An 8th grade class will take a trip to the museum on a school bus. The cost is$5 per student, plus $30 to park the bus in the city lot.Use a function to help you answer this question: What is the total cost if thereare either 20 or 25 students going?A. $130 or $155OB. $100 or $125C. $225D. $150 or $45

Answer:

\(A) x+y=100 \\ ..\ 5x + y = 420\)

Step-by-step explanation:

From the question we are told that:

Five-dollar bill  x

One-dollar bill  y

Total number of bills \(N=100\)

Worth of bills \(w=420\)

Generally the equation for Total number of bills  is mathematically given by

Since it is made up of five and one dollar bills

Therefore

  \(x+y=100\)

Hence the Equation for Total worth of bills is

 \(5x+y=420\)

The System of equations used is

\(A) x+y=100 \\ ..\ 5x + y = 420\)

Answer:

\( - x - 7\)

Step-by-step explanation:

\((4x - 6) - (5x + 1)\)

A minus before the parentheses changes the signs in the parentheses to the opposite:

\( 4x - 6 - 5x - 1\)

Subtract the number with x's seperately from the plain numbers:

\(4x - 5x - 1 - 6\)

\( - x - 7\)

Answer:

Complement: 63°

Supplement: 153°

Step-by-step explanation:

NOTE: Supplementary angles are two angles that have a sum of 180°. Complementary angles are two angles that have a sum of 90°.

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A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot. The weight of the tabletop, in pounds, is 1032.

The volume of the rectangular tabletop is the product of the length, breadth, and height of the given tabletop.

Volume of rectangular tabletop= (length x width x height)

The tabletop will have a length of eight feet, a width of three feet, and a thickness of one inch.

Volume of rectangular tabletop= (length x width x height)

                                                 = \(8 \times 3 \times 1\\\\24\)

A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot.

The weight of the tabletop, in pounds = 43 x 24

                                                              = 1032 pounds

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The amount of baking powder would they need to used 1 teaspoon of salt will be 6 teaspoons.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The Mosley family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.

Now,

Since, The Mosley family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.

Hence, The amount of baking powder would they need to used 1 teaspoon of salt = 2 × 3

                         = 6

Thus, The amount of baking powder would they need to used 1 teaspoon of salt will be 6 teaspoons.

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The two expressions are equivalent because they both represent the same concept: a number that is less than 3 but negative. In the first expression, -x, the negative sign in front of the x indicates that the value of the expression is the opposite of x. So if x is a positive number, then -x will be a negative number, and vice versa. In the second expression, x > -3, the greater than sign indicates that the value of x is greater than -3. Since we know that x is negative, this means that x is less than -3.

Therefore, both expressions represent the same thing: a number that is less than 3 but negative. This is why they are equivalent.

Answer:

  t(r) = log(r)/log(5) = log₅(r)

Step-by-step explanation:

You want the inverse of r(t)=5^t.

An exponential function is solved using logarithms.

  \(r = 5^t\qquad\text{given}\\\\\log(r)=t\cdot\log(5)\qquad\text{take logarithms}\\\\\boxed{t(r)=\dfrac{\log(r)}{\log(5)}}\qquad\text{divide by the coefficient of t}\)

The change of base formula can be used to simplify this a bit.

  \(\boxed{t(r)=\log_5(r)}\)

__

Additional comment

The latter form of the inverse function can be found directly at the first step by taking logarithms base 5.

The notation here is slightly different from the usual "inverse function" notation, where we designate the inverse of f(x) using f⁻¹(x). The notation we have used recognizes that the function r(t) generates ordered pairs (t, r), and the inverse function t(r) generates ordered pairs (r, t).

You are welcome to make use of whatever inverse function notation will satisfy your grader.

Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

The simplified form of the univariate monomial expression as requested in the task content is; 1.6 y⁴.

It follows from the task content that the simplified form of the univariate monomial expression is to be determined.

Since the given expression is;

32 y⁶ / 20 y²

The expression can be simplified as follows;

( 32 / 20 ) • y⁶ / y²

= 8/5 • y⁴

= 1.6 y⁴.

On this note, it can be inferred that the simplified form of the expression is; 1.6 y⁴.

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The value of x is for the two rectangular table to have the same area is 6 or -1.

The dimensions of table one is x+4 and x, hence the area is:

Area = length * breadth

A = (x + 4)(x)

A = x² + 4x

The dimensions of table two is 2x + 3 and x - 2, hence the area is:

Area = length * breadth

A = (2x + 3)(x - 2)

A = 2x² - 4x + 3x - 6

A = 2x² - x - 6

Since both tables have same area, hence:

x² + 4x = 2x² - x - 6

x² - 5x - 6 = 0

x² - 6x + x - 6 = 0

x(x - 6) + 1(x - 6) = 0

(x + 1)(x - 6) = 0

x = -1 or 6

The value of x is 6

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 Range of a function is defined by the set of output values.

Range of the function given in graph will be -∞ < y ≤ 12

From the graph attached,

Output values of the function (values on y-axis) vary from negative infinity to f(x) = 12.

  Therefore, approximate range of the function will be defined by -∞ < y ≤ 12

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Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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Answer:

D) 240 ft²

Step-by-step explanation:

The formula for the surface area of a square pyramid is 2(B)(H) + B² , so, 2×8×11 + 8²= 240.

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Answer:

1&2 are -2x^(3)+3x^(2)+x or Factored is −-x(2x^(2)-3x-1)

3&4 are 2x^(4)-3x^(3)-x^(2) or Factored is x^(2)(2x^(2)-3x-1)

5 is Yes

Step-by-step explanation:

1. (x+1*2x^(2)-x)(-1)

2x^(3)-x^(2)+2x^(2)-x(-1)

2x^(3)-3x^(2)-x(-1)

-2x^(3)+3x^(2)+x

−-x(2x^(2)-3x-1)

2. (2x^(2)-x*x+1*2x)(-1)

2x^(3)-x^(2)+2x^(2)-x(-1)

2x^(3)-3x^(2)-x(-1)

-2x^(3)+3x^(2)+x

−-x(2x^(2)-3x-1)

3. (x+1*2x^(2)-x)(x)

2x^(3)-x^(2)+2x^(2)-x(x)

2x^(3)-3x^(2)-x(x)

2x^(4)-3x^(3)-x^(2)

x^(2)(2x^(2)-3x-1)

4. (2x^(2)-x*x+1*2x)(x)

2x^(3)-x^(2)+2x^(2)-x(x)

2x^(3)-3x^(2)-x(x)

2x^(4)-3x^(3)-x^(2)

x^(2)(2x^(2)-3x-1)

5. (2x^(2)-x*x+1*2x)(x)=(x+1*2x^(2)-x)(x)

(2x^(2)-x*x+1*2x)(x)-2x^(2)-x=(x+1*2x^(2)-x)(x)-2x^(2)-x

(x+1)(x)=(x+1)(x)

(x+1)(x)-(x+1)=(x+1)(x)-(x+1)

X=X

Angle ∠EBD is congruent to angle ∠DBA. Option D is the true statement.

An angle bisector is the line segment that bisects the angle into two equal halves.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,

Ray BE is a bisector of angle CBA,

∠CBE = ∠EBA = 60°

∠EBD = ∠EBA - ∠DBA

∠EBD = 60 - 30 = 30

So,

∠EBD = ∠DBA [DB becomes angle bisector of angle EBA]

Thus, ∠EBD is congruent with ∠DBA is the only correct answer among the option.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Which of the following statements is true if ray BE is a bisector of angle CBA?

A. Ray BD is a bisector of angle CBA.

B. ∠EBD is congruent to ∠CBE.

C. Ray BE is a bisector of angle ABE.

D. ∠EBD is congruent to ∠DBA.

Answer:

Step-by-step explanation:

inorder to solve the area of the shaded area;°/360ñRsquared

arc length you use ;°/360ñD

A salary slip for the month of March 2023 with information given below.

Salary Slip - March 2023

Employee Details:

Name: [Employee Name]

Employee ID: [Employee ID]

Designation: [Employee Designation]

Earnings:

Basic Salary: [Basic Salary]

House Rent Allowance (HRA): [HRA]

Dearness Allowance (DA): [DA]

Incentive: [Incentive]

Total Earnings: [Total Earnings]

Deductions:

Provident Fund (PF): [PF]

Insurance: [Insurance]

Loss of Pay (LOP): [LOP]

Total Deductions: [Total Deductions]

Net Pay: [Net Pay]

Breakdown:

Basic Salary: 50% of CTC (18L) = [Basic Salary]

HRA: 20% of Basic Salary = [HRA]

DA: 12% of Basic Salary = [DA]

Incentive: 75% of target completion = [Incentive]

Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]

PF: 12% of Basic Salary = [PF]

Insurance: Rs. 2500 = [Insurance]

LOP: [LOP]

Total Deductions = PF + Insurance + LOP = [Total Deductions]

Net Pay = Total Earnings - Total Deductions = [Net Pay]

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Answer:

$18

Step-by-step explanation:

If Susan, Jacky, and Tom split $27 equally, we must:

\(\frac{27}{3} = 9\)

Each person gets $9 individually. Jacky has $9 and Tom has $9, so together it totals $18.

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Answer:

Step-by-step explanation:

g(x) = |x-3| is neither even nor odd; the graph is not symmetric about the y-axis (as characterizes even functions), and is not symmetric about the origin either.

g(x) = x + x is actually g(x) = 2x, which is an odd function.  The graph is symmetric about the origin.

Answer:

the surface area of the rectangular prism is 572cm².

Step-by-step explanation:

The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:

2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²

So the surface area of the rectangular prism is 572 square centimeters.

if a number (lets say 'y' is that number) is equal to (I.e. y = )..mathematically

now y is equal to twice the smaller number ( lets say that the smaller number is 'x' ) plus (+) 3 . that brings us to the linear equation...

y = 2x + 3;

also the second part of the question says that the same number ( I.e. 'y' here ) is twice the sum of smaller number (I.e. '2x' here ) and 1.

which gives us 2nd equation I.e.

y = 2x + 1 ;

the question is to find the possible number of solutions for both these equation

to find solution means to find all those points or say numbers which would satisfy both these equations

now for the first equation..

lets say ( y = 5 ) this means ( 2(1) + 3 )

so the solution will be ( 1, 5)

now for the second equation..

we will proceed with whatever data we know..

I.e. we know that value of ' y ' is 5, as we assumed

putting value of y in 2 nd equation we get ( 2(2)+1 )

I.e solution will be ( 2, 5)

now what does this signify...?

it signifies that there is no such point that will satisfy both these equations simultaneously..

hence we can say that there is no solution possible for this situation.

Answer:

yes

Step-by-step explanation:

No, Savannah is incorrect. Doubling the length, width, and height of a right rectangular prism will not double its surface area.

Surface area is the total area of an object's exposed faces, including any external surface area. It is a measure of the size of a surface and is usually expressed in square units such as square meters or square centimeters. Surface area is a two-dimensional measurement, since it only takes into account the area of a surface, and not its thickness or volume.

The surface area of a right rectangular prism is calculated by multiplying the length by the width and then multiplying that number by two and adding the two products together.

For example, the surface area of a right rectangular prism with a length of 15 cm, a width of 10 cm, and a height of 5 cm is calculated as follows:

Surface area = (15 cm * 10 cm) + (15 cm * 5 cm) = 150 cm2 + 75 cm2 = 225 cm2

Doubling the length, width, and height of this right rectangular prism would give us a prism with a length of 30 cm, a width of 20 cm, and a height of 10 cm. The surface area of this new prism would be calculated as follows:

Surface area = (30 cm * 20 cm) + (30 cm * 10 cm) = 600 cm2 + 300 cm2 = 900 cm2

As you can see, doubling the length, width, and height of the right rectangular prism does not double its surface area - the surface area has increased by four times (900 cm2/225 cm2 = 4).

In conclusion, doubling the length, width, and height of a right rectangular prism does not double its surface area; rather, it increases the surface area by a factor of four.

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No, Savannah is incorrect. Doubling the length, width, and height of a right rectangular prism will not double its surface area.

Surface area is the total area of an object's exposed faces, including any external surface area. It is a measure of the size of a surface and is usually expressed in square units such as square meters or square centimeters. Surface area is a two-dimensional measurement, since it only takes into account the area of a surface, and not its thickness or volume.

The surface area of a right rectangular prism is calculated by multiplying the length by the width and then multiplying that number by two and adding the two products together.

For example, the surface area of a right rectangular prism with a length of 15 cm, a width of 10 cm, and a height of 5 cm is calculated as follows:

Surface area = (15 cm * 10 cm) + (15 cm * 5 cm) = 150 cm2 + 75 cm2 = 225 cm2

Doubling the length, width, and height of this right rectangular prism would give us a prism with a length of 30 cm, a width of 20 cm, and a height of 10 cm. The surface area of this new prism would be calculated as follows:

Surface area = (30 cm * 20 cm) + (30 cm * 10 cm) = 600 cm2 + 300 cm2 = 900 cm2

As you can see, doubling the length, width, and height of the right rectangular prism does not double its surface area - the surface area has increased by four times (900 cm2/225 cm2 = 4).

In conclusion, doubling the length, width, and height of a right rectangular prism does not double its surface area; rather, it increases the surface area by a factor of four.

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Answer:

1244 DCD

Step-by-step explanation:

The height of the can of cylinder shape is 9.14 cm.

What is a cylinder?

In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases separated by a curved surface at a specific distance. These bases frequently have a circular shape (like a circle), and an axis connects their respective centres.

We are given the diameter as 4 cm.

So, the radius is 2cm.

Also, it is given that the surface area of the can is 140 square centimeters.

So, using the surface area of cylinder, we get

⇒Area = 2πr (h + r)

⇒140 = 2π * 2 (h + 2)

⇒140 = 4π (h + 2)

⇒140 = 4 * 3.14 * (h + 2)

⇒140 = 12.56 * (h + 2)

⇒11.14 = h + 2

⇒h = 9.14

Hence, the height of the can of cylinder shape is 9.14 cm.

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A kilowatt-hour is about 1 3.6 x 10⁶ joules.

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

A kilowatt-hour is about 3.6 x 10⁶joules.

The above statement means that we convert 3.6 x 10⁶joules from joules to kilowatt-hour

Using the above as a guide, we have the following:

The given parameter can be represented using the following equation

3.6 x 10⁶joules = x kilowatt-hour

Rewrite as

x kilowatt-hour = 3.6 x 10⁶joules

As a general rule of conversion, we have

1 kilowatt-hour = 3.6 x 10⁶joules

So, we have the following representation

x kilowatt-hour = 1 kilowatt-hour

Evaluate the quotient

x = 1

Hence, the expression that completes the blank is 1 (one)

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