Question:
Which set of ordered pairs (x,y) could represent a linear function?
[tex]\mathbf{A}= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\}[/tex]
[tex]\mathbf{B}= \,\,\left\{(-1, -8),\,\,(0, -3),\,\,(1, 3),\,\,(2, 8)\right\}[/tex]
[tex]\mathbf{C}= \,\,\left\{(-9, 5),\,\,(-3, 3),\,\,(3, 0),\,\,(9, -2)\right\}[/tex]
[tex]\mathbf{D}= \,\,\left\{(1, -8),\,\,(2, -6),\,\,(3, -3),\,\,(4, 0)\right\}[/tex]
Answer:
[tex]\mathbf{A}= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\}[/tex]
Step-by-step explanation:
Given
Ordered pairs A - D
Required
Which represents a linear function?
To do this, we simply calculate the slope (m) of each ordered pairs.
[tex]m = \frac{y_2 - y_1}{x_2-x_1}[/tex]
Considering A:
[tex]\mathbf{A}= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\}[/tex]
Consider the following pairs
[tex](x_1,y_1) = (2,9)[/tex] and [tex](x_2,y_2) = (4,5)[/tex]
[tex]m = \frac{5 - 9}{4 -2} = \frac{-4}{2} = -2[/tex]
Consider the another pairs
[tex](x_1,y_1) = (2,9)[/tex] and [tex](x_2,y_2) = (6,1)[/tex]
[tex]m = \frac{1 - 9}{6 -2} = \frac{-8}{4} = -2[/tex]
Consider the another pairs
[tex](x_1,y_1) = (2,9)[/tex] and [tex](x_2,y_2) = (7,-1)[/tex]
[tex]m = \frac{-1 - 9}{7 -2} = \frac{-10}{5} = -2[/tex]
The slope is uniform all through.
i.e.
[tex]m = -2[/tex]
Hence, this can be a linear function
Considering B:
[tex]\mathbf{B}= \,\,\left\{(-1, -8),\,\,(0, -3),\,\,(1, 3),\,\,(2, 8)\right\}[/tex]
Consider the following pairs
[tex](x_1,y_1) = (-1,-8)[/tex] and [tex](x_2,y_2) = (0,-3)[/tex]
[tex]m = \frac{-3 - (-8)}{0 - (-1)} = \frac{-3 +8}{0 +1} = \frac{5}{1} = 5[/tex]
Consider the another pairs
[tex](x_1,y_1) = (-1,-8)[/tex] and [tex](x_2,y_2) = (1,3)[/tex]
[tex]m = \frac{3 - (-8)}{1 - (-1)} = \frac{3 +8}{1 +1} = \frac{11}{2} = 5.5[/tex]
The calculated slopes are not equal.
i.e.
[tex]m = 5[/tex] and [tex]m = 5.5[/tex]
Hence, this can't be a linear function
Considering C:
[tex]\mathbf{C}= \,\,\left\{(-9, 5),\,\,(-3, 3),\,\,(3, 0),\,\,(9, -2)\right\}[/tex]
Consider the following pairs
[tex](x_1,y_1) = (-9,5)[/tex] and [tex](x_2,y_2) = (-3,3)[/tex]
[tex]m=\frac{3-5}{-3-(-9)} = \frac{3-5}{-3+9} = \frac{-2}{6} = -\frac{1}{3}[/tex]
Consider the another pairs
[tex](x_1,y_1) = (-9,5)[/tex] and [tex](x_2,y_2) = (3,0)[/tex]
[tex]m=\frac{0-5}{3-(-9)} = \frac{0-5}{3+9} = \frac{-5}{12} = -\frac{5}{12}[/tex]
The calculated slopes are not equal.
i.e.
[tex]m = -\frac{5}{12}[/tex] and [tex]m = -\frac{1}{3}[/tex]
Hence, this can't be a linear function
Considering D:
[tex]\mathbf{D}= \,\,\left\{(1, -8),\,\,(2, -6),\,\,(3, -3),\,\,(4, 0)\right\}[/tex]
Consider the following pairs
[tex](x_1,y_1) = (1,-8)[/tex] and [tex](x_2,y_2) = (2,-6)[/tex]
[tex]m = \frac{-6 - (-8)}{2 - 1} = \frac{6 + 8}{1} = \frac{14}{1} = 14[/tex]
Consider the another pairs
[tex](x_1,y_1) = (1,-8)[/tex] and [tex](x_2,y_2) = (3,-3)[/tex]
[tex]m = \frac{3 - (-8)}{-3 - 1} = \frac{3 + 8}{-4} = \frac{11}{-4} = -\frac{11}{4}[/tex]
The calculated slopes are not equal.
i.e.
[tex]m = -\frac{11}{4}[/tex] and [tex]m = 14[/tex]
Hence, this can't be a linear function
From the calculations above:
Only (A) can be a linear function
Answer:
Step-by-step explanation:
Simplify (combine like terms) 4x + 2x
Answer:
6x
Step-by-step explanation:
Answer:
4x+2x= 6x
Step-by-step explanation:
When combining like terms you add the numbers with the same variable your answer is 6x
g(x) is the transformation the parent function f(x)=x2 after being reflected over the x-axis and translated 4 units left. What is the equation for g(x)?
Answer:
Reflection across the x-axis: y = − f ( x ) y = -f(x) y=−f(x) The concept behind the reflections about the x-axis is basically the same as the reflections about the y-axis. The only difference is that, rather than the y-axis, the points are reflected from above the x-axis to below the x-axis, and vice versa.
the equation for g(x) after reflected over x axis and translated 4 units left
[tex]g(x)=-(x+4)^2[/tex]
Given :
Parent function is [tex]f(x)=x^2[/tex]
When a graph is reflected over x-axis then f(x)=-f(x)
When a graph is translated 'a' units left then we add 'a' with
f(x) becomes f(x+a)
Parent function f(x) is reflected over x-axis , multiply -1 with f(x)
so , [tex]f(x)=-x^2[/tex]
Now we translate 4 units to the left, add 4 with x
[tex]g(x)=-x^2\\g(x)=-(x+4)^2[/tex]
The final equation of g(x) is
[tex]g(x)=-(x+4)^2[/tex]
Learn more : brainly.com/question/9111027
please explain how you got your answer
Write the expression as a monomial in its standard form:
25a^4*(3a^3)^2
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Answer:
[tex]225a^{10}[/tex]
Step-by-step explanation:
The rules of exponents apply:
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
__
[tex]25a^4\cdot(3a^3)^2=25a^4\cdot3^2a^{2\cdot3}=25\cdot9a^4\cdot a^6\\\\=225a^{4+6}=\boxed{225a^{10}}[/tex]
WHICH FUNCTION BEST REPRESENTS THIS GRAPH?
Answer:
y=-2+1
Step-by-step explanation:
Write a situation to represent the integer -17.
Answer: 12
Step-by-step explanation:
27 8/9 divided by 6 5/8
Answer:4 100/477
Step-by-step explanation:You need to divide it.And first you change the mixed numbers 27 8/9 and 6 5/8 to improper fraction .27 8/9 as a improper fraction is 251/ 9 . 6 5/8 as a improper fraction is 53/ 8 .ANd now you divide 251/ 9 by 53/ 8.In order to divide fractions you need to do KCF which stand for Keep ,change,flip .SO you have 251/ 9 divide 53/ 8 ,now you KEEP 251/9 ,Change the division sign to multiplication ,and flip 53/8 to 8/53.And now you multiply 251/9 by 8/53 which gives you 2008/ 477.Lastly you change 2008/ 477 which is a improper fraction to a mixed number which is 4 100/477.
h + 9.7 = - 9.7
pls help me I'm stuck
Answer:
SimplifyingH + 9.7 = -9.7Reorder the terms:9.7 + H = -9.7Solving9.7 + H = -9.7Solving for variable HMove all terms containing H to the left, all other terms to the right.Add -9.7 to each side of the equation.9.7 + -9.7 + H = -9.7 + -9.7Combine like terms: 9.7 + -9.7 = 0.00.0 + H = -9.7 + -9.7H = -9.7 + -9.7Combine like terms -9.7 + -9.7 = -19.4H = -19.4SimplifyingH = -19.4Answer: h = - 19.4
Step-by-step explanation:
h + 9.7 = - 9.7
h + 9.7 - 9.7 = - 9.7 - 9.7
h = - 19.4
Someone please help me on these 2 problems!
1) function 2) not a function
the first one is a function because its y values are the same number (3), which means it is a horizontal line and horizontal lines are functions.
the second one is not a function because the coordinates cannot have different inputs but different outputs. each input must have only one output.
the coordinates for the second one are:
(2,5); (1,1); (1,2); (3,2)
and a function cannot have two same x-coordinates. it must pass the vertical line test which is a way to tell if something is a function or not. since the second graph does not pass the vertical line test, it is not a function
hope this helps :)
Morgan is a real estate agent and most recently made $12,500 on the sale of a home. Her commission she earns in selling homes is 12%. What was the sale price of the home that Morgan sold? Round to the nearest dollar amount
Answer:
$104,167 approx.
Step-by-step explanation:
Step one:
Given data
Morgan made $12,500 on the sale of a home.
Her commission she earns in selling homes is 12%
Step two:
let the cost of the home be x
So 12% of x= 12,500
12/100*x= 12,500
0.12*x=12,500
0.12x=12,500
divide both sides by 0.12
x= 12,500/0.12
x=$104,166.66
x=$104,167
somebody please help me!!!!!
Answer:
62% and 64%
Step-by-step explanation:
no computer access = 21 + 165 = 186/300 = 0.616 = 62%
no email access = 27 + 165 = 192/300 = 0.64 = 64%
Answer:
(a) 62%
(b) 64%
Step-by-step explanation:
To find the answer to part "a" you need to divide the total number of shoppers without computer access at home by the total number of shoppers (300).
186/300 = 0.616 = 0.62
0.62 is equivalent to 62%
To find the answer to part "b" you need to divide the total number of shoppers without an email account (Regardless of computer access) by the total number of shoppers (300).
192/300 = 0.64
0.64 is equivalent to 64%.
I hope this helps!
Help please due in 30 minutes
Answer:
the last one
Step-by-step explanation:
uv
A block of ice weighs 12 tonne.
The block is a cube with side length 81cm.
Find the density of the ice.
Give your answer in kilograms per cubic metre.
Answer:
81 cm is 0.81 metre
12 tonne is 12000 kg
Volume of a cube is a^3
V=0.531441
D=M/V
=12000/0.531441
Density is 22580.11708 kg per m cube
Step-by-step explanation:
if 9 calculators cost £96.30. How much do 13 calculators cost
Step-by-step explanation:
First, you want to start by creating an equation to find the unit rate
calculators = c
9c = 96.30
Solve!!!
9c/9 = 96.3/9
c= 10.7
A calculator costs $10.70 (Sorry I will be using the dollar sign instead)
Now you want to set an expression for 13 calculators
13c
Substitute 10.7 in
13(10.7)
Multiply them
$139.10
13 calculators cost $139.10
I hope this helps!!!
Mariah purchases three hair barrettes by using a gift card, which starts with a balance of $35.79. Which expression models her purchase? 3 b minus 35.79 35.79 + 3 b 35.79 b minus 3 35.79 minus 3 b
Answer:
35.79 minus 3 b
Step-by-step explanation:
Mariah purchases three hair barrettes by using a gift card, which starts with a balance of $35.79.
Let the number of barrettes be represented by b
She purchases 3 barrettes
Hence = 3 × b = 3b
Hence, the expression that models her purchase is given as:
$35.79 - 3b
Answer:
35.79-3b
Step-by-step explanation:
The value of the gift card 35.75 minus the cost of 3 barrettes (3b).
so 3b stands for 3 barrettes.
Please show the working. (Standard form)
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Answer:
12.8 light-years
Step-by-step explanation:
Multiply the distance by the conversion factor.
(1.208×10^14 km) × (1 light-year)/(9.461×10^12 km)
= (1.208/9.461)×10^(14-12) light-year ≈ 12.8 light-year
_____
Additional comment
The term "standard form" in this context is somewhat ambiguous. In some parts of the world, "standard form" is "scientific notation." In that form, the distance is 1.28×10^1 light years.
Use the equation of the line of best fit,
y = 0.94x + 7.96, to answer the questions below. X is the number of year of experience. Y is used for the hourly pay rate. Give exact answers, not rounded approximations.
(a) What is the predicted hourly pay rate for a cashier with 7 years of experience?
(b) What is the predicted hourly pay rate for a cashier who doesn't have any experience?
(C) For an increase of one year of experience, what is the predicted increase in the hourly pay rate?
Answer:
a)14.75
b)7.96
c)0.94*1+7.96
Step-by-step explanation:
If c= 16, solve for b. (Timed!!!)
Answer:
b is 8√3 ⇒ A
Step-by-step explanation:
In the given triangle
∵ The Δ is the special right triangle 30°: 60°: 90°
∴ There is a ratio between its sides
∵ a is opposite to the angle of measure 30°
∵ b is opposite to the angle of measure 60°
∵ c is opposite the angle of measure 90°
∴ a: b: c = 1: √3: 2
∵ c = 16
→ By using the ratio between its sides
→ 30°: 60°: 90°
→ 1 : √3: 2
→ a : b : 16
→ By using cross multiplication
∵ b × 2 = √3 × 16
∴ 2b = 16√3
→ Divide both sides by 2
∴ b = 8√3
help fast i’ll mark brainliest
what is the sum of this sequence 1+3+5+7+...+999
Answer:
250,000
Step-by-step explanation:
the equation of this arithmetic sequence is 1 + 2n
1 + 2n = 999
2n = 998
n = 499
[tex]\mathrm{\sum _{n=0}^{499}1+2n}[/tex] = 250,000
If c= 6, solve for a.
Answer:
A=3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
this is an isosceles right triangle, a special triangle where if hypothenuse is x,the legs are a/sqrt2
c=6
a=6/[tex]\sqrt{2}[/tex]=3[tex]\sqrt{2}[/tex]
Which graph has a rate of change of zero?
Answer:
The horizontal line
Step-by-step explanation:
Answer:
The horizontal line has a rate of change of 0, since it has a slope of 0Step-by-step explanation:
On the other hand, the vertical line has an undefined slope.
Slope is rise/run or change n y over change in x.
If the y axis coordinate never changes, then rise = 0. The only number that changes is x. x changes 1 for every 0 y changes. 0/1 = 0.
In a vertical line, however, the x coordinate is the one that doesn't change. We reverse the number from before, but we have a problem 1/0 is an undefined number since you cannot divide by 0.
Answer is second graph shown
one more than the product of 6 and a number v?
Plzzzzzz help me:(
And PLZZZ answer right
Thank u!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!:)
take like 10 secs. im just not smart
Answer:
A
Step-by-step explanation:
Answer:
B.
hope it helps...........
All of the middle-school mathletes solve math problems at the same pace. Working together, six mathletes complete all of the summer homework in 22 hours. How many hours will the homework take if the number of mathletes? PLEASE HELP
Answer:
44 hours
Step-by-step explanation:
because if its half it will take twice as long
Answer:
44 hours
Step-by-step explanation:
If you decrease the amount of participants in half, the amount of time that it takes per work load automatically doubles. So if the original amount of hours that it took with six participants is 22. If we cut six into half, then 22 hours would double into 44. Then it would become 44 hours with three people. Also, for check, I did have this problem for RSM.
a)
9 + n = 5 quel est le chiffre qui manque
Answer:
Votre réponse sera n=-4
Step-by-step explanation:
9+n=5
9-9+n=5-9 (Soustraire 9 des deux côtés)
n= -4
J'espère que cela t'aides :)
Percents
Michael is leaving a 15% tip for his waitress. What percent of the
original price will he pay? Write your answer as a percent, decimal,
and fraction.
Answer:
115%, 1.15, 115/100
Step-by-step explanation:
Please give me the correct answer
See below
Step-by-step explanation:
[tex]A = {9}^{2} = 81 \\ \\ A = {12}^{2} = 144 \\ \\ x = \sqrt{81 + 144} \\ \\ = \sqrt{225} \\ \\ = 15\\\\A = {15}^{2} = 225 [/tex]
line k goes through the points ( 8,15) and (-4,9). if line p is parallel to line k, what is the slope of line p?
Answer:
Line p will have a slope of 1/2
Step-by-step explanation:
The slope of line k is
m = ( y2-y1)/(x2-x1)
= ( 9 -15)/(-4 -8)
= -6/-12
= 1/2
If the lines are parallel, they have the same slope
Line p will have a slope of 1/2
Step-by-step explanation:
We can find the slope of a line through the formula
[tex]\frac{y1 - y2}{x1-x2}[/tex]
Where x1 and y1 are the coordinates of the first point, and x2 and y2 are the coordinates of the second point.
So we substitute the values we are given into this formula:
[tex]\frac{15-9}{8-(-4)}[/tex]
and simplify:
[tex]\frac{6}{12}[/tex]
and simplify again:
[tex]\frac{1}{2}[/tex]
And so the slope of line k is 1/2x. Since line p is parallel to line k, the slope of line p is also 1/2x.
Do y’all know the answer to this math question?
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Answer:
BC = 35
Step-by-step explanation:
The sum of the segments is the overall length.
AB +BC = AC
(2x +6) + (6x +5) = 51 . . . . substitute given values
8x +11 = 51 . . . . . . . . . . . . . collect terms
8x = 40 . . . . . . . subtract 11
x = 5 . . . . . . . . . divide by 8
BC = 6x+5 = 6(5) +5 . . . . . . . . use the value of x to find BC
BC = 35
Can someone please help me!
Answer:??? sry
Step-by-step explanation: