Find the recursive rule for the following sequence. -3, 2, 7, 12, 17,

Answer:

The last option, (x+2)(x-3)(x-1)

Step-by-step explanation:

The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,

⇒ f (x) = (x - 1) (x - 2) (x - 3)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

Function is,

⇒ f (x) = x³ - 2x² - 5x + 6

Now, We can factor the function as;

Since, 1 is a root of function as it satisfy the function.

So, One factor is,

⇒ (x - 1)

Find another roots as;

(x - 1) ) x³ - 2x² - 5x + 6 ( x² - x - 6

         x³ - x²

        ----------

             - x² - 5x

            - x² + x

            -------------

                    - 6x + 6

                    - 6x + 6

                    ------------

                           0

Hence,

⇒ f (x) = x³ - 2x² - 5x + 6

⇒ f (x) = (x - 1) ( x² - x - 6 )

⇒ f (x) = (x - 1) ( x² - 3x - 2x - 6)

⇒ f (x) = (x - 1) ( x (x - 3) - 2 (x - 3))

⇒ f (x) = (x - 1) (x - 2) (x - 3)

Hence, The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,

⇒ f (x) = (x - 1) (x - 2) (x - 3)

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The price of a two-year bond is 101.78 and the correct option is C.

Given that a 9% annual coupon and a yield to maturity of 8%.

Simple yield is the amount of interest received by a bond issuer divided by the current market price of the associated bond.

Implicit Face value, FV=$100

Time, N=2 years

Coupon, C=(9/100)×$100=9

The yield of maturity, r=8%=0.08

Now, we will find the bond price using the formula

Price of bond = C× [1-{1/ (1+r)ⁿ}/r] +M/ (1+r)ⁿ

Substitute the values in this formula, we get

Price of bond=9×[1-{1/(1+0.08)²}/0.08]+100/(1+0.08)²

Price of bond=9×[1-{1/(1.08)²}/0.08]+100/(1.08)²

Price of bond=9×[1-{1/1.1664}/0.08]+100/1.1664

Price of bond=9×[(1-0.857)/0.08]+85.73

Price of bond=9×[0.143/0.08]+85.73

Price of bond=9×1.7875+85.73

Price of bond=16.0875+85.73

Price of bond=101.78

Hence, the price of a two-year bond with a 9% annual coupon and a yield to maturity of 8% is 101.78.

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Applying the angles of intersecting secants theorem, the measure of arc XY is: 32°.

According to the angles of intersecting secants theorem, m∠XZY = 1/2(arc VW - arc XY).

Plug in the values:

39 = 1/2(110 - arc XY)

2(39) = 110 - arc XY

78 = 110 - arc XY

78 - 110 = - arc XY

-32 = - arc XY

Arc XY = 32°

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Answer: 77 degrees

mLON is the total angle. mLOM is part of the angle, and is 55 degrees. To find the missing degree, subtract the part we know from the part the whole. In this case, subtract 55 from 132. mMON is 77 degrees.

Answer:

Step-by-step explanation:

Consistent Independent = exactly ONE solution

Consistent Dependent = INFINITELY many solutions

Inconsistent = NO solution

The selling price of an equipment costing $150.00 with 35% markup is $202.50

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given that the mark up is 35%, hence:

Markup = [(selling price - cost price)/cost price] * 100%

Substituting:

$202.50

Selling price = $202.50

The selling price of an equipment costing $150.00 with 35% markup is $202.50

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Answer:

[tex]\huge\boxed{\sf n = 49}[/tex]

Step-by-step explanation:

[tex]x^2-14x+n[/tex] ---------------(1)

We need to solve it using the following formula:

[tex]a^2-2ab+b^2=(a-b)^2[/tex]

Writing the middle term in the expression as 2ab

[tex](x)^2-2(x)(7)+n[/tex]

Form the expression, we come to now that

So, the we can write the expression as:

[tex](x)^2-2(x)(7)+(7)^2\\\\x^2-14n+49[/tex]

Comparing expression (1) with the above expression, we get:

[tex]\rule[225]{225}{2}[/tex]

Answer:

1) y > x² + 4x - 5, y > x + 5

2) Rational

Step-by-step explanation:

For a parabola, if the shade is inside the curve then the value of y will be greater or equal to:

For a line, if the shade is above it then the value of y will be greater or equal to:

Therefore, since parabola doesn't have solid curve (--- graph) then the inequality is ">"

Therefore, the inequality for parabola is y > x² + 4x - 5

For a line, it does not have solid graph so the inequality is ">"

Therefore, the inequality for line is y > x + 5

-----------

The graph of function describes the shape of rational function. It cannot be exponential as exponential only has one curve. It cannot be logarithm  for same reason as exponential. It cannot be polynomial as polynomial is continuous function but the graph is discontinuous at specific point x = 0.

That being said, all choices except rational are all continuous function by default but rational function isn't and since the graph is discontinuous then we can say that it's rational function.

Answer: 4n - 7 = 21, n = 7

Step-by-step explanation:

A difference indicates subtraction of two terms. Four times a number indicates that a number of any value has to be multiplied by 4.

Hence, the equation that is represented by the question is

[tex]4x - 7 = 21[/tex]

We can also solve this equation (i.e., find the value of x that makes this equation true).

Adding 7 to both sides, we get

[tex]4x - 7 + 7 = 21 + 7[/tex]

Since the -7 and 7 add to 0, the equation becomes

[tex]4x = 28[/tex]

To get x by itself, we can divide both sides by 4, making the equation

[tex]x=7[/tex]

Hence, x must be 7 to make the equation true, or 7 is a solution to the equation.

area is multiplication

perimiter is adding the numbers on each side, for example, if the right side is 7, the left side will be 7. Add them and it will givey ou 14

Considering the definition of an inequality, the inequality that can be used to determine x is 20x + 10≤ 80

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

A rental car company charges $20 per day to rent a car and $0.10 for every mile driven.

Addison wants to rent a car, knowing that:

On the other hand, x represents the maximum number of days Alyssa can afford to rent for while staying within her budget.

Then, the inequality that can be used to determine x is:

20x + 0.1×100≤ 80

So:

20x + 10≤ 80

In summary, the inequality that can be used to determine x is 20x + 10≤ 80

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Answer:

the third option, x = –3, –1, 3

Step-by-step explanation:

The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

The optimization equation is given as

z=−3x+5y

The constraints are given as:

x+y≥−2

3x−y≤2

x−y≥−4

Next, we plot the constraints on a graph and determine the points of intersections

See attachment for the graph

From the attached graph, the points of intersections are

(-3, 1), (3, 7) and (0, -2)

So, we have:

(0, -2)

(-3, 1)

(3, 7)

Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

So, the complete parameters are:

Optimization Equation:

z=−3x+5y

Constraints:

x+y≥−2

3x−y≤2

x−y≥−4

Vertices of the feasible region

(0, -2)

(-3, 1)

(3, 7)

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The kind of symmetry that would be shown in the design is an axial symmetry.

It should be noted that an axial symmetry simply means a symmetry around an axis.

In this case, the capital letter E has an acid of symmetry. Therefore, an axial symmetry is appropriate.

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Answer:

[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]

Step-by-step explanation:

[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]

Put f(x) = y

[tex]\displaystyle y=\frac{x}{5} -2[/tex]

Swap x and y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Now, solve for y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Add 2 to both sides

[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]

Multiply 5 to both sides

[tex]5(x+2)=y[/tex]

Distribute

[tex]5x + 10 =y[/tex]

Put y = f⁻¹(x)

[tex]\boxed{f^{-1}(x)=5x+10}[/tex]

[tex]\rule[225]{225}{2}[/tex]

The resulting equation will represent a line whose slope is 1/2 times the slope of the line

The equation of the line is given as:

y = 3x/a + 5

The constant a is a positive constant.

So, when the value of a in the equation is doubled, we have:

y = 3x/2a + 5

A linear equation is represented as

y = mx + b

Where m represents the slope.

So, we have:

m1 = 3/a

m2 = 3/2a

Substitute m1 = 3/a in m2 = 3/2a

m2 = 1/2 * m1

Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line

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In Economics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

This ultimately implies that, all producers of any product generally work to maximize their profits and make them as large as possible, in order to enable them break even and successful.

Based on the information provided, we can logically deduce that this function has its roots at x = 0 and x = 26 and its vertex is a minimum. Thus, this quadratic function which describes the relationship between the number of products produced and the overall profit margin is an increasing function:

Therefore, once they hit 26 items they break even again. The worst case scenario is that they produce 13 items, as they will have a profit of -50 dollars because the minimum point is at (18, -35). Also, the first root tells us that the profit will be 0 when 0 products are sold.

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The answer is 14.

First, we need to find X using the first statement.

Now, we have to substitute this in the required expression.

Answer:

D

Step-by-step explanation:

As the function approaches a certain x-value, it makes a very sharp turn and doesn't touch the axis as you can see in the graph. It does that because if the x-value is applied to the function, it would make it undefined. In this case, the graph is approaching x = -3 and x = +7 since at those points, the lines for the graph change suddenly. You would look for a function that if x is -3 or 7, it makes the y-value undefined.

Another way to easily do this would be to substitute values that are in front of the value that the graph is avoiding like 6 or 8 for 7 and -2 and -4 for -3. You can see if the y-values that would output from substituting those numbers are correct.

Answer:

[tex]\sqrt{65}[/tex], so [?] = [65]

Step-by-step explanation:

This is a classic Pythagorean Theorem problem :)

We are given a right triangle with 2 sides, so all we have to do is plug it into the formula a² + b² = c², or in simple terms: the square of one side plus the square of the other equals the square of the hypotenuse.

line h is going to bisect the diameter of the circle (8) so one side will be 4. We're given 9 as our hypotenuse, so:

(4)² + (h)² = (9)².

16 + h² = 81

h² = 81 - 16, h² = 65, h = [tex]\sqrt{65}[/tex].

1. The solution to the first percent puzzle is as follows:

                              75%         66²/₃         11¹/₉

          33¹/₃%        25%          22¹/₅%      3⁷/₁₀%

         50%         37¹/₂%          33¹/₃%      5¹/₂%

        50%          37¹/₂%          33¹/₃%      5¹/₂%

2. The solution to the second percent puzzle is as follows:

                           10%             90%

         50%           5%              45%

         50%           5%              45%

A percent puzzle is a puzzle that engages students to practice working with percentages.

The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.

The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.

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Answer:

81

Step-by-step explanation:

The reason why the expression x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c is because they follow the FOIL Technique

We want to explain why x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c.

Now, using the FOIL Technique we can say that the factors are;

(x + p)(x + q)

Expanding this gives;

x² + px + qx + pq

⇒ x² + (p + q)x + pq

Now, applying that to the trinomial; x² + 6x + 8, we can say that;    

p + q = 6, and pq = 8

Thus, solving simultaneously gives;

p = 2 and q = 6.

Thus;

x² + 6x + 8 = (x + 2)(x + 6)

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Answer:

lcm of 3,6,9 is 18

The general-form equation of the circle is:

A. [tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

This circle has center at (4,4), hence:

[tex]x_0 = 4, y_0 = 4[/tex]

The radius is of 3 units(distance of A and B from the center), hence the equation is:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 4)^2 + (y - 4)^2 = 3^2[/tex]

We expand the equation to find the general form, hence:

[tex]x^2 - 8x + 16 + y^2 - 8y + 16 = 9[/tex]

[tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]

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Answer is (n + 3) + (n - 7)

Simplified to 2n - 4

Using “n” for number

Answer:

perpendicular

Step-by-step explanation:

We'll find the slope of both lines and see what it tells us.

If the slopes are the same, the lines are parallel. If the slopes are opposite sign and flipped (negative reciprocals) then they are perpendicular.

The slope is y-Y on top of a fraction and x-X on the bottom.

Slope of AB:

m = 2-1 / -3 -5

= 1/-8 = -1/8

Slope of CD:

m = 7- -1 / 2-1

= 8/1 = 8

Since the slopes are -1/8 and 8, the lines are perpendicular, because they are opposite sign and flipped (negative reciprocals)

Answer: [tex]10^4[/tex]

Step-by-step explanation:

Assuming we are using the common log (base 10),

[tex]\log 3ty=6\\\\\log 3y +\log t=6\\\\2+\log t =6\\\\\log t=4\\\\t=10^4[/tex]

Answer:

M = $2.5; V = $5

Step-by-step explanation:

We need to set up a system of equations to find the price for both movies (M) and video games (V).

We can use 2M + 5V = 30 and 8M + 3V = 35

We can use elimination:

[tex]-4(2m+5v=30)\\8m+3v=35\\\\-8m - 20v = -120\\8m+3v=35\\-17v=-85\\v=5\\\\2m+5(5)=30\\2m+25=30\\2m=5\\m=5/2 ;m=2.5[/tex]