Find the 9th term of the arithmetic sequence with 9=10 and d= - ½

Answer:

12

Step-by-step explanation:

Given that,

f(x) = 2x² - 3x + 7

To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.

Let us solve it now.

f(2.5) = 2(2.5)² - 3×2.5 + 7

f(2.5) = 12.5 - 7.5 + 7

f(2.5) = 12

Answer:

\(f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}\)

The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.

The sum of all the sides of the square or the product of the four and the edge length of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,

4(x + 2) = 40

Simplify the equation, then we have

4(x + 2) = 40

(x + 2) = 10

x = 10 - 2

x = 8

The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.

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The complete question is given below.

Solve it to find the value of x. Also, find the actual length of each square perimeter of the square is 40 cm and side length is (x + 2).

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Hi!

A hypotenuse is the longest leg in a right triangle.

A right triangle is a triangle that has one 90 degree angle.

The hypotenuse is always directly across from the right angle.

In pictures, right angles are represented by a square.

Therefore, the side with the hypotenuse is side 3, because we can see that the angle between side 1 and side 2 is the right angle, and the hypotenuse would be directly across.

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Image = other parts of a right triangle:

Answer:

D

Step-by-step explanation:

The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

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Answer:

The formula

Step-by-step explanation:

just do pi times the circle's radius squared.

(pi x r squared)

To show that the point (å, ä) is on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ), we need to demonstrate two things: that the point lies on the line segment, and that it is equidistant from the endpoints.

1. Determine the midpoint of the line segment:

  - The midpoint coordinates (\(x_{mid, y_{mid\)) can be found using the midpoint formula:

    \(x_{mid\) = (x1 + x2) / 2 and \(y_mid\) = (y1 + y2) / 2, where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

    In this case, we have (x1, y1) = (Ů, ü) and (x2, y2) = (ĝ, ġ).

2. Calculate the midpoint coordinates:

  - Substitute the values into the midpoint formula to find (x_mid, y_mid).

3. Find the slope of the line segment:

  - Use the slope formula: slope = (y2 - y1) / (x2 - x1).

    Apply the formula to the endpoints (Ů, ü) and (ĝ, ġ) to determine the slope of the line segment.

4. Determine the negative reciprocal of the line segment's slope:

  - Take the negative reciprocal of the slope calculated in the previous step. The negative reciprocal of a slope m is -1/m.

5. Write the equation of the perpendicular bisector:

  - Using the negative reciprocal slope and the midpoint coordinates (\(x_{mid\), \(y_{mid\)), write the equation of the perpendicular bisector in point-slope form: y - \(y_{mid\) = \(m_{perp\) * (x - \(x_{mid\)), where \(m_{perp\) is the negative reciprocal slope.

6. Substitute the point (å, ä) into the equation:

  - Replace x and y in the equation of the perpendicular bisector with the coordinates of the point (å, ä). Simplify the equation.

7. Verify that the equation holds true:

  - If the equation is satisfied when substituting (å, ä), then the point lies on the perpendicular bisector.

By following these steps, you can demonstrate that the point (å, ä) lies on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ).

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Answer:

This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.

Step-by-step explanation:

x < 3 or x > 5

This means, x is less than 3, but greater than 5.

Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.

Answer:

x < -2 or x > 5

Step-by-step explanation:

We want to write the compound inequality.

There is an open circle at -2 and a line going to the left.

x < -2

There is an open circle at 5 and a line going to the right.

x > 5

We use an or since they are not connected.

x < -2 or x > 5

Answer:

Step-by-step explanation:

on the 250ml ÷ 140 ml = 1L and 78757ml

on the 200 ml ÷ 150 ml = 1L and 333ml

on the 150 ml ÷ 160 ml = 9375ml

on the 100 ml ÷ 170 ml = 58832ml

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we get that 6.255 × 10¹⁰  larger than 1.5 × 10⁸ by 417 times.

We are given two expressions:

6.255 × 10¹⁰ and 1.5 × 10⁸

We need to tell that how much times is 6.255 × 10¹⁰  larger than 1.5 × 10⁸.

We will do this with the help of division.

So, we get that:

= 6.255 × 10¹⁰  ÷ 1.5 × 10⁸

= 6.255 × 10¹⁰⁻⁸  ÷ 1.5

= 6.255 × 10²  ÷ 1.5

= 625.5 ÷ 1.5

= 417

Therefore, we get that 6.255 × 10¹⁰  larger than 1.5 × 10⁸ by 417 times.

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The domain restrictions for (f/g)(x) are (c) x = 0, 6

From the question, we have the following parameters that can be used in our computation:

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Answer:

80in²

Step-by-step explanation:

Hey There!

So the first step of this problem is to find the width of the scale drawing

To do so we need to find the scale factor

To find the scale factor we divide the length of the room by the length of the scale factor

32/8=4

so the scale factor is 4

now to find the width

40/4=10

so the width of the scale drawing is 10 in

now we can find the area given the length and the width

10x8=80in²

so we can conclude that the area of the scale drawing is 80in²

we should distribute the 133 quintals of wheat among the mills in the following way:

Mill 1: 63.3 centners

Mill 2: 38.4 centners

Mill 3: 75 centners

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, One mill can grind 19 centners of wheat in 3 hours. 32 centners of the second - in 5 hours, and 10 centners of the third - in 2 hours.

Let's first find out the efficiency of each mill, which is the amount of wheat it can grind per hour:

Mill 1:

19 centners / 3 hours = 6.33 centners per hour

Mill 2:

32 centners / 5 hours = 6.4 centners per hour

Mill 3: 1

0 centners / 2 hours = 5 centners per hour

We can see that Mill 2 is the most efficient, followed closely by Mill 1, and Mill 3 is the least efficient.

Let's call the number of hours that each mill will work "x".

The amount of wheat each mill can grind in "x" hours is:

Mill 1: 6.33x centners

Mill 2: 6.4x centners

Mill 3: 5x centners

The LCM of 3, 5, and 2 is 30.

Therefore, if each mill works for 30 / 3 = 10 hours,

30 / 5 = 6 hours,

30 / 2 = 15 hours respectively,

they will all finish at the same time.

The amount of wheat each mill will grind in the allotted time is:

Mill 1: 6.33 x 10 = 63.3 centners

Mill 2: 6.4 x 6 = 38.4 centners

Mill 3: 5 x 15 = 75 centners

This distribution will ensure that all three mills start working at the same time and finish grinding at the same time

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Complete question:

One mill can grind 19 centners of wheat in 3 hours. 32 centners of the second - in 5 hours, and 10 centners of the third - in 2 hours. How should 133 quintals of wheat be distributed among these mills in such a way that they start working at the same time and finish grinding at the same time?​

The point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

Given that:

y = total cost

x = miles

We are also given the system of linear equations that models the scenario given as:

y = 0.27x + 27 --> equation 1

y = 0.21x + 45 --> equation 2

To find the value of x, make both equations equal to each other and solve:

0.27x + 27 = 0.21x + 45

Combine like terms

0.27x - 0.21x = -27 + 45

0.06x = 18

Divide both sides by 0.06

0.06x/0.06 = 18/0.06

x = 300

To find the value of y, plug in the value of x into equation 1, and find y:

y = 0.27(300) + 27

y = 81 + 27

y = 108

Thus, the point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

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a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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The successor of -34 is -33 using the formula "n+1".

A phrase that follows or is right after a specific number, term, or value is known as a successor.

The successor of n is "n+1" if n is a number (and n belongs to any whole number).

The terms just after, immediately after, and next number/next value are also used to describe a successor.

As is common knowledge, integers are collections of numbers that range from negative infinity to positive infinity.

The integers are.........., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.................. The preceding and following numbers will also be negative integers if the provided number is a negative integer.

So, the successor of -34:

= -34 + n

= -34 + 1

= - 33

Therefore, the successor of -34 is -33 using the formula "n+1".

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Answer:

Midsegment theorem for Traoezoids

Step-by-step explanation:

I hope it helps you

He would have saved $87,221.02  after 1 year

He would have saved $268,335.90   after 3  years

What is an ordinary annuity?

An ordinary annuity means a fixed amount invested at specific intervals, in this case, $7,185.51 is invested monthly, which means that its future value can be computed using the future value formula of an ordinary annuity as shown below:

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

FV=future value of an ordinary annuity

PMT=monthly payment invested every month

r=monthly interest rate=annual interest/12

N=number of months that monthly payments were

FV after 1 year:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in 1 year=12

FV=$7,185.51*(1+0.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*(1.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*0.02528845698324970/0.00208333333333333

FV=$87,221.02

FV after 3  years:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in  3 years=36

FV=$7,185.51*(1+0.00208333333333333)^36-1/0.00208333333333333

FV=$268,335.90

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The volume of the composite figure is 6,330.24 in^3

We know that the volume of half a sphere of radius R is:

V = (2/3)*pi*R^3

Here we know that pi = 3.14 and R = 12 inches, then the volume is:

V = (2/3)*3.14*(12 in)^3 = 3,617.28 in^3

And the volume of a cone of height H and radius R is:

v = (1/3)*pi*R^2*H

So here the volume is:

v = (1/3)*3.14*(12in)^2*18in = 2,712.96 in^3

Then the total volume is:

3,617.28 in^3 +  2,712.96 in^3 = 6,330.24 in^3

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The total surface area is A≈747.7ft²

The area of the two bases and the area of the curved surface are added to determine the cylinder's total surface area. Consequently, the following is the formula for the cylinder's total surface area:

The area of the two bases plus the area of the curved surface equals the cylinder's total surface area. Due to the cylinder's round bases, their combined area will be equal to r2 + r2. We already know that a cylinder's curved surface area is 2rh.

(r2 + r2 + 2rh) is the cylinder's total surface area.

⇒ 2πr² + 2πrh

A=2πrh+2πr²

A=2·π·7·10+2·π·72≈747.69905ft²

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Answer:

Option C: -$1500 is the correct answer.

Step-by-step explanation:

Given that:

Total amount invested in business = $24,000

Loss suffered in first quarter = $4500

As the amount is shared by Brian, Steve and Rita equally, therefore,

Loss of each person = \(\frac{Loss}{Number\ of\ people}\)

Loss of each person = \(\frac{4500}{3} = \$1500\)

As loss is defined by decrease in the investment,

Loss of each person = -$1500

Hence,

Option C: -$1500 is the correct answer.

Answer:

-$1,500

I hope this helps

Answer:

6

Step-by-step explanation:

i took the test

The height of the prism is 49.2 feet

The given parameters are:

The area of the trapezoid is:

Area = 0.5 * (Sum of opposite sides) * Height

So, we have:

1280 = 0.5 * 52 * Height

This gives

1280 = 26 * Height

Divide both sides by 26

Height = 49.2

Hence, the height of the prism is 49.2 feet

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Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

his is the day that immediately proceeds the last and final spring sabbat, ... The fact that Beltane and Samhain happen in unison twice a year lends ... You know all those Halloween recipes you've been saving on Pinterest for years now? ... Halloween and Samhain product brands as you can all year long.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

G(2)= 2^2 +4(2)

Solve via order of operations

G(2)=4 +8

G(2)=12

Given:

The selling price of 12 eggs is equal to the cost of 15 eggs.

To find:

The gain percentage.

Explanation:

Let us assume the cost price of 1 egg is $1.

So, the cost price of 15 eggs is $15.

According to the problem,

The selling price of 12 eggs is $15.

So, the selling price of 1 egg is,

Then, the gain percentage is,

Therefore, the gain percentage is 25%.

Final answer:

The gain percentage is 25%.