Answers
Hi! I'm happy to help! (sorry for the wait, my computer crashed)
A linear function is where one variable is independent (x), and another is dependent. This means that we use x to solve for y, y depends on x to be found.
To solve this, we use an equation call slope intercept form, which states that y=mx+b.
There is only 1 solution line. (to solve for how to find y, you only have to have two verifications)
For our first table, we have x as 1, 2, 3,and 4. y is 3, 6, 12, and 24.
For our first set, with x is one and y is 3, there are infinite solutions, so we have to test and see if it matches the second set of x is 2 and y is 6.
How I like to check for what m will be, I check the first two y values. The first two are 3 and 6. They have an increase of 3, so m will be 3. (this only works when x increases by 1)
With m being 3, we can solve for b, to complete the equation:
3=(3(1))+b
3=3+b
With this, b must equal 0
3=3+0
Now, we just have to check if this equation matches all of the other x values:
6=(3(2))+0
6=6+0
__________________________________
12=(3(3))+0
12=9+0
12≠9
This equation doesn't seem to work, so this is not a linear function.
For our next table, our first two y values are 2 and 5, which have a increase of 3, so our m will be 3 again.
Now, let's solve for b:
2=(3(1))+b
2=3+b
In this case, b will be -1 because 2=3-1
Now, let's check if this matches up with our other values:
5=((3)2)-1
5=6-1
_______________________________
9=((3(3)-1
9=9-1
9≠8
This equation doesn't work, so it is not a linear function.
For our next table, we have our first two y values as -3, and -5. This has a decrease of 2, so our m will be -2.
Now, let's solve for b:
-3=((-2)1)+b
-3=-2+b
In this equation, b will be -1 because -3=-2-1.
Now, let's check our other values:
-5=(-2(2))-1
-5=-4-1
___________________________________________
-7=(-2(3))-1
-7=-6-1
______________________________________________
-9=(-2(4)-1
-9=-8-1
All of these values match, so this is a linear function.
If you wanted to (you don't have to, but if you needed verification) you could check the fourth problem.
Has a decrease of 2, so m would be -2. Plug it in:
-2=(-2(1))+b
-2=-2+b
b would be 0.
Check it on the second problem:
-4=(-2(2))+0
-4=-4+0
Check the third:
-2=(-2(3))+0
-2=-6+0
-2≠-6
The fourth table doesn't match either, so it is not a linear function.
You should choose option 3 because it is a linear function.
I hope this was helpful, keep learning! :D
Related Questions
8 216 899 (nearest million)
Answers
Answer:
8 milliom
Step-by-step explanation:
its ez
The wood on the back deck of a house needs waterproofing. The shape of the deck
is a rectangle with the length of 40 feet and a width of 3 yards. A gallon can of
waterproof stain covers 50 square feet and costs $19.99 per can plus 8% sales tax.
You go to the hardware store to purchase the waterproof stain needed to complete
the job. You give the cashier $150. How much change do you receive, or how much
additional cash must you find in order to be able to pay for all of the stain you need?
You must show all calculations.
Area of Rectangle = length X width
You cannot split up a can of stain.
You must show all calculations.
Answers
Dimensions of a rectangular deck = [tex]40[/tex] feet by [tex]3[/tex] yards
Width of the deck is in yards, so convert it into feet.
Since, [tex]\frac{1}{3}[/tex] yards = 1 foot
Therefore, 1 yard = [tex]3[/tex] feet
And [tex]3[/tex] yards = [tex]3\times 3[/tex] feet
= [tex]9[/tex] feet
Therefore, dimensions of the rectangular deck = [tex]40[/tex] feet by [tex]9[/tex] feet
Area of the deck = Length × Width
= [tex]40\times 9[/tex]
= [tex]360[/tex] square feet
∵ [tex]50[/tex] square feet of deck is stained by number of cans = 1
∴ 1 square feet will be stained by number of cans = [tex]\frac{1}{50}[/tex]
∴ [tex]360[/tex] square feet will be stained by cans = [tex]\frac{360}{50}[/tex] = [tex]7.2[/tex]
We can not purchase can in fractions or parts.
Therefore, number of cans to be purchased = [tex]8[/tex]
Cost of waterproof stain per can = $[tex]19.99[/tex] plus [tex]8[/tex]% sales tax
Therefore, actual cost of 1 can to be paid for the waterproof stain
= [tex](19.99 + 19.99\times \frac{8}{100})[/tex]
= [tex]19.99+1.5992[/tex]
= $[tex]21.5892[/tex]
Cost of [tex]8[/tex] cans = [tex]21.5892\times 8[/tex]
= $[tex]172.71[/tex]
I have paid $[tex]150[/tex] to the cashier.
Therefore, additional money to be paid = [tex]172.71-150[/tex]
= $[tex]22.71[/tex]
Learn more,
https://brainly.com/question/17424783
Integral sin(3x+3)dx
Answers
Step-by-step explanation:
steps are in picture above.
Note:if you have any question please let me know.
Is 4.357216436 rational
Answers
Answer: It is a rational number.
Step-by-step explanation: Because rational numbers can also be terminating decimals.
Please help me find the value of “ find the value m
Answers
Answer:
Add those angles together. PQT is the sum of the angles PQS and SQT
3x+13+6x-2
add like terms
9x-11
angle PQT is equal to 9x-11.
Step-by-step explanation:
. If 26039 apples aré shared equally among 13 boys. How many does each boy receive?
Answers
Answer:
2003 apples for each boy
Answer:
26o39÷3 =2,003
therefore; each boy gets 2,003 apples
Jade, May and Nel are saving money in a bank account. May has saved €5 more than Jade. Nel has saved twice
as much as May. The three of them have saved €115 in total. How much did each of them save? (Assume that
Jade saved €x)
Answers
Answer:
Money saved by Jade = € 25
Money saved by May = € 30
Money saved by Nel = € 60
Step-by-step explanation:
Money saved by Jade = € x
Money saved by May = x + 5
Money saved by Nel = 2* (x + 5) = 2*x + 2*5 = 2x + 10
Total = € 115
x + x + 5 + 2x + 10 = 115
x + x + 2x + 5 + 10 = 115
Combine like terms
4x + 15 = 115
Subtract 15 from both sides
4x = 115 - 15
4x = 100
Divide both sides by 4
x = 100/4
x = € 25
Money saved by Jade = € 25
Money saved by May = 25+ 5 = € 30
Money saved by Nel = 2*25 + 10 = 50 + 10 = € 60
Answer:
Jade=€25
May=€30
Nel=€60
Step-by-step explanation:
Since Nel has 2 units, May has one and you do not know Jane but it is only €5 less, you want to plus 5 to make Jane have one unit like May, so:
115+5=120 (4 units）
120 divide 4= 30 (1 unit)
Jade=30-5=€25
May=€30
Nel=30x2=€60
Hope this helps! Thanks.
Convert 5420 into base five numeral
Answers
2x+7y=-6
4x-y=18\
show step by step how it is solved
Answers
Answer: (60/13, 6/13)
Concept:
There are three general ways to solve systems of equations:
Elimination SubstitutionGraphingHere, we are going to use elimination since all the variables are in the corresponding position.
Solve:
Given
[tex]\left \{ {{2x+7y=-6} \atop {4x - y=18}} \right.[/tex]
Multiply the first equation in order to eliminate [x]
[tex]\left \{ {{4x + 14y = -12} \atop {4x - y = 18}} \right.[/tex]
Subtract the second equation from the first equation to eliminate [x]
[tex]14y-y=-12+18[/tex]
[tex]13y=6[/tex]
Divide 13 on both sides
[tex]13y/13=6/13[/tex]
[tex]\boxed{y=\frac{6}{13} }[/tex]
Substitute [y] value in order to get [x] value
4x - y = 18
4x - 6/13 = 18
4x = 18 + 6/13
4x = 240/13
[tex]\boxed{x=\frac{60}{13} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A design for a banner includes a striped background. The stripes are colored in the repeating order: yellow, blue, orange, green, and purple. What calor is the 37th stripe?
Answers
Answer:
purple.orang.blue.yellow and green
purple.orang.blue.yellow and green
(1)
What is the interest on Rs.1880.90 for one year at simple
interest 5 1/2
%?
Answers
Formula for simple interest = total = start value x ( 1 + interest rate x time)
Total = 1880.90 x ( 1 + 0.055 x 1)
Total = 1,984.35
Interest = total - starting amount
Interest = 1984.35-1880.90 = 103.45
Interest: £103.45
Answer:
Given :-Perimeter = 1880.9
Time = 1 years
Rate = 5 (½) years
To Find :-Interest
Solution :-SI = PRT/100
5½ = 11/2 %
» SI = 1880.9 × 11 × 1/2 × 100
» SI = 1880.9 × 11/200
» SI = 103.4
Intersection of 2 lines form a
Answers
Answer:
i believe that`s called a linear pair. the opposite sides of the lines create matching angles.
Question 1
A factory has to transport raw materials to a project site. The total weight of the raw material will not be less than 1,500 tons. The factory manager plans
to use two different trucking firms, Big Red has heavy duty trucks that can transport 200 tons at a cost of $50 per truckload. Common Joe is a more
economical firm, costing only $20 per load, but its trucks can transport only 90 tons. The factory manager does not wish to spend more than $450 on
transportation. The availability of trucks is the same for both firms.
Part A
What inequality will show the number of trucks used to transport the required raw material? Replace the inequality sign with the equal sign. Go to
your math tools and open the Graph tool to graph the resulting equation and paste it into the box below. Describe which part of the graph should
be shaded and whether the line should be dashed or not.
Answers
Answer:
simple answer
Step-by-step explanation:
You work at McDonalds making $12 per hour, this week you are scheduled to work
4:30pm - 10pm Wednesday - Saturday. How much will your gross pay be for the WEEK?
(you are on the clock the entire shift)
Answers
Answer:
7$
Step-by-step explanation:
Reduce the fraction 21 /35
Answers
Answer:
3/5
Step-by-step explanation:
21/35
Divide both the top and bottom by 7
21/7 = 3
35/7 = 5
3/5
Answer:
3/5
Step-by-step explanation:
Find gcf for 21 and 35….7
Divide both by 7…. 3 and 5
Arrange 3 as numerator and 5 as denominator….3/5
Please help!
Please do not just give the answer, also explain please because I need to know how to do this.
Find the value of X
Answers
Answer:
x = 6.5
Step-by-step explanation:
In order to solve this problem, you need to use trigonometry (sin, cosine, tangent).
Sin = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Tangent = opposite/adjacent
We need to use tangent in this case because 10 is the opposite side from the 57° angle, and x is right next to it, making it adjacent. So, our equation would look like this:
tan (57)° = 10/x
Multiply both sides by x
x (tan (57)°) = 10
Divide both sides by tan (57)°
10 / tan (57)° = 6.49408 = 6.5
Step-by-step explanation:
We are given two angles measures and one side. Notice the given angle and the side that is opposite to that given angle is given. We need to find side x. But can we also find the angle opposite of the side we are trying to find. Yes we can
Remeber that triangles interior angles add up to 180.
Remeber that triangles interior angles add up to 180.One angle measure 90 and the other measure is 57 so
[tex]90 + 57 + x = 180[/tex]
[tex]x = 33[/tex]
So the angle opposite of the side we are trying to find is 33.
Since we know two angles and two sides that are opposite of those two angles respectively, we can use what is called Law of Sines
[tex] \frac{b}{ \sin(b) } = \frac{c}{ \sin(c) } [/tex]
where the numerator are the side measures, and the denominator are the angle measures.
Plug in the respectively values. Angle 57 is opposite of 10 and Angle 33 is opposite of x.
[tex] \frac{10}{ \sin(57) } = \frac{x}{ \sin(33) } [/tex]
Multiply both sides by sin 33 to isolate x.
We get
[tex]x = 6.494[/tex]
Round if needed
In other words, apply law of sines when you have two angles and two sides that are opposite of those angles respectively.
The sum of the angle measures of a quadrilateral is 360°. Write and solve an equation to find the value of x.
Answers
Answer:
x = 70
Step-by-step explanation:
The sum of the angle measures of a quadrilateral is 360°
76 + 92 + 122 + x = 360
168 + 122 + x = 360
290 + x = 360
x = 360 - 290
x = 70
You can ever CROSS-CHECK
76 + 92 + 122 + 70
290 + 70
= 360
thus cross-checked
3 If 5 is added to the difference of 3 times of 4 and 7 then find the number.
Answers
Answer: 10
Concept:
There are few vocabularies that describe each operation:
Addition: added to, the sum of, plusSubtraction: subtracted from, the difference of, minusMultiplication: multiplied with, the product of, timesDivision: divided by, the quotient of, divideRefer to the list above to answer the question
Solve:
Given worded expression
5 is added to the difference of 3 times of 4 and 7
Convert to numerical expression
3 × 4 - 7 + 5
Simplify by multiplication
=12 - 7 + 5
Simplify by addition/subtraction
=5 + 5
=[tex]\boxed{10}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
4 1/6 = 3 1/3c
WAHT?!? HOW IN THE WORLD DO YOU EVEN DO THIS?!?
Answers
Answer:
1 1/4 =c
Step-by-step explanation:
4 1/6 = 3 1/3c
Change the mixed numbers to improper numbers
4 1/6 = ( 6*4+1)/6 =25/6
3 1/3 = ( 3*3+1)/3 = 10/3
25/6 = 10/3c
Multiply each side by 3/10
25/6 * 3/10 = 10/3c * 3/10
3/6 * 25/10 = c
1/2 * 5/2 =c
5/4 =c
Change back to a mixed number
1 1/4 =c
Can someone help me please I don’t get this (due today)
Answers
Sure, I will help you.
25. Measure of MP=152 degrees.
26. Measure of QNL=208 degrees.
27. Measure of WT=155 degrees.
28. Measure of WTV=205 degrees.
I believe that these answers are correct, but if not, please let me know. If you have any questions, feel free to ask.
Please help explanation if possible
Answers
Answer:
x=-2 y=3
Step-by-step explanation:
you should multiple second equation by -5 and collect all terms then put -2 from x
PLS HELP MEEEEE I HAVW TO SUBMIT THIS SOON
Answers
Answer:
(100×m) + d
where m is the month number of your birthday
and d is the day number of your birthday
Step-by-step explanation:
[(((m × 4) + 14) × 25) - 230] + d - 120
》[((4m + 14) × 25) - 230] + d - 120
》100m + 350 - 230 -120 + d
》100m + d
what is cos 0 when sin 0 = 2/5
Answers
Answer:
cos 0 = 1
.................
350 rounded to the nearest hundred is
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{350 rounded to the nearest hundred is...}[/tex]
[tex]\huge\text{Rounding is basically is the}\\\huge\text{approximation of the given number.}[/tex]
[tex]\huge\bullet\huge\text{ So, when you are looking at 350, you are}\\\huge\text{asking yourself is it closer to 300 or 400.}\\\huge\text{If you are looking at the number correctly}\\\huge\text{you would see it is closer to \underline{\underline{400}} when you}\\\huge\text{rounded to NEAREST HUNDRED.}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your ANSWER/RESULT is: \bf 400}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
please help easy maths
Answers
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
The y intercept occurs when x = 0.
All you have to do is read the table until you come to x = 0.
When you do, read down to get the y value.
The answer is A (0,2)
[tex]\sqrt{9x^2[/tex]
Answers
Answer:
3x
Step-by-step explanation:
[tex] \sqrt{9 {x}^{2} } [/tex]
[tex] \sqrt{9} \sqrt{ {x}^{2} } [/tex]
[tex] \sqrt{ {3}^{2} } \sqrt{ {x}^{2} } [/tex]
[tex] \sqrt{ {3}^{2} } x[/tex]
[tex] = 3x[/tex]
what is the length of the diameter ?
Answers
Answer:
you can measure it in ruler
Let f(x) = -20x^2 + 14x + 12 and g(x) = 5x - 6. Find f/g and state it’s domain.
Answers
Greg can complete a landscaping job in six days and Jeff can complete the same job in four days. Working together, and how many days could they complete the job?
Answers
Answer:
2.4 days
Step-by-step explanation:
they could complete the job in :
(6×4)/(6+4) = 24/10 = 2.4 days
[tex]\\ \rm\longmapsto \dfrac{ab}{a+b}[/tex]
[tex]\\ \rm\longmapsto \dfrac{6(4)}{6+4}[/tex]
[tex]\\ \rm\longmapsto \dfrac{24}{10}[/tex]
[tex]\\ \rm\longmapsto 2.4days[/tex]
what is the value of x in the equation 11+7x=-17
Answers
[tex]\\ \rm\Rrightarrow 11+7x=-17[/tex]
[tex]\\ \rm\Rrightarrow 7x=-7-11[/tex]
[tex]\\ \rm\Rrightarrow 7x=-28[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{-28}{7}[/tex]
[tex]\\ \rm\Rrightarrow x=-4[/tex]
Answer: x = -4
Step-by-step explanation:
Given equation
11 + 7x = -17
Subtract 11 on both sides
11 + 7x - 11 = -17 - 11
7x = -28
Divide 7 on both sides
7x / 7 = -28 / 7
[tex]\boxed{x=-4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions