please solve and explain

1) n²+n is always an even integer

2. n² +n is always an even integer when n is even

3. n² +n is always an even integer when n is odd

Since, if n is an integer,

Then n = even or odd,

If n = even ⇒  = even

⇒ = even+ even = even  

Now, If n = odd ⇒  = odd   ( square of a odd number is always odd )

⇒  = odd + odd = even

Hence, however, n is odd or even,

is always an even number.

⇒ Options 1), 2) and 3) are correct.

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The future value of the account after 25 years is $210,595.95.

We can use the formula for future value of an annuity:

FV = P * (1 + r)^n + PMT * ((1 + r)^n - 1) / r

Where

Substituting the given values, we get:

FV = 19675.13 * (1 + 0.0925)^25 + 3000 * ((1 + 0.0925)^25 - 1) / 0.0925

Simplifying and evaluating, we get:

FV = $210,595.95

Therefore, the future value of the account after 25 years is $210,595.95.

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Answer:

Step-by-step explanation:
<ABC is 72 degrees.

1) This triangle is isosceles because two sides are equivalent. Thus, <C and <B are the same.
2) We know that <A + <B + <C = 180 in total
3. x + 2x + 2x = 5x
5x = 180
x = 36
4. <ABC = 2x = 2(36) = 72

Answer:

725

Step-by-step explanation:

8250-1000= 7250

(7250x10)/100=725

10% of 7250=725

Answer: 7,150

Step-by-step explanation: It says that you have a deductible of $1,000 and a co-insurance of 10% so you add the $1,000 with the 10% and that will give you $1,100. Then we have the medical bill which is $8,250 so what we will do next is to minus the $8,250 from the $1,100 that we got from the $1,000 and 10% so, when we minus the $8,250 with $1,100 we will get $7,150 and that is your answer.

I hope this helps!

Answer:

Step-by-step explanation:

The height of a tree would be the height of its root node, or equivalently, the depth of its deepest node.

The relative minimum of the function include the following: -2.

In this exercise, you are required to determine the relative minimum of the function with respect to the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

Based on the information provided about this quadratic function, we can reasonably infer and logically deduce that that its vertex is at x equals negative three and y equals negative two.;

Vertex (h, k) = (-3, -2)

Therefore, the relative minimum is equal to -2.

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Answer: True

9/4 = 2 1/4

Step-by-step explanation:

:) See the images below to know more.

Answer:

  C. Vertical angles

Step-by-step explanation:

Given angles 5 and 8 where line c crosses line a, you want to know what type they are.

Where two lines cross, four angles are formed. They all share the vertex point where the lines intersect. If they share a side (and no interior space), they are adjacent angles that form a linear pair. As such, they are supplementary.

In the given figure the supplementary angle pairs where line c crosses line a are ...

  (5, 6), (6, 8), (7, 8), (5, 7)

If the angles do not share a side, but are formed from opposite rays, they are "vertical angles" and are congruent.

The vertical angle pairs there are ...

  (5, 8), (6, 7)

Angles 5 and 8 are vertical angles, choice C.

__

Additional comment

Angle pairs (1, 8) and (2, 7) are "alternate exterior angles." Angle pairs (3, 6) and (4, 5) are "alternate interior angles."

Assuming lines b and c are parallel, considering also angles where line b crosses line a, there are additional supplementary pairs of angles:

  (1, 2), (2, 4), (3, 4), (1, 3), (1, 6), (1, 7), (2, 5), (2, 8), (3, 5), (3, 8), (4, 6), (4, 7)

When parallel lines are crossed by a transversal, all of the acute angles are congruent, all of the obtuse angles are congruent, and the acute angles are supplementary to the obtuse angles. The angles are referred to by different names (and different theorems), depending on where they are in relation to the transversal and the parallel lines.

The problem here is mostly concerned with vocabulary. The "how to do this" is "learn the vocabulary."

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Answer:

5. 1 line

6. none

7. 2 lines

8. 1 line

9. 1 line

Answer: the point that were left are 429

Step-by-step explanation:

i got this by multiplying 660 and 35% or .35 and got 429 and the amount left is 65% and to get that you would subtract 100% and 35% which gets you 65%.

I promise its right please rate and like and if you want give  brainliest

Answer:

a

Step-by-step explanation:

x² - 6x + 9 = 25 ( subtract 25 from both sides )

x² - 6x - 16 = 0 ← in standard form

(x + 2)(x - 8) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 8 = 0 ⇒ x = 8

Answer:

6^2 + 4(1/2)(6)(9) = 36 + 108 =

144 square meters

The equation in standard form is (x- (-12))² + (y - 0)²  = (√164)²

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

Using the completing square method on the given equation:

24x + y² = -x² + 20

x²+ 24x + y² = 20

[x² + 24x + (12)²] + [y² + 0x + (0)²] = 20 + (12)²

(x + 12)² + (y + 0)² = 164

(x - (-12))² + (y - 0)² = 164

(x- (-12))² + (y-0)²  = (√164)²

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Answer:

y = (1/25)x^2 - 1

Step-by-step explanation:

To begin, we can use the fact that the x-intercepts of the parabola are at (5, 0) and (-6, 0) to determine the x-intercepts form of the equation. The x-intercepts form of a parabola is given by:

(x - r)(x - s) = 0,

where r and s are the x-coordinates of the x-intercepts.

Using this form, we can write:

(x - 5)(x + 6) = 0

Expanding this equation gives:

x^2 + x - 30 = 0

Next, we use the fact that the vertex of the parabola is at (0, -1) to determine the y-intercept form of the equation. The y-intercept form of a parabola is given by:

y = a(x - h)^2 + k,

where (h, k) is the vertex.

Substituting (0, -1) into this equation gives:

y = a(x - 0)^2 - 1

Simplifying gives:

y = ax^2 - 1

Now we can use the fact that the parabola passes through the point (5, 30) to determine the value of a. Substituting x = 5 and y = 0 into the equation above gives:

0 = a(5)^2 - 1

Solving for a gives:

a = 1/25

Substituting this value of a into the equation above gives the final equation of the parabola:

y = (1/25)x^2 - 1

5/0-6/0-41=

hope that helps okay :) if not really really sorry

0.3895 Answer

Step-by-step explanation:

I thought you meant it on paper.

Answer:

0.3895

Step-by-step explanation:

Write out the division problem: 389.5 ÷ 1000.

Since we're dividing a decimal number by 1000, we can simply move the decimal point three places to the left to convert 1000 to 1.000: 389.5 ÷ 1.000.

Moving the decimal point three places to the left also means we need to add three trailing zeroes to the dividend: 389.5 becomes 389.500.

Now we can perform the long division: divide 3 by 1, write the quotient 3 above the 8, and subtract 3 from 8 to get 5 as the new remainder. Bring down the next digit 8 to get 58.

Divide 58 by 1, write the quotient 58 above the 9, and subtract 58 from 89 to get 31 as the new remainder. Bring down the next digit 5 to get 315.

Divide 315 by 1, write the quotient 315 above the decimal point, and subtract 315 from 389 to get 74 as the new remainder.

Since there are no more digits to bring down, we've reached the end of the long division. The final quotient is 0.3895.

Don't forget to include the decimal point in the answer, since we moved it three places to the left in step 2. The final answer is 0.3895.

So, 389.5 ÷ 1000 = 0.3895.

since the now has a value of ten so the p is equalled to 59

Yes, the project consists on single set of ordered pairs numbered 1 through 30 on coordinate planes for all class students is a suitable one.

Ordered pair is a composition of the x- coordinate (i.e., abscissa) and the y coordinate (i.e, ordinate), that's two values written in a fixed order within. In mathematics, an ordered pair ( pair means two objects) so, (a, b) is a pair of objects in particular order. The order in the pair is very significant, that is ordered pair (a, b) is different from the ordered pair (b, a). Now, Ms. todd provide a project to students which consists a single set of ordered pairs numbered 1 through 30, for all students in her class. We can easily graph a ordered pair on coordinate plane. Coordinate plane is a 2-D graph made using x-coordinate and y-coordinate. There is two axis x-axis and y-axis. So, first they collect all possible ordered pairs from 1 to 30 like ( 1,1),( 1,2),(1,3),..........(1,30), (30,1),.....,(30,30) ... etc. In this coordinate plane consists 30 numbers value on y-axis and 30 on x-axis. Then, draw on graph. Hence, it is suitable.

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Answer:

The unit rate is 35 pages per minute.

Step-by-step explanation:

Divide 175 by 5, or 175/5  to get the unit rate, which is 35.

the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."

How to solve the question?

To calculate the overall gain or loss, we need to first find the total cost of buying the shares and the total revenue from selling them.

For the 40 shares of Zycodec purchased at its lowest price of 29.39, the total cost would be:

40 shares x $29.39/share = $1,175.60

For the 95 shares of Unix purchased at its highest price of 16.12, the total cost would be:

95 shares x $16.12/share = $1,531.40

The total cost of purchasing both stocks would be:

$1,175.60 + $1,531.40 = $2,707

Now, we need to find the total revenue from selling the shares. The closing price of Zycodec is 34.95, so the revenue from selling 40 shares would be:

40 shares x $34.95/share = $1,398

The closing price of Unix is 15.78, so the revenue from selling 95 shares would be:

95 shares x $15.78/share = $1,499.10

The total revenue from selling both stocks would be:

$1,398 + $1,499.10 = $2,897.10

The overall gain or loss would be the difference between the total revenue and total cost:

Overall gain/loss = total revenue - total cost

Overall gain/loss = $2,897.10 - $2,707

Overall gain/loss = $190.10

Since the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."

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The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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The value of cos(2θ) is 1/2

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

If cos(tetha) = √3/2

this means the adjascent is √ 3 and the hypotenuse is 2

therefore ;

opp = √ 2²- √3)²

= √4-3

= √1

= 1

therefore sin(tetha) = 1/2

cos(2θ) = cos²(tetha) -sin²(tetha)

cos²(tetha) = (√3/2)² = 3/4

sin²(tetha) =( 1/2)² = 1/4

cos(2θ) = 3/4 - 1/4 = 2/4 = 1/2

therefore the value of cos(2θ) is 1/2

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Answer: 14

Step-by-step explanation:

Answer: x^2 + 17x/2 + 15

Step-by-step explanation:

i promise this is right

the area of the rhombus is approximately 74.60 square units.

How to solve the question?

To find the area of a rhombus using decomposition, we first need to draw its diagonal lines. Let's label the points where the diagonals intersect as points A and B.

Now we can decompose the rhombus into two congruent triangles, ABC and ABD, where AB is the diagonal and AD and BD are half of the diagonals.

We can find the length of AD and BD using the Pythagorean theorem. Since x=4 units and y=6 units, we have:

AD²= (x/2)² + h²

AD² = (4/2)²+ 5²

AD²= 4² + 5²

AD² = 41

AD = sqrt(41)

Similarly, we can find the length of BD:

BD²= (y/2)² + h²

BD²= (6/2)² + 5²

BD²= 3²+ 5²

BD²= 34

BD = √(34)

Now we can find the area of each triangle:

Area of ABC = (AB * BD) / 2

Area of ABC = (2 * √(41) * √(34)) / 2

Area of ABC = √(1394)

Since the rhombus is made up of two congruent triangles, its total area is twice the area of one triangle:

Area of rhombus = 2 * Area of ABC

Area of rhombus = 2 * √(1394)

Area of rhombus ≈ 74.60 square units

Therefore, the area of the rhombus is approximately 74.60 square units.

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the answer is (a) 30.To find the first term that appears in both sequences, we can simply compare the terms in each sequence until we find a match

what is sequence ?

In mathematics, a sequence is a set of numbers, called terms, arranged in a specific order. Each term in the sequence is obtained by applying a certain rule or formula to the preceding term(s) in the sequence.

In the given question,

Using Rule 1, we can create the first sequence:

10, 30, 90, 270, 810

Using Rule 2, we can create the second sequence:

58, 51, 44, 37, 30

To find the first term that appears in both sequences, we can simply compare the terms in each sequence until we find a match.

We see that the number 30 appears in both sequences as the fifth term of the second sequence and the second term of the first sequence.

Therefore, the answer is (a) 30.

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The Junior class sold 165 slices of pizza.

Let x represent the number of hamburgers sold and y represent the number of slices of pizza sold.

The total amount from sales: 1.35x + 0.75y = 292.50

They sold 40 more slices of pizza than hamburgers: y = x + 40

Now, we'll solve the system of equations using the substitution method:

Substitute the second equation into the first equation:
1.35x + 0.75(x + 40) = 292.50

Distribute $0.75 through the parentheses:
1.35x + 0.75x + 30 = 292.50

Combine like terms:
2.10x + 30 = 292.50

Subtract 30 from both sides of the equation:
2.10x = 262.50

Divide both sides by 2.10 to solve for x:
x = 125

Now that we know there were 125 hamburgers sold, we can use the second equation to find the number of slices of pizza sold:

y = x + 40
y = 125 + 40
y = 165
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An appropriate tree diagram.
            /    \

           /      \

   0.6 /         \ 0.4

       /             \

     R               NR

    / \                /  \

  /     \             /       \

0.6    0.4    0.6    0.4

 R     NR     R        NR

Where R represents rain and NR represents no rain.

By using the multiplication principle, we can calculate the probabilities of all the outcomes by multiplying the probabilities along each path. The probability of there being no rain today and no rain tomorrow is the probability of following the path NR-NR, which has a probability of

P(NR-NR) = P(NR|NR) * P(NR) = 0.4 * 0.4 = 0.16

Hence, the probability that there will be no rain today and no rain tomorrow is 0.16 or 16%.

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A population has a mean μ=135 and a standard deviation Ï=28.

The mean of the sampling distribution of sample means is equal to the population mean, that is 135.

The standard deviation of the sampling distribution of sample means can be calculated by using the formula

SE = Ï /[tex]\sqrt{n}[/tex]

Where Ï is the population standard deviation and n is the sample size.

By putting the given values we get

SE = 28 / [tex]\sqrt{57}[/tex] = 3.7

Hence, the mean of the sampling distribution of sample means is 135, and the standard deviation is 3.7.

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The actual height of the tower is 160 feet.

Given that, a scale model of a tower is 24 inches.

The scale is 1.5 inches:10 feet.

We know that, 1 foot = 12 inches

So, the scale 1.5 inches : 120 inches.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

1.5/120 = 24/The actual height of the tower

1.5×The actual height of the tower = 24×120

The actual height of the tower=2880/1.5

= 1920 inches

In feet = 1920/12

= 160 feet

Therefore, the actual height of the tower is 160 feet.

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The line tangent to f(x) = x + sin(x) is parallel to the secant line connecting the endpoints at x = π on the interval [-2π, 2π].

Let's begin by finding the slope of the secant line connecting the endpoints of the function. The endpoints of the function on the interval [-2π, 2π] are (-2π, -2π + sin(-2π)) and (2π, 2π + sin(2π)), which evaluate to (-2π, 0) and (2π, 0), respectively.

The slope of the secant line is

m = (0 - 0)/(2π - (-2π)) = 0

Since we want the tangent line to be parallel to the secant line, the slope of the tangent line should also be 0. We can find the equation of the tangent line using the point-slope form

y - (x + sin(x)) = 0

y = x + sin(x)

To find the points on the interval where the tangent line is parallel to the secant line, we need to find the values of x where the derivative of f(x) is equal to 0 (i.e., where the slope of the tangent line is 0). The derivative of f(x) is

f'(x) = 1 + cos(x)

Setting this equal to 0 and solving for x, we get

cos(x) = -1

x = π

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The given question is incomplete, the complete question is:

At how many points on the interval [-2pi, 2pi] is the line tangent to f(x)=x+sin x parallel to the secant line connecting the function endpoints?