PLEASE READ THIS EXPLANATION: It is an EXTREMELY foundational concept in algebra that must be understood. Ask questions in the comments if you do not understand anything because I love helping others learn! Do not be shy. :)
Alright, so let's just understand the problem. The interval [3,6] means that the smallest x-value is x=3 and the largest x-value is x=6, and they both INCLUDE x=3 and x=6 (It would exclude x=3 and x=6 if it was like interval (3,6) with parentheses). Since f(x) is an exponential function, the change per x is not consistent and its growth actually grows as it continues in the direction of infinity, so that is why the average rate of change is interesting and very much relies on what range there is. The average rate of change from x=3 to x=6 will be far smaller than the average rate of change farther down the road at x = 99999 and x = 100003.
So, how do we find the average rate of change? All you have to do is find the slope between two points. Simple as that.
So, how do we apply that here? Imagine a graph with two points, one point at x = 3 and one point at x = 6 and we do not know the y-value of either of these points. So, that's our first step!
We need to first find how much it grows at x=3 and x=6 separately to find the the y-value of these points. f(x) = 2^x for x = 3 means y = 8, and f(x) = 2^x for x = 6 means y = 64. We now have two points:
(3, 8) and (6, 64)
Now, all we have to do is find the slope between these lines. All we have to do is use the normal formula for finding slope:
(y₂ - y₁) / (x₂ - x₁) OR (y₁ - y₂) / (x₁ - x₂)
Most people use the first one, but they give you the exact same answer, so don't ever think it's impossible to use the second one. Let's just use the first formula anyway.
(3, 8) = (x₁, y₁)
(6, 64) = (x₂, y₂)
Now, let's use the formula (remember you can use either one because it won't affect your answer):
(y₂ - y₁) / (x₂ - x₁) = (64 - 8) / (6 - 3) = 56 / 3 = 18 and 2/3
So, the average rate of change is 18 and 2/3 or 18.666666667.
solve each of the following equations show solution set on a number line 3x-1=8
Answer:
x=3
Step-by-step explanation:
here u go!!! :)
answer
Algunos estudiantes se repartieron una bolsa de galletas. Todos tomaron la misma cantidad y sobraron 5
Which of the following expressions is a factor of 2x2 – 112 + 15?
Answer:
Step-by-step explanation:
where are the expressions?
a spinner has 8 equal sections,6 are green .find probability that will land on green
Answer:
P(A) and P(B) = P(A) x P(B)
P(A) = number gray/total number of sections = 6/8 = 3/4
P(B) = number of reggae songs/total number of songs = 2/8 = 1/4
P(A) and P(B) = (3/4)(1/4) = 3/16
Step-by-step explanation:
Answer: 3/4 (0.75)
Step-by-step explanation:
6 out of 8 sections are green.
So there is a 6/8 probability that it will land on green.
6/8 = 3/4.
Can someone please help me
Answer:
19.0 cm
Step-by-step explanation:
a^2+b^2=c^2
1^2+b^2=19^2
1+b^2=361
(subtract one from both sides)
b^2=360
(now square root to get rid of the ^2)
[tex]\sqrt{b^2}[/tex]=[tex]\sqrt{360}[/tex]
b=18.97 rounded to the tenths place is 19.0
Answer:
The length of the other leg is 19 cm (rounded to the nearest tenth).
Step-by-step explanation:
In order to solve this, we need to know the Pythagoras theorem which states that...
[tex]c^{2} = a^{2} +b^{2}[/tex] (Where c is the length of the hypotenuse and a and b are the lengths of the legs)
Now just substitute the values to find the length of the other leg, and we get...
[tex]c^{2} = a^{2} +b^{2}\\19^{2} = 1^{2} + b^{2} \\b^{2} = 19^{2} - 1^{2} \\b^{2} = 361 - 1\\b^{2} = 360\\b = \sqrt{360} \\[/tex]
b ≅ 19
Therefore the length of the other leg is around 19 cm.
Find the volume of the clinder in the terms of π
Answer:
A) 127.16π m³
Step-by-step explanation:
Volume of a cylinder:
V = πr²h
Given:
r = 3.4
h = 11
Work:
V = πr²h
V = π(3.4²)(11)
V = π(11.56)(11)
V = 127.16π
Answer:
hey bestie, its 127.16
Step-by-step explanation:
3.4 squared is 11.56
and 11.56 times 11 is 127.16
I need help with this elimination problem
Add up the same sides of both equations to eliminate x :
(x - 2y) + (-x + 3y) = 8 + (-5)
(x - x) + (-2y + 3y) = 8 - 5
y = 3
Then
x - 2y = x - 6 = 8 → x = 14
If a quadrilateral has exactly one pair of congruent, opposite angles, then the quadrilateral is a ______
help me please!:(
this is geometry
Answer:
23.9cm^3
Step-by-step explanation:
[tex]\sqrt{176[/tex]
Answer:
13.2664991614
Step-by-step explanation:
Answer: 13.2664991614
hope this helps <3
Identify the terms and coefficients of each expression.
7 + 8p - 2^r
terms:
coefficient:
g^2- 14h + 10
terms:
coefficients :
Find the radius of a sphere with a volume of 180 cubic feet. Round your answer to the nearest tenth.
Answer:
3.50ft
Step-by-step explanation:
Given data
Volume= 180ft^3
The expression for the volume of a sphere is given as
Volume=4/3πr^3
substitute
180=4/3*3.142*r^3
180=12.568/3*r^3
180=4.189*r^3
r^3= 180/4.189
r^3= 42.969
cube root both sides
r= ∛ 42.969
r= 3.50ft
Hence the radius is 3.50ft
What is the value of x?
A. 30
B. 42
C. 39
D. 85
Answer:
39
Step-by-step explanation:
102 + 39 + x = 180
180 - 141 = 39
39 is x
Hope this helps!
Find the indicated measure. Round answers to the nearest hundredth.
On a farm, the farmer decides to give pizza to her 18 ducks as a special treat. She orders 3 pizzas, and the total price is $26.28. What is the unit price of each pizza?
$4.38
$8.76
$23.28
$78.84
Answer:
$8.76
Step-by-step explanation:
$26.28 / 3 = $8.76 per pizza
Find the surface area of this prism. Please help 20 points!!!!!
Answer:
ima say 260. .................
Answer:
umm 247
Step-by-step explanation:
helppppppppp id.k this
Answer:
-432 ,-2 ,2 ,72
Step-by-step explanation:
The Answer Is 2,592
This is because this is a geometric sequence, every number is multiplied by -6 to find the next number in the sequence.
Solve for x LT1 10th grade level
Answer:
x = 5
Step-by-step explanation:
Because the red-marked lines are parallel, we know that the ratios are the same
5x : 45 = 20 : 36
5x/45 = 20/36
5x * 36 = 20 * 45
5x * 4 = 20 * 5
5x * 1 = 5 * 5
x = 5
plsssss helppp sooonnnn
Answer:
4 and -6≤x<0
Step-by-step explanation:
6. 4
7. -6≤x<0
Fig. A shows a paper cup in the shape of an inverted right circular cone. Its base radius is 4 cm and its slant height is 8.5 cm.
(a) Find the capacity of the paper cup.
(b) The paper cup is cut along PQ to form the sector in Fig. B. Find
(i) the area of the sector,
(ii) the angle of the sector.
(a)
Height of the cup
= [tex]\sqrt{ {8.5}^{2} - {4}^{2} }[/tex]
= 7.5 cm
The capacity of the cup
= [tex] \frac{1}{3} \times \pi \times {4}^{2} \times 7.5[/tex]
= 126 cm³ (cor. to 3 sig. fig.)
(b)(i)
The area of the sector
= [tex]\pi \times 4 \times 8.5[/tex]
= 107 cm² (cor. to 3 sig. fig.)
Can you help me for (b)(ii)?
9514 1404 393
Answer:
16π/17 radians ≈ 169.41°
Step-by-step explanation:
The arc length of the sector is the circumference of the cone:
C = 2πr = 2π(4 cm) = 8π cm
The angle and arc length are related by ...
s = rθ . . . . . θ in radians
8π cm = (8.5 cm)θ
θ = 8π/8.5 = 16π/17 . . . . radians
bii) The angle of the sector is 16π/17 radians ≈ 169.41°.
Answer:
169° (3sf)
Step-by-step explanation:
the area of a circle multiplied by the angle over 360 gives you ans.
x/360 × π × r²=34π -> ur ans frm part i
x × π(8.5²)=12240π
x × 72.25=12240
x=169.41°
3, 6, 9, 10, 10, 11
What is the range of the data?
What is the second quartile Q2 (or what is the median)?
What is the interquartile range? (Q1-13)
Answer:
Range : 8
Q2: 9.5
Interquartile range is 2.5
factorise x squared - 3x
Answer:
x squared -3× =x(x-3)
Step-by-step explanation:
Since the common factor is x,one comes out to multiply the other to give it x squared and since one x has been written outside already we just write the 3 so that when we multiply it we will get the answer we were asked to factorise
Determine if the number when converted to a decimal will result in a repeating or terminating decimal
5 divided by 10
what is the definition of an expression
Answer:
the process of making known one's thoughts or feelings.
Step-by-step explanation:
Next time you ask a question please tell us if it's in a math term or something, I did it in the Ela/reading term.
the process of making known one's thoughts or feelings.
For example, if you make someone laugh their expression would be happy or suprised. Expression is just a way of seeing someones thoughts and feelings.
Hope this helps!
Have a great day!
- Hailey: )
Please please please help me
Answer:
D. 17
Step-by-step explanation:
1. Set up an equation (2x + 5) + (3x + 10) = 100
2. 2x + 3x= 5x and 5 + 10 = 15
3. The equation simplified 5x + 15 = 100
4. Move the 15 to the other side of the equation. 5x = 100 - 15
5. 5x = 85
6. Finally, divide 85/5
7. Our final answer is 17.
What is the measure of the third angle
Answer:
43
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given two angles: 47 and 90
Do 180 minus 47 + 90 to get the third angle
[tex]x = 180 - (47 +90)\\x = 180 - 137\\x = 43[/tex]
The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
Find the slope of the line, and complete the sentences below.
100-meter Race
ty
100
80
Distance (m)
60
40
20
0
0
2
10
4 6 8
Time (s)
The slope of the line is Choose..
The slope represents
Choose.
Answer:
l
Step-by-step explanation:
Describe the properties of equality that Kira used. The first step is to use the property of equality to combine the constant terms. The second step is to use the property of equality to isolate the variable.
Answer:
1. Subtraction property
2. Division property
Step-by-step explanation:
Question has missing details.
Kira's steps are:
[tex]\frac{7}{2} - 2x = \frac{11}{2}[/tex]
[tex]\frac{7}{2}- \frac{7}{2} - 2x = \frac{11}{2}- \frac{7}{2}[/tex]
[tex]- 2x \div -2= \frac{4}{2} \div -2[/tex]
[tex]x = -1[/tex]
Required
The properties used
For the first step, we have:
[tex]\frac{7}{2} - 2x = \frac{11}{2}[/tex]
To get to step 2, Kira subtracted [tex]\frac{7}{2}[/tex] from both sides.
i.e.
[tex]\frac{7}{2}- \frac{7}{2} - 2x = \frac{11}{2}- \frac{7}{2}[/tex]
This property is subtraction property
In the second step, where x is isolated.
[tex]- 2x \div -2= \frac{4}{2} \div -2[/tex]
Both sides of the equation were divided by -2 to give:
[tex]x = -1[/tex]
This property is division property
Answer:
person above correct
what is the sum of the following equation? 8/10+60/10=
Answer:
as a mixed number it's 6 4/5
Answer:
6.8
[tex]6\frac{4}{5}[/tex]
Step-by-step explanation:
Select all the expressions that are equivalent to x2+4x. (^2 means raising something to the 2nd power.)
Answer:
(x+4)x
Step-by-step explanation:
The factor of the expression into an equivalent form x² + 4x would be; x(x + 4)
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To derive equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.
We need to factor the expression into an equivalent form x² + 4x
This expression could also be given by;
x² + 4x
Then factor out x we get;
x² + 4x = x(x + 4)
Hence, the expression into an equivalent form x² + 4x would be; x(x + 4)
Learn more about expression here;
brainly.com/question/14083225
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