How is the graph of g(x)=(x-3)³ related to the graph of f(x) = x²?

Answer:

0

Step-by-step explanation:

The y-coordinates are the same, so the line is horizontal. Therefore, the slope is zero.

The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.

Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.

Let the slope of the line joining A (7,-6)  and B(6,-6)  be m.

We know that the slope of a line is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope of the line

= (6-7) / (-6+6)

= -1 / 0

= undefined

Since the slope is undefined we can say that the straight line is parallel to the y axis.

we know that tan 90° = ∞

So any line parallel to this line will have the same slope as the y axis.

Hence the slope of the given line is undefined or infinity.

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[tex]\boldsymbol{\sf{\dfrac{4}{6}+\dfrac{1}{4} }}[/tex]

We reduce the fraction 4/6 to its lowest expression by extracting and canceling 2.

    [tex]\boldsymbol{\sf{\dfrac{4}{6}=\dfrac{4\div2}{6\div2}=\dfrac{2}{3} }}[/tex]

                            [tex]\boldsymbol{\sf{\dfrac{2}{3}+\dfrac{1}{4} }}[/tex]

Convert 2/3 and 1/4 to fractions with like denominators.

                [tex]\boldsymbol{\sf{\dfrac{2\times4}{3\times4}+\dfrac{1\times3}{4\times3} \iff \ \dfrac{8}{12}+\dfrac{3}{12} }}[/tex]

Since 8/12 and 3/12 have the same numerator, we join numerators and add.

                         [tex]\boldsymbol{\sf{\dfrac{8+3}{12}= }}\boxed{\boldsymbol{\sf{\frac{11}{12} }}}[/tex]

Answer: p(t) = 100×1.0153^(12t)

1.53% per month

In general, the function will be written ...

 p(t) = (initial value)×(growth factor)^t

where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...

 growth factor = 1 + growth rate

Here, the growth rate is given as 20% per year, so the growth factor per year is ...

 1 +20% = 1.20

The initial value is given as 100, so we can write the exponential function as ...

 p(t) = 100×1.20^t

__

The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.

 p(t) = 100×(1.20^(1/12))^( 12t)

 p(t) = 100×1.0153^(12t) . . . . population exponential function

This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...

 1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change

Step-by-step explanation:

The probability of choosing a blue marble is 0.59.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

The jar contains 7 red marbles and 10 blue marbles.

The probability of choosing a blue marble will be:

= Number of blue marbles / Total marbles

= 10/17

= 0.59

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The polynomial function for the given zeros is  x⁷+9x⁶+20x⁵-22x⁴-87x³+37x²+114x-72

Polynomial function:

An expressions that may contain variables of varying degrees, non-zero leading coefficients, positive exponents, and constants is known as polynomial function.

Given,

Here we have the value of zeros as x = -1, 3, 2, 4 and n = 5.

Now, we have to find the polynomial function from it.

Let us consider if a polynomial function f(x) has zeros x = -1, x = 3, x = 2, and x =  4, then it has factors 

=> (x - 1)³ (x + 3)² (x +2) (x + 4)

Here there are four factor, in these polynomial so it can be Quintic Function.

Now, we have to expand this one to get the resulting polynomial,

=> x⁷+9x⁶+20x⁵-22x⁴-87x³+37x²+114x-72

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Answer: 7

Step-by-step explanation:

Median is the middle number of a data set.

You need to first start off with listing the shoe sizes in numerical order:

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9.5

You have a total of 11 numbers in the set, so you can choose the sixth number in the set, which is 7.

So, 7 is the median number.

The median of current data is 6.5 while by adding 9.5 to the data group the median changes to 6.75.

Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.

For example;

Set { 1,2,2,3,4,5,6} here mode is 2 and median is 3.

As per the given data,

5.5, 6, 7, 8.5 6.5,6.5, 8, 7.5, 8 5

Write the above data in increasing order,

5,5.5,6,6.5,6.5,7,7.5,8,8.5

The median is the middle value thus, 6.5 will be the median.

Now let's add 9.5 to the data group,

5,5.5,6,6.5,6.5,7,7.5,8,8.5,9.5

Now we have two middle values 6.5 and 7

Median = (6.5 + 7)/2 = 6.75

Hence "The median of current data is 6.5 while by adding 9.5 to the data group the median changes to 6.75".

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Answer:

D and E

Step-by-step explanation:

Dilations shrink or enlarge, but do not change angle measurements.

Factoring the given polynomial expression with the greatest common factor gives 3x⁴(6x - x³ + 4)  

From the question, we are to factor the giving polynomial expression with the greatest common factor

The given polynomial expression is

18x^5-3x^7+12x4

This can be properly written as

18x⁵ - 3x⁷ + 12x⁴

First, we will determine the greatest common factor of the coefficients in the expression.

The coefficients in the expression are 18, 3, and 12.

The greatest common factor of 18, 3, and 12 is 3.

Now, we will determine the greatest common factor of x⁵, x⁷, and x⁴.

The greatest common factor of x⁵, x⁷, and x⁴ is x⁴.

Thus,

The greatest common factor of the polynomial expression is 3x⁴.

Now,

Factoring the polynomial with the greatest common factor

18x⁵ - 3x⁷ + 12x⁴

3x⁴(6x - x³ + 4)

Hence, the result of factoring the polynomial is 3x⁴(6x - x³ + 4)  

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Answer:

D

Step-by-step explanation:

The amount that you have to pay for the time is $300.

From the information, the person is buying some television time and the station tells you that they reach 120,000 people and they quote you $2.50 CPM

The cost will be:

= Total people × Cost per thousand

= 120000/1000 × $2.50

= 120 × $2.50

= $300

The amount is $300.

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The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

A system contains two or more linear equations that can be solved or graphed together at once.

This statement is true.

For example,

The two linear equations can be:

ax + by = c ____(1)

dx + ey = F _____(2)

We can solve this equation using the substitution method or elimination method.

We can find the point of intersection.

And we can solve and graph together at once.

Thus,

The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.

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Answer: Substituting x = 2y + 4 into the equation 6x + 8y = 7.

Step-by-step explanation:

       Since they solved for x, their next step will likely being solving by substitution, where you substitute for one variable to solve the other one.

       There are a few different ways to solve systems of equations, so this might not be her next step.

For the 95% confidence interval for the number of toys that are from China in a random sample of 210 toys, using the z-distribution, we have that:

a) The critical value would be of z = 1.96.

b) The standard error is of: 0.0316

c) The margin of error is of: 6%.

d) The expected number of toys in the sample is of: 147.

e) The lower limit of the interval is of: 64%.

f) The upper limit of the interval is of: 76%.

A confidence interval of proportions has the bounds obtained by the rule presented below as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate and the sample size for this problem are given as follows:

[tex]\pi = 0.7, n = 210[/tex]

Hence the expected number of toys in random sample of 210 toys is of:

0.7 x 210 = 147.

The standard error is calculated as follows:

[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.7(0.3)}{210}} = 0.0316[/tex]

The margin of error is the multiplication of the critical value and of the standard error, hence:

M = 1.96 x 0.0316 = 0.06 = 6%.

The bounds of the interval are the estimate plus/minus the margin of error, hence they are given as follows:

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Answer: cu

Step-by-step explanation: cmu

Answer:

x = [tex](\frac{z-y}{5}) ^{2}[/tex]

Step-by-step explanation:

5[tex]\sqrt{x}[/tex] + y = z ( subtract y from both sides )

5[tex]\sqrt{x}[/tex] = z - y ( divide both sides by 5 )

[tex]\sqrt{x}[/tex] = [tex]\frac{z-y}{5}[/tex] ( square both sides to clear the radical )

([tex]\sqrt{x}[/tex] )² = [tex](\frac{z-y}{5}) ^{2}[/tex]

x = [tex](\frac{z-y}{5}) ^{2}[/tex]

Answer:

a_n = (4/7)(-7)^(n - 1)

Step-by-step explanation:

a1 = 4/7 = 4/7 × 1 = (4/7)(-7)^0

a2 = -4 = 4/7 × (-7) = (4/7)(-7)^1

a3 = 28 = 4/7 × (-7)(-7) = (4/7) × (-7)^2

etc.

a_n = (4/7)(-7)^(n - 1)

Using cosine law,

d^2 = 65^2 + 35^2 - 2(65)(35)cos140

= 8935.5022

d = sqrt(8935.5022)

= 94.5 m

Angle = inverseCos(35sin40 / 94.5) = 76.23 degrees South of East

Answer:

One number is 16 and the other number is 20

Step-by-step explanation:

Let x = one number

Let y = the other number

x + y = 36

x - y = 4  Or x = 4 + y

Substitue in 4 + y for x in the first equaion

4 + y + y = 36  Combine like terms

4 + 2y  = 36  Subtract 4 from both sides

2y = 32  Divide both sides by 2

y = 16

Substitute 16 for y in either of the orginal equaions

x + y = 36

x + 16 = 36  Subtract 16 from both sides

x = 20

The equivalent expression for 11(9a+3b) is 33(3a+b)

How should an equivalent be written?

The numerator and denominator must be multiplied or divided by the same number when writing equivalent fractions. This explains why these fractions have the same value when they are simplified.

How does math equivalent work?

We need to multiply the denominator of 7 by a number that will give us 21 in order to obtain equivalent fractions, which requires multiplying both the numerator and the denominator by the same number. We may find an equal fraction by multiplying the numerator and denominator by 3, so 3 times 7 gives us 21.

Given expression: 11(9a+3b)

Take 3 outside from the expression, we get,

= 33(3a+b), which is called the equivalent expression

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To solve we must expand the terms and then simplify and finally multiply.

The expressions are two algebraic expressions which are equivalent when they both take the same numerical value, for any value of the domain of each of the variables.

So the Result of the Expression is 99a + 33b

¡Hope this helped!

The range of the function f(x) = |x| - 4 is [-4, ∞).

For any function y = f(x), Domain is the set of all possible values of y that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

We have -

f(x) = |x| - 4

According to question, we have -

f(x) =  |x| - 4

We will draw the graph of the function -

f(x) = |x| + 4

Range is the set of value along the [y] - axis.

We can see that, the values of range of [y] variable is from -

[-4, ∞)

Therefore, the range of the function f(x) = |x| - 4 is [-4, ∞).

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Answer:

nu tg hi yum

Step-by-step explanation:

The solution of the function is x = 12

Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.

Consider a right-angle triangle ABC, right-angled at C. In that case, side AB will be the hypotenuse. Also, if we chose AC as the base and BC as the perpendicular. Then, for ∠BAC, value of sinθ = Perpendicular/ hypotenuse = BC/AB

6cos(5x) = 3

divide both sides by 6, we have

cos(5x) = 3/6

cos(5x) = 0.5

taking the anti cosine of both sides

5x = Arc cos 0.5

5x = 60

x = 60/5

x = 12°

In conclusion, the value of x = 12°

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The value of R(x) is - [1-7x]

What is division in algebra?

The four basic arithmetic operations of addition, subtraction, multiplication, and division are used to connect variables and constants in algebraic expressions. The procedure of multiplying and dividing algebraic expressions is the opposite of each other. You can divide algebraic expressions using the long division method, the division of a monomial by another monomial, or the division of a polynomial by another polynomial.

Dividend: The number or value that we divide is known as a dividend.

Divisor: The number that divides the dividend is known as a divisor

Quotient: The result obtained from the division process is known as a quotient

Remainder: The number left over after the division process is known as the remainder.

In the given question;

f(x) is dividend and

d(x) is divisor

Q(x) is the quotient

And we have to find the remainder i.e. R(x)

After dividing [tex]\frac{4x^3-8x^2+2x-1}{2x+1}[/tex] we get

Q(x) =[tex]2x^2-5x[/tex]

and R(x) = [tex]-[1-7x][/tex]

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Answer: 9/2

Step-by-step explanation:

[tex]\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}[/tex]

The simplified probability that all randomly chosen student has a schedule that excludes music theory is given as follows:

p = 1/14.

The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

In the context of this problem, these numbers of outcomes are given as follows:

The symbol [tex]C_{n,x}[/tex] represents the number of combinations of x elements that can be obtained from a set of n elements, and the combination formula is presented as follows:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Considering the formula presented above, the numeric values of the combinations are obtained as follows:

Hence the simplified probability is of:

p = 4/56 = 1/14.

As the quotient of 56 and 4 is of 14.

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Forming the two telephone charge plans in a slope intercept equation form, like Y=mx + b, is as follows:

The slope intercept equation is an equation of a straight-line with its slope (constant unit rate) combining the x and y intercepts.

Generally, the formula y = mx + b depicts the slope intercept equation with the following values:

y = y coordinate

m = slope

x = x coordinate

b = y intercept

                           Plan A   Plan B

Fixed cost (b)      $25        $50

Variable cost (m)  50          25

x = monthly            12          12

y = the total cost for the period

Thus, Plan A will have a total cost of 50x + 25 and Plan B will have a total cost of 25x + 50.

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Answer:

Step-by-step explanation:

Let the number be x and y.

Solve the system by substitution:

Find x:

The equation of the line passing through (-6,-10) and having slope m = 1/6  in Standard From is  x - 6y = 54   .

In the question ,

it is given that ,

the required line passes through the point (-6,-10) ,

and has slope(m) = 1/6 ,

So , the equation of the line that passes through the given point and slope ,

is given by ,

(y - (-10)) = 1/6(x -(-6))

(y + 10) = 1/6(x + 6)

On cross multiplication ,

we get ,

6(y + 10) = x + 6

6y + 60 = x + 6

x - 6y = 60 - 6

x - 6y = 54

Therefore , The equation of the line passing through (-6,-10) and having slope m = 1/6  in Standard From is  x - 6y = 54   .

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