Determine if the following table represents a linear function. If so, what’s the rate of change?
The values in the table represent a linear function.
The correct option is; Yes; The rate of change = 3/2
What is a linear function?A linear function is a function forms a straight line when plotted on the coordinate plane.
The values in the table represent a linear function, where we get;
The first difference is constant
The subsequent x-values increase by the same value
The increase the subsequent x-values is; 4 - 2 = 6 - 4 = 8 - 6 = 2, which is a constant
The first difference in the y-values is; 6 - 3 = 9 - 6 = 12 - 9 = 3
The first difference is a constant, 3, therefore, the values in the table represent a linear function.
The slope or rate of change is the ratio of the first difference to the difference in subsequent x-value, therefore;
The rate of change = 3/2
The correct option is therefore; Yes, rate of change = 3/2
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(x+7)+3y simply I need help plsssss
Answer:
move 7
Step-by-step explanation:
x + 3 y + 7
Plot the graph of the linear equation. 3x-2y=6
Answer:
First point : (0, -3)
Second point : (2, 0)
Y-intercept : -3
Step-by-step explanation:
To tackle a question like this, the first thing you want to do is put the equation into y = mx + b form.
1.) 3x - 2y = 6
2.) -2y = -3x + 6 (bring 3x to the other side, using inverse operations)
3.) y = 1.5x - 3 (divide -2 on both sides, to isolate the variable y)
Now that you have the y-intercept (-3), you have your y value. Finally, just substitute the variable y from the original equation to solve for the x value.
1.) 3x - 2(-3) = 6
2.) 3x + 6 = 6 (multiply (-2) and (-3))
3.)3x = 0 (subtract 6 on both sides using inverse operations)
4.) x = 0
Now you have your first point which is (0, -3)!
To get your last point, just substitute your y coordinate from the original equation to get x.
1.) 3x - 2(0) = 6
2.) 3x - 0 = 6
3.) 3x = 6
4.) x = 2
Then, substitute the x coordinate from above in the original equation to get the y coordinate.
1.) 3(2) - 2y = 6
2.) 6 - 2y = 6
3.) -2y = 0
4.) y = 0
Second coordinate : (2, 0)
I hope this explanation was helpful!
Write an integer to represent spending $50
The integer that represents spending $50 is -50
Let U be the set of whole numbers from 5-10 inclusive. Set A= {5, 7, 9}, Set B = {5, 8, 10}. AU~B <---------
Answer:
Suppose the universal set is U = all whole numbers from 1 to 9. If A = {1, 2, 4}, then Ac = {3, 5, 6, 7, 8, 9}. As we saw earlier with the expression Ac ...
Let U be the set of whole numbers from 5-10 inclusive. Set A={5, 7, 9 ...
Two of the dozen eggs in a carton
are cracked. About what percent of the
carton is cracked?
Answer:
17%
Step-by-step explanation:
2/12 or the eggs are cracked. That means 1/6 of the eggs are cracked.
1/6 approximately equals 0.167
So, it is approximately 16.7%, or if you round it up, 17%.
Answer:
16.67 %
Step-by-step explanation:
two of a dozen is 2/12 simplified is 1/6 and 1/6 in a percentage is 16.67%
Write the expression using exponents. g⋅g⋅g⋅g⋅g
please answer this, i am so confused
The bag of dog food would last for 21 days.
The bag contains 42 cups of dog food. If the dog eats [tex]2\frac{1}{3}[/tex] cups everyday, the amount of cup in the bag decreases by [tex]2\frac{1}{3}[/tex] cups everyday. This can be represented with this expression: 42 - [tex]2\frac{1}{3}[/tex]d. Where d represents the number of days.
In order to determine the number of days in which the bag would be emptied, this equation can be used:
Number of days the dog food would last = number of cups in the cup / amount the dog eats each day
42 ÷ [tex]2\frac{1}{3}[/tex]
42 ÷ [tex]\frac{7}{3}[/tex]
42 x [tex]\frac{3}{7}[/tex] = 21 days
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225 people must be split into 9 equal groups how many people in each group
Answer:
25
Step-by-step explanation:
division
Answer:
If 225 people are split into 9 equal groups each group will have 25 members in it
PLEASE HELP look at this screenshot is it a, b, c, or d
Answer:
D.
Step-by-step explanation:
e
LJKHLJU;KL['KLO'KOIOYUOYU
Answer:
what is your question all I see is numbers and shapes
Find the graphed solution to the inequality. 3(x-9) < -18
Closed or open, left or right?
Answer:
open left
Step-by-step explanation:
We can distribute the left side to get [tex]3x-27<-18[/tex].
We can then add [tex]27[/tex] to both sides of the equation to get [tex]3x<9[/tex].
We can finally divide both sides of the equation to get [tex]x<3[/tex].
Because it's a [tex]<[/tex] and not a [tex]<=[/tex], it is closed. And because the inequality opens to the right, it faces to the left.
So, it is a open left graph.
Hey ! Can anyone help me with this question please ? Thank you
Answer:
x = 102°
Step-by-step explanation:
a straight line = 180°
180 - 78° = 102°
Answer:
x°+78°=180°[supplementry angle]
x°=180°-78°
x°=102°
answer
o differences between constructing an inscribed regular hexagon and constructing an inscribed square.
Answer:
a daddy
Step-by-step explanation:
Question 6(Multiple Choice Worth 1 points)
(05.03 LC)
What is the initial value of the equation shown?
y = -4x - 3
O-4
O-3
03
04
9514 1404 393
Answer:
(b) -3
Step-by-step explanation:
The "initial value" is the constant in the equation. It is the value that remains when the x-term is removed. It is the result of evaluating the equation when x=0.
y = -4(0) -3 . . . . substitute x=0
y = 0 -3
y = -3 . . . . the "initial value"
Calculus, derivatives. Please help! Show work, if possible. Thanks! :)
Answer:
a. y=4
b. graph the given and y=4
Step-by-step explanation:
The given is y= 8 sin(x) cos(x)
to get y' which is the slope of the tangent line we take the derivative
for this problem, the derivative involves the constant rule (which states that the derivative a constant times a value is just the constant times the derivative of said value) and the multiplication rule (assuming that the two parts in question are represented by the variables a and b then the derivative of a*b = a*b'+b*a')
thus we get 8*(sin(x)*-sin(x)+cos(x)*cos(x))
-8sin^2(x)+8cos^2(x)
You can also leave the 8 differentiated out depending on the form you need.
Now that we have the derivative we can plug pi/4 into this equation to get the slope of the tangent line at that point
=8sin^2(pi/4)+8cos^2(pi/4)
this would equal -8*1/2 +8*1/2 which equals 0
the slope of the tangent at this point would be zero
To get the point for point slope form we plug the pi/4 into the given equation to get a y value and get the point (pi/4, 4)
this means the point slope equation would be
y-4=0(x-pi/4)
y-4=0
y=4
To graph you would just enter the given equation and the equation for the tangent line into a graphing software or calculator and see if the line is tangent at the point (pi/4, 4)
what percent of 60 is 15? Please help 10points
25% of 60 is 15
If divide 15 by 60 we find that it is eqyivalent to the ratio of 1/4. 1/4 is the same as 25%.
Answer:
25%
Step-by-step explanation:
25% means one fourth. 15 is exactly 1/4, or 25% of 60.
Hope it helps you! :)
[tex]GraceRosalia[/tex]
HELPPPPPPPPPPP. please explain how u got the answer
Step-by-step explanation:
the key is x = 0.
also I see in the first table no "run-away" effect of some values, so my first suspicion is : it is linear.
let's test it.
a linear function is a line :
y = ax + b
remember, x = 0 is a key element.
y = a×0 + b
-3 = a×0 + b
-3 = b
so, we know, the line function is
y = ax - 3
now, for the a. let's use the next xy pair (1, 1).
1 = a×1 - 3
4 = a
aha ! our line function is therefore
y = 4x - 3
verify with the next 2 points (2, 5) and (3, 9)
5 = 4×2 - 3 = 5 correct
9 = 4×3 - 3 = 9 correct
linear type and equation confirmed.
the second table :
yes, we see relatively big y values compared to the x values.
and the y values follow the powers of 2
so it seems to to be exponential.
64 = 2⁶
32 = 2⁵
16 = 2⁴
8 = 2³
so, while x increases, the powers of 2 decrease. so, we must build something like y = 2^x, but it must run contrary to the increase in x.
the old trick : c-x.
again, x= 0 is key. when x = 0 we get the biggest y (64). that means that gives us c.
64 = 2^(c-x) = 2^(c-0) = 2^c = 2⁶
=> c = 6
so, we suspect the exponential function
y = 2^(6-x)
let's verify with the other points
(1, 32)
32 = 2^(6-1) = 2^(5) = 32 correct
(2, 16)
16 = 2^(6-2) = 2^(4) = 16 correct
(3, 8)
8 = 2^(6-3) = 2^(3) = 8 correct
so, yes, it is the exponential function
y = 2^(6-x)
Solve the following for x:
4x + y = z
a.x = z - y - 4
b.x = z/4
c.x = z-y/4
d.x = z+y/4
Explain
Answer:
[tex]x = \frac{1}{4} z - \frac{1}{4} y[/tex]
Step-by-step explanation:
4x + y = z
4x = z - y
x = 1/4z - 1/4y
The length of a rectangle is one more than twice its width. If the perimeter of the rectangle is 134
centimeters, find its length.
Answer: We can set up the formula: 2L +2W = 110. We can also set up length as 2x+1 and width as x so plug this in: 2 (2x+1)+2x=110. Expanded to: 4x+2+2x=110. Rewritten as: 6x=108.
Step-by-step explanation:
I need help on this I've been struggling to solve
Answer:
ok
Step-by-step explanation:
Evaluate.
(a−2b)3 when a=−3 and b=−1/2
Enter your answer in the box.
Answer:
[tex]-3.5[/tex]
Step-by-step explanation:
[tex](a-2b)^{3} \\=a^{3}-6a^{2} b+6ab^{2}-8b^{3}[/tex]
Given that,
[tex]a=(-3)\\b=(-1/2)[/tex]
So,
[tex](a-2b)^{3} \\=a^{3}-6a^{2} b+6ab^{2}-8b^{3}\\=(-3)^{3}-6* (-3)^{2} *\frac{-1}{2} +6*(-3)*(\frac{-1}{2} )^{2} -8*(\frac{-1}{2} )^{3} \\= (-27)-6*9*\frac{-1}{2} +-18*\frac{1}{4} -8*\frac{-1}{8} \\=(-27)-6*-4.5-4.5+1\\=-27+27-4.5+1\\=-3.5[/tex]
Hope this helps you
Let me know if you have any other questions :-)
Hayden has 7 shells . Elly has 5 fewer shells than Hayden . Beth has 2 shells . How many shells do they have in all?
Answer:
11 i think
Step-by-step explanation:
Which of the following is an equation of the line In the graph? A.3x-y=4 B.3x+y=4 C.-3x-y=4 D.-3x+y=4m
9514 1404 393
Answer:
B. 3x+y=4
Step-by-step explanation:
The constant on the right is positive, so the signs of the coefficients match the signs of the respective intercepts. The graph shows both x- and y-intercepts are positive, so the equation will have positive coefficients everywhere. The appropriate choice is ...
3x +y = 4
Help please 6th grade math
Answer:
Step-by-step explanation:
-1
a) 6 * (-3)
b) (-5) x4
c) (-9) * (-2)
Answer:
A:-18
B:-20
C:18
Step-by-step explanation:
if i sell 329 ham sandwiches this week how many ham sandwiches did i sell each day this week.
Answer:
you would have sold 47 ham sandwiches each day of the weed
Answer:
Your answer would be 47 ham sandwiches.
Step-by-step explanation:
It is very simple you would just do 329/7=47
Find the gradient of the line
3y + 2x = 1
how to guys
Answer:
-2/3
Step-by-step explanation:
The gradient of a line is its slope. You can just convert the equation to slope-intercept form (y=mx+b where "m" is the gradient/slope):
3y + 2x = 1
3y = 1 - 2x
y = 1/3 - 2/3x
y = -2/3x + 1/3
So, as we can see, -2/3 is the gradient/slope of the line.
Use a variation model to solve for the unknown value.
Answer:
x+y=12
Step-by-step explanation:
a teacher has 7 pack of 12 pencils and 2 packs of 54 pencils.the teacher shares these pencils out into 8 pencil pot.how many pencils with be in each pot?
Answer:
24
Step-by-step explanation: