If the sum of the first n terms of a sequence is n² - n + 1. Find the 5th term

Alternate Interior angles

x = 25

By careful observation of the diagram, we would see that both angles are at the opposite sides of the transversal. At the same time, they are at the interior of the two parallel lines.

This means that <108 and <4x + 8 are alternate interior angles.

Since the two lines intersecting the transversal are parallel, the alternate interior angles are equal

That is,

4x + 8 = 108

4x = 108 - 8

4x = 100

x = 100/4

x = 25

We already know that the solution is (9, -3/5), let's show that

Let's plug our solution into the equation

The second equation is true!

The solution set of the inequality x-15≤6/9 is  x≤47/3.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is x-15≤6/9

x minus fifteen lesser than or equal to six by nine.

x is the variable and minus is the operator,

x-15≤6/9

On the right side the numerator and denominator is divided by 3

x-15≤2/3

Add 15 on both sides

x≤2/3+15

x less than or equal to two by three plus fifteen.

x≤2+3(15)/3

When three is multiplied with fifteen we get 45.

x≤45+2/3

So when forty five and two are added we get 47.

x≤47/3

Hence, the solution set of the inequality x-15≤6/9 is  x≤47/3.

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Complete quesstion,

Find the solution set of the  inequality x-15≤6/9

Answer:

I think that there might be some complex differential equation

stuff going on here if this were in the real world, but for the sake of this problem... may I suggest that the tank is filling up  at a rate of

1/8 of a tank per hour...

it is evaporating at a rate of 1/12 tank per hour

you can subtract the rates

1/8 - 1/12 = 12/96- 8/96 = 3/96 = 1/32 tank/hr

so to fill the tank it should take 32 hours...

I think the logic and math work... lets see if someone else will verify this analysis?

Step-by-step explanation:

By solving a system of equations we can see that there are 400 main-floor seats and 200 balcony seats.

Let x = number of seats on the main-floor

y = number of balcony seats

We know that if all the seats are sold, then the total income is $4,200, we can write the equation:

x*8 + y*5 = $4,200

And if 25% of the main-floor and 40% of the balcony seats are sold, then we get an income of $1200, then we can write:

0.25*x*8 + 0.4*y*5 = $1,200

x*2 + y*2 = $1,200

2(x + y) = $1200

x + y = $600

x = 600 - y

putting the value of x in equation1)

8(600-y) + 5y = 4200

4800 - 8y + 5y = 4200

3y = 600

y = 200

and x = 600 - 200 = 400

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Answer:

Step-by-step explanation:

cos theta = (adjacent side) / (hypotenuse) = 1/6.  The adjacent side has length 1 and the hypotenuse length 6.  The opposite side has length

√(6^2 - 1^2) = ÷√35

and so sin theta = (opp side) / (hypotenuse) = (√35) / 6

and tan theta = [(√35) / 6] / (1/6), or √35

When the input x is -18, the output h is 14. The answer is obtained using substitution method.

What is substitution method?

One of the algebraic techniques for solving simultaneous linear equations is the substitution approach. It entails changing any variable's value from one equation to the other by substituting it in. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

Now, we are given h = 17+x/6

So, when the input x is -18, using substitution method,

h=17+(-18/6)

=17+(-3)

=17-3

=14

Hence, when the input x is -18, the output h is 14.

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Answer:

C. 2 and 6

Step-by-step explanation:

2 and 6 are the zeros because they are both on X

The value of y at x = 121.9 for the expression y = 3x - 245 will be 120.7.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that the expression is y = 3x - 245. The value of x is 121.9.

The solution for the value of y will be calculated as:-

y = 3x - 245

y = ( 3 x 121.9 ) - 245

y = 365.7 - 245

y = 120.7

Therefore, the value of y for the given expression will be 120.7.

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The complete question is given below.

Find the value of y for the expression y = 3x - 245 at x = 121.9.

The solution to the linear programming problem is:

Maximum value of z = 120

x₁ = 0, x₂ = 6

To solve the given linear programming problem using the graphical method, we first need to plot the feasible region determined by the constraints and then identify the optimal solution.

The constraints are:

x₁ + x₂ ≥ 12

x₁ + x₂ ≤ 6

x₁, x₂ ≥ 0

Let's plot these constraints on a graph:

The line x₁ + x₂ = 12:

Plotting this line on the graph, we find that it passes through the points (12, 0) and (0, 12). Shade the region above this line.

The line x₁ + x₂ = 6:

Plotting this line on the graph, we find that it passes through the points (6, 0) and (0, 6). Shade the region below this line.

The x-axis (x₁ ≥ 0) and y-axis (x₂ ≥ 0):

Shade the region in the first quadrant of the graph.

The feasible region is the overlapping shaded region determined by all the constraints.

Next, we need to find the corner points of the feasible region by finding the intersection points of the lines. In this case, the corner points are (6, 0), (4, 2), (0, 6), and (0, 0).

Now, we evaluate the objective function z = 15x₁ + 20x₂ at each corner point:

For (6, 0): z = 15(6) + 20(0) = 90

For (4, 2): z = 15(4) + 20(2) = 100

For (0, 6): z = 15(0) + 20(6) = 120

For (0, 0): z = 15(0) + 20(0) = 0

From the evaluations, we can see that the maximum value of z is 120, which occurs at the corner point (0, 6).

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Answer:

38

Step-by-step explanation:

Let the missing number be 10x + y, where x is the tens digit, and y is the ones digit.

5 + 7 + 1 + 3 + 7 + 2 + x + y = (1/5)(57 + 13 + 72 + 10x + y)

25 + x + y = (1/5)(142 + 10x + y)

125 + 5x + 5y = 142 + 10x + y

4y = 5x + 17

y = (5/4)x + 17/4

y = 1.25x + 4.25

x must be 1 less than a multiple of 4.

Try x = 3.

y = 1.25 × 3 + 4.25

y = 8

The number is 3(10) + 8 = 38

Check:

5 + 7 + 1 + 3 + 7 + 2 + 3 + 8 = 36

57 + 13 + 72 + 38 = 180

36 = (1/5)(180)

36 = 36

38 is correct.

Step-by-step explanation:

no this is a test I cant hlep i will tell ms.jules you are searching for the answers

Answer:

16

Step-by-step explanation:

Q(M + P)

4(3 + 1)

4(4)

16

Improper integrals: Improper integrals are integrals with an infinite region of integration or integrands that have an infinite discontinuity within their limits.

Improper integrals are classified into two types: Type I and Type II.

Let's see both of them below:

Type I Improper Integrals:

If the limit, as b approaches a from the right-hand side, of the integral of f(x) from a to b does not exist, then the Type I improper integral is represented by ∫a to ∞ f(x)dx, or∫−∞ to a f(x)dx.

Because the integral of f(x) from a to b has no limit as b approaches a from the right-hand side, this occurs.

Type II Improper Integrals: If f(x) has an infinite discontinuity in the interval (a,b) or at b, then the Type II improper integral is represented by∫a to b f(x)dx = lim h→b- ∫a to h f(x)dx or ∫b to ∞ f(x)dx = lim n→∞ ∫b to n f(x)dx. This occurs since the interval of integration contains an infinite discontinuity.

In other words, if f(x) has an infinite discontinuity in (a,b) or at b, the integral of f(x) from a to b, or from b to infinity, does not converge.

Partial fractions decomposition of (9x²-4)/[(x-9)²(x²-9)(x²+9)] can be given as shown below:

For a given rational function whose denominator is a product of quadratic factors, partial fractions are a method of reducing it to a sum of simpler fractions. In order to locate the coefficients A, B, C, D, E, and F in partial fraction decomposition of the given rational function, follow the steps below.

The denominators of partial fraction can be shown as follows;

\($$\frac{9{x}^{2}-4}{\left(x-9\right)^{2}\left(x^{2}-9\right)\left(x^{2}+9\right)}=\frac{A}{x-9}+\frac{B}{\left(x-9\right)^{2}}+\frac{C}{x+3}+\frac{D}{x-3}+\frac{E}{x^{2}+9}+\frac{F}{x+3}$$\)

Multiply both sides of the equation by the common denominator, which is; (x - 9)²(x + 3)(x - 3)(x² + 9)

\($$9{x}^{2}-4=A\left(x-9\right)\left(x+3\right)\left(x-3\right)\left(x^{2}+9\right)+B\left(x+3\right)\left(x-3\right)\left(x^{2}+9\right)\)+\($$C\left(x-9\right)\left(x-3\right)\left(x^{2}+9\right)+D\left(x-9\right)\left(x+3\right)\left(x^{2}+9\right)+E\left(x-9\right)\left(x+3\right)\left(x-3\right)+F\left(x-9\right)^{2}\left(x+3\right)$$\)

Substitute the value of x=-3 to get the value of C.

\($$9(-3)^{2}-4=C(-3-9)(-3-3)(-3^{2}+9)+\cdots$$\)

\($$=C(-12)(-6)(-18)=C(12)(6)(18)$$\)

Therefore, C = \($ \frac{- 1}{27}$\)

Substitute the value of x=3 to get the value of D.

\($$9(3)^{2}-4=D(3-9)(3+3)(3^{2}+9)+\cdots$$\)

\($$=D(-6)(6)(18)=D(6)(-6)(18)$$\)

Therefore, D = \($ \frac{1}{27}$\)

Let \($x^{2}+9=y$\)

Substitute the values of A, B, E, and F to get the value of C.

\($$9{x}^{2}-4=A(x-9)(x+3)(x-3)(x^{2}+9)+\cdots$$\)

\($$+B(x+3)(x-3)(x^{2}+9)+C(x-9)(x-3)(x^{2}+9)+D(x-9)(x+3)(x^{2}+9)+\cdots$$\)

\($$+E(x-9)(x+3)(x-3)+F(x-9)^{2}(x+3)$$\)

\($$9{x}^{2}-4=\left[A(x-9)(x+3)(x-3)+\cdots\right]+\left[B(x+3)(x-3)(x^{2}+9)+\cdots\right]$$\)

\($$+\left[\frac{-1}{27}(x-9)(x-3)(x^{2}+9)+\cdots\right]+\left[\frac{1}{27}(x-9)(x+3)(x^{2}+9)+\cdots\right]+\left[E(x-9)(x+3)(x-3)\)\($$+\cdots\right]+\left[\frac{F}{(x-9)}(x-9)^{2}(x+3)+\cdots\right]$$\)

\($$=\frac{1}{y-9}\left(\frac{A}{x-9}+\frac{B}{(x-9)^{2}}+\frac{C}{x+3}+\frac{D}{x-3}\right)+\frac{E}{y}+\frac{F}{y-9}$$\)

Multiply both sides by \($x^{2}-9$\) to get rid of the y variable.

\($$9{x}^{2}-4=\frac{A(x+3)(x-3)(y-9)}{y-9}+\frac{B(x-9)(y-9)}{(x-9)^{2}}+\frac{C(x-9)(x+3)(y-9)}{x+3}$$\)

\($$+\frac{D(x-9)(x+3)(y-9)}{x-3}+\frac{E(x+3)(x-3)}{y}+\frac{F(x-9)(y-9)}{y-9}$$\)

\($$=A(x+3)(x-3)+B(x-9)+C(x-9)(x+3)+D(x-9)(x+3)+E(x+3)(x-3)(x^{2}+9)+F(x-9)^{2}(x+3)$$\)

Let's solve the above equation.

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The probability that a student enrolled in algebra is also enrolled in health is 0.8.

Let's denote the event of a student being enrolled in algebra as A and the event of a student being enrolled in health as H. We are given that 25% of the students are enrolled in algebra (P(A) = 0.25) and 20% of the students are enrolled in both algebra and health (P(A ∩ H) = 0.20).

We want to find P(H|A), the probability that a student is enrolled in health given that the student is enrolled in algebra.

Using the conditional probability formula:

P(H|A) = P(A ∩ H) / P(A)

We substitute the given values:

P(H|A) = 0.20 / 0.25

Simplifying this expression:

P(H|A) = 0.80

Therefore, the probability that a student enrolled in algebra is also enrolled in health is 0.80, or 80%.

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Answer:

The planet's speed is 18,950,000 km per 940 days

which equals

20,159.5744680851 kilometers per day

Dividing that by 24 gives us the planetary speed in km / hour which is

839.982269503546 kilometers per hour.

I have no idea what 3sf means so I can't answer that.

Step-by-step explanation:

The equation of the parabola with focus (-2, 5) and directrix y = 3 is y = \((1/4)x^2 + x + 5.\)

To write the equation of a parabola with focus (-2, 5) and directrix y = 3, we can use the standard form of the equation of a parabola:

\((x - h)^2 = 4p(y - k)\)

Where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus or directrix.

First, let's determine the vertex of the parabola. The vertex lies halfway between the focus and the directrix, so its y-coordinate is the average of the y-coordinates of the focus and the directrix:

Vertex y-coordinate = (5 + 3) / 2 = 8 / 2 = 4

Since the directrix is a horizontal line, the vertex has the same y-coordinate as the directrix. Therefore, the vertex is (h, k) = (-2, 4).

Next, let's determine the value of p. The distance from the vertex to the focus (or directrix) is p. In this case, the focus is (-2, 5), so the distance from the vertex to the focus is:

p = 5 - 4 = 1

Now we can write the equation of the parabola using the vertex and the value of p:

\((x - (-2))^2 = 4(1)(y - 4)\)

\((x + 2)^2 = 4(y - 4)\)

Expanding the square on the left side:

(x + 2)(x + 2) = 4(y - 4)

(x^2 + 4x + 4) = 4y - 16

Simplifying the equation:

\(x^2 + 4x + 4 = 4y - 16\)

x^2 + 4x + 20 = 4y

Rearranging the terms:

4y = x^2 + 4x + 20

Finally, dividing both sides by 4 to isolate y, we get the equation of the parabola:

\(y = (1/4)x^2 + x + 5\)

So, the equation of the parabola with focus (-2, 5) and directrix y = 3 is y = \((1/4)x^2 + x + 5.\)

To sketch the parabola, plot the focus (-2, 5) and the directrix y = 3 on a graph. The vertex is also located at (-2, 4). The parabola opens upwards because the coefficient of x^2 is positive. Use the equation to plot additional points and sketch the curve symmetrically around the vertex.

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Given Jessica and Laura's expenditure on shirts and pants, the equation to solve for the price of each shirts and pants is:

3s + 4p = 90

4s + 2p = 70

Let

Cost of each shirts = s

Cost of each pants = p

Jessica:

3s + 4p = 90 (1)

Laura:

4s + 2p = 70 (2)

Multiply (2) by 2

8s + 4p = 140 (3)

8s + 4p = 140 (3)3s + 4p = 90 (1)

Subtract (1) from (3) to eliminate p

8s - 3s = 140 - 90

5s = 50

s = 50/5

s = $10

substitute s = 10 into (1)

3s + 4p = 90 (1)

3(10) + 4p = 90

30 + 4p = 90

4p = 90 - 30

4p = 60

p = 60/4

p = $15

Therefore, the cost of each shirts is $10 and the cost of each pants is $15

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Answer:

you use division then add then you get the answer

Step-by-step explanation:

Answer:

50+45x

Step-by-step explanation:

Answer:

x² + (y + 3)² = 25

Step-by-step explanation:

the centre (C) of the circle is at the midpoint of the diameter.

using the midpoint formula

midpoint = ( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

with (x₁, y₁ ) = P (3, 1 ) and (x₂, y₂ ) = Q (- 3, - 7 )

C = ( \(\frac{3-3}{2}\) , \(\frac{1-7}{2}\) ) = ( \(\frac{0}{2}\) , \(\frac{-6}{2}\) ) = (0, - 3 )

the radius r is the distance from the centre to either P or Q

using the distance formula

r = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = C (0, - 3 ) and (x₂, y₂ ) = P (3, 1 )

r = \(\sqrt{(3-0)^2+(1-(-3)^2}\)  

 = \(\sqrt{3^2+(1+3)^2}\)

 = \(\sqrt{3^2+4^2}\)

 = \(\sqrt{9+16}\)

 = \(\sqrt{25}\)

 = 5

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (0, - 3 ) and r = 5 , then

(x - 0 )² + (y - (- 3) )² = 5² , that is

x² + (y + 3)² = 25

Answer:

12 feet

Step-by-step explanation:

pls follow me and Mark as brainliest

The Expression that represents how much Margo will have to pay for the storage unit if Carissa contributes is 14m + 2 while Margo will pay $86 if she uses the storage unit for 6 months.​

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

Let m represent amount of monthly payments

Margo's payment = 17m + 3

Carissa's payment = 3m + 1

The payment will be = 17m + 3 - (3m + 1)

Total payment = 14m + 2

For 6 months, m = 6

Substituting in the equation 14m + 2

Payment for 6 months = 14(6) + 2

Payment = $86

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Answer:

p=12

Step-by-step explanation:

DBC = 180

ABE = 180

ABC + DBA = 180

ABC = (5p -28)

DBA + (12p -4)

CBD = ABC + DBA = 180

-------------------------------------------------

180 = (5p - 28) + (12p + 4)

180 = 17p - 24

204 = 17p

12 = p

p = 12

------------------------------------------------------

180 = (5(12) - 28) + (12(12) +4)

180 = 60 - 28 + 144 +4

180 = 180

Answer:

x=5

Step-by-step explanation:

6:5

x:4, so x =5

The side also looks a little bigger than 4.

Hope it Helps

Answer:

44 pairs of boots

Step-by-step explanation:

As per two options given to Alice,

1). Wages of $33 for each day work + commission of $2.5 for every pair sold.

 If Alice sells x pairs of boots in a day, then total amount earned by Alice,

 = (33 + 2.5x)

2). Commission of $3.25 for every boot sold.

  If Alice sold x pairs of boots, total earnings of the day = 3.25x

If earning of Alice is equal in both the plans,

(33 + 2.5x) = 3.25x

3.25x - 2.5x = 33

0.75x = 33

x = 44

Therefore, for the sales of 44 pairs of the boots Alice will earn equal by both the plans.

Answer:

the answer is 1   1/4

Step-by-step explanation:

1/4 multiple 5= 5/4 or 1   1/4

Answer:

40 cm^3

5 x 8 x 1

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

6=x

Step-by-step explanation:

y= 18; y= 3x

18=3x

18/3 = 3x/3

6=x

Hope this helps!