Part A:
To find the average rate of change, let us first write out the equation to find it.
Δy/Δx = average rate of change.
Finding average rate of change for Section A
Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5
Δx = 1- 0 = 1
Plug the numbers in: Δy/Δx = 5/1 = 5
Therefore, the average rate of change for Section A is 5.
Finding average rate of change for Section B
Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36
Δx = 3 - 2 = 1
Plug the numbers in: Δy/Δx = 36/1 = 36
Therefore, the average rate of change for Section B is 36.
Part B:
(a) How many times greater is the average rate of change of Section B than Section A?
If Section B is on the interval [2,3] and Section A is on the interval [0,1].
For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.
(b) Explain why one rate of change is greater than the other.
Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.
2y = - 3x - 6
For the function provided below, you need to solve for slope intercept form, the x intercept and the y intercept. You must show all work for credit.
The x intercept of the equation is (-2,0) , the y intercept of the equation is (0,-3) and The slope intercept form of the equation is [tex]y = -1.5x -3[/tex] .
What is slope intercept form?The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope intercept form is given as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the y-intercept.
What are intercepts?Using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0and a x-intercept or horizontal intercept is a point where the graph of a function or relation intersects the x-axis of the coordinate system. As such, these points satisfy y = 0
According to the question
The equation : [tex]2y = - 3x - 6[/tex]
The x intercept of the equation :
as a x-intercept or horizontal intercept is a point where the graph of a function or relation intersects the x-axis of the coordinate system. As such, these points satisfy y = 0 .
Therefore,
at y= 0
[tex]0 = -3x -6[/tex]
[tex]6 = -3x[/tex]
[tex]x = -2[/tex]
So,
x intercept of the equation is (-2,0)
The y intercept of the equation :
As a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.
Therefore
at x= 0
[tex]2y = -3*0 - 6[/tex]
[tex]2y = -6 \\ y = -3[/tex]
y intercept of the equation is (0,-3)
Now, The slope intercept form of the equation [tex]2y = - 3x - 6[/tex]
As slope intercept form is given as
y = mx + b
We will convert equation to standard slope intercept form
i.e
Dividing equation by 2 both side
[tex]y = -1.5x -3[/tex]
So,
m = -1.5
Hence, The x intercept of the equation is (-2,0) , the y intercept of the equation is (0,-3) and The slope intercept form of the equation is [tex]y = -1.5x -3[/tex] .
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A+b/a-b =5/3 what are the following ratios? a+b/3b
witch expression an be placed on the right side of the equal sign to form an equation 5 + 2/3 ? K12 6 grade
c-3=6
x+8=18
y-5=4
Please Show your Work For each problem.
Answer:
1. 9
2. 10
3. 9
Step-by-step explanation:
c-3=6
+3 +3
-----------
c = 9
x+8=18
-8 -8
------------
x = 10
y-5=4
+5 +5
------------
y = 9
hope this helps! :D brainliest would be very, very much appreciated!! <3
Can u help me w this
Answer:
a) 15, b) 36
Step-by-step explanation:
Answer:
a is 15, b is 6
Step-by-step explanation:
a. 5x+3=17. subtract 3 on both sides then u get 5x=14 then you simply by dividing by 5 on each side which gives you x= 14/5 = 2.5 so ..... 5x+1= 15
b. first you rearrange the terms to -3y+5=6, then you subtract 5 from each side so it's 3y = 1. then divide both of the equation by the same term ( -3) to get y= -1/3. so 5 - 3y² = ..... 3× -1/3 = -1 and -1² = -1 so 5 - (-1) = 6
Which of the following sets is equal to {1, 2, 3, ...)?
{x| xER, x>1}
{x|xER, x> or equal to 1}
{x|xEN, x> or equal to 1}
Answer:
[tex]\{x~ | ~x\in \mathbb{N}, x \geq 1\}[/tex]
Step-by-step explanation:
Let f(x)=5(3)x−4. Evaluate f(6).
Given that:
f(x) = 5(3)x-4
f(6) = 5(3)(6) - 4 ⇛15(6) - 4 ⇛90-4 ⇛86Ans.
Which is the solution to the inequality?
Y+ 15 < 3
A. y <-12
B. y >-12
C. y <18
D. y> 18
Answer: A
Step-by-step explanation:
Subtract 12 from both sides:
y + 15 - 15 < 3 - 15
Simplify:
y < -12
5. What is the correct expanded form for the number 84.76?
80 + 4 + 0.07 + 0.006
80 + 4 + 0.7 + 0.06
0 +
800 + 40 + 0.7 + 0.06
O 80 + 4 + 0.7 + 0.6
4
Answer:
80+4+0.7+0.06
There is no step by step.
An angle measures 13.8° more than the measure of its complementary angle. What is the measure of each angle?
When sum of two angles is 90°, then each of those two angles will be considered to be the complementary angle of each other.Example : 60° and 30° are two angles, and their sum is 90°. So, 60° and 30° are complementary angles.
[tex]\qquad[/tex]____________________
Explanation :-Measure of an angle is 13.8° more than the measure of it's complementary angle. We are asked to find measure of each angle!Solution :-One of the complementary angles be "x" . Then the other angle becomes " (x + 13.8)° "Sum of these two angles is equal to 90° . Since they are complementary angles.[tex] \bf{\underline{\underline{\dag According\ to\ the\ question:-}}} [/tex]
[tex]\qquad[/tex][tex] \pink{\bf\longrightarrow {x\ +\ x\ +\ 13.8°\ =\ 90⁰} }[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 2x + 13.8° = 90° [/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 2x = 90° - 13.8° [/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 2x = 76.2° [/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow x = \cancel{\dfrac{76.2°}{2}} [/tex]
[tex]\qquad[/tex][tex] \pink{\bf \longrightarrow x = 38.1° }[/tex]
Then –
[tex]\qquad[/tex][tex] \bf \longrightarrow x +13.8° [/tex]
[tex]\qquad[/tex][tex] \tt \longrightarrow 38.1° + 13.8° [/tex]
[tex]\qquad[/tex][tex] \tt \longrightarrow 51.9° [/tex]
The measures of the two given angles is 38.1° and 51.9°.[tex]\qquad[/tex]______________________
For which value of x is inequality 3(1+x)<+6true?
Answer: For in the inequality to be true, X must be less than or equal to 1. That represented as an in equality is X < 1.
x<1 true
Step-by-step explanation:
3(1+x)<+6= 3×1+3×X<+6=3+3x<6 then3x=6-3 solution 3x=3 devide by 3 both sides the answer is x=1 hence x<1 verified
Pls help I’ll brainlest ASAP
Answer:
Slope = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
rise over run = slope
slope 1/4 y-intercept 3 step by step
Graph the solution to this inequality on the number line. 1/3x−3<−1 5/6
Answer:
x < 3 1/2
Step-by-step explanation:
first solve the inequality for x
1/3 x - 3 < -1 5/6
add 3 to both sides
1/3x < 1 1/6
multiply both sides by 3
x < 3 1/2
then just graph x < 3 1/2 on a number line
Answer: Open arrow pointing left on 3.5
Step-by-step explanation: Got correct answer from test review
Multiply
(5x+y)(6x-7y)
Answer:
30x2−29xy−7y2
Step-by-step explanation:
=(5x+y)(6x+−7y)
=(5x)(6x)+(5x)(−7y)+(y)(6x)+(y)(−7y)
=30x2−35xy+6xy−7y2
=30x2−29xy−7y2
Write an equation of the line passing through (-2,1) and (3,2). Give the answer in standard form
how do i delete my answer because apparently my answer is wrong so yes i don't know how to delete it so i'm just editing it and have a good day people
Answer:
y=[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
y=m-+x so y=slope+or-y-intercept
i was doing this task in math and I came across this:
x-12x=0.88x
.
can someone plz explain why is this equal to this?
I understand it's simplified, but how?
Answer:
mx+b+a= x-12x=0.88x
Step-by-step explanation:
Solve. 9(8 - x) = 3x brainly EEE PLSS
Answer:
x=6
Step-by-step explanation:
9(8-x)=3x
9 x 8=72
72-9x=3x
72=12x
72/12=6
x=6
Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in simplest form.
64,16,4,…
This is a (geometric/arithmetic) sequence and the (common ratio/common difference) is equal to ____.
Step-by-step explanation:
this is clearly not a linear sequence (the terms don't have the same difference).
so, it has to be a geometric sequence.
the common ratio is r.
s2 = s1 × r
16 = 64 × r
r = 16/64 = 1/4
control :
s3 = s2×r
4 = 16 × 1/4 = 4
correct.
Common ratio is 1/4
What is geometric progression ?A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term. It is represented by:
a, ar, ar2, ar3, ar4, and so on.
Where a is the first term and r is the common ratio.
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 1/4
gives the next term. In other words, [tex]a_n=a_1r^n^-^1[/tex]
Hence, common ratio r = 1/4
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1) write the measurement 4009 mm into the place value table below
a) what is 4009 mm in cm
b) what is 4009 mm in m
2) how many millimeters is 6 liters
Answer:
a)400.9 cm
b)4.009 m
c) 181.71 mm
Step-by-step explanation:
a) First know that when you move from cm to mm you multiply by 10 and when you move from mm to cm you divide by 10 because 1mm= 0.1 cm
so 4009mm/10 = 400.9cm
b) when you move from m to mm you multiply by 1000 but when you move from mm to m you divide by 1000 ,so 4009/1000 = 4.009
c) 1litre= 1000000mm³
6litre= x
xlitre= 6000000 litre mm³
divide by litre
x= 6000000 mm³
but according to the question we are not looking for cubic mm but mm the fore remove cubic by insterting cube root
x= 181.71 mm
: . c)181.71 mm
Which triangle has vertices (–3, –5), (7, 4), (0, 4)?
Answer:
see attached
Step-by-step explanation:
The one that matches the triangle shown in the attachment has the given vertices.
One bridge in Maryland is 6,946 meters
long. It is 46 times as long as another
nearby bridge. How long is the shorter
bridge? Explain.
Answer:
151 meters
Step-by-step explanation:
6946/46=151 meters
Answer:
Step-by-step explanation:
If you want to be formal, let the shorter bridge = x
46x = 6946 Divide by 46
x = 6946/46
x = 151
So the shorter bridge is 151 meters long.
WILL BRAINLIST IF YOU GET CORRECT AND HURRY
A pair of linear equations is shown below: y = −3x + 5 y = x + 2 Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)
A: On a graph, find the point of intersection of two lines, the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.
B: On a graph, find the point of intersection of two lines, the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2.
C: On a graph, find the point of intersection of two lines, the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1.
D: On a graph, find the point of intersection of two lines, the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.
Answer:
answer is b
Step-by-step explanation:
please help ill mark brainliestO
Answer:
8 cm
Step-by-step explanation:
According to the condition,
[tex]\dfrac{PQ}{RS} = \dfrac{QT}{ST}\\\\\implies \dfrac{9}{3} = \dfrac{QT}{4}\\\\ \implies 3 =\dfrac{QT}{4}\\\\\implies QT = 3 \times 4 = 12~ \text{cm}\\\\\text{Hence}~ QS =QT - ST = 12 -4 = 8~ \text{cm}[/tex]
Which of the following is described below?
This object goes forever in opposite
directions. It is infinitely skinny, as it is a
set of points that are all lined up.
A. Point
B. Line
C. Ray
D. Segment
Answer:
B. line
Step-by-step explanation:
A line would fit this description best. A ray wouldnt work because it goes on infinitely in one direction. A point wouldnt work because it is a dot that marks a location, and a segment is bound by 2 points, and cannot go on forever.
The given description would be best fitting to a "line", which is the correct answer would be an option (B).
What is the line?A Line is formed by a set of points traveling in a straight line but in opposite directions. It has no breadth, no depth (curvature), and no termination, which implies 'it will not finish,' hence it moves in a straight line in opposing directions indefinitely.
This object goes forever in opposite directions. It is infinitely skinny, as it is a set of points that are all lined up.
This description would be best suited to a line.
A ray would not operate since it extends in one direction indefinitely. A point would not work since it is a dot that indicates a position, but a segment is constrained by two points and cannot continue indefinitely.
Hence, the correct answer would be an option (B).
Learn more about the Slope of the Line here:
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The sum of two numbers is 58.25. The second number is 14 less than 2 times the first number. What are the two numbers?
plz fast
Answer:
The first number is 24.08 and the second number is 34.17
Find the midpoint of Segment AB if A (-5, 6) and B(1.-3).
Midpoint Formula: (X: + X2, Y + y2)
2 2
Answer:
(-2, 1.5)
Step-by-step explanation:
x-coordinate = ½(1 - 5) = -2
y-coordinate = ½(-3 + 6) = 1.5
The American Opportunity Credit is?
Answer fast plzz... i will give brainly
Answer:
1.15 inches
Step-by-step explanation:
of the negative number, and of the
16
6 The sum of a negative number,
negative number is – 13.2. What is the negative number?
Answer:
semoga jawabannya benar
Step-by-step explanation:
Korelasi Rank Spearman digunakan untuk mencari hubungan atau untuk menguji signifikansi hipotesis asosiatif bila masing-masing variabel yang dihubungkan berbentuk Ordinal.
Answer:
179.2
Step-by-step explanation:
166 = x + -13.2
166 - -13.2 = 166 + 13.2 = 179.2
