if you have a table of values like those above and you can find the value for f(n), how would you go about finding the value of f(n-1)? How do f(n) and f(n-1) compare to each other?

Answer:

Z = ky/x where y=12, x=-12 and z=-6

-6= k(12)/-12

-k = - 6

K = 6

Answer:

7x

Step-by-step explanation:

The vertex is (3,16) and the quadratic equation in vertex form is [tex]f(x)=(x-3)^{2}+16\\[/tex].

Any equation in algebra that can be put into standard form is called a quadratic equation (from the Latin quadratus, which means "square").

As well as being referred to as the roots or zeros of the expression on the left-hand side of the equation, the values of x that satisfy it are known as solutions of the equation. There are only two possible answers to a quadratic equation. A double root is said to exist if there is only one solution. In the case where all of the coefficients are real values, there are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or all three of the aforementioned options. If complex roots are taken into account, then a quadratic equation will always have two roots, with a double root counting as one. An equivalent equation  can be created from a quadratic equation.

Calculations:

[tex]f(x)=x^{2} -6x+25\\ = x^{2} -2.x.3+(3^{2} )-(3^{2} )+25\\=(x-3)^{2} -9+25\\=(x-3)^{2}+16\\[/tex]

Comparing this from the vertex, y=[tex]a[/tex][tex](h-x)^{2} +k\\[/tex]

h=3 and k=16

Hence, vertex is (3,16).

[tex]f(x)=(x-3)^{2}+16\\[/tex]

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Answer:

[tex]15 \frac{1}{6}=15.167\:\:\sf(nearest\:thousandth)[/tex]

Step-by-step explanation:

[tex]15 \frac{1}{6}=15+\dfrac{1}{6}[/tex]

Convert ¹/₆ into a decimal by using long division:

[tex]\large \begin{array}{r}0.1\:6\:6\phantom{..}\\6{\overline{\smash{\big)}\,1. 0 \:0\: 0\: \phantom{.}}}\\{-~\phantom{(}\underline{0.6\:0\phantom{-)}}\\0.4\:0\:\:\phantom{))}\\-~\phantom{()}\underline{0.3\:6\:\:\phantom{))}}\\0.0\:4\:0\:\:\phantom{}\\-~\phantom{()}\underline{0.0\:3\:6\:\:\phantom{}}\\0.0\:0\:4\:\:\phantom{}\\\end{array}[/tex]

Therefore, ¹/₆ = 0.166666.....

[tex]\begin{aligned}\implies 15 \frac{1}{6} & =15+\dfrac{1}{6}\\\\& = 15 + 0.166666...\\\\& = 15.166666...\\\\& = 15.167\:\:\sf(nearest\:thousandth)\end{aligned}[/tex]

Tau is correct, the sum between -(1 ³/₄) and (2 ¹/₂) is equal to the difference between (2 ¹/₂) and (1 ³/₄)

Remember that the sum between a number A and a negative number -B is written as:

A + (-B)

And that is equal to the difference between A and B.

A - B

In this case, Tau says that the sum between:

-(1 ³/₄) and (2 ¹/₂)

Is written as:

(2 ¹/₂) + (-(1 ³/₄) )

(2 ¹/₂)  - (1 ³/₄)

And, using the above property, we conclude that this is equal to the difference between (2 ¹/₂) and  (1 ³/₄)

So Tau is correct.

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Answer: 13 pieces

Step-by-step explanation:

4 m * 100 cm/1 m=

4 * 100/1=

4*100=400 cm.

400/30=

(10+390)/30=

10/30 + 390/30=

1/3 + 13 ==> 13 pieces

Work Shown:

1 meter = 100 cm

4 meters = 400 cm

400/30 = 13.33 approximately

That rounds down to 13

You'll have 400-13*30 = 400-390 = 10 cm of ribbon leftover.

Answer:135

Step-by-step explanation:6075/45=135 hope this helps

Answer:

135

Step-by-step explanation:

Let x be the number of sessions.

Create an equation.

45x=6075

Divide 45 from both sides.

x=135

135 practice sessions.

Hope this helps! :)

The properties used, in order, are:

We start by writing the linear equation:

3*(x + 2) = 4x + 1

The first step is using the distributive property to distribute the left product.

3x + 6 = 4x + 1

Then we use the addition property of equality to subtract 4x in both sides, we will get:

-x + 6 = 1

And we use it again to subtract 6 in both sides:

-x = 1 - 6 = -5

Finally, we multiply both sides by -1 (multiplication property of the equality)

x = 5

That is the solution of the linear equation.

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Use a decimal number to fill in the blank. a 16 input mux has 4  select lines.

What is a decimal number?

How do you write decimal numbers?

To write a decimal in word form, follow these steps:

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The simplified equation of the X/3 ≥-33 is will be X ≥ -99.

Solving a math problem is another way of saying simplifying an expression. When you simplify an expression, you are attempting to write it in the most straightforward manner feasible. Finally, no more adding, subtracting, multiplying, or dividing should be required.

To make anything simpler or simpler to reduce it to the fundamentals. to reduce in scope or complexity: to streamline management procedures.

Given  = X/3>-33

This can be written as:

X/3 ≥-33

X ≥ -33 * 3

X ≥ -99

The simplified equation of the X/3 ≥-33 is will be X ≥ -99.

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The reasonable Domain and Range for the situation.

Given that

To find

So, according to the question

We have,

So, we can say that

          Total charges = 8 (total number of peoples in a party)

Let's assume

                                 Total charges = y , and

Total number of peoples in a party =  x

Then, we get a equation of this problem,

                y = 8x ------------(1)

So, the domain of this equation will be greater then and equal to 64. and range will be greater then and equal to 8 and less then and equal to 40.

Answer:

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The total area under the normal curve is 1.

Why is there a standard deviation?

the total area under the normal curve is 1.

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The factors of the expression  w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)

(w - 4) will be the height

(w + 10) will be the length

Given,

The length of the enclosure for the pancake tortoise will be greater than the height, that is: l > h

The volume of enclosure = w³ + 6w² - 40w

Where w is the width.

Now, factorize the expression:

w³ + 6w² - 40w = 0

10 - 4 = 6

10 × (-4) = -40

Therefore, the factors of the expression  w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)

Here, we know that length is greater than height.

So, (w - 4) will be the height and (w + 10) will be the length.

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Answer: 16

Step-by-step explanation:

Let's say x=Geometric mean.

4*64=x*x

x*x=256    

x^2=256

x=16

The difference between depths in January and July is equal to: D. 16 feet.

An absolute value function can be defined as a type of function that consist of an algebraic expression, which placed within absolute value symbols

In order to determine the difference between depths, we would calculate the magnitude of the depth for each of the month.

For January, we have:

January depth = 20 - 6

January depth = 14 feet.

For July, we have:

July depth = 20 - 22

July depth = -2 feet.

Now, we can calculate the difference between depths in January and July:

Difference = 14 - (-2)

Difference = 14 + 2

Difference = 16 feet.

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Answer:

-5+12=7

Step-by-step explanation:

7-12=-5

Answer:

-5

Step-by-step explanation:

x + 12 = 7

x + 12 - 12 = 7 - 12

x = -5

The quotient of the equation (-y5 - 9y) = y

The term "quotient" is used frequently in mathematics, and it may also refer to a fraction or a ratio as well as the integer portion of a division (in the case of Euclidean division)[2] (in the case of proper division). In the Euclidean division sense, and in the proper division sense, the quotient is "6 with a remainder of 2" when 20 (the dividend) is divided by 3 (the divisor). A quotient in the second meaning is only the proportion of a dividend to its divisor.

According to the given value,

-y*5-9y=y

Mutiply

-5y-9y=y

Combine like terms

-14y=y

Rearrange the terms

-14y -y= O

Combine the terms

-15y =O

divide on both sides

y=o

Hence , the Quotient is 0.

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Answer:

[tex]10\frac{11}{20}[/tex]

Step-by-step explanation:

[tex]5\frac{1}{2} + 3\frac{4}{5} + 1\frac{1}{4}[/tex]

1.Find the LCM(Least Common Multiple).

That would be 20.

2.Multiply so all denominators are equal.

[tex]5\frac{10}{20} + 3\frac{16}{20} + 1\frac{5}{20}[/tex]

3. Add

[tex]9\frac{31}{20}[/tex]

4. Simplify

[tex]10\frac{11}{20}[/tex]

Check to discover if an issue even exists before attempting to address it. not just to you, but also to those it will effect. You may create the criteria to compare and evaluate the potential remedies by developing an understanding of what makes this a problem in the first place.

Before programming starts, evaluation enables us to think through a problem's solution, ensure that it satisfies the original design requirements, yields the right answer, and is appropriate for the task at hand.

Three methods can be used to evaluate your problem-solving skills: asking for examples of times you've previously solved an issue; posing you with potential scenarios and asking you to reply; and observing how you use your problem-solving abilities in various exams and activities.

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The inverse function of f(x) = (x + 2)/(x - 3) is given as follows:

[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]

The function in this problem is defined as follows:

f(x) = (x + 2)/(x - 3).

Using the notation y = f(x), it is given as follows:

y = (x + 2)/(x - 3).

To obtain the inverse, the first step is exchanging the variables x and y, as follows:

x = (y + 2)/(y - 3).

Now the variable y must be isolated to obtain the inverse function, as follows:

xy - 3x = y + 2

xy - y = 3x + 2

y(x - 1) = 3x + 2

y = (3x + 2)/(x - 1).

Hence the inverse function is given by:

[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]

Meaning that the fourth option is correct.

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Based on the triangle sum theorem:

20° + (y - 10)° + 4y° = 180

y = 34

The triangle sum theorem states that if we add up all the three interior angles in a triangle, the sum we would get would be equal to 180 degrees.

Given the following are interior angles of a triangle:

Based on the triangle sum theorem, we have the following equation:

20° + (y - 10)° + 4y° = 180

Solve for y

20 + y - 10 + 4y = 180

10 + 5y = 180

5y = 180 - 10

5y = 170

5y/5 = 170/5

y = 34

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Step-by-step explanation:

so, we have a kite here.

a kite is a quadrilateral, that is totally symmetric along one of its diagonals.

the sum of all internal angles of a quadrilateral is always 360°.

remember, the sum of all angles around one point on one side of a line is always 180°.

a full circle airways represents 360°.

the inner angle at 140° is

180 - 140 = 40°

the inner angle at 250° is

360 - 250 = 110°

the inner angles at x and its opposing corner are equal (due to the symmetry) and are in sum with the other 2 inner angles 360°.

so, we have for the inner angles

360 = 110 + 40 + 2×xinner

210 = 2×xinner

the inner angle of x = 105°.

x (the outer angle of the inner angle of x) is

x = 360 - 105 = 255°

Answer:

25

Step-by-step explanation:

j(k + 2)

5(3 + 2)

5(5)

25

Answer:

Graph the solution to this inequality on the number line.

0.3(x − 4) > -0.3

Step-by-step explanation:

Answer:

9y

Step-by-step explanation:

[tex]\bullet\; \tt{(3y)^2} = 3^2y^2 = 9y^2}[/tex]

[tex]\bullet\; \tt y^{-1} = \dfrac{1}{y}\\\\\bullet\;(3y)^2 \times y^{-1} = 9y^2 \times \dfrac{1}{y } = \dfrac{9y^2}{y}\\\\\\bullet \tt \dfrac{y^2}{y} = y\\\\\tt \bullet \dfrac{9y^2}{y} = 9y[/tex]

Answer:

B

Step-by-step explanation:

9+(−2)^3

=9+ −8

=1

Answer:

b is your answer

Answer:

34-5=29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

hope it helps and have a nice day! :)