a person walking across a circular park or a circular table to be bordered.
Circumference is a linear value with the same units as length. A circle is a closed round figure whose boundary points are all equidistant from a fixed point known as the center. The area and circumference of a circle are the two most important metrics of a circle.
The formula for the circumference of a circle is
C = 2πr
We have given that radius = 7.6m
So, the circumference is
C = 2π(7.6)
= 38π
= 119. 43
Thus, circumference is 119.43
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Andrew and Dustin picked $3$ and $2$ pounds of strawberries, respectively. Their neighbor, Jessica, saw them and asked if she could share the strawberries with them. Andrew and Dustin agreed and the three of them shared the strawberries evenly. After the meal, Jessica gave Andrew and Dustin $\$5$ to thank them. If Andrew and Dustin distribute the $\$5$ fairly, how much does Andrew get?
Answer:
4
Step-by-step explanation:
Of the total 5 pounds of strawberries, each person ate 5/3 pounds. Thus, 3-5/3=4/3 pounds of Andrew's strawberries were given to Jessica and 2-5/3=1/3 pounds of Dustin's strawberries were shared. The ratio of pounds shared by Andrew to those shared by Dustin is 4/3:1/3 , or 4:1, so to be fair, the money should be split in the same ratio. Therefore, Andrew should get $4 and Dustin should get $1 .
Thanks to my dad for the help
Answer:
4
Step-by-step explanation:
right on aops
your friends are planning a party for their parents anniversary. The caterer charges a delivery fee of $100 plus an additional $35.75 per person. if they can spend no more than $530, how many people can they invite? remember you cannot serve a partial person.
Answer:
3815699985588888548555006
The sum of two numbers is 5. Three times the first is thirteen more than ten times the second. Find the numbers
The two numbers with the sum of 5 are 0 and 5
How to determine the two numbers?The sum of the numbers is given as
Sum = 5
The relationship between the numbers is given as
Three times the first is thirteen more than ten times the second.
This can be rewritten as
3x = 15 + 10y
Where x and y represent the numbers
This means that
x + y = 5
Make x the subject
x = 5 - y
Substitute x = 5 - y in 3x = 15 + 10y
3(5 - y) = 15 + 10y
Expand
15 - 3y = 15 + 10y
Evaluate the like terms
13y = 0
This gives
y = 0
Substitute y = 0 in x =5 - y
x = 5 - 0
Evaluate
x = 5
Hence, the numbers are 0 and 5
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Clytie looked at her social studies test. She received a grade of 85%. If there were 33 questions on the test, how many did Clytie get right?
There were 33 questions on Clytie's test and she got a grade of 85%.
The number of right answers was:
[tex]\frac{85}{100}\cdot33[/tex]The result is approximately 28, thus:
Clytie got 28 answers right
4 1/2 + 3 5/6 in a fraction
Answer:
8 1/3
Step-by-step explanation:
4 1/2 + 3 5/6
First, we must convert the fraction to a common denominator.
1/2 = 3/6
4 3/6 + 3 5/6
3/6 + 5/6 = 8/6 = 1 2/6 = 1 1/3
1 1/3 + 4 + 3 = 8 1/3
The answer is 8 1/3.
Answer: 8 1/3
Step-by-step explanation:
4 1/2 + 3 5/6
So what we do is we make them have the same denominator
1/2 = 3/6
Now... 3/6 + 5/6 = 8/6
8/6 will have to be converted into a mixed number so...
that will be 1 2/6
now we add the two whole numbers 4 and 3 which is 7
7+1=8
8 + 2/6 = 8 2/6
now simplify that and you get 8 1/3
Write a justification for each step.
16. 5x3 = 4(x + 2)
Answer:
1.75 = x
Step-by-step explanation: I'm not sure if you meant 5x3 or 5 times 3 so I did the one that made sense
5 x 3 = 4(x+2)
First step: distribute so 5 x 3 = 4x + 8
Second step: 5 x 3 = 15 15 = 4x+8
Third step: Subtract 8 from both sides 15 - 8 = 7 7 = 4x
Fourth step: Divide by 4 on both sides 7/4 = 1.75 1.75 = x
What is 7 to the power of two?
Find the slope of the line graphed below.
Slope = 1
Slope of the line shown in the graph is 1.
What is slope?The slope of a line indicates its steepness.
The slope is defined as the ratio of the vertical change between two points, known as the rise, to the horizontal change between those same two points, known as the run.To find the slope of a line given the coordinates of two points on the line, use the slope formula. The slope formula is m=(y2-y1)/(x2-x1), or the difference between the y and x values.From the graph we can plot two points (2 , 2) and (4 , 4).
Equation to find slope ,
m = y2 - y1 / x2 - x1
By substituting values,
m = 4 - 2 / 4 - 2
= 2 / 2
= 1
∴ Slope ( 2 , 2) and ( 4 , 4 ) = 1.
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Coordinate distance Decimal (6,-5) and (9,-1)
After applying distance formula, we have come to find that, distance from coordinate (6,-5) to coordinate (9,-1) is 5 unit.
What is a coordinate plane?A coordinate plane is a surface with two dimensions made up of two number lines. It is created when the origin, the point at which the X-axis and Y-axis intersect, is reached. To locate points, one uses the numbers on a coordinate grid.
A coordinate plane is useful for graphing points, lines, and many other things. It serves as a map and provides clear instructions for getting from one place to another.
The formula for distance of two given points is
Distance =√((x₂ – x₁)² + (y₂ – y₁)²)
Here, (x₁, y₁) is (6,-5) and
(x₂, y₂) is (9,-1)
Substituting the given values we get
Distance = √((9 – 6)² + ((-1) – (-5))²)
= √((3)² + (4)²)
= √(9 + 16)
= √(25)
= 5
Thus, Distance from point (6,-5) to point (9,-1) is 5 unit.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
s=/a
s=-/a,a>0
it inchs
Step-by-step explanation:
Tickets to a baseball game cost $3 for a child’s ticket and $5 for an adult ticket. At the last game, $521 was collected when 139 people attended the game. Which value could replace x in the table so that a single-variable equation can be written and solved to determine the number of child’s tickets, c, sold?
Answer: x = 139-c is used to replace and there are 87 child's ticket.
Step-by-step explanation:
Let the number of child's ticket be 'c'.
Total number of people attended the game = 169
Let the number of adult's ticket be 'x'.
Cost of each child's ticket = $3.
Cost of each adult ticket = $5.
Total amount collected = $521
So, According to question, it must be look like this :
3c+5x=$521
Here, we need to replace x , so that a single variable equation can be written and solved to determine the number of child's tickets sold.
x+c=139
x=139-c
So, our single variable equation becomes
3c+5(139-c)=$521
3c+695-5c=521
-2c=521-695
-2c=-174
Hence, x = 139-c is used to replace and there are 87 child's ticket.
This is the correct answer to this question.
C. 139 – c
What is 157.8- (3^2+ 6) times 3
Please show your work
In linear equation,112.8 is the solution .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.= 157.8 - ( 3² + 6) × 3
= 157.8 - ( 9 + 6) × 3
= 157.8 - 15 × 3
= 157.8 - 45
= 112.8
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Can someone help me with this
rude!we dont us such words here change it please
Classify each linear equation.
No Solution
:: 3x = 3(x + 3)
:: -2(x + 3) = -2x - 6
Infinitely Many Solutions
:: 2x + 2 = 2(x + 1)
::5(X + 1) = 5x +1
A linear equation is a mathematical expression that may be written as x 1+ldots +a n+x n+b=0, where x 1, ldots, and x n are the variables and display style b, a 1, ldots, and a n are the coefficients, which are frequently real integers.
What in mathematics is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and which includes only a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is referred to as a "linear equation of two variables" on occasion.A linear equation is a mathematical expression that can be written as x 1+ldots +a n+x n+b=0, where x 1, ldots, and x n are variables and b, a 1, ldots, and a n are coefficients, which are frequently real integers.To learn more about Linear equation refer to:
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What’s the answer plsss
The angle of inclination of the line to the nearest tenth of a degree is 25.4°.
So, the correct option is Option(c).
What is the Angle of Inclination?A line's angle inclination is the angle created by the line's intersection with the x-axis. Using a horizontal "run" of 1 and m for slope, the angle of inclination, theta = tan⁻¹(m), or m = tan⁻¹(m), may be calculated.
Given:
The length of the sides of the given triangle are,
Base = 9.7
Perpendicular = 4.6
So, Angle of Inclination = tan θ = Perpendicular/Base
θ = tan⁻¹(4.6/9.7)
θ ≅ 25.4°
Therefore, the angle of inclination of the line to the nearest tenth of a degree is 25.4°.
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The table below gives values of an invertible function f(x):
Part A
f(0)
that means the value of f(x) for x=0
looking at the table
For x=0 ----> f(x)=4
therefore
f(0)=4
Part B
f(x)=0
looking at the table
f(x)=0 when the value of x=1
therefore
f(1)=0
Part C
f^-1(0)
For f(x)=0 -----> the value of x=1
therefore
f^-1(0)=1
Part D
f^-1(x)=0
looking at the table
For x=0 -----> f(x)=4
therefore
f^-1(4)=0
the life of an electric component has an exponential distribution with a mean of 10 years. what is the probability that a randomly selected one such component has a life more than 7 years?
The probability is 0.4647.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or the likelihood of a statement being true.The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty. The higher the probability of an event, the more likely the event will occur. A simple example is tossing a fair coin. Both outcomes are equally likely because the coin is fair. The probability of heads or tails is 1/2. These concepts are an axiomatic mathematical formalization of probability theory that is widely used in research fields such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy. Infer the expected frequency from the event. Probability theory is also used to explain the underlying dynamics and laws of complex systems.To learn more about probability from the given link :
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The sum of one-fourth of a number and twelve is twelve less
than the number. What is the number?
