These tables represent a quadratic function with a vertex at (0, -1). What is
the average rate of change for the interval from x = 8 to x = 9?
OA. -82
OB. -17
C. -65
D. -2
x y
0
1
23456
125
-10
-17
-26
-37
Interval
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
Average rate
of change
-1
-3
-5
-7
-9
-11
3-2
1-2
3-2
1-2
3-2
Answers
Answer:
B
Step-by-step explanation:
We can notice that based on the given pattern, the average rate of change from [tex]x=n[/tex] to [tex]x=n+1[/tex], where [tex]n \in \mathbb{Z}[/tex], is [tex]-2n-1[/tex].
So, the average rate of change from [tex]x=8[/tex] to [tex]x=9[/tex] is [tex]-2(8)-1=-17[/tex].
The rate of change for the interval from x = 8 to x = 9 is -17.
What is Rate of change?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.
The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.
We know the standard form of quadratic function
y = a (x - b)² + c with vertex (b, c)
Since the vertex is (0, -1) then b= 0, c= -1.
Then, the quadratic equation is:
y= ax² - 1 passes through (1, 2), (2, -5),.....
So, the rate of change in interval (8, 9) is
= y(9)- y(8)/ (9-8)
= -9² -1 - 8² - 1/ 1
= -17.
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Related Questions
Johnny has some nickels and dimes in his pocket, and the change is worth $0.75. He has twice as many dimes and nickels. How many of each type of coin does Johnny have? // system of equations questions it requires 2 equations and to define the x and y
Answers
=====================================================
Work Shown:
x = number of nickels
y = number of dimes
5x = value of the nickels only (cents)
10y = value of the dimes only (cents)
5x+10y = total value of all the coins = 75 cents
One equation we can form is 5x+10y = 75.
"he has twice as many dimes as nickels" tells us that y = 2x. We can replace every copy of y with 2x and solve for x as shown in the steps below.
5x+10y = 75
5x+10(y) = 75
5x+10(2x) = 75 ... plug in y = 2x
5x+20x = 75
25x = 75
x = 75/25
x = 3
This value leads to y = 2x = 2*3 = 6
Johnny has 3 nickels and 6 dimes.
------------------
Check:
1 nickel = 5 cents
3 nickels = 3*5 = 15 cents
1 dime = 10 cents
6 dimes = 6*10 = 60 cents
3 nickels + 6 dimes = 15 cents + 60 cents = 75 cents = $0.75
The answers are confirmed.
(for 100 points)
Multiply (3.84 x 10−9)(7.6 x 1015). Write the final answer in scientific notation.
plus brainly
Answers
Answer:
2.9 × 1025
(scientific notation)
= 2.9e25
(scientific e notation)
Step-by-step explanation:
hope this helped
Answer:
2.9184 × 10⁷Step-by-step explanation:
(3.84 × 10⁻⁹) (7.6 × 10¹⁵) = Rearrange the product(3.84 × 7.6) × 10⁻⁹ ⁺ ¹⁵ = Simplify29.184 × 10⁶ = Move the decimal to the left by one digit2.9184 × 10⁷ Answerwhat is 15×86 2/3 please answer asap I need help
Answers
elect the correct word to fill in each blank. as the sample size increases, the degrees of freedom (i) which moves the t (ii) a z - (i) first blank - (ii) second blank a. decreases b. further from c. closer to d. increases
Answers
As the sample size (n) increases, the number of degrees of freedom increases, and the t-distribution approaches a normal distribution.
What is degrees of freedom ?
The variety of degrees of freedom is the amount of values within the final calculation of a datum that are liberal to vary. Estimates of applied math parameters are often primarily based upon totally different amounts information|of knowledge or data.
Main Body:
Degrees of freedom typically equals the quantity of observations (or items of information) minus the quantity of parameters calculable. once you perform regression, a parameter is calculable for each term within the model, and and every one consumes a degree of freedom. Therefore, as well as excessive terms during a multivariate analysis model reduces the degrees of freedom on the market to estimate the parameters' variability.
Hence the number of degrees of freedom increases,as the sample size (n) increases.
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Lily ordered a replacement part for her
desk. It was shipped in a box that
measures 4 in. by 4 in. by 14 in. What is
the greatest length in whole inches that
the part could have been?
Answers
Thus the largest length is 15 inches
Size (l) is 14 inches.
Size (w) = 4 inches.
Height is 4 inches (h).
The distance between one bottom corner and the opposite top corner is known as d. Find s, the diagonal across the bottom of the box, first.
[tex]w^2 + l^2 = s^2[/tex]
Replace the prescribed measures.
[tex]4^2 + 14^2 = s^2[/tex]
Simplify.
[tex]16 + 196 = s^2[/tex]
[tex]21^2= s^2[/tex]
To determine d, use the expression for s.
[tex]h^2 + s^2 = d^2[/tex]
Plug in s2 = 212 and h = 4.
4^2 + 21^2 = d^2
Simplify.
16 + 21^2 = d^2
228 = d2
On both sides, take the square root.
√228 = √d2
15.1 ≈ d
Therefore, the part's maximum possible length was 15 inches.
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Homer told Bart that if he wanted the new video game, Bonestorm, he would have to score an 85% or higher on his next math quiz. Mrs. K gave the class a pop quiz and Bart scored 22/25. Use your skills converting a fraction to a percent and decimal and calculate whether Bart will get his new video game.
Answers
Bart is doing a quiz and gets 22/25
25 *? = 100
? = 4
So multiply 22 by 4
Then you get 22*4%
Which is 88%
Determine whether each ordered pair is a solution of the inequality. x+2y>10
Answers
The ordered pair of a solution of the inequality are (10, 0) and (0, 5).
The given inequality is x+2y>10.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Graph the inequality by finding the boundary line, then shading the appropriate area.
The solution of the inequality is (10, 0) and (0, 5).
Hence, the ordered pair of a solution of the inequality are (10, 0) and (0, 5).
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Help Algebra 2 Bionomical radical expressions
Answers
The product of the radical expression is - 49 + 13√7. option B is the correct answer
From the question, we have
(7-√7)(-6+√7)
= (7) × (-6) + (-√7) × (√7) + (-√7) × (-6) + (7)(√7)
= -42 - 7 + 6√7 + 7√7
= - 49 + 13√7
The product of the radical expression is - 49 + 13√7
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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PLEASE HELP FAST
the question is on the screenshot
Answers
Answer:
Since 1 scoop of ground coffee makes 1 cup of coffee, Andy can make 24 cups of coffee from the jar.
Step-by-step explanation:
Select all equations that can result from adding these two equations or subtracting one from the other.
{x+y=123x−5y=4
A -2x−4y=80
B -2x+6y=80
C 4x−4y=164 x minus 4 y is equal to 16
D 4x+4y=164 x plus 4 y is equal to 16
E 2x−6y=-82 x minus 6 y is equal to
F 5x−4y=285 x minus 4 y is equal to 28
Answers
The two equations that can be formed by adding or subtracting is
4x−4y = 16 and 2x − 6y = -8 .
the two equations are : x + y = 12 and 3x − 5y = 4
Adding we get :
x + y = 12
3x − 5y = 4
4x -4y = 16
Subtracting we get:
x + y = 12
3x − 5y = 4
-2x + 6y = 8 or 2x - 6y = -8
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the unknown parameters variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
It will be regarded as a phrase. In the following section of this article, you will discover the distinction between an equation and an expression.
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10 points!!!!!! help now it is due now!!!!!!!!
Answers
Answer:
Step-by-step explanation:
Write the value of x when y is = 7
x = 7
x = -1
x = -4
Determine the equation of the line that is perpendicular to the given line, through the given point
y = x -1 ; (-6,2)
Answers
The equation of the line is y=-x-4
How to find whether line is perpendicular or not?
Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane. Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.
The given line is
y=x-1
the slope of it is 1
As the slopes of perpendicular lines are negative reciprocals
So, the slope of the perpendicular line is -1
As the point is(-6,2)
y=mx+b
y=(-1)x+b
2=-1(-6)+b
2=6+b
b=2-6
b=-4
∴The equation of the line that is perpendicular is y=-x-4
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PLEASE HELP the pics down below
Answers
I believe that f(2) would be 10 and f(-2) would be -5.
960 times 1.0 times 10^6
Answers
Answer:960000000
Step-by-step explanation:
Answer: 960000000
Step-by-step explanation:
960 times 1.0 times 10^6 look it up !!
Canada computer charges 18.70/h plus 20.00 for a service call. the repairs person came to do maintenance on all of the school's computers. if the job took three and a half hours, what was the bill?
Answers
Using a linear equation to solve this problem, the charge for a 3.5 hour job is 85.45 dollar.
How much was the bill?To find how much was the bill, we need to write an equation or linear equation for this.
For every linear equation, it takes the form of y = mx + c.
Where m and c are the slope and intercepts of the straight line.
In this case, our linear equation can be written as
y = 18.70x + 20
where x = number of hours worked.
If the job took three and a half hour which is 3.5 hours, we can substitute this into the equation and solve.
y = 18.70(3.5) + 20
y = 85.45
The charge is 85.45 dollar.
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Write and olve a real-word proublem that involve dividing a decemal by a decimal
Answers
We have elaborate below a real-world problem that involves a decimal divided by a decimal.
Since we are given a problem that says that Jake owns a bakery amd he makes 8.5 boxes of cupcakes in 15.5 hours, the question is how many cupcakes he makes in 1 hour .So the time taken is 15.5 and the number of cupcakes made in the 15.5 hours is 8.5. So 15 .5hours=8.5 cupcakes, now dividing both sides by 15.5, we get: 1 hour=8.5/15.5 =0.54 = 1 cupcake, therfore, it needs 1 hour to make 1 cupcake. Here we had two quantities in form of decimals, so there division of expression of decimal dividing a decimal.
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Given that r is a vector 125 km due north, and s is a vector 164 km due south, what are the
hr
magnitude and direction of the sum r + s?
Answers
Answer:
39 km due southStep-by-step explanation:
Since the two vector have opposite directions, their sum will be the difference of magnitudes:
r + s = 164 - 125 = 39And the direction is the same with the vector with greater magnitude, so it is south.
Answer:
Magnitude = 39 km
Direction = South
Step-by-step explanation:
Formula we use,
→ r + s
Now the required answer will be,
→ r + s
→ 164 + (-125)
→ 164 - 125
→ 39 km
Thus, answer is 39 km due south.
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.
Answers
The polynomial function with third degree, zeros of −3, −1, and 4, and a y-intercept of −13 is y = -13/12 (x³ - 13x + 12)
Polynomial function:
polynomial function means a functions of single independent variables, in which variables can occur more than once, raised to an integer power.
Given,
Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.
And we need to construct a polynomial function with the stated properties and reduce all fractions to lowest terms.
We know that the standard form for the third degree polynomial function is written as,
=> y = K (x + zeros1) (x + zeros2) (x + zeros3)
The third degree, zeros of the function is -3, -1 and -4.
Now, we have to apply it on the general form,
=> y = K (x -3) (x - 1) (x + 4) ----------------------(1)
Here we know the value of y intercept is -13 then the value of x is 0.
So, it can be written as,
=> -13 = K(0 - 3) (0 - 1) (0 + 4)
=> -13 = K (12)
Therefore, the value of K = -13/12
Now, apply the values on the equation (1), then we get,
=> y = -13/12 (x -3) (x - 1) (x + 4)
Therefore, the third degree polynomial function is,
=> y = -13/12 (x³ - 13x + 12)
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whats the answer to this
Answers
A Linear equation in point slope form using the first point 3/4h , 9 in that can be used to determine the level of chocolate syrup in dispenser after x hours is y = -4x + 12 .
In the question ,
it is given that
in 3/4 hours the the level of chocolate syrup was 9 inch ,
So , the first point is (3/4,9) .
in 5/4 hours the level of chocolate syrup in the dispenser was 7 inch .
So , the second point is (5/4,7)
to find the linear equation we first need to find the slope .
Slope = (7-9)/(5/4-3/4)
= -2/(2/4)
= -4
So , the equation in slope intercept form having point (3/4 , 9) and slope -4 is .
(y - 9) = -4(x - 3/4)
y - 9 = -4x + 3
y = -4x + 3 + 9
y = -4x + 12
Therefore , The linear equation is y = -4x + 12 .
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if 1 + 2 = 3 then what does 1+2 equal
Answers
1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
1 + 2 = 3
As we know, from the definition:
Arithmetic can be defined as, an operation in which we do the addition of numbers, subtraction, multiplication, and division.
For the addition of two numbers:
The two numbers are 1 and 2:
Draw a vertical line 1: |
Draw two vertical lines 2: | |
Count the lines: | | | = 3
Thus, 1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.
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Can anybody solve this for me?
Answers
Answer:
1. -3
2. 6
3.less than
Step-by-step explanation:
6. In parallelogram ABCD find m¿A. (G.CO.11)
D
B. 70°
C. 110°
D. 200°
A
(6x +20)°
(4x+10°
6
Answers
Answer: b
Step-by-step explanation:
I WILL GIVE BRAINLIST!!
Which postulate would prove that triangle ABC triangle DEC?
A) ASA
B) SAS
C) SSS
D) AAS
Answers
Answer:
ASA
Step-by-step explanation:
1) the angles are congruent where they intercept in blue
2) the sides that are congruent are between the two congrunet angles the blue ones and the given ones
Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answers
Answer:
Angles 2, 3, 6, and 7 will be the same with 41 degrees!
Angles 1, 4, 5, and 8 are the same with 139 degrees!
Step-by-step explanation:
Opposite angles are the same so that makes angles 2, 3, 6, and 7 the same at 41 degrees!
The same rule applies to angles 1, 4, 5, and 8 and we have to subtract!
180 - 41 = 139 degrees!
Have an amazing day!!
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Write the equation of the line that contains the following point and slope. (-2, -7) m = 4/5
Answers
The equation of the line that passes through the point and slope (-2, -7) m = 4/5
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The line contains the following point and slope. (-2, -7) m = 4/5
y - y1 = m(x - x1)
y + 7 = 4/5(x + 2)
y = 4x/5 + 8/5 - 7
y = 4x/5 - 27/5
Thus, the equation of the line that passes through the point and slope (-2, -7) m = 4/5
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Which point represents the origin? number line from minus 5 to 5 with point M at minus 4, J at minus1, W at 0, and K at 2. Question 1 options: Point W Point J Point M Point K
Answers
The point that represent the origin in the number line is Point W
What is a number line?A number line is a horizontal representation of numbers in parts with equal intervals
The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values at right
number line on -5 to 5 will have the origin at the center and te center here is zero which is similar to p
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Numerical factors of a term is also it's coefficient true or false
Answers
A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables. For example, in the term 2x, 2 is the coefficient.
Solve the equation by Factoring.
n²-n-56=0
A) (6,3)
C) (-6,7)
B) -7, 8)
D) -8,8
Answers
Step-by-step explanation:
n^2 - n -56 = 0
n^2 -8n +7n-56 = 0
n(n-8) +7(n-8) = 0
(n+7)(n-8) = 0
n = (-7,8)
option B
Order the group of rates from least to greatest. 100 oz/min, 2500 g/min, 10 lb/min
Answers
enter the value of x + 26
Answers
This answer is correct if you have the same assignment as I did. Where the central angle and the angle between the tangents are supplementary
x=26=180 now subtract 26 and you get 154