The graph shows the quadratic function f(x) . What is the average rate of change for the quadratic function from x = 10 to x = 12? Enter your answer in the box.
Answers
Explanation:
1) The average rate of change is the total (net) change of the function divided by the time elapsed (or the distance between the two input data).
2) For example, given:
Initial value of the function, for t = a: f(a)
Final value of the function, for t = b: f(b)
Then, the average rate of change = change on the function / change on hte input variable = [ f(b) - f(a) ] / [ b - a]
3) This is an example with a quadratic function:
f(x) = 3x^2 - 2x + 20
for x = 10, f(10) = 3 (10)^2 - 2(10) + 20 =3(100) - 20 + 20 = 300
for x = 12, f(12) = 3 (12)^2 - 2(12) + 20 = 3(144) -24 + 20 = 428
average rate of change: [ f(12) - f(10) ] / (12 - 10) = [428 - 300] / (2) = 128 / 2 = 64.
This very same procedure you can use whenever you know the function.
If what you have is the graph of the function, just take f(12) and f(10) from the graph, and calculate [f(12) - f(10) ] / (12 - 10) = [ f(12) - f(10) ] / 2.
Answer:
3
Step-by-step explanation:
Related Questions
Let's say we have a square whose sides all measure 14 inches. Determine to two decimal places the dimensions of the square that has twice the area of this square.
Answers
so the area = 14 x 14 = 196 square inches
Double the area:
196 x 2 = 392 square inches
To find one side of the square:
[tex] \sqrt{392} [/tex] = 19.80 inches (2 d.p.)
The dimensions of the square that has twice the area of the given square is 19.80 in.
What is scaling ?
It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.
It is given that :
the side of square measure = 14 inches
so the area of square will be :
A = a²
= 14 x 14
= 196 square inches
The square that has twice the area of this square means double the area :
196 x 2 = 392 square inches
To find one side of the square:
A = a²
a = √A
= √392
= 19.80 inches
Therefore, the dimensions of the square that has twice the area of the given square is 19.80 in.
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the sum of a number times 4 and 21 is greater than or equal to 24. use the variable w for the unknown number
Answers
4w >= 24 - 21
4w >= 3
w >= 3/4
w >= 0.75
What is the inequality of the problem and the symbol
Answers
Answer this question: a family of 4 people consumes 5000 grams of fish every week. how much fish will the family consume in an year? find the answer in kilograms.
Answers
1 week = 5000 grams
5000g x 52weeks = 260,000g
260,000g = 260 kg
The family consumes 260 kilograms of fish in a year.
1 week = 5000 grams
5000g x 52weeks = 260,000g
260,000g = 260 kg
Therefore family consumes 260 kilograms of fish in a year
Ana participated in a charity walk. She raised $0.25 for each 1/2 mile that she walked.The first day Ana walked 11 miles.The second day, she walked 14 miles.How much money did Ana raised?
Answers
11 + 14 = 25.
She walked a total of 25 miles.
Each mile is two half-miles, so 25 miles is 50 half-miles.
She raised $0.25 for each 1/2 mile, so she raised $0.25 * 50 = $12.50
After walking for 2 days she raised a total of $12.5.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, Ana participated in a charity walk. She raised $0.25 for each 1/2 mile that she walked.
Since, for 1/2 miles she earns money = 0.25
Thus,
For 1 mile she will earn a total of money = 0.25* 2
For 1 mile she will earn a total of money = 0.5
Since Ana ran for 2 days, The first day Ana walked 11 miles. On the second day, she walked 14 miles.
So,
Total of miles she walked = 11 + 14
The total of miles she walked = 25
Thus,
She raised a total amount of money = 25 *0.5
She raised a total amount of money = 12.5$
Therefore, after walking for 2 days she raised a total of $12.5.
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There are a few ways to increase the rate of a reaction. When the amount of a substance in a given volume is increased, this is altering the__________.
Answers
The amount of material/volume is the material’s concentration.
The rate is the reaction is increase by altering the concentration.
Answer:
Concentration.
Step-by-step explanation:
Concentration: It is define as the amount of substance per unit volume.
Or
Concentration is defined as the ratio of solute in a solution to either solvent or total solution.
Concentration usually is expressed in terms of mass per unit volume.
When the amount of a substance in a given volume is increased then it alter the concentration of reactant.When the concentration of reactant is increase then the rate of reaction increases.Because when the concentration is increases then more ions or molecules interact to form new compounds therefore, the rate of reaction increases.When the concentration of reactant decrease then less number of ions or molecules interact to form new compounds therefore, the rate of reaction decreases.
the Jade restaurant has a large aquarium on display in its lobby.The base of the aquarium is 5 feet by 2 feet. The height of the aquarium is 4 feet . How manny cubic feet of water are needed to completely fill the aquarium?
Answers
V = width * length * height.
Given:
Width = 2 ft
Length = 5 ft
Height = 4 ft
Therefore the volume is
V = 2*5*4 = 40 ft³
Answer: 40 ft³
In a candy store, a $5.00 jar of candy is labeled "50% off " what is the discount? What is the sale price of the jar of candy?
Answers
Discount $= Price times discount %
=$5.00 * 50%
=$5.00 * 0.50
=$2.50 discount amount
STEP 2:
Sale price= Original $ - Discount amount
=$5.00 - $2.50
=$2.50 sale price
ANSWER: Discount amount is $2.50 and the sale price is also $2.50.
Hope this helps! :)
the soccer club has planned a trip to a tournament . the cost of the van is $192. when 2 students who are not members of the club join the trip , thw transportation cost per person drops by $3.20. how mant soccer club members are gpoing to the tournament
Answers
Answer:
10 soccer club members are going to the tournament.
Step-by-step explanation:
Let x be the number of soccer club members who are going to the tournament,
Given,
The cost of transportation of x students = $ 192
⇒ The cost of transportation of 1 student = [tex]\frac{192}{x}[/tex]
⇒ The cost of transportation of (x+2) student = [tex]\frac{192}{x-2}[/tex]
According to the question,
[tex]\frac{192}{x}-\frac{192}{x+2}=3.20[/tex]
[tex]192(\frac{1}{x}-\frac{1}{x+2})=3.20[/tex]
[tex]192(\frac{x+2-x}{x(x+2)})=3.20[/tex]
[tex]\frac{384}{x^2+2x}=3.20[/tex]
[tex]3.2x^2+6.4x=384[/tex]
[tex]3.2x^2+6.4x-384=0[/tex]
By the quadratic formula,
[tex]x=\frac{-6.4\pm \sqrt{40.96+4915.2}}{6.4}[/tex]
[tex]\implies x = \frac{-6.4\pm 70.4}{6.4}[/tex]
[tex]\implies x = 10\text{ or } x = -12[/tex]
Since, the number can not be negative,
Hence, 10 soccer club members are going to the tournament.
To find the number of soccer club members going to the tournament, we set up an equation based on the total cost of the van and the drop in cost per person when two additional students join. Solving the quadratic equation reveals that the number of soccer club members is 10.
Explanation:The question asks us to determine the number of soccer club members going to the tournament given that the cost of the van is $192 and that the cost per person drops by $3.20 when 2 additional students join the trip. Let's denote the number of club members as 'x'. Before the 2 students join, the cost per person is $192 / x. After they join, the cost per person becomes $192 / (x + 2), which is $3.20 less than the original cost per person, so:
192 / x - 192 / (x + 2) = $3.20
Multiplying through by x(x + 2) to clear the denominators gives us:
192(x + 2) - 192x = 3.20x(x + 2)
This simplifies to:
192x + 384 - 192x = 3.20x^2 + 6.4x
The term 192x cancels out on both sides, so we have:
384 = 3.20x^2 + 6.4x
To solve for 'x', we divide both sides by 3.20:
120 = x^2 + 2x
Now we solve the quadratic equation x^2 + 2x - 120 = 0. Factoring this equation, we get (x + 12)(x - 10) = 0. Thus, x can be -12 or 10. However, since we can't have a negative number of club members, the number of soccer club members is 10.
what are the solutionso of 8x^2 = 6 + 22x
Answers
[tex]0 = -8x^2+22x+6[/tex]
Factor out a -2:
[tex]0 = -2(4x^2-11x-3)[/tex]
Factor this equation:
[tex]0 = 4x^2-11x-3[/tex]
I will use the AC method. To use it, first multiply a and c (in ax^2 + bx +c):
[tex]4*-3 = -12[/tex]
Now, look for two numbers that multiply to -12 and add to -11. Obviously these numbers are -12 and 1. (-12*1 = -12 and -12+1 = -11). Now, because of rules, you set it up in a Punnett square:
4x^2 -12x
x -3
Now, we find common factors of the terms in rows:
_x_______-3__
4x| 4x^2 -12x
1 | x -3
So, you can use this to write an equivalent expression to the quadratic given:
[tex](x-3)(4x+1)[/tex]
Now, we known the factors are (solve for x): 3 and -1/4.
Rearranging the quadratic equation, (Ax² + Bx + C = 0)
8x² - 22x - 6 = 0
Simplify. Divide both sides of the equation by 2.
4x² - 11x - 3 = 0
Using the quadratic formula. Identify first the value of the coefficients.
A = 4
B = -11
C = -3
Using the quadratic formula:
[tex]x = \frac{-B +- \sqrt{B^2 - 4AC} }{2A} [/tex]
Substitute A, B and C
[tex] x_{1} = \frac{-(-11) + \sqrt{(-11)^2 - 4(4)(-3)} }{2(4)}[/tex]
x = 3
[tex] x_{1} = \frac{-(-11) - \sqrt{(-11)^2 - 4(4)(-3)} }{2(4)}[/tex]
x = [tex]- \frac{1}{4} [/tex]
An even function must always have what characteristic?
A) rotation symmetry about the origin
B) be a polynomial with even exponents on x
C) a line of symmetry on the x-axis
D) a line of symmetry on the y-axis
Answers
Find the measure of angles A,B,C,D
Answers
B = 180-90 = 90
C = 180 - 90 - 25 = 65
D = 180-65 = 115
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Find 2 numbers if Their sum is −7 and their difference is 14
Answers
The larger number is (-7+14)/2 = 3.5.
The smaller number is (-7-14)/2 = -10.5.
_____
The two equations a+b=-7, a-b=14 can be solved to get these results. It is genrally convenient to solve them by adding one to the other, or subtracting one from the other.
In the diagram Shown a 2 foot wide flower border surrounds the heart shaped pond.What is the area of the border?
Answers
Answer:
Area of the border is 142.80 ft²
Step-by-step explanation:
The given figure consist of three figures = 2× semicircles + 1 square.
We will calculate area of the figure including border
Area of one semicircle = (1/2)π×r²= (1/2)×π×(12/2)² = (1/2)π×(6)² = 18π ft²
Area of square = side² = 12² = 144 ft²
Total area = 144 + 18π + 18π = (144 + 36π) ft²
Now we will calculate area without border.
Area of the semicircle = (1/2)π×r² =(1/2)π×[(12-4)/2]²=(1/2)π×(4)² = 8π ft²
area of square = side²= (12-4)²= 8² = 64 ft²
Total area = 64 + 8π + 8π = (64 + 16π) ft²
Now the area of the border = Area with border - Area without border
= (144 + 36π) - (64 + 16π) = 20π + (144 - 64) = 20π + 80
= 20×3.14 + 80 = 142.80 ft²
Area of the border = 142.80 ft²
The area of the flower border surrounding the heart-shaped pond is approximately 142.80 square feet.
The given figure consists of three parts: two semicircles and one square. Let's calculate the area of the border step by step:
1. Area of the Semicircles:
- The semicircles form the rounded top of the heart shape.
- Each semicircle has a radius of half the width of the pond, which is [tex]\(12 \, \text{ft}\)[/tex].
- Area of one semicircle = [tex]\(\frac{1}{2} \pi r^2\)[/tex]
[tex]\[ = \frac{1}{2} \pi (6)^2 = 18\pi \, \text{ft}^2\][/tex]
- Total area contributed by both semicircles = [tex]\(2 \times 18\pi = 36\pi \, \text{ft}^2\)[/tex]
2. Area of the Square:
- The square section of the pond has sides of [tex]\(10 \, \text{ft}\)[/tex] each.
- Area of the square = side squared
[tex]\[ = 10^2 = 100 \, \text{ft}^2\][/tex]
3. Total Area Including Border:
- Total area = Area of semicircles + Area of square
[tex]\[ = 144 + 36\pi \, \text{ft}^2\][/tex]
4. Area Without Border:
- To find the area without the border, we subtract the area of the pond from the total area:
[tex]\[ = 100 + 16\pi \, \text{ft}^2\][/tex]
5. Area of the Border:
- The area of the border is the difference between the total area and the area without the border:
[tex]\[ = (144 + 36\pi) - (100 + 16\pi) = 20\pi + 80 = 20 \times 3.14 + 80 = 142.80 \, \text{ft}^2\][/tex]
Therefore, the area of the flower border surrounding the heart-shaped pond is approximately 142.80 square feet.
Lisa needs to score at least 12 points on her next turn to win the game. Write an inequality to represent the number of points Lisa needs to win the game
Answers
L ≥ 12 will be the inequality for this situation.
Final answer:
Lisa needs to score at least 12 points to win, so the inequality to represent this scenario is 'p >= 12', where 'p' is the number of points she scores on her next turn.
Explanation:
To represent the number of points Lisa needs to win the game with an inequality, we can let p stand for the points she will score on her next turn.
Since she needs to score at least 12 points, the inequality would be p \">= 12".
This reads as 'p is greater than or equal to 12,' meaning Lisa needs to score 12 or more points to win.
Volume of a Cylinder
Answers
The problem says to use 3 for pi. The radius is half the top of the cylinder, which is 2 in / 2 = 1 in. The height is given to be 12 in.
Our equation becomes...
Volume = 3* (1)^2 * 12 = 36 in^3
Molly says that 4/8 is always the same 1/2. Andrew says that 4/8 and 1/2 are equivalent fractions, but they could be different amounts.
Answers
Does anyone know these answers
Answers
If g=x-9 and if x=15what isg
Answers
g = 6
the answer is g =6
Substitute 15 for x in g = x - 9
g = 15 - 9
Now, Solve
g = 15 - 9 = 6
6 is your answer
1. A cake in the shape of a circus tent is used as a centerpiece at a celebration. The cake consists of a cylinder and a cone. The cylinder has a diameter of 12 inches and a height of 14 inches. The cone has a height of 6 inches. What is the volume of the cake? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. Show your work.
(Please show me how you get your answers)
I nEED HELP!
Answers
1) The cylindrical part.
2) The cone of the tent.
Note: In order to find the total volume of the cake, we have to add the volumes of both of the above-mentioned part.
1.
The volume of the cylinder = [tex] \pi *r^{2}*h[/tex] --- (A)
We have the height = h = 14 inches.
Radius = r = Diameter / 2 = 12/2 = 6 inches.
and [tex]\pi [/tex]= 3.14
Put the above values in equation (A);
(A) => The volume of the cylinder = (3.14) * (6 x 6) * (14) = 1582.56 inches cubed
2.
The volume of the cone = [tex]\pi *r^{2}* \frac{h}{3} [/tex] --- (B)
Since the cake is in "circus tent" shape, therefore, the radius of the cone should be equal to the radius of the cylinder.
Radius of the cone = r = 6 inches.
Height of the cone = h = 6 inches.
and [tex]\pi [/tex]= 3.14
Put the above values in equation (B);
(B) => The volume of the cone = (3.14) * (6 x 6) * (6 / 3) = 226.08 inches cubed
The volume of the cake = Volume of the cylinder + Volume of the cone
[tex]V_{cake}[/tex] = 1582.56 + 226.08 = 1808.64 inches cubed
Ans: The volume of the cake = 1808.64 [tex]in^{3}[/tex]
-i
Can someone pls help me??
Answers
what's 2x-y=-3 in slope intercept form
Answers
The equation of line is slope intercept form is y = 2x + 3
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
2x - y = -3 be equation (1)
Adding 3 on both sides of the equation , we get
2x - y + 3 = 0
Adding y on both sides of the equation , we get
y = 2x - 3
Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Therefore , the value of A is 2x - 3 , where the slope is m = 2
Hence , the equation of line is y = 2x - 3
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Final answer:
To convert the equation 2x-y=-3 into slope-intercept form, y must be isolated. The steps involve rearranging the equation to solve for y, resulting in the slope-intercept form y = 2x + 3, where the slope (m) is 2 and the y-intercept (b) is 3.
Explanation:
To convert the equation 2x-y=-3 into slope-intercept form, we need to solve for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope, and b represents the y-intercept.
Let's solve for y:
Start with the original equation: 2x - y = -3.Add y to both sides: 2x = y - 3.Next, add 3 to both sides to isolate y: 2x + 3 = y.The equation is now in slope-intercept form, with m = 2 and b = 3, which is y = 2x + 3.Therefore, the equation 2x - y = -3 in slope-intercept form is y = 2x + 3.
az-qb=yz solve for z and justify each step
Answers
We assume that A, q, and, b, are real numbers (where y could be a variable).
Step 2:
Terms with z to the left of the equation. Independent terms of z to the right of the equation.
Az - yz = qb
Step 3:
Common factor z.
z (A - y) = qb
Step 4:
Clear z.
z = qb / (A - y)
Answer:
z = qb / (A - y)
What is the value of x? Enter your answer in the box
x =
Answers
18x + 90 = 180
18x = 180 - 90
18x = 90
x = 90/18
x = 5
18x + 90 = 180
18x = 90
x = 5
answer
x = 5
A
B
C
D?
Which is the answer please help x
Answers
64/100 = 0.64
Divide top and bottom by 4.
64/4 = 16
100/4 = 25
Answer 16/25 <<<<====
I NEED HELP ON QUESTION #4
Answers
9w ×0 is already 0.
0 - 12 = -12
-12 doesn't equal 9w - 12.
Hope this helps!
Write an algebraic expression for the word phrase. five fewer than d days d – 5 5 + d 5 – d d + 5
Answers
Answer:
(d-5)
Step-by-step explanation:
we know that
The phrase"five fewer than d days" is equal to subtract 5 from the number d
so
d minus 5-----> (d-5)
Answer:
d-5
Step-by-step explanation:Just trust
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What is the area of Triangle PQR on the grid?
2 square units
3 square units
4 square units
8 square units
Answers
PQ = 2 units
height = 4 units
area = 2*4 = 8/2 = 4 square units
2×4/2=4 square units
what is the answer t
3a equals 9
Answers
Simply divide both sides by 3.
3a ÷ 3 = 9 ÷ 3
Simplify.
a = 3
~Hope I helped!~
Negative 18=r-3
What r and how did you get it
Answers
To solve for r, add 3 to both sides of the equation.
Explanation:To solve for r, you need to isolate it on one side of the equation. Begin by adding 3 to both sides of the equation to cancel out the -3 on the right side. This gives you -15 = r. Therefore, the value of r is -15.
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