2. Chen said that the vertex for any quadratic function f(x) = ax² + bx + c can be
found at the point (-2, c). Do you agree or disagree with Chen? Explain.

The formula for g(x) in terms of h(x) is: g(x) =  h(x - 5) -1

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The turning point (stationary point) of the curve.

the minimum point of a parabola that opens upwards

the maximum point of a parabola that opens downwards

To find the series of translations that transform the graph of y = h(x) onto y = g(x), compare the vertices of both graphs.

Vertex of h(x) = (-5, 7)

Vertex of g(x) = (0,6)

Find the difference of coordinates, the rule of translation right and up

x = 0 - (-5) = 5

y = 6- (7) = -1

h(x) translated 7 units right = h(x - 5)

h(x - 7) translated 5 units up = h(x - 5) -1

Therefore, the formula for g(x) in terms of h(x) is: g(x) =  h(x - 5) -1

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Answer:

number 1 and 2

Step-by-step explanation:

polynomial expressions have 4 or more numbers

Answer:

The first and last examples are polynomials

Step-by-step explanation:

The second example is not a polynomial because you cannot have fractional exponents.

The third example is not a polynomial because by cannot have variables in the denominator.

If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x), then the,

(a) Mean = 3.42544

(b) Variance = 7.91

Given data,

If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x) as defined in the following table:

x              0         1               2                  3          4          5         6        7     8      

P(X=x)    0.06528   0.3870     0.03062       0.0968      0.06913        0.0968      0.04846                0.01252            0.1935

Mean = Σ [tex]x p(x)[/tex]

Mean = (0 * 0.06528) + (1*0.3870) + (2*0.03062) + (3*0.0968) + (4*0.06913) + (5*0.0968) + (6*0.04846) + (7*0.01252) + (8*0.1935)

Mean = 0 + 0.3870 + 0.06124 + 0.2904 + 0.2765 + 0.484 + 0.2907 + 0.0876 + 1.548

Mean = 3.42544

Mean = Σ [tex]x p(x)[/tex] = 3.42544

Σ [tex]x^{2} p(x)[/tex] = (0 * 0.06528) + ([tex]1^{2}[/tex]*0.3870) + ([tex]2^{2}[/tex]*0.03062) + ([tex]3^{2}[/tex]*0.0968) + ([tex]4^{2}[/tex]*0.06913) + ([tex]5^{2}[/tex]*0.0968) + ([tex]6^{2}[/tex]*0.04846) + ([tex]7^{2}[/tex]*0.01252) + ([tex]8^{2}[/tex]*0.1935)

Σ [tex]x^{2} p(x)[/tex] = (0 * 0.06528) + (1*0.3870) + (4*0.03062) + (9*0.0968) + (16*0.06913) + (25*0.0968) + (36*0.04846) + (49*0.01252) + (64*0.1935)

Σ [tex]x^{2} p(x)[/tex] = 0 + 0.3870 + 0.1224 + 0.8712 + 1.106 + 2.42 + 1.744 + 0.613 + 12.38

Σ [tex]x^{2} p(x)[/tex] = 19.6436

Variance = Σ [tex]x^{2} p(x)[/tex] - ( Σ [tex](xp(x))^{2}[/tex])

Variance = 19.6436 - [tex](3.42544)^{2}[/tex]

Variance = 19.6436 - 11.7336

Variance = 7.91

Therefore,

If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x), then the,

(a) Mean = 3.42544

(b) Variance = 7.91

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Answer:

f⁻¹(x) = [tex]\frac{\sqrt{x}}{2}[/tex] , -[tex]\frac{\sqrt{x} }{2}[/tex]

Step-by-step explanation:

f(x) = 4x²

rewrite as:

y = 4x²

Interchange the variables, then solve for y:

x = 4y²

y² = x/4

y = √x/2, -√x/2

Answer:

f⁻¹(x) = [tex]\frac{\sqrt{x}}{2}[/tex] , -[tex]\frac{\sqrt{x} }{2}[/tex]

The zeros of the quartic equation x⁴ - 2 · x² - 63 are x₁ = √(1 - √62), x₂ = √(1 + √62), x₃ = - √(1 - √62) and x₄ = - √(1 + √62).

In this problem we find a quadratic-like quartic equation, that is, a quadratic equation of the form:

y = a · x⁴ + b · x² + c

Where a, b, c are real coefficients.

From this expression in standard form we must determine its roots by using an application of algebra properties known as completing the square, which is transforming a part of the function into cubic square trinomial.

First, write the expression and equal it to zero:

x⁴ - 2 · x² - 63 = 0

Second, complete the square and simplify:

(x⁴ - 2 · x² + 1) = 63 - 1

(x² - 1)² = 62

x² - 1 = ± √62

x² = 1 ± √62

x = ± √(1 ± √62)

Third, write all the zeros of the quartic equation:

x₁ = √(1 - √62), x₂ = √(1 + √62), x₃ = - √(1 - √62), x₄ = - √(1 + √62)

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Third grade class :: 148 books

Fourth grade class :: 175 books

Total :: 323 books

1 box = 9 books.

323/9 =

36 box....

The Consistent System Of Linear equations have at least one Solution , and the inconsistent system of linear equations have No Solution .

Let the system of two linear equations be given as :  [tex]a_{1}x +b_{1}y =c_{1}[/tex] and [tex]a_{2}x +b_{2}y =c_{2}[/tex] ;

Case(i) If the equations satisfies the condition :  [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex] ,

then linear equations has a unique solution and solutions are called as consistent .

Case(ii) If the equations satisfies the condition :  [tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]  ,

then linear equations has infinitely many solution and the solutions are called consistent .

Case(iii) If the equations satisfies the condition : [tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]  ,

then the linear equations has No Solution and the solutions are called as inconsistent .

Therefore  , if system has at least one solution , then solutions are consistent .

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The 10 years continuous growth rate as calculated is 0.9259 % per year and the equation to model the population growth of the United States, and is used it to estimate the population in 2020 is  P = 281.4e^(0.009 259t); 338.6 million  .

Given,

P₀ = 281.4 million

P  = 308.7 million

To calculate the growth rate

t = 2010 - 2000 = 10 yr

P = P₀e^(rt)

308.7 = 281.4e^(10r)

e^(10r) = 1.0970

10r = ln1.0970

r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259  

r = 0.9259 % per year

To find the equation of population model

P = 281.4e^(0.009 259t)

here , P is in millions and

the number of years passed since 2002 is represented as t.

P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203

P = 338.6 million

Therefore, the population in 2020 is assumed to be 338.6 million.

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There are 460 bass fish present if a sample of 1,000 fish is collected.

We can determine how much of one quantity is in the other by comparing two amounts of the same units and finding the ratio. Ratios can be divided into two groups. One is the part-to-whole ratio, and the other is the part-to-part ratio. The link between two distinct entities or groupings is depicted by the part-to-part ratio.

Given table shows about type and number of fish,

Type of Fish              Bass      Eel       Gar

Number of Fish          92         56       52

total number of fishes = 92 + 56 + 52 = 200

to find the number of Bass fish if the total fishes are 1000,

= (1000)92/200

= 460

Hence, there are 460 Bass fish present if a sample of 1,000 fish is collected in the lake.

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Answer: 146

Step-by-step explanation:

The answer to the above question is B. Multiply the first equation by -2 and add the second equation.

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."

Given,

[tex]2x - 2y = 24\\4x + 7y=-40\-4x +4y = -96\\4x+7y = -40\\11y = -136\\y = -136/11[/tex]

The answer to the above question is B. Multiply the first equation by -2 and add the second equation.

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The plant root is growing at a rate of 3.81 centimeters per month.

To find the number of centimeters that the plant root is growing per month, you need to convert the number of inches to centimeters. One inch is equal to 2.54 centimeters, so to convert from inches to centimeters, you need to multiply the number of inches by 2.54.

In this case, the plant root grows 1.5 inches per month. Multiplying this by 2.54 gives us 3.81 centimeters, which is the correct answer. Therefore, the plant root is growing at a rate of 3.81 centimeters per month.

The other answer choices are not correct because they do not give the correct number of centimeters that the plant root is growing per month.

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A particular plant root grows 1.5 inches per month, then 3.81 centimeters the plant root are growing per month.

In the given question, a particular plant root grows 1.5 inches per month.

We have to find how many centimeters the plant root is growing per month.

As we know that 1 inch = 2.54 centimeters

To convert 1.5 inches in centimeters we multiply 1.5 by 2.54 because in 1 inch has 2.54 centimeters. After multiply we can easily find the answer in centimeters.

So 1.5 inch = 1.5*2.54 centimeters

1.5 inch = 3.81 centimeters

Hence, a particular plant root grows 1.5 inches per month, then 3.81 centimeters the plant root are growing per month.

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The option that best describes the pattern of association for the scatterplot graph is; There is a positive nonlinear association.

In statistics, we say that two random variables have a positive correlation if Y tends to increase as X increases.

Meanwhile, we can say that two random variables have a negative correlation if Y tends to decrease as X increases.

Now, when there is a relationship between the x and y variables, we can say that there is some type of association such as linear, quadratic, exponential e.t.c

Now, in this given scatterplot, we can see that y almost certainly increases as x increases and as such this is a positive correlation. Similarly, we see that it is not a linear relationship as it looks like an exponential curve. Thus, it is a non linear association.

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Answer:

The option that best describes the pattern of association for the scatterplot graph is; There is a positive nonlinear association.

Step-by-step explanation:

The radical exponent for five to the three fourths power all raised to the two thirds power is C. the square root of five.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this situation, five to the three fourths power all raised to the two thirds power will be:

= 5^3/4(^2/3)

= 5^1/2

The correct option is C

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All the situation are Exponential relationship accept the last one.

A linear function is modeled by the following rule:

y = mx + b

In which: m is the slope, which is the rate of change, that is, the change in y divided by the change in x. b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.

Given that "you work as a taxi driver. you earn an average of $75 in tips each day".

That is, 75^x

This is a Exponential equation.

2. The number of visitors to the eiffel tower in paris increases by 1.5% each year.

This is a Exponential equation.

The number of tadpoles in the pond triples each day.

This is a Exponential equation.

Also, every year 39 million cars cross the golden gate bridge in san francisco.

This is a Linear equation.

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The general form of an exponential decay function is f(a) = P . (1 - r)ᵃ,  while the general function of growth function is f(a) = P . (1 + r)ᵃ.  Hence, if the factor (1 - r) is less than 1, it is a decay function, while if the factor  (1 + r) is greater than 1, it is a growth function

The general exponential decay function can be written as:

f(a) = P . (1 - r)ᵃ

Where:

P = initial quantity

f(a) = remaining quantity at time a

a = time period

r  = decay rate

(1 - r) = decay factor

On the other hand, the general exponential growth function can be written as:

f(a) = P . (1 + r)ᵃ

where:

r = growth rate

(1 + r) = growth factor

Hence, the difference between decay function and growth function is: the factor in decay faction is less than 1, while in growth function, the factor is greater than 1.

Example:

f(a) = 6 . (0.25)ᵃ

This is an exponential decay function because the factor is less than 1, that is 0.25

f(a) = 10 . (3)ᵃ

This is not an exponential decay function, but a growth function,  because the factor is greater than 1, that is 3

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Answer:

A

Step-by-step explanation:

[tex]\frac{4}{5}[/tex] x - [tex]\frac{3}{2}[/tex] = [tex]\frac{1}{4}[/tex]

multiply through by 20 ( the LCM of 5, 2, 4 ) to clear the fractions

16x - 30 = 5 ( add 30 to both sides )

16x = 35 ( divide both sides by 16 )

x = [tex]\frac{35}{16}[/tex]

The one-third of the job will take md/3n days. The result is obtained by using the concept of inverse proportion.

Inverse proportion is a proportionality relationship when one value increases and the other decreases.

Assuming that the workers are working at the same rate, the more workers will complete the job more quickly. It means the more workers that do the job, the less time needed. We use inverse proportion to solve this problem.

We have workers and time to complete a job. Let's say e is the time for n workers to complete the job.

By the inverse proportion concept, we get

m/n = e/d

e = md/n days

To complete one-third of the job, they need

⅓e = ⅓ (md/n)

⅓e = md/3n

Hence, it will take md/3n days to complete the one-third of the job.

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The amount of customers  exceed 285 and when there are 47 tables of 4 and 16 tables of 5 the number so new customers is 17.

Given,

The numbers of customers one at a time is 285

At 12 pm it has 216 customers.

Part A :

To check new amount of customers exceeds 285 or not.

Also given 147 new customers.

So by substituting values:

216 x (1 - 1/3) + 147

= 144 + 147

= 291

Since 291 > 285

Therefore the new number of customers exceed 285.

Part B :

To find number of customers in the restaurant  when there are 47 tables of 4 and 16 tables of 5.

47 x 4 + 16 x 5

= 188 + 80

= 268

So, 285 - 268

= 17

Therefore there are  17 new customers in the restaurant.

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Answer:

  (8, 12)

Step-by-step explanation:

You want to solve the system ...

Add the two equations:

  (2x -y) +(y -x) = (4) +(4)

  x = 8 . . . . . . . . . . . . simplify

  y = 4 +x . . . . . . rearrange the second equation

  y = 4 +8 = 12

The solution is (x, y) = (8, 12).

The property of the triangle congruence state that a ≅ B then B ≅ A are:

The triangle is a polygon that has 3 edge and vertices. Triangle is one of the basic shape in the geometric. The area of the triangle is formulated as base of the triangle * height of triangle x 0,5. The value of three triangle edge degree is 180°.

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The value of the expression [(x² + 7x + 10) / (x² + 4x + 4)] · [(x² + 3x + 2) / (x² + 6x + 5)] will be 1.

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.

The expression is given below.

⇒ [(x² + 7x + 10) / (x² + 4x + 4)] · [(x² + 3x + 2) / (x² + 6x + 5)]

Simplify the expression, then we have

⇒ [(x² + 7x + 10) / (x² + 4x + 4)] · [(x² + 3x + 2) / (x² + 6x + 5)]

⇒ [(x + 5)(x + 2) / (x + 2)(x + 2)] · [(x + 2)(x + 1) / (x + 5)(x + 1)]

⇒ 1

The value of the expression [(x² + 7x + 10) / (x² + 4x + 4)] · [(x² + 3x + 2) / (x² + 6x + 5)] will be 1.

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Answer:see photo #4

Step-by-step explanation:

Answer:

3.  x^10

4.  648

Step-by-step explanation:

See the attached worksheet

Answer:

20 per kilogram. then it is necessary to know just what units are being used for the purchase. This information is given under 'Comparative Costs per Unit'.

Step-by-step explanation:

Answer:

3,744 [tex]cm^{2}[/tex]

Step-by-step explanation:

Front is a trapezoid

a = 1/2([tex]base_{1}[/tex] + [tex]base_{2}[/tex])h

a = 1/2(29 +12)24

a = 492

the back is the same value 492

Bottom

29 x 30 = 870

Right sides

30 x 26 = 780

Left side

25 x 30 = 750

Top

12 x 30 = 360

492 + 492 + 870 + 780 + 750 + 360 = 3744[tex]cm^{2}[/tex]

Answer:

y=50+25x

Step-by-step explanation:

x= 25 each hour

add by 25

and it will give you your output.

The equation of the line passing through the points (1,3) with slope = -4 is

y = -4x + 7

The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

m = (y - y1) / (x - x1)

where m = -4

y1 = 3

x1 = -1

-4 = (y - 3) / (x - 1)

-4(x - 1) = y - 3

-4x + 4 = y - 3

y = -4x + 7

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The volume of the cylinder is approximately 478.9 cm3.

To find the volume of a cylinder, you can use the formula:

[tex]Volume = \pi r^2h[/tex]

where r is the radius of the base of the cylinder and h is the height of the cylinder.

In this case, the radius of the cylinder is 1.045 cm and the height is 30.48 cm, so the volume is approximately 478.9 cm3. This is found by plugging the given values into the formula and rounding to the nearest tenth:

Volume = [tex]\pi (1.045 cm)^2(30.48 cm)[/tex] = 478.9 cm3.

So, the volume of the cylinder is approximately 478.9 cm3.

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Complete Question:

A graduated cylinder (approximate as a regular cylinder) has a radius of 1.045 cm and a height of 30.48 cm. What is the volume of the cylinder in cm3 (use 3.141 for TT)? Round to the nearest tenths.

The false statement is that the membership rates are increasing 20% each year.

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

We are given the equation models the number of members, M, of a gym t years after the gym opens.

[tex]M = 1,800 (1.02) ^t[/tex]

Now if the t time is 3 year then;

[tex]M = 1,800 (1.02) ^t\\\\M = 1,800 (1.02) ^3\\\\M = 1910.14[/tex]

So the last option is True.

Now we can see that the model shows exponential growth. so it is true also.

From the equation the inital part is that  1,800 members joined the gym when it first opened. that is also true.

Hence, the statement is false.

•The membership rates are increasing 20% each year.

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