The graph shows the function f(x).
Which value is closest to the average rate of change from x = 1 to x = 4?
A.−3.5
B.−2.3
C. −1.4
D .−0.3
Answers
Answer:
Option B is correct
-2.3
Step-by-step explanation:
Average rate of change(A(x)) for the function f(x) over the interval [a, b] is given by:
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex] ....[1]
We have to find the average rate of change from x = 1 to x = 4.
From the graph as shown below
For x = 1
f(1) = 3
and
For x = 4
f(4) = -3.9
Using [1] we have;
[tex]A(x) = \frac{f(4)-f(1)}{4-1}[/tex]
Substitute the given values we have;
[tex]A(x) = \frac{-3.9-3}{3}[/tex]
⇒[tex]A(x) = \frac{-6.9}{3}[/tex]
Simplify:
[tex]A(x) = -2.3[/tex]
Therefore, -2.3 value is closest to the average rate of change from x = 1 to x = 4
Related Questions
how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution
Answers
To solve this, set up the following equation using the given values: that you have some quantity of a 20% solution, a quantity of a 50% solution, and that you need to have 12 gallons of a 30% solution. We will use a variable, x, together with the "goal" quantity of 12 gallons to solve this problem with only one unknown, even though we really have two unknowns (the quantity of 20% solution and that of the 50% solution).
Remember that when writing out percentages, a 20% solution is also a 0.2 solution, and a 50% solution is a 0.5 solution.
Let x = an unknown quantity of the 20% (or 0.2) solution. We therefore have 0.2x, since we have x gallons of the 20% solution. (Remember that "of" is a key word that denotes multiplication).
Therefore, 12 - x is the other unknown and is multiplied by the 0.5 (50%) solution, since we have this quantity of the 50% solution. Really, we could say that we have 0.5y (if we want to introduce another variable; however, it is much simpler to put the other quantity in terms of x, which is easy to do, since we know that the two unknown quantities must amount to 12 gallons). Now, we must multiply our second unknown, 12 - x, by 0.5. This gives us 0.5(12 - x).
Our two unknown quantities, 0.2x and 0.5(12 - x) add up to 12 gallons of a 30% solution. Putting all the words together to form an equation we get:
0.2x + 0.5(12 - x) = 0.3(12)
Now we expand the equation (call it distributing out the parentheses).
0.2x + 6 + 0.5x = 3.6
Combine like terms:
-0.3x + 6 = 3.6
Solve for x:
-0.3x = -2.4
x = 8
Plug x = 8 back into the equation to check that this is possible.
x = 8, and 12 - x = 4
0.2(8) + 0.5(12 - (8)) = 0.3(12)
0.2(8) + 0.5(4) = 0.3(12)
3.6 = 3.6
Check
To create 9 gallons of a 30% alcohol solution, mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution by setting up and solving a system of equations based on volumes and concentrations.
Explanation:To find out how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of a 30% alcohol solution, we can set up a system of equations based on the volumes and concentrations of the solutions. Let's let x represent the volume of the 20% solution and y represent the volume of the 50% solution.
Since the total volume of the mixture should be 9 gallons, we have our first equation:
x + y = 9Next, we consider the concentration of alcohol in the final mixture. The amount of pure alcohol from the 20% solution is 0.20x gallons, and from the 50% solution, it is 0.50y gallons. The final mixture has a concentration of 30%, so the total amount of alcohol in the 9 gallons mixture is 0.30 * 9 gallons. This gives us our second equation:
0.20x + 0.50y = 0.30 * 9Now we have a system of two equations with two variables that can be solved using methods such as substitution or elimination. After solving, we find that x = 6 gallons and y = 3 gallons. Therefore, to obtain 9 gallons of a 30% alcohol solution, you'd need to mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution.
Explain why the equation (x-4)^2-10=15 has two solutions. Then solve the equation to find the solutions.
Please show all your work! (30 points)
Answers
Let's solve it first so that we can understand whats going on in the equation
(x-4)²-10=15
add 10 to both sides
(x-4)²=25
square root both sides
(Okay, so here is where the problem can have 2 solutions. Because the square root of 25 could be (5*5) or it could be (-5*-5). If it's positive five then...
x-4=5
add 4 to both sides
x=9
if it's negative 5 then...
x-4=-5
add 4 to both sides
x=-1
So the answer could be x=-1 or x=9.
It has two solutions because there are two possibilities for the answer to the square root of 25.
I hope this help, and if you have any more questions, please feel free to ask me.
Have a nice day!
What are the zeros of the polynomial function f(x) = (x – 6)(x – 2)(x + 7)?
Answers
So,
x - 6 = 0
⇒ x = 6
x - 2 = 0
⇒ x = 2
x + 7 =0
⇒ x = -7
Thus the zeros of the given function are x = 6, x = 2 and x = -7
Which type of triangle is formed by joining the vertices A(-3, 6), B(2, 1), and C(9, 5)?
Answers
[tex]AB= \sqrt{ (2+3)^{2} + (1-6)^{2} } =5 \sqrt{2} \\ \\ BC= \sqrt{ (9-2)^{2} + (5-1)^{2} } =\sqrt{65} \\ \\ CA = \sqrt{ (-3-9)^{2} + (6-5)^{2} } = \sqrt{145} \\ \\ [/tex]
None of the side lengths are equal, so the triangle formed by the given vertices is a Scalene Triangle. Moreover, the Pythagorean theorem is also not satisfied with given side lengths, so the triangle is NOT a Right Angled Triangle.
At Jason's car rental shop it costs a flat rate of $100 to rent a car, which covers the cost of driving up to 75 miles. For every mile over 75 it costs an additional $0.10. Write a piecewise function modeling this situation, where x represents the miles driven and y represents the total cost.
Answers
5,895÷36
show all your work
Answers
____
The calculator is certainly faster.
Which expression is equivalent to 10x^6y^12/-5x^-2y^-6? Assume .x=0.y=0.
Answers
(10x ^ 6y ^ 12) / (- 5x ^ -2y ^ -6)
Rewriting we have:
(10 / -5) * ((x ^ 6y ^ 12) / (x ^ -2y ^ -6))
(-2) * ((x ^ 6y ^ 12) / (x ^ -2y ^ -6))
Then, for power properties:
(-2) * (x ^ (6 - (- 2)) and ^ (12 - (- 6)))
(-2) * (x ^ (6 + 2) and ^ (12 + 6))
(-2) * ((x ^ 8y ^ 8)
For x = 0, y = 0, we have:
(-2) * ((0 ^ 8) (0 ^ 8))
0
Answer:
An expression that is equivalent when x = 0 and y = 0 is:
0
Answer:B on edge
Step-by-step explanation:
Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL
method. Which method is most efficient? Explain.
Answers
FOIL stands for
first-multiply the first term in each set of parenthesis
outer-multiply the outer term in each of the perenthesis
inner- multiply the inner term in each of the parenthesis
last- multiply the last term in each of the parenthesis
(3x+8)(x+1)
(3x*x)=3x^2
(3x*1)=3x
8*x=8x
8*1=8
thus we shall have:
3x^2+3x+8x+8
=3x^2+11x+8
Distributive property:
(3x+8)(x+1)
3x(x+1)+8(x+1)
3x^2+3x+8x+8
=3x^2+11x+8
Both methods are efficient, it all depends with the users preference
Final answer:
To simplify (3x+8)(x+1), we can use the FOIL method, the Distributive Property, or a multiplication table, all leading to the same simplified expression: 3x² + 11x + 8. The FOIL method is typically the most efficient for binomials.
Explanation:
The question asks to simplify the expression (3x+8)(x+1) using a table, the Distributive Property, and the FOIL method and to determine which method is most efficient.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last and represents a quick way to multiply two binomials:
First: Multiply the first terms in each binomial (3x×x = 3x²).
Outer: Multiply the outer terms (3x×1 = 3x).
Inner: Multiply the inner terms (8×x = 8x).
Last: Multiply the last terms in each binomial (8×1 = 8).
Adding these products together, we get 3x² + 3x + 8x + 8, which simplifies to 3x² + 11x + 8.
Using the Distributive Property
This involves expanding the expression by multiplying each term in the first polynomial by each term in the second: (3x+8)(x) + (3x+8)(1), which also simplifies to 3x² + 11x + 8.
Using a Table
Create a table where you list each term of the first polynomial in the first row and the terms of the second polynomial in the first column, and then fill in the table with the products of the intersecting terms. The sum of these products will also yield 3x² + 11x + 8.
While all three methods will give the correct answer, the FOIL method is generally seen as the most efficient for this particular problem, as it provides a straightforward, step-by-step process that is easy to follow and remember for multiplying two binomials.
Mrs. Daly's reading classes were surveyed about their reading preferences. the data is summarized in the table below.
given that a student is in 9th grade, what is the probability that they like to read non-fiction novels, based on this data?
Answers
Answer:
0.60
Step-by-step explanation:
What is the mode of these numbers? A 40. B 43. C 26 and 31. D. 31 and 43
Answers
pleae help thanks a bunch
Answers
You use the Pythagorean theorem to solve this
[tex] a^{2} + b^{2} = c^{2} [/tex]
Put in the values it tells you to
[tex]a^{2} + 4.4^{2} = 5.5^{2} [/tex]
Square the numbers
[tex]a^{2} + 19.36 = 30.25[/tex]
Subtract 19.36 from both sides
[tex] a^{2} = 10.89[/tex]
Take the square root of both sides
a = 3.3
The answer is 3.3
Hope this helps!
If a+5=b, then what is the value of (b−a)^4?
Answers
(b-a)^4
((a+5)-a)^4
Simplification, as follows:
((a+5)-a)^4
(5)^4 the a’s cancel
625
The value of (b-a)^4 when a+5=b is 625.
A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?
Answers
The dog will win the race.
the answer would be 90% because when you multiply 30% x 30% =90% its the same as 3 x 3 = 9
PLZ HURRY!!
If a Professional basketball player earns $3 million playing 125 games per year and plays an average of 40 minutes per game, how much does he earn per second of playing time?
Answers
24,000/40= 600 per minute
600/60= 10 per second
$10 per second.
PLEASE HELP!!!! THIS LINEAR EQUATIONS!!!
Answers
[tex]120x + 60y \geqslant 600[/tex]
We use the 'more than or equal sign' as the consultant needs to make at least $600 - so exactly $600 or more than $600
Marta wants to use her mothers recipe. Her mother's recipe makes enough soup for 10-12 people, but Marta wants to make only 1/3 of that amount. If the original recipe requires 2 1/2 pounds of chicken, how many pounds of chicken will Marta need for her soup?
Answers
However, first we need to turn 2 1/2 into an improper fraction to make the multiplication simpler. To do this, we should multiply the unit (2) by the denominator (2) and add the numerator (1).
2*2=4, 4+1 = 5, therefore, 2 1/2 = 5/2
Now, we have to multiply 5/2 by 1/3. To do this, we just multiply the two numerators and the two denominators together.
5/2 * 1/3 = 5*1/2*3=5/6
Therefore, Marta needs to use 5/6 pounds of chicken for the recipe.
Hope this helps!
I WILL MARK BRAINLIEST PLEASE HURRY
Answers
according to the given equation the centre of this circle is in the poit (6;7) and its radius =4 units.
Using this data, it is possible to define right choice: D.
answer: graph D.
Centennial park is evaluating the capacity of the park and have determined that 15 people can comfortably stand in a section that is 5ft by 8ft , the park has dimensions that are 400yds by 200 yds estimate the number of people who can fit in the park
Answers
We have been given that 15 people can comfortably stand in a section that is 5ft by 8ft .
Hence, the area of this section is given by
[tex]A=5\times 8\\ A=40 ft^2[/tex]
Hence, we can say that 15 people can comfortably stand in an area 40 square feet.
Now, we know that 1 yard is equal to 3 feet.
Hence, the area of the section 400yds by 200 yds is equal to
[tex]400\times 3 \times 200 \times 3\\ =720000 ft^2[/tex]
Now, in 40ft^2, 15 people can stand comfortably.
Hence, in 720000 ft^2, number of people can stand comfortably is
[tex]\frac{15}{40} \times 720000\\ \\ =270000[/tex]
Therefore, 270000 people can stand in the park of dimension 400 yds by 200 yds
How to solve this please?
2x - 5 = 4
Answers
2x-5=4
First lets get the 2x by itself so we have to add 5 on both sides.
2x-5=4
+5 +5
2x=9
Now we need to get the X by itself so divide each side by 2
[tex] \frac{2x}{2} = \frac{9}{2} [/tex]
Now we are left with the following
X=[tex] \frac{9}{2} [/tex]
We must simplfy the fraction
2 will go into 9 four times with 1 left over. So the mixed fraction answer would be:
x=[tex]4 \frac{1}{2} [/tex]
As a decimal you would just divide 9 and 2
x=4.5
Hope this helped!
Or in decimal form, 4.5
Hope this helps. - M
Andrew drove 55 mph on his trip. Which of the following equations best represents the distance he drove if x stands for the number of hours?
Answers
X= The hours
I hope this helps!!
Answer
Using speed formula:
[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]
Let y represents the distance in miles and x represents the time in hours.
As per the given statement:
Andrew drove 55 mph on his trip.
Using formula;
we have;
[tex]55 = \frac{y}{x}[/tex]
Multiply both sides by x we have;
[tex]y = 55x[/tex]
Therefore, the equation best represents the distance he drove is [tex]y = 55x[/tex]
After being rearranged and simplified, which two of the following equations could be solved using the quadratic formula?
Answers
1. degree = 2 (i.e. the highest power equals exactly two)
2. the linear term (e.g. 4x, or -5x...) and constant term (e.g. 5, -30, pi, etc.) may or may not be present.
Now let's simplify and examine the given equations, and see if each can be solved with the quadratic formula:
A.
[tex]5x^3+2x-4=2x^2[/tex]
[tex]5x^3+-2x^2+2x-4=0[/tex]
The degree (highest power) is three, so it is not "exactly two". NO.
B.
[tex]5x^2-3x+10=2x^2+21[/tex]
[tex]3x^2-3x-11=0[/tex]
The degree (highest power) is two, so it is "exactly two". YES.
C.
[tex]5x^2-3x+10=5x^2[/tex]
[tex]0x^2-3x+10=0[/tex]
[tex]-3x+10=0[/tex]
The degree (highest power) is one, so it is not "exactly two". NO.
D.
[tex]x^2-6x-7=2[/tex]
[tex]x^2-6x-9=0[/tex]
The degree (highest power) is two, so it is "exactly two". YES.
Note that it is very important to simplify the equations before checking the degree.
If you need further explanations, please feel free to post in comments.
Answer:
The Answer will Be B and D
Step-by-step explanation:
Lupe has 14 stickers that she wants to give to 2 friends. She wants each friend to have the same number of stickers. Select the three statements that describe how Lupe should give the stickers to her friends. Each friend gets 14÷2 stickers. Each friend gets 2 of the 14 stickers. Each friend gets 142 stickers. Each friend gets 7 of the 14 stickers.
Answers
Answer:
The correct options are 1, 3 and 4.
Step-by-step explanation:
It is given that Lupe has 14 stickers that she wants to give to 2 friends.
Total number of stickers Lupe has is 14.
The number of friends is 2.
She wants each friend to have the same number of stickers. It means each friend will get half of 14.
The number stickers Lupe should give to her friends is 14 divided by 2.
[tex]\text{Number of stickers}=14\div 2[/tex]
Write this value in fraction form.
[tex]\text{Number of stickers}=\frac{14}{2}[/tex]
[tex]\text{Number of stickers}=7[/tex]
It means the correct statements are
1. Each friend gets 14÷2 stickers.
3. Each friend gets (14)/2 stickers.
4. Each friend gets 7 of the 14 stickers.
Hence correct options are 1, 3 and 4.
Josh is hiking Glacier National Park. He has now hiked a total of 1 7 km 17 km17, space, k, m and is 2 km 2 km2, space, k, m short of being 1 2 2 1 start fraction, 1, divided by, 2, end fraction of the way done with his hike. Write an equation to determine the total length in kilometers ( h ) (h)left parenthesis, h, right parenthesis of Josh's hike.
Answers
17 + 2 = 19 km is 1/2 of the total length, that is,
19 = (1/2)h
(1/2)h = 19 multiply both sides by 2
h = 2*19
h = 38 km
The total length in kilometers is 38 km.
hey can you please help me posted picture of question
Answers
1. The figure shows a parabola whose vertex is (0,0).
2. The x² indicates that the red parabola shown in the figure is vertical
3. and the sign - indicates that the red parabola opens down.
Therefore, you can conclude that the red parabola has the equation f(x)=-x²
So, the answer is B.
Shifting 4 units down means subtracting 4 from the function value.
So, G(x) = 4 - x²
Thus,
F(x) = G(x) - 4
F(x) = 4 - x² - 4 = - x²
Therefore, the correct answer is option B
hello can you please help me posted picture of question
Answers
you just have to find the solution to Y.
[tex]( \frac{-b}{2a},y( \frac{-b}{2a})) [/tex]
b = coefficient of x term = 8
a = coefficient of squared term = 2
So,
[tex] \frac{-b}{2a}= \frac{-8}{4}=-2 [/tex]
and
[tex]y(-2)=2(-2)^{2}+8(-2)+1=-7 [/tex]
Therefore, the vertex occurs at (-2, -7)
So, the correct answer is option C
What is the surface area of a cylinder with a radius of 5 ft and a height of 2 ft?
Answers
Answer:
Its B.
Have a great day! OwO
Use multiplying by 1 to find an expression equivalent to 3/14 with a denominator of 14 y.
Answers
now, "same" could be anything whatsoever, you name it, a whole polynomial, a whole anything whatsoever.
[tex]\bf \cfrac{\sqrt{2}}{\sqrt{2}}=\cfrac{\sqrt{3}}{\sqrt{3}}=\cfrac{100000000}{100000000}=\cfrac{eggs}{eggs}=\cfrac{miles}{miles}=\cfrac{\frac{\quad \sqrt{3}}{\sqrt[5]{17}}\quad }{\frac{\sqrt{3}}{\sqrt[5]{17}}}=\cfrac{whatever}{whatever}=1[/tex]
now, that said, let us use 1 in this case then ... hmmmm we simply need a "y" in the denominator, so we simply multiply the denominator AND numerator by "y", y/y = 1 btw.
[tex]\bf \cfrac{3}{14}\cdot \cfrac{y}{y}\implies \cfrac{3y}{14y}[/tex]
Dynatashia has a list of items she needs to buy at the store. She has written down the items and the advertised prices as shown: Hamburger – $3.99 per pound Hamburger buns – $1.29 2-liter soda – 3 for $2.00 Dynatashia buys 1.5 pounds of hamburger, 1 package of buns and 3 of the 2-liter bottles of soda. Her receipt is shown below. 2-ltr soda 2@3/$2 $1.34 Hambrg 1.5 lb@3.99 $5.99 Hbuns 1@1.69 $1.69 2-ltr soda 1@3/$2 $0.67 Determine if Dynatashia's receipt is correct. a. Yes, Dynatashia's receipt is correct. b. No, Dynatashia paid too much for soda. c. No, Dynatashia paid too much for hamburger. d. No, Dynatashia paid too much for buns.
Answers
Answer:
D. No, Dynatashia paid too much for buns.
Step-by-step explanation:
We are given that,
The actual cost of the items are,
Items Cost
Hamburger $3.99 per pound
Buns $1.29 per packet
2-liter soda $2 per 3 bottle
As, she bought 1.5 pounds of hamburgers, 1 packet of buns and 3 bottles of 2-liter soda.
So, she has to pay,
For hamburger = 1.5 × 3.99 = $5.99
For buns = 1.29 × 1 = $1.29
For soda bottles = $2
But from the receipt, we see that she pays,
For hamburger = 1.5 × 3.99 = $5.99
For buns = 1.69 × 1 = $1.69
For soda bottles = 1.34 + 0.67 = $2
That is, she has to pay $1.29 for the packet of the buns but she paid $1.69 for the buns.
Hence, the receipt is not correct as Dynatashia paid too much for the buns.
Answer: D
Step-by-step explanation:
edg
A bookstore costs $90 a day to keep open, and spends $12 for each book it sells. the store charges $18 for each book it sells. If n represents the number of books sold, which equation represents the revenue function for this bookstore?
Answers
Answer:
[tex]R=6n-90[/tex]
Step-by-step explanation:
Let
R------> the revenue function
n------> the number of books sold per day
we know that
In this problem
[tex]18n[/tex] -----> represent the profit
[tex](12n+90)[/tex] -----> represent the cost
so
The revenue is equal to the profit minus the cost
[tex]R=18n-(12n+90)[/tex]
[tex]R=n(18-12)-90[/tex] ------> equation that represent the revenue function
Simplify
[tex]R=6n-90[/tex]
how many ounces of 30% hydrochloric acid solution and 80% hydrochloric acid solution must be mixed to get 10 oz of 50% hydrochloric acid solution
Answers
This diagram tells you the constituents 80% and 30% solution are in the proportion 20:30 or 2:3 or 4:6 to make the mix having 50% hydrochloric acid. Note that the numbers 4 and 6 add to 10, the number of ounces of solution we want.
4 ounces of 80% solution must be mixed with 6 ounces of 30% solution to make 10 ounces of 50% solution.