The average rates of change of a function f(x) and g(x) are their slopes
The average rate of change of the function f(x) is always less than the average rate of change of the function g(x)
How to determine the average rate of change?The average rate of change of a function f(x) over the interval [a,b] is calculated as:
[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]
The average rates of change of the functions over the intervals are:
A. 0 ≤ x ≤ 3
[tex]m_1 = \frac{f(3) - f(0)}{3 - 0} = \frac{5 * 3 - 5 *0}{3 - 0} = 5[/tex] ---- f(x)
[tex]m_2 = \frac{g(3) - g(0)}{3 - 0} = \frac{25 * 3 - 25 *0}{3 - 0} = 25[/tex] --- g(x)
B. 0 ≤ x ≤ 2
[tex]m_1 = \frac{f(2) - f(0)}{2 - 0} = \frac{5 * 2 - 5 *0}{2 - 0} = 5[/tex] ---- f(x)
[tex]m_2 = \frac{g(2) - g(0)}{2 - 0} = \frac{25 * 2 - 25 *0}{2 - 0} = 25[/tex] --- g(x)
C. 3 ≤ x ≤ 6
[tex]m_1 = \frac{f(6) - f(3)}{6 - 3} = \frac{5 * 6 - 5 *3}{6 - 3} = 5[/tex] ---- f(x)
[tex]m_2 = \frac{g(6) - g(3)}{6 - 3} = \frac{25 * 6 - 25 *3}{6 - 3} = 25[/tex] --- g(x)
D. 1 ≤ x ≤ 2
[tex]m_1 = \frac{f(2) - f(1)}{2 - 1} = \frac{5 * 2 - 5 *1}{2 - 1} = 5[/tex] ---- f(x)
[tex]m_2 = \frac{g(2) - g(1)}{2 - 1} = \frac{25 * 2 - 25 *1}{2 - 1} = 25[/tex] --- g(x)
From the above computation, we can see that:
The average rate of change of the function f(x) = 5x is always less than the average rate of change of the function g(x) = 25x
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4x + y = 10
7x + 2y = 17
Answer:
x = 3, y = - 2
Step-by-step explanation:
By substitution method,
4x + y = 10 -------> equation 1.
7x + 2y = 17 -------> equation 2.
From equation 1,
y = 10 - 4x ------> equation 3.
Substitute equation 3 in 2,
7x + 2 ( 10 - 4x ) = 17
7x + 20 - 8x = 17
7x - 8x = 17 - 20
- x = - 3
x = 3
Substitute x = 3 in equation 1,
4 ( 3 ) + y = 10
12 + y = 10
y = 10 - 12
y = - 2
Hence,
x = 3
y = - 2
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pa brainliest kung ayaw, edi wag** char
Samir recorded the number of different types of pets his friends have in the table shown below:
Cats 2
Dogs 4
Rabbits 1
Guinea Pigs 4
Which of the following plots represents the data in the table?
How many triangles can be constructed with side lengths of 1. 8 cm, 3. 4 cm, and 5. 6 cm?
0
1
more than one
please explain your answer
Answer:
0.
Step-by-step explanation:
1.8 + 3.4 = 5.2.
The sum of two sides is less than the length of the third side (5.6 cm) so the answer is 0 triangles,
Can someone help me please
Answer:
The Area of the shaded region :
(x²)(4x-1) - (5x)(x+7) =
4x³ - x² - 5x² - 35x =
4x³ - 6x² - 35x
I NEEED HELLPPP write this using exponents question
Answer:
D. [tex](-2)^6[/tex]
Step-by-step explanation:
There are six (-2), so it would be D. since C. would just mean [tex]2^6[/tex] and turn that negative.
You can check using a calculator that (-2)(-2)(-2)(-2)(-2)(-2) would equal 64 while C. equals -64. So the correct answer would be D.
A scale says that it's readings are accurate to within 1%, meaning that when an object
is weighed using that scale, the reading will have an error of at most 1%.
Gillian puts a math textbook on a scale, and the scale reads 1,999.8 grams. What is
the difference between the maximum and minimum possible values for the textbook's
actual weight?
Answer:
Step-by-step explanation:
well, 1% of 1999.8=19.998, so it would be + - 1,999.99
Nine wolves, eight female and one male, are to be released into the wild three at a time. If the male wolf is to be in the first released group and order does not matter, in how many ways can the first group of three wolves be formed? 28 ways 36 ways 56 ways 84 ways.
The first group of three wolves can be formed in 28 ways.
We have been given that Nine wolves, eight female and one male, are to be released into the wild three at a time.
What is the meaning of combination?
A combination is a combination of n things taken k at a time without repetition.
We need to choose 1 male wolf out of 1 wolf male. So we can choose one wolf as
[tex]c(1,1)=\frac{1!}{1!(1-1)!} =\frac{1!}{1!}=1!=1[/tex]
We can choose 1 male wolf in only 1 way.
Since the female wolfs are identical that means order doesn't matter, so we will use combinations.
We can choose 2 female wolves out of 8 as
[tex]C(8,2)=\frac{8!}{2!(8-2)!} =\frac{8\times 7 \times 6!}{2\times 1\times 6!} =\frac{8\times 7}{2} =28[/tex]
Therefore, we can choose 2 female wolves out of 8 female wolves in 28 ways.
We have to find number of ways in which the first group of three wolves can be formed we will multiply the ways of choosing 1 male wolf and 2 female wolves.
Number of ways farming first group of three wolves
1(28)=28
Therefore, the first group of three wolves can be formed in 28 ways
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What is the measure of < L
Answer:
C.
Step-by-step explanation:
Because of the K And j = K and L.Those are equal of the length.
And also, I believed the angel of K is 130 degrees ...
I hope it can help you a lots...Thanks.
Answer:
C
Step-by-step explanation:
typical property of isoceles triangle
properties:
1.- Base angles are equal
2. has two sides equal
☆the two above are key to identifying an isoceles triangle
the one above satisfies no.2
brainliest please
how do i use a model to tell whether the fractions are equivalent? numbers: 1/2 and 5/10 grade 4
Answer:
ok so 5/10ths is also 3/6ths or 2/4ths or 1/2
Step-by-step explanation:
A consumer agency wants to determine which of two laundry detergents, A or B, cleans better. Fifty 1-square-foot sections of fabric are randomly selected and cut from different bolts of fabric. They are then subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale of 1–10, with 1 being the least clean to 10 being the most clean. The mean rating for detergent A is found to be significantly greater than the mean rating for detergent B.
Which of the following is a valid conclusion?
Inferences can be made about the population of fabric from which the pieces were cut. The conclusion can be made that detergent A cleans better than detergent B for the fabric from these bolts.
Inferences cannot be made about the population of fabric from which the pieces were cut. The conclusion can be made that detergent A cleans better than detergent B for the fabric from these bolts.
Inferences can be made about the population of fabric from which the pieces were cut. The conclusion cannot be made that detergent A cleans better than detergent B for the fabric from these bolts.
Inferences cannot be made about the population of fabric from which the pieces were chosen. The conclusion cannot be made that detergent A cleans better than detergent B for the fabric from these bolts.
The conclusion about the detergents in the sampling is D.Inferences cannot be made about the population of fabric from which the pieces were chosen.
What is sampling?Sampling is the selection of a subset of individuals that are gotten from a statistical population in order to estimate the characteristics of the whole population.
In this case, inferences cannot be made about the population of fabric from which the pieces were chosen. The conclusion cannot be made that detergent A cleans better than detergent B for the fabric from these bolts.
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What is the following product?
30. 10
2.110
3.10
4./10
10/5
Step-by-step explanation:
300220302/5=0.42Hope it helps you
Solve for e:2e-13+8=135
Answer:
e = 70
Step-by-step explanation:
2e - 13 + 8 = 135
2e - 5 = 135
2e = 135 + 5
2e = 140
divide both sides by 2
e = 70
Mark and Henry win some money and share it in the ratio 1:3. Mark gets £9. How much did Henry get?
Answer:
£27
Step-by-step explanation:
1:3 = M:H
Mark gets £9
1 = £9
3: £9 x 3 = £27
Answer: the answer is £27
Step-by-step explanation: it is related to ratio if mark gets 9 so 9 times 3 . Equals to 27 . You can make criss cross way . 1 won't make the answer different. Hope it helps
bro no one is helping??
Answer:
A-6 , B-19 , C-55 , D-119 , E-70
Step-by-step explanation:
Subtract 68 from 138 to find out how many 8th graders in total, and that will get you blank E.
Subtract 64 from 70 (E) to find out blank A.
Add 6 and 13 get the total for TV, blank B.
To get blank C, you need to subtract 13 from 68.
For the last blank, blank D, you need to add 55 (blank C) and 64, which will give you 119.
32 The area of a parallelogram is (32 + sqrt(2)) square feetIf the length of the base is (4 + sqrt(2)) feet, find the height of the parallelogram in simplest radical form
The height of the parallelogram that has an area of (32 + √2) ft² and base of (4+√2) ft is 9(7 + 2√2) / 7 ft
How to calculate area of a parallelogram?area of parallelogram = bh
where
b = baseh = heightTherefore,
area = (32 + √2) ft²
base = (4+√2) ft
Therefore,
area of a parallelogram = bh
(32 + √2) = (4+√2)h
divide both sides by (4+√2)
h = (32 + √2) / (4+√2)
h = (32 + √2) / (4+√2) × (4-√2) / (4-√2)
h = (32 + √2) (4-√2) / 16 - 4√2 + 4√2 - 2
h = 128 + 32√2 + 4√2 - 2 / 14
h = 126 + 36√2 / 14 ft
h = 18(7 + 2√2) / 14 ft
h = 9(7 + 2√2) / 7 ft
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What is the displacement current between the plates if the separation of the plates is r and they have an area of a?
A displacement current simply means the limited shift of electric components which occur when the voltage is applied to the capacitor.
What is displacement current?Your information is incomplete. Therefore, an overview of the displacement current will be given.
A displacement current simply defines the terms of the rate of change of the electric displacement field.
It's the current due to the changing of the electric field that is inside the plate of the capacitor.
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Sally needs to wrap a birthday gift. The gift has a length of 15 in, a width of 13 in,
and a height of 9in. Use the Surface Area formula for a Rectangular Prism to figure
out how much wrapping paper Sally will need to wrap the gift. Write a paragraph,
using the RACE format, explaining how you got your answer.
Answer:
849in 2
Step-by-step explanation:
sally needs to wrap a birthday gift.
the surface area of the gift is 894 in 2.
the formula for surface area of a rectangular prism is S = 2(lw + lh + wh).
to use the formula . i added (lw + lh+ wh) then multiplied it by 2 . so sally will need 894in2 of wrapping paper for the gift.
9 markers cost $7. 50. How much would 7 markers cost
Answer:
5.83
Step-by-step explanation:
9 / 7.50 = 0.833(repeating)
8.33(repeating) * 7 = 5.833(repeating)
Simplify 5.833(repeating)
Answer:
5.83
Step-by-step explanation:
Given the equation 47=38+n, tell which value is a solution from the solution set n={7, 9, 11, 13}
First, let's solve this equation by subtract 38 from both sides:-
[tex]\bigstar[/tex] 47-38=n
hence, the answer is:-
9=n
or
[tex]\bigstar{\underline{\boxed{\pmb{n=9}}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Please answer number 6. Thank you.
4³root192-4³root375 +2³root 24. find the simplify
Answer:
512√3 - 320√15 + 16√6
Step-by-step explanation:
4^3√192 simplified is 64√192. This can be simplified even further to 512√3. 4^3√375 simplified is 64√375, which is 320√15. 2^3√24 simplified is 8√24, which is 16√6. Therefore the answer is 512√3 - 320√15 + 16√6.
Hi! Please help. (Geometry Btw)
Answer:
It is C
Step-by-step explanation:
Reflection in X axis
Reflecting over the x axis, the x values remain the same and the y values become opposite.
answer: c. (X,y) becomes (x,-y)
Which is the pattern for factoring the sum of cubes
Answer:
a³ +b³ = (a +b)(a² -ab +b²)
Step-by-step explanation:
The patterns for factoring the sum and difference of cubes are similar. The sign of the second term in each factor is reversed from one pattern to the other.
a³ -b³ = (a -b)(a² +ab +b²)
a³ +b³ = (a +b)(a² -ab +b²) . . . . . pattern for factoring sum of cubes
Find the area of the trapezoid
Check the picture below.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ h=2\\ a=3\\ b=9 \end{cases}\implies A=\cfrac{2(3+9)}{2}\implies A=12[/tex]
Please helpppp neeed doneeee asappp
Answer:
abnormal condition of sardines
Step-by-step explanation:
what?
Please help me with complement or supplement of an angles.
Answer: 101 degrees
Step-by-step explanation:
is 56/72 and 7/9 proportional
Answer:
Yes. They are proportional.
Step-by-step explanation:
[tex]\frac{56}{72} =\frac{7}{9}[/tex]
[tex]0.777=0.777[/tex]
The left side 0.777 is equal to the right side 0.777, which means that the given statement is always true.
True
You woke up at 9:00 am 5 hours later still doing school work then you took a nap for 2 hours what time was it is when you woke up
The length of cassidy's bed is 9 1/4 if the area of the comforter is 69 3/8 square feet what is the width of the comforter
area of triangle = W × B
area of a triangle is = 552/8
552/8 = 37/4 × W
552/8 = 37W/4
8•37W = 4•552
296W = 2208
W = 7.5
width : 7.5 feet
Explanation:
area of rectangle : Length * Width
Given,
area : 69 3/8length : 9 1/4solve:
[tex]\rightarrow \sf 69\dfrac{3}{8} = 9\dfrac{1}{4} * Width[/tex]
[tex]\rightarrow \sf \dfrac{69.375}{9.25} = width[/tex]
[tex]\rightarrow \sf width = 7.5[/tex]
13. What is the equation in standard form of the circle
represented by
x2 + y2 - 10x - 6y = 23?
A (x+5)2+(y + 3)2 = 23
B. (x + 5)2+(y + 3)2 = 57
C. (x-5)+(y - 3)2 = 23
D. (x - 5)2+(y - 3)2 = 57
The standard form of a circle shows the center and the radius
The equation of the circle in standard form is (x + 5)^2 + (y - 4)^2 = 57
How to determine the equation?The standard equation of a circle is:
(x - a)^2 + (y - b)^2 = r^2
Where:
Center= (a,b)
Radius = r
Assume that:
(a,b) = (-5,3)
r = [tex]\sqrt{[/tex]57
The equation of the circle would be:
(x + 5)^2 + (y - 4)^2 = ([tex]\sqrt{57[/tex])^2
Evaluate the exponent
(x + 5)^2 + (y - 4)^2 = 57
Hence, the equation of the circle in standard form is (x + 5)^2 + (y - 4)^2 = 57
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