Consider the table that includes the input and output values of a function.
Which best describes the constant difference for the function?
a constant second difference of –6
a constant second difference of 8
a constant third difference of –6
a constant third difference of 8
Answers
The first option is correct and it best describes the constant difference for the function as a constant second difference of –6.
What is a function?A function f(x) is the relation between a set of inputs resulting and producing the desired output value of y for each input.
From the given information:
x f(x) first difference second difference third difference
-2 0 - - -
-1 -10 (-10-0)/-1--2 = -10 - -
0 -12 (-12 - 10)/0 -- 1= -2 (-2-10)/2 = -6 -
1 -12 (-12--12)/1-0 = 0 (0-2)/2 = -1 (-1+6)/2 = 5/2
2 -16 (-16--12)/2-1 = -2 (-2-0)/2 = -1 (-1+1)/2 = 0
Therefore, we can conclude that the constant difference for the function is a constant second difference of –6.
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Answer:
A
Step-by-step explanation:
Related Questions
f(x) = x². What is g(x)?
Answers
g(x) is the inverse of f(x)
[tex]f(x) = {x}^{2} [/tex]
[tex]g(x) = \sqrt{x} [/tex]
Find the midpoint of the line segment whose endpoints are given. (9,3), (10,- 10)
Answers
Answer:
Step-by-step explanation:
(xm , ym ) = x1 + x2 / 2 and y1 + y2 / 2
= 9 +3 / 2 = 10 -10 / 2
= 12/2 = 0/2
= 6 = 0
So midpoints are (6 , 0)
Answer:
midpoint = [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
Step-by-step explanation:
To find the midpoint of a line segment, you have to find the average of the x and y-values of the end-points, i.e., add the x-coordinate values and divide the answer by 2, and do the same for the y-coordinate values.
• midpoint = [tex](\frac{x_{2} + x_1}{2}, \frac{y_2 + y_1}{2} )[/tex]
= [tex](\frac{9 + 10}{2}, \frac{3 + (-10)}{2} )[/tex]
= [tex](\frac{19}{2}, \frac{-7}{2} )[/tex]
= [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
226,710 - 724,435 =
How to work this out without calculator
Answers
solve for x -
[tex]\bold{x {}^{2} - 4 = 0}[/tex]
ty! ~
Answers
Answer:
x² - 4 = 0
x² = 4
x =± √4
x = +2 or x = -2.
Answer:
2 and -2 (±2)
Step-by-step explanation:
Step 1: Move -4 to the other side of the equal sign; we get x² = 4.
Step 2: A lot of people miss the negative answer! The square root of 4 is equal to both positive 2 and negative 2.
Hope this helped! Please mark me as Brainliest b/c I really need it!!!FAST!
A right rectangular prism has a square base and a height of 2.5 meters. If the length of a side of the square base is 4 meters, what is the volume of the prism?
Answers
Answer:
69 there hope it helps ;)
Step-by-step explanation:
420
2
What is the equation of the line that is perpendicular to y=x+4 and that passes through (5,-4)?
--5v-20
K
Answers
Perpendicular lines have slopes that are negative reciprocals of each other, so since the slope of the given line is 1, the slope of the line we want to find is -1.
Substituting into point-slope form,
[tex]y+4=-1(x-5)\\\\y+4=-x+5\\\\\boxed{y=-x+1}[/tex]
help
You invest $1000 in an account that has an annual interest rate of 4%, compounded monthly for 12 years. What is the equivalent interest rate and how many times will the money be compounded?
Answers
The equivalent interest rate is 4.07%.
The money will be compounded 12 times.
What is the equivalent interest rate?
The equivalent interest rate is the actual interest rate that an account earns after accounting for number of compounding.
Effective interest rate = (1 + APR / m ) ^m - 1
M = number of compounding
(1 + 0.04/12)^12 - 1 = 4.07%
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I will give lots of points please help
Answers
Answer:
a) 81π in³
b) 27 in³
c) divide the volume of the slice of cake by the volume of the whole cake
d) 10.6%
e) see explanation
Step-by-step explanation:
Part (a)The cake can be modeled as a cylinder with:
diameter = 9 inheight = 4 in[tex]\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in[/tex]
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
[tex]\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}[/tex]
Part (b)[tex]\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}[/tex]
If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.
[tex]\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}[/tex]
Part (c)The volume of each slice of cake is 27 in³.
The volume of the whole cake is 81π in³.
To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:
[tex]\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}[/tex]
Part (d)Probability is approximately 10.6% (see above for calculation)
Part (e)If the four slices of cake are cut and passed out before anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, until the marble is found. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.
e total cost, in dollars, for a company to produce r headsets per day is modeled by the function C,
where C(r) = (-5)2 + 35 for 5 < r ≤ 25. The company sells each headset for $20. On one day, the
company produced 15 headsets. According to the model, what will be the profit on the sale of these
headsets? (Profit equals total sales minus total cost.)
O $215
O $225
O $240
O $300
Answers
‐10+35=25 and 25 × 20=300
Find how many numbers between 23^2 and 25^2.
Answers
Answer:
Step-by-step explanation:
We know that, 252 = 625
And, 262 = 676
Now, 676 - 625 = 51
So, there are 51 - 1 = 50 numbers lying between 252 and 262
Find all real zeros of the function.
Answers
Answer:
Zeros: 0, 1, and 7
Step-by-step explanation:
Given function: f(x) = 3x(x - 1)²(x - 7)²
To find the zeros (also known as the x-intercepts) of the function, first substitute f(x) = 0 into the equation and simplify.
1. Substitute f(x) = 0:
[tex]\sf f(x) = 3x(x - 1)^2(x - 7)^2\\\\\Rightarrow 0 = 3x(x - 1)^2(x - 7)^2[/tex]
2. Divide both sides by 3:
[tex]\sf \dfrac{0}{3} = \dfrac{3x(x - 1)^2(x - 7)^2}{3}\\\\\Rightarrow 0=x(x-1)^2(x-7)^2[/tex]
3. Separate into possible cases:
[tex]\sf a)\ x = 0\\b)\ (x - 1)^2 = 0\\c)\ (x - 7)^2 = 0[/tex]
4. Simplify:
[tex]\sf a)\ x = 0\ \textsf{[ already simplified ]}[/tex]
[tex]\sf b)\ (x - 1)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 1)^2}=\sqrt{0}\\\\\Rightarrow x-1=0\ \textsf{[ add 1 to both sides ]}\\\\x-1+1=0+1\\\\\Rightarrow x=1[/tex]
[tex]\sf c)\ (x - 7)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 7)^2}=\sqrt{0}\\\\\Rightarrow x-7=0\ \textsf{[ add 7 to both sides ]}\\\\x-7+7=0+7\\\\\Rightarrow x=7[/tex]
Therefore, the zeros of this function are: 0, 1, and 7.
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6z + 10= -2 solve this problem
Answers
Answer:
z = -2
Step-by-step explanation:
Answer:
[tex]\boxed{\bf z = - 2}[/tex]
Step-by-step explanation:
[tex]\bf 6z + 10 = - 2[/tex]
Subtract 10 from both sides.
[tex]\bf 6z + 10 - 10= - 2 - 10[/tex]Simplify.
[tex]\bf 6z = - 12[/tex]Divide both sides by 6.
[tex]\bf \cfrac{6z}{6} = \cfrac{ - 12}{6} [/tex]Simplify.
[tex]\bf z = - 2[/tex]_________________________
whats the answer? :(
Answers
Answer:
D) 8[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
5[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex] = 8[tex]\frac{1}{2}[/tex]
What is one possible value of 2x
Answers
Answer:
really good
Step-by-step explanation:
thanks for your help you with that do not have a copy of the receipt for your time to help you with theQuestion
Find the distance between the points (-5, 8) and (-3,0).
Answers
To calculate the distance between two points we use this formula:
[tex] \boxed{ \boxed{{d \: = \: \sqrt{(x_2 \: - \: x_1)^{2} \: + \: (y_2 \: - \: y_1)^{2} } }}}[/tex]
______________________We organize the values:x₁ = -5 x₂ = -3 y₁ = 8 y₂ = 0______________________
We apply the values already obtained to the formula to get the distance:
[tex]d \: = \: \sqrt{( - 3 \: - \:( - 5))^{2} \: + \: (0 \: - \: 8)^{2} }[/tex]
[tex]d \: = \: \sqrt{( - 3 \: - \: ( - 5))^{2} \: + \: ( - 8)^{2} }[/tex]
[tex]d \: = \: \sqrt{( - 3 \: + \: 5) ^{2} \: + \: 64 } [/tex]
[tex]d \: = \: \sqrt{ {2}^{2} \: + \: 64 } [/tex]
[tex]d \: = \: \sqrt{4 \: + \: 64} [/tex]
[tex]d \: = \: \sqrt{68} [/tex]
[tex]d \: = \boxed{ \bold{ \: 2 \sqrt{17} \: units}}[/tex]
Answer:[tex] \huge{\boxed{ \bold{2 \sqrt{17} \: units }}}[/tex]
MissSpanishWhat number comes next in the sequence?
1, 1, 2, 3, 5, 8, 13, 21, 34, ?
Answers
Answer:
55
Step-by-step explanation:
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
5+8 = 13
8+13 = 21
13+21 = 34
21 +34 = 55
PLEASE GIVE BRAINLIEST
The following excerpt comes from the International Bottled Water Association
"In 2012, total U.S. bottled water consumption increased to 9.67 billion gallons, up from 9.1 billion gallons in 2011. In fact, 2012's consumption growth was the strongest it has been in five years. In addition,
per-capita consumption is up 5.3 percent in 2012, with every person in America drinking an average of 30.8 gallons of bottled water last year. Bottled water increased in absolute volume more than any other
beverage category in the U.S. Bottled water sales increased by 6.7 percent in 2012, and now total $11.8 billion."
(i) Estimate the per capita consumption from 2011 from data in the statement. Express your answer rounded correctly to the nearest tenth of a gallon.
Answers
Using proportions, the estimate of the per capita consumption from 2011 is of 29.2 gallons.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
From the data, the 2012 consumption was 5.3% percent higher than in 2011, that is 105.3% of 1.053x. This consumption was of 30.8 gallons, hence:
1.053x = 30.8.
x = 30.8/1.053
x = 29.2.
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Assuming two hikers begin at a trail start, which scenarios must be true based on the table? Check all that apply.
Melissa and Corey started on different trails.
Melissa hiked up the trail for a longer period of time than Corey.
Melissa and Corey crossed paths between 60 and 90 minutes.
Corey began his descent before Melissa.
As Melissa’s time increased from 0 to 60 minutes, her elevation decreased.
Answers
The true statements are (A), (B) and (D)
What is data?Data is information that has been translated into a form that is efficient for movement or processing.
As, from the given table we can see that
Melissa and Corey started on different trails.Melissa hiked up the trail for a longer period of time than Corey.Corey began his descent before Melissa.Learn more about this concept here:
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Dwayne is selling hamburgers and cheeseburgers. he has 100 burger buns. each hamburger sells for $3, and each cheeseburger sells for $3.50. which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80? h c ≤ 80 3h 3.5c ≤ 100 h c ≤ 80 3h 3.5c ≥ 100 h c ≤ 100 3h 3.5c ≤ 80 h c ≤ 100 3h 3.5c ≥ 80
Answers
Let h represent hamburgers and c represent cheeseburgers
h + c ≤ 100 - The number of burgers sold
3h + 3.5c ≥ 80 - Amount that each burger sells for
Solve the linear programming problem.
Minimize and maximize
P = 10x + 5y
Subject to
2x+3y 230
2x+y ≤ 26
-2x+3y ≤ 30
x, y 20
Answers
The minimized value is 50 and the maximized value is 130
How to minimize and maximize the function?The objective function is:
P = 10x + 5y
Subject to
2x+3y ≤30
2x+y ≤ 26
-2x+3y ≤ 30
x, y >0
Next, we plot the graph of the constraints (see attachment)
From the graph, the vertices of the feasible regions are:
(0, 10),(12, 2) and (6,14)
Substitute these values in P = 10x + 5y
P = 10(0) + 5(10) = 50
P = 10(12) + 5(2) = 130
P = 10(6) + 5(14) = 130
Hence, the minimized value is 50 and the maximized value is 130
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6(2x² - 5) = [?]
x = -3
Answers
x = -3
[tex]6( {2x}^{2} - 5) \\ \\ 6(2 \times { (- 3)}^{2} - 5) \\ \\ 6(2 \times ( 9) - 5) \\ \\ 6( 18 - 5) \\ \\ 6 \times ( 13) \\ \\ 78.[/tex]
=6(2*9-5)
=6(18-5)
=6*13
=78
I need help with number 10 please
Answers
Answer:
Liz
Step-by-step explanation:
if the chart is correct only 3 people spent more than 2 1/2 hours on homework when 9 people spent less than 2 1/2 hours on homework
A kitchen measures 20 feet long and 10 feet wide. A scale drawing is made using a scale factor of 124.
What is the length of the kitchen in the scale drawing?
5/12
5/6
5/4
Drag and drop a number to correctly complete the statement.
The length of the kitchen in the scale drawing is Response area ft.
Answers
The length of the kitchen in the drawing using the scale factor is: B. 5/6.
How to Find Length Using Scale Factor?We are given a scale factor of 1:24.
Let the length of the kitchen in the drawing = x
Actual length of kitchen = 20 ft.
Using the scale factor, we have:
1/24(20) = 20/24
= 5/6
The length of the kitchen in the drawing is: B. 5/6.
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If the odds against an event are 3:5, then the probability that the event will fail to occur is
Answers
Answer:
3/8
Step-by-step explanation:
probability = wanted outcomes / total outcomes
odds = wanted outcomes / unwanted outcomes
Odds of 3:5 losing means 3 losing outcomes and 5 winning outcomes.
The total outcomes is 8
The probability of losing which is the probability that the event will fail to occur is 3/8.
Which expression is equivalent to 36x² - 25?
O (18x)²+(-5)²
O (18x)²-(5)²
O (6x)²+(-5)²
O (6x)²-(5)²
Answers
Answer:
[tex] \boxed{ \rm(6x)²-(5)²}[/tex]
Step-by-step explanation:
Given expression/polynomial :
[tex]3 6{x}^{2} - 25[/tex]
Let's evaluate.
We can re-write the polynomial as
[tex]6 {}^{2} x {}^{2} - 5 {}^{2} [/tex]Further
[tex]{(6x) {}^{2} - 5 {}^{2} }[/tex]Hence, the expression is equivalent to last Choice, (6x)²-(5)².
-Regards, Hannah :)
What is the value for y?
What is the value of x?
Enter your answer in the box.
x =
Equiangular triangle A B C. Angles A, B, and C are marked congruent. The length of side A C is labeled as 5 x minus 22. The length of side A B is labeled as 4 x minus 10. The length of side B C is labeled as 3 x plus 2.
Enter your answer in the box.
y =
An isosceles triangle A B C with horizontal base B C and vertex A is above the base. Side A C and C B are labeled with single tick mark. All the three angles are labeled. Base angles C A B is labeled as 50 degrees and angle C B A is labeled as 2x degrees. The angle A C B is labeled left parenthesis 5 y plus 10 right parenthesis degrees.
Answers
1. The value of x in the equilateral triangle is: 12
2. x = 25; y = 14
What is an Equilateral Triangle?If a triangle has three sides that are marked congruent, then the triangle is an equilateral triangle.
1. Since triangle ABC is an equilateral triangle and its sides are equal, therefore:
5x - 22 = 3x + 2 [congruent sides]
Solve for x
5x - 3x = 22 + 2
2x = 24
2x/2 = 24/2
x = 12
The value of x is: 12.
2. Base angles of an isosceles triangle are congruent, therefore:
2x = 50
x = 50/2
x = 25
Thus, using the triangle sum theorem, we have:
2x + 50 + 5y + 10 = 180
Plug in the value of x and find y
2(25) + 50 + 5y + 10 = 180
50 + 50 + 5y + 10 = 180
110 + 5y = 180
5y = 180 - 110
5y = 70
y = 70/5
y = 14
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Which of the following linear equations represents the data chart?
X Y
1 6
2 5
3 4
4 3
y=x+5
y=x+3
y = -x + 7
None of these choices are correct.
Answers
Answer: y = -x + 7
Step-by-step explanation:
The slope is [tex]\frac{5-6}{2-1}=-1[/tex], so we know the equation is of the form [tex]y=-x+b[/tex].
Substituting in the coordinates (1,6) to find b,
[tex]6=-1+b\\\\b=7[/tex]
Thus, the equation is y = -x + 7
Graph the inequality.
y > |x-2| -5
Answers
Here is the graph! I hope this helps!
Answer:
^this means graph C.
Step-by-step explanation:
Statement: "Three less than four times a number is greater
than or equal to 41."
Answers
Answer:
x≥11
Step-by-step explanation:
4x-3≥41
4x≥41+3 -44
x≥44/4 = 11
Help me with this question please!!!
Answers
a) 2/8 = 1/4
b) There are 3 females who can speak French and 2 males who can speak French, so the probability is 3/5
