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All of the graphs and associated functions and equations serve as examples of quadratic functions.

The locations where the graph's line or curve crosses the x-axis are known as the zeros of a function. The line dividing a graph into equal halves is known as the axis of symmetry.

The minimum or greatest point on a graph is the vertex of a function. If a quadratic function expands upward, its vertex is lowest; if not, it is maximum.

The worksheet is given below:

Using the stated definitions, the worksheet's answers are:

Graph 1

Zeros: -4 and 0

Axis of symmetry: x = -2

Min or Max: Maximum

Vertex: (-2, 4)

Graph 2

Zeros: 2

Axis of symmetry: x = -2

Min or Max: Minimum

Vertex: (-2, 0)

Graph 3

Zeros: -3 and 3

Axis of symmetry: x = 0

Min or Max = Minimum

Vertex: (0, -9)

Graph 4

Zeros: -5 and -3

Axis of symmetry: x = -4

Min or Max = Maximum

Vertex: (-4, -1)

Graph 5

Zeros: 3 and 7

Axis of symmetry: x = 5

Min or Max = Minimum

Vertex: (5, -4)

Graph 6

Zeros: None

Axis of symmetry: x = 24

Min or Max = Minimum

Vertex: (2, 5)

Graph 7

Zeros: 1 and 5

Axis of symmetry: x = 3

Min or Max = Minimum

Vertex: (3, -4)

Graph 8

Zeros: -2 and 0

Axis of symmetry: x = -1

Min or Max = Maximum

Vertex: (-1, 1)

Graph 9

Zeros: 5

Axis of symmetry: x = 5

Min or Max = Minimum

Vertex: (5, 0)

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The Ruiz family's laptop has the greater initial resale value. During the first four years, the resale value of the Sawyer family's laptop decreases at an average rate faster than​ the resale value of the Ruiz family's laptop.

The initial resale value of the laptops for both families are the same, as the function f(x) models the resale value for both families and does not differentiate between them.

During the first four years, the average rate of change in the resale value of the Sawyer family's laptop can be found by finding the average rate of change of the function f(x) over the interval [0, 4]. The average rate of change during this interval can be approximated by finding the average rate of change over a smaller interval within [0, 4]. For example, finding the average rate of change over the interval [0, 1] and then multiplying by 4 to find the average rate of change over the entire interval [0, 4].

Correct Question :

The Sawyer and Ruiz families each bought a laptop computer at the same time resale values in dollars of the laptops are modeled by the given function where X is the number of years that each family has owned the laptop.

The ____ family's laptop has the greater initial resale value. During the first four years, the resale value of the Sawyer family's laptop decreases at an average rate ____ the resale value of the Ruiz family's laptop.

1st blank:

Ruiz

Sawyer

2nd blank:

slower than

equal to

faster than​

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The above function should be used to complete the table based on the given domain as follows;

x         0      1     2     3    4    

f(x)      -6     -5   -3     1    9

In order to use the given exponential function to complete the table, we would have to substitute each of the values of x (x-values or input values) into the exponential function and then evaluate as follows;

When the value of x is 0, the exponential function is given by;

f(x) = 2^x - 7

f(0) = 2^0 - 7

f(0) = 1 - 7

f(0) = -6.

When the value of x is 1, the exponential function is given by;

f(x) = 2^x - 7

f(1) = 2^1 - 7

f(1) = 2 - 7

f(1) = -5.

When the value of x is 2, the exponential function is given by;

f(x) = 2^x - 7

f(2) = 2^2 - 7

f(2) = 4 - 7

f(2) = -3.

When the value of x is 3, the exponential function is given by;

f(x) = 2^x - 7

f(3) = 2^3 - 7

f(3) = 8 - 7

f(3) = 1.

When the value of x is 4, the exponential function is given by;

f(x) = 2^x - 7

f(4) = 2^4 - 7

f(4) = 16 - 7

f(4) = 9.

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The length of the side ML of the trapezoid JKML is 58 units.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.

We know the midsegment of a trapezoid is half of the sum of the two parallel sides.

Therefore, {(3x + 11) + (10x - 12)}/2 = 45.

3x + 11 + 10x - 12 = 90.

13x - 1 = 90.

13z = 91.

x = 91/13.

x = 7.

So, The length of ML is 10(7) - 12 = 70 - 12 = 58 units.

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The shape of the banana curve is a parabola, the number of zeros is 1, the zeros of the polynomial are (-3, 4), and the quadratic polynomial is a(x² - 16).

(i) The shape of the banana curve from the figure is a parabolic shape.

(ii) The number of zeros of the polynomial for the shape of the banana is 1.

(iii) To find the zeroes of f(x) = x² - x - 12, we need to solve the equation x² - x - 12 = 0 using the quadratic formula.

x = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = -1, c = -12

x = (1 ± √(1 + 48)) / 2

x = (1 ± √49) / 2

So, the zeroes are (1 + 7) / 2 = 4 and (1 - 7) / 2 = -3.

(iv) If the representation of the banana curve whose one zero is 4 and the sum of the zeroes is 0, then the equation is x = -4 and x = 4.

The quadratic polynomial is f(x) = a(x - 4)(x + 4) = a(x² - 16).

Since the coefficient a is not given, we cannot determine the exact polynomial, but we know it must be of form f(x) = a(x² - 16).

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--The given question is incomplete; the complete question is

"The below quadratic function can model the natural shape of a banana. Now, we know that a parabolic shape must have a quadratic function, therefore an equation in standard form of f(x) = ax² + bx + c. To find an equation for the parabolic shape of the banana, we need to find the values of a, b, and c. From the banana picture above, we can see that a quadratic function is able to model the banana quite accurately, with a=0.1, b=0, and c=0. Therefore, the equation is f(x) = 0.1x²

(i) Name the shape of the banana curve from the above figure.

(ii) Find the number of the zeroes of the polynomial for the shape of the banana.

(iii) If the curve of banana represented by f(x) = x² - x - 12. Find its zeroes.

(iv) If the representation of banana curves whose one zero is 4 and the sum of the zeroes is 0, then find the quadratic polynomial.​"--

A statement which is false include the following: D. In the ordered pair (9, 7), 7 is the x-coordinate.

In Mathematics, an ordered pair is a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate and the y-coordinate on the coordinate plane of any graph such as the following:

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(6 - 3)² + (7 - 7)²]

Distance = √[3² + 0²]

Distance = √9

Distance = 3 units.

In conclusion, in the ordered pair (9, 7), 9 is the x-coordinate while 7 is the y-coordinate.  

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The value of n is 1.03.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

3.2-5.1-3n+5=0

Now,

-3n=-3.2+5.1-5

-3n=-3.1

n=3.1/3

n=1.03

Therefore, the answer of given algebra will be 1.03

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Answer: I got 13x^2+4x+7, I hope this helps

Answer:

450 meters is 0.45 kilometers.

Ella bought 12 mini cakes. The solution has been obtained using the unitary method.

What is a unitary method?

In the unitary technique, the value of a single unit is determined first, and then the value of the required number of units is determined. Simply expressed, the unitary approach is used to determine the value of a single unit from a specified multiple.

We are given that the bakery charges $35 for 7 mini cakes

So, the charge for 1 mini cake is

⇒$35/7 = $5

Now, Ella has bought mini cakes for $60.

So, the number of mini cakes bought by her are

⇒$60/$5 = 12

Hence, Ella bought 12 mini cakes.

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The value of the bulldozer at year 2.5 is 93593.67 and at year 5 is 66451.16.

A construction company bought a new bulldozer for $125,000. The bulldozer depreciates exponentially and after 2 years the value of the bulldozer is $80,000. What is the value at year 2. 5 and 5Let V0 be the initial value of the bulldozer, and k be the depreciation rate. We know that the value of the bulldozer after 2 years is V2 = V0 * e^(-k * 2) = 80000.

So, k = -ln(V2/V0) / 2.

The value of the bulldozer at year 2.5 can be calculated as:

V2.5 = V0 * e^(-k * 2.5)

The value of the bulldozer at year 5 can be calculated as:

V5 = V0 * e^(-k * 5)

Plugging in V0 = 125000 and k = -ln(V2/V0) / 2, we get:

V2.5 = 125000 * e^(-k * 2.5) = 93593.67

V5 = 125000 * e^(-k * 5) = 66451.16

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The value of x in the above triangle, according to the supplied assertion, is 21.

The Pythagorean Theorem states that the squared on the tangent line (the side across from the right angle) of a right triangle, or, in standard mathematical notation, a2 + b2, are equal to the numbers on the legs. A triangle is a two-half polygon in geometry that has 3 components and three vertices. The most important attribute of a triangle is that its inside angles sum to 180 degrees. The right triangle angle sum attribute is what is known as.

x+x+7/x+7 = 9+12/12

2x+7/x+7 = 27/12

8x+28 = 7x+49

8x-7x = 49-28

x = 21

Therefore, the of x is 21

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Using the factor method, the other x-intercept for the parabola defined by the equation is; (-5, 0)

We are given the equation of the parabola as;

y = -x² - 7x - 10

We are given one of the x-intercepts as (-2, 0). Thus, let us factorize the equation of the parabola by setting it to zero to get;

-x² - 7x - 10 = 0

Let's factor it as;

-x² - 2x - 5x - 10

Factorizing it out gives;

-x(x + 2) - 5(x + 2) = 0

Thus, we now have;

(-x - 5)(x + 2) = 0

Thus, the other x-intercept is at;

-x - 5 = 0

x = -5

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A total of 31 child tickets were sold that day.

System of Equations:

Problems with two unknown values require a system of equations containing two variables.

A unique solution is obtained only when the lines formed by the equations intersect at only one point.

Let C be the number of child tickets and A be the number of Adult tickets

Now, like most coin, cost, or earnings problems, you can make a number balance and a money balance and get two equations for the two unknowns defined above:

4C=adults, because four times as many tickets were sold

6.50C+9.80(4C)=1436.80

6.50C+39.2C=652.50

45.7C=1436.80

C=31

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The solution to the equation 2-x³ = 4x + 3 is x=1.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

To find the solution to the equation 2-x³=4x+3, we can set the two sides of the equation equal to each other and solve for x.

2-x³ = 4x + 3

x³ - 4x - 1 = 0

To solve this equation, factor it or use the cubic formula.

One possible solution is x = 1, which can be verified by substituting it back into the original equation.

Another way to find the solution graphically, we can plot the graphs of y = 2-x^3 and y = 4x+3 on the same coordinate plane. The points at which the two graphs intersect are the solutions to the equation.

The graph of y = 2-x^3 is a downward facing parabola and the graph of y = 4x+3 is a line with slope 4 and y-intercept 3.

The intersection point of the parabola and the line is the solution x=1

It is not possible to find the other solutions graphically because the parabola doesn't intersect with the line again.

Therefore, the solution is obtained as x = 1.

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Answer:

0.51

Step-by-step explanation:

45 / (45 + 6 + 37) = 0.51

The probability that all three letters are identical is the product of the probability that each individual letter is identical, which is (1/26) * (1/26) * (1/26) = (1/26)^3.

The probability that all three letters selected are identical would be (1/26)^3, assuming that the pool of letters contains an equal number of each letter of the alphabet (a, b, c, ..., z) and that each letter is selected independently and with replacement. This is because there is only a 1 in 26 chance of selecting any given letter on the first draw, and the same is true for the second and third draws. Since all three draws are independent, the probability that all three letters are identical is the product of the probability that each individual letter is identical, which is (1/26) * (1/26) * (1/26) = (1/26)^3.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

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If Pablo’s goal is to walk a total of 10(3/4) miles each week. He walked 2(1/4) miles on Sunday, 1(3/8) miles on Monday, and 1(7/8) miles on Tuesday , then the equation to find the number of miles he needs to walk is "15/8 + 11/8 + 9/4 + x = 43/4" .

the goal of Pablo to walk in a week is = 10(3/4) = 43/4  ;

the distance he walked on Sunday is = 2(1/4) = 9/4  ;

the distance he walked on Monday is = 1(3/8) = 11/8 ;

the distance he walked on Tuesday is = 1(7/8) = 15/8  ;

let the remaining distance be = x miles ;

So , this situation can be represented in equations as :

⇒ 15/8 + 11/8 + 9/4 + x = 43/4 ;

making the denominator same by taking LCM as 8  ,

we get ;

⇒  15/8 + 11/8 + 18/8 + 8x =  43/4

⇒  15/8 + 11/8 + 18/8 + 8x/8 = 43/4

⇒  15 + 11 + 18 + 8x = 8 × 43/4  ;

⇒  44 + 8x = 86  ;

⇒ 8x = 86-44 = 42 ;

⇒ x = 42/8 = 5.25

Therefore , Pablo still needs to cover 5.25 miles to reach his weekly goal .

The given question is incomplete , the complete question is

Pablo’s goal is to walk a total of 10(3/4)  miles each week. He walked 2(1/4)  miles on Sunday, 1(3/8)  miles on Monday, and 1(7/8)  miles on Tuesday. Write the equation that he can use to find the number of miles he needs to walk the rest of the week to reach his goal ?

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The price of the stock models exponential is 500, The rate of exponential growth or exponential decay is 19%.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x) = 500(1 − 0.19 )x² models the price of a share of stock over time.

The quantity decreases slowly at regular intervals by a fixed percent.

The price of the stock models exponential is 500.

The rate of exponential growth or exponential decay is 0.19×100=19%

f(x) = 500(1 − 0.19 )x²

f(x)=500(0.81)x²

f(x)=500(0.81)x² is the equivalent function of  f(x) = 500(1 − 0.19 )x²

Hence, The price of the stock models exponential is 500, The rate of exponential growth or exponential decay is 19%.

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Answer:

433345344 Answer

Step-by-step explanation:

Answer:

A. 190-25

Step-by-step explanation:

Answer:

A or B

Step-by-step explanation:

Because 190 - 125 will give you the difference of 190 and 125

Denominator can be defined as the bottom number in a fraction that shows the number of equal parts an item is divided into. It is the divisor of a fraction

The given problem is

13x^6

51 x^4

From here, we must exclude all values that make the denominator equal to zero.

This is defined if and only if

x ≠ 0

Even the given expression can be simplified to obtain:

13x^6

51 x^4

The exclusion is

x ≠ 0

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Answer:

x = 0

Step-by-step explanation:

I got it correct on Odyssey. Feel free to let me know if you need any help in the future  : )

The angle of each measure is:

m<DEC= 129°

m∠BCE = 51°

m∠ADE = 57°

m∠EDB = 123°

m∠DBC = 57°

Angle of measure is the measure of an angle formed by two rays with a common endpoint. Angle of measure is important to many mathematical and scientific fields, including geometry, trigonometry, and physics.

In geometry, angles are used to define shapes and measure the size of an object. For example, angles are used to determine the angles of a triangle, or the angles between the sides of a rectangle. Angle of measure is also important in trigonometry, as it is used to calculate the lengths of sides and angles in a triangle, as well as the area of a triangle.

Angle of measure is also used in engineering, navigation, and surveying. When designing a building or structure, angles are used to determine the strength and stability of the structure, as well as the angles of the beams and walls. In navigation, angles are used to calculate the direction of a ship or aircraft. Finally, in surveying, angles are used to measure the angles between points on a map or a landscape.

Given,

m∠DEC= (12x-3)°, m∠BCE= (7x-26)°, and m∠DAE= 72°

∠DEC+∠BCE = 180°

12x-3+7x-26 = 180°

19x - 29 = 180°

19x = 180+29

x = 209/19

x = 11

Substitute x=11 in m∠DEC= (12x-3)°, we get

m∠DEC= 129°

Substitute x=11 in m∠BCE= (7x-26)°, we get

m∠BCE = 51°

To find m∠ADE,

m∠ADE + m∠DAE + m∠DEA=180°

m∠ADE + 72° + 51° = 180°

m∠ADE = 57°

To find m∠EDB,

m∠EDB + m∠ADE=180°

m∠EDB = 180° - 57°

m∠EDB = 123°

To find m∠DBC,

m∠DBC = m∠ADE are corresponding angles, so

m∠DBC = m∠ADE = 57°

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A boat can travel approximately distance 116 miles on 39 number of gallons of gasoline.

To calculate the distance a boat can travel on 39 gallons of gasoline, you must divide the distance (174 miles) by the amount of gasoline (58 gallons), and then multiply the result by the new amount of gasoline (39 gallons).

the distance a boat can travel on 39 gallons of gasoline, you must divide the distance (174 miles) by the amount of gasoline (58 gallons), and then multiply the result by the new amount of gasoline (39 gallons).

174 miles ÷ 58 gallons x 39 gallons = 116.37 miles

Therefore, a boat can travel approximately 116 miles on 39 gallons of gasoline.

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Answer:

56 Primitive feet

Step-by-step explanation:

Are 5 ways for four people with different heights to line up single-file so that exactly two people are taller than the person immediately behind them.

Let's call the four people A, B, C, and D, and let's assume that their heights are distinct and that A is the shortest. Then, there are 3! = 6 ways for them to line up single-file without any restrictions on their heights. However, this counts the cases where A is taller than B, which is not allowed.

To correct for this overcounting, we can subtract the number of ways where A is taller than B, which is 2! = 2, since there are 2! ways to arrange B, C, and D in this case.

However, this also subtracts the case where A is taller than both B and C, which is not allowed.

So, we need to add the number of ways where A is taller than both B and C, which is 1, since there is only 1 way to arrange B, C, and D in this case. Therefore, by PIE, the number of ways for A, B, C, and D to line up single-file so that exactly two people are taller than the person immediately behind them is:

6 - 2 + 1 = 5

So, there are 5 ways for four people with different heights to line up single-file so that exactly two people are taller than the person immediately behind them.

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Answer:

You can find the unit rate for each cereal an see which one is a better deal.  You divide and quantity of cereal by the price.

72 words per minute

Step-by-step explanation:

Say one box of cereal has 100 ounces and it cost $4.50 and another box of cereal has 150 ounces for $5.25

4.50/100 = .045 cents per ounce the other box would be

5.25/150 = .035 cents per ounce.

1800/25 = 72

We can start solving the problem using systems of equations. Let x be the cost of each balloon and y be the cost of each banner. We know from the problem that:

1x + 1y = 3 (the cost of 1 balloon and 1 banner is $3)

5x + 2y = 9 (the cost of 5 balloons and 2 banners is $9)

We can use the first equation to solve for one of the variables in terms of the other, and substitute that into the second equation. Then we can solve for the remaining variable.

From equation 1:

y = 3 - x

We can substitute this into equation 2:

5x + 2(3 - x) = 9

Which simplifies to:

5x + 6 - 2x = 9

3x = 3

x = 1

So each balloon costs $1

We can now substitute x=1 in the first equation:

1*1 + 1y = 3

y = 2

So each banner costs $2

Step-by-step explanation:

Let us assume the cost of

In first case , cost of 1 1 balloon and 1 banner is $3 . We can set up a equation as ,

1*x + 1*y = 3

x + y = 3 . . . . . (i)

In second case, cost of 5 balloons and 2 banners is $9 . So ,

5*x + 2*y = 9

5x + 2y = 9 . . . . . (ii)

From equation i and ii , we have ,

5(3-y) + 2y = 9

15 - 5y + 2y = 9

15 - 3y = 9

3y = 15 -9

3y = 6

y = 2

And we had ,

x + y = 3

x + 2 = 3

x = 3 - 2

x = 1

Hence,

and we are done!

The number of ways to load the cars onto the truck is  [tex]^{25}C_3[/tex] i.e. 2300 ways.

To find the number of ways to load the cars on the truck we can use the formula for combination, which is given by -

C(n,k) = n! / (k! (n-k)!)

where n is the total number of cars (25), k is the number of cars we want to choose (3)

Using this formula, we can calculate the number of ways to load the cars as follows -

C(25,3) = 25! / (3! (25-3)!) = 252423 / (321) = 2300

Hence, there are 2300 ways to load 3 cars out of 25 onto the truck for transport.

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The equation relating the number of hours worked and the total amount earned will be y = 14x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the table, the two points will be written as (1.25, 17.50) and (3.75, 52.50). Then the equation of the line is given as,

(y - 17.50) = [(52.50 - 17.50) / (3.75 - 1.25)](x - 1.25)

y - 17.50 = 14(x - 1.25)

y - 17.50 = 14x - 17.50

y = 14x

The equation relating the number of hours worked and the total amount earned will be y = 14x.

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The missing table is attached below.