Given:
Consider the function is:
[tex]f(x)=\dfrac{x^2}{3}[/tex]
To find:
The average rate of change over the interval 2 ≤ x ≤ 4.
Solution:
We have,
[tex]f(x)=\dfrac{x^2}{3}[/tex]
At [tex]x=2[/tex],
[tex]f(2)=\dfrac{2^2}{3}[/tex]
[tex]f(2)=\dfrac{4}{3}[/tex]
At [tex]x=4[/tex],
[tex]f(4)=\dfrac{4^2}{3}[/tex]
[tex]f(4)=\dfrac{16}{3}[/tex]
The average rate of change of a function f(x) over the interval [a,b] is:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
So, the average rate of change over the interval 2 ≤ x ≤ 4 is:
[tex]m=\dfrac{f(4)-f(2)}{4-2}[/tex]
[tex]m=\dfrac{\dfrac{16}{3}-\dfrac{4}{3}}{2}[/tex]
[tex]m=\dfrac{\dfrac{16-4}{3}}{2}[/tex]
On further simplification, we get
[tex]m=\dfrac{12}{3\times 2}[/tex]
[tex]m=\dfrac{12}{6}[/tex]
[tex]m=2[/tex]
Therefore, the average rate of change over the interval 2 ≤ x ≤ 4 is 2.
Find the 15th term in the following arithmetic sequence : 1, 6, 11, 16, ...
Hint: Write a formula to help you. 1st term + common difference(desired term - 1)
Answer:
a₁₅ = 71
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 1 and d = 6 - 1 = 5 , then
a₁₅ = 1 + (14 × 5) = 1 + 70 = 71
Step-by-step explanation:
hear is your answer in attachment
Terrific Tents has a new two-person tent. If the material costs $0.02 per square inch, find out how much it costs to make each two-person tent.
Answer:
$280
Step-by-step explanation:
Please find attached the image of the tent
cost of the tent = cost per square inch x total surface area of a triangular prism
total surface area of a triangular prism = (perimeter x height) + 2(area of a triangle)
Area of a triangle = 1/2 x base x height = 1/2 x 40 x 50 = 1000in²
1000 x 2 = 2000
Perimeter = 50 + 50 + 50 = 150
150 x 80 = 12,000
total surface area = 12,000 + 2000 = 14,000
Total cost = 14,000 x 0.02 = $280
A rectangle has a length of 2x+7 and a width of 3x+8.
Write and simplify an expression for the perimeter of that rectangle
Answer:
2(2x+7)=4x+14
2(3x+8)=6x+16
4x+14+6x+16
4x+6x+14+16
The answer is:
10x+30
What is the image of (-8,-8) after dilation by a scale factor of {1/4} centered at the origin?
Answer:
(-2, -2)
Step-by-step explanation:
To scale a factor by 1/4, you just need to divide the numbers by 4, or multiply them by 1/4.
-8/4=-2
Answer:
It would be (-2, -2)
evaluate 9!/6!3!
plz helppp:)))
Answer:
84 :-)
Step-by-step explanation:
A school survey asked students which candidate they supported for class president. the survey data are shown in the relative frequency table.
Answer:
C. 24%
Step-by-step explanation:
hope it works
Answer:
39%
Step-by-step explanation:
Quadrilateral R S T Q is shown. Angle R is 132 degrees, angle Q is 56 degrees, and angle T is 79 degrees.
What is the measure of angle S?
48o
56o
93o
101o
Answer:
C) 93o
Step-by-step explanation:
Trust the process
edge 2021
Answer:
Got a 100% on the Unit Test on Edge and 93 is the correct answer like the person above added! :D
please help!! i will help you back!!
Answer:
c = 50
Step-by-step explanation:
Using the Pythagorean Theorem:
Plug in the values of a = 14, and b = 48
[tex]a^{2} +b^{2} =c^{2}\\14^{2} +48^{2} =c^{2} \\c^{2} = 2500\\c = \sqrt{2500} \\c = 50[/tex]
What is the length of CD???
Can someone help me? It's urgent and thank you!
Answer:
15.2%
Step-by-step explanation:
There are 12 marbles in total and there are 5 red marbles, so the probability of getting a red marble is 5/12. There are now 11 marbles and there are 4 blue marbles. So the probability of getting a blue marble is 4/11.
You multiply these 2 values together.
5/12 * 4/11 = 20/132 = 0.1515
This is about 15.2%
Answer:
option b : 15.2 %
Step-by-step explanation:
5 Red , 4 Blue, 3 Yellow
Total balls = 12
[tex]Probability \ of \ choosing \ red = \frac{5C_1}{12C_1} = \frac{5}{12}\\\\Probability \ of \ choosing \ blue \ without \ replacement = \frac{4C_1}{11C_1} = \frac{4}{11}\\\\Probability \ of \ red \ and \ then \ blue = \frac{5}{12} \times \frac{4}{11} = 0.1515\\\\Probability \ in \ percentage = 0.1515 \times 100 = 15.15 = 15.2 \%[/tex]
Which of the following is acceptable justifications to use in geometry when justifying statements about segments and
angles?
A Theorems, Defintions, Postulates, Conjectures
B. Patterns, Defintions, Conjectures, Assumptions
C. Theorems, Defintions, Assumptions, Properties
D. Theorems, Defintions, Postulates, Properties
Please select the best answer from the choices provided
ОВ
оооо
ОС
Answer:
D.
Theorems, Defintions, Postulates, Properties
Step-by-step explanation:
Find the product mentally.
(r - s)^2
A) r^2 - 2 rs + s^2
B) r^2 - rs + s^2
C) 2 r^2 - rs - s^2
Step-by-step explanation:
A is the answer to the question
A) r^2 - 2rs+s^2
...............................
Which graphs present functions?
A. graph B and D
B. graph A only
C. graph D only
D. graph C and graph D
What is the measure of Rsl?
Answer:
x = 13
Step-by-step explanation:
[tex](9x + 27) = (6x + 66) \\ 9x - 6x = 66 - 27 \\ 3x = 39 \\ x = \frac{39}{3} \\ x= 13 [/tex]
Pls help ahahahhahaha
Step-by-step explanation:
x=30° { ins angle inscribed angle Standing on arc are equal }
hope it helps
stay safe healthy and happy...Help Please... 15 points :)
Answer:
√100 = 10, √36 = 6, √225 = 15
Step-by-step explanation:
100 can be made by 10^2 (10 x 10), 36 has factors of 6 and can be made by 6^2, and 225 can be made by 15^2.
[tex] \sqrt{100} = \sqrt{10 \times 10} [/tex] = [tex]\boxed{10}[/tex]
[tex] \sqrt{36} = \sqrt{6 \times 6} [/tex] = [tex]\boxed{6}[/tex]
[tex] \sqrt{225} = \sqrt{15 \times 15} [/tex] = [tex]\boxed{15}[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
what percent of 80 is 42
Answer:
52.5 percent of 80 is 42.
help please, kind of confused
Answer:
Step-by-step explanation:
Yikes. This is quite a doozy, so pay attention. We will begin by factoring by grouping. Group the first 2 terms together into a set of parenthesis, and likewise with the last 2 terms:
[tex](2d^4+6d^3)-(18d^2-54d)[/tex] and factor out what's common in each set of parenthesis:
[tex]2d^3(d+3)-18d(d+3)[/tex]. Now you can what's common is the (d + 3), so factor that out now:
[tex](d+3)(2d^3-18d)[/tex] BUT in that second set of parenthesis, we can still find things common in both terms, so we continue to factor that set of parenthesis, carrying with us the (d + 3):
[tex](d+3)2d(d^2-9)[/tex] BUT that second set of parenthesis is the difference of perfect squares, so we continue factoring, carrying with us all the other stuff we have already factored:
[tex](d+3)2d(d+3)(d-3)[/tex]. That's completely factored, but it's not completely simplified. Notice we have 2 terms that are identical: (d + 3):
[tex]2d(d+3)^2(d-3)[/tex] is the completely factored and simplified answer, choice 3)
Describe the transformation of f(x) to g(x).
(answers and graph in picture) PLSSSS HELP
Answer: b
Step-by-step explanation:
becuz now brainliest
The transformation of a function may involve any change. The correct option is A.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)Given the function of f(x) as sin(x), Now it can be seen the graph of the two functions is parallel, but the function f(x) has a y-intercept of 0, while h(x) has a y-intercept of 1. Therefore, we can write,
h(x) = f(x) + 1
The function is shifted up by 1 unit.
Hence, the transformation of the function is correctly described in the first option.
Learn more about Transforming functions:
https://brainly.com/question/17006186
#SPJ5
If y varies directly as x, and x=9 when y =15, find the value of y when x=33
Answer:
y = 55
Step-by-step explanation:
Direct variation is
y = kx where k is a constant
15 = k*9
15/9 =k
5/3 = k
The equation is y = 5/3 x
Let x = 33
y = 5/3 * 33
y = 55
there are 15 tickets in a box each bearing one of the a number from 1 to 15 one ticket is drawn at random from the box find the probability of event that the ticket drawn shows an even number and shows a number which is multiple of 5
Answer:
(i) no. of favourable out comes =7 i.e. {2,4,6,8,10,12,14}
∴ P=
15
7
(ii) no. of favourable outcomes =3 i.e {5,10,15}
∴ P=
15
3
=
5
1
Step-by-step explanation:
thats my answer thank you
Please help its due at 11 am
Answer:
maximum
Step-by-step explanation:
This graph has a maximum because the parabola faces downwards. If the parabola faced upwards, then the graph would be minimum.
Hope this helps
Answer:
Maximum so sorry if Wong
Find the value of x
Does anybody know this?
Answer:
x = 45 °
Step-by-step explanation:
We know that the sum of all angles if right angle triangle is 180 °.
90 ° + x + x = 180°
90 ° + 2 x = 180 ° ...( combine like terms)
2 x = 180 ° - 90 °.. ( subtract 90° from 180° )
2 x = 90°
x = 90° /2 ....( divide by 2 )
x = 45 °
Solve the following for y: 4x + 2y = −2 (5 points)
y = −2x + 1
y = 2x + 1
y = −2x − 1
y = 2x − 1
Answer:
Step-by-step explanation:
4x + 2y = −2
Divide by two on both sides
2x+y = -1
subtract 2x from both sides
y = -1 -2x = -2x -1
Answer:
y = -2x - 1
Step-by-step explanation:
4x + 2y = -2
→ Minus 4x from both sides
2y = -4x - 2
→ Divide both sides by 2
y = -2x - 1
Solve the following system by using substitution.
4x+2y=18
y=x+3
which following algebraic statements are true
Answer:
All of them are true.
Step-by-step explanation:
x^2 y - z / x^2 is true. x^2, when divided by itself, cancels itself out, so the equation that is left is y - z.
For the second one, a/c + b/c is true because when you add a + b = it will change; it will be added together. the remaining c will stay the same, as it is the denominator/the same, so you keep it as it is.
For the final one, you distribute ^2 to (a+b), so they become a^2 + b^2.
This means that all of the statements are true.
1, 2, 5, 9, Rule i-
what is the rule
Answer:
it is an infinite rule guiding it
Help answer pleaseeeeeee
Answer:
Your answer is C.
Step-by-step explanation:
I answered it on paper. When it comes to explaining I have to be person to person. But I hope this helps. :)
The vertex form of the equation of a parabola is y = 2(x + 4)2 - 7.
What is the standard form of the equation?
HELP FAST LOL HAHAHAH
Answer:
184
Step-by-step explanation:
First, note that the sides that are opposite to each other are congruent (this will come into play in a second). We can find the area of each triangle by doing 0.5(b)(h) (aka half * base* height). Since we've established tha opposite sides are congruent and the triangles are opposite to each other, they must be congruent. That means that the area is going to be the exact same for both triangles. So, we get the expression (0.5)(6)(4)(2), which comes out to 6*4 = 24. Then, to find the area of the 2 rectangles that are the sides, just do 5*10*2 = 100 square meters for both rectangles combines. Lastly, we need to find the area of the floor. The dimensions of the floor are 6 and 10, so we just do 6*10 = 60. Now, add all those numbers together. We get 100+60+24 = 184. Hope this helps! Let me know if anything is still confusing.
