What is the total surface area of the square pyramid below?

Simplified expression for the amount is 5(36+23m) .

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Step 1: Form an equation for the amount of money Troy has received after m months.

If the total months that Troy's grandfather has given him money is m, then the number of months that Troy's mother has given him money is m - 3.

⇒ Total amount in account = 300 + 75m + 40(m - 3)

                                             = 300 + 75m + 40m-120

                                             =180 + 115m

                                            =5(36+23m)

Hence, Simplified expression for the amount is 5(36+23m) .

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The equations which are represents in the graph are  y  = 0.86x & y =  -2.4x + 6

The equation of a straight line is a relationship between x and y coordinates, The two points form of equation of a straight line is y-y₁ =  y₂-y₁/x₂-x₁(x-x₁),

Given that,

A graph, In which two lines are given,

Line 1 is passing through following points,

(0, 0) and (1.75, 1.5)

Line 2 is passing through following points,

(2.5, 0) and (0, 6)

Equation of line 1

y - 0 =  (1.5-0)/(1.75-0) (x - 0),

y  =  0.86(x - 0),

y  = 0.86x,

Equation of line 2,

y - 6 =  (0 - 6)/(2.5 - 0)(x - 0),

y - 6 =  -2.4 (x - 0),

y - 6 =  -2.4x

y =  -2.4x + 6

Hence, the equations are y  = 0.86x & y =  -2.4x + 6

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Step 1: To calculate the cost of 5kg of breakfast cereal, we need to multiply the cost of 1kg by 5.

Step 2: R36 x 5 = R180

Step 3: Therefore, 5kg of breakfast cereal will cost R180.

The area of the figure made up of a semicircle and a triangle is 63.25 ft²

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

The figure is made up of a semicircle and a triangle.

The semicircle has a diameter of 10 feet. Hence:

Area of semicircle = (1/2) * π * diameter²/4

Substituting:

Area of semicircle = (1/2) * π * 10²/4 = 39.25 ft²

The triangle has a base of 8 ft and height of 6 ft. hence:

Area of triangle = (1/2) * base * height

Substituting:

Area of triangle = (1/2) * 8 ft * 6 ft = 24 ft²

The area of the figure = Area of triangle + Area of semicircle

Area of figure = 24 ft² + 39.25 ft² = 63.25 ft²

The area of the figure is 63.25 ft²

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Answer:

1/2 base * height = 16 in^2

1/2 * 8 in * H = 16 in^2

H = 32 in^2 / 8 in = 4 in         Equation # 4

The line representing the equation part of the constraint 7x1 + 4x2 28 goes through the following two points e. none of the above.

The equation of a line can be represented as y = mx + b, where m is the slope of the line and b is the y-intercept. The line representing the equation of a constraint, such as 7x1 + 4x2 = 28, would be a straight line in a two-dimensional graph.

The points given in the options a, b, c, and d are pairs of x and y coordinates. To determine if any of these points lie on the line representing the constraint equation, we would need to substitute the x and y values into the equation and see if the equality holds.

For example, for option a, if we substitute x = 4 and y = 0 into the equation, we get 7 * 4 + 4 * 0 = 28, which is not true. Hence, none of the given points in the options lie on the line representing the constraint equation.

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The curve will get shifted left side by four units. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = g(x)

If the g(x) is replaced with g(x + 4). Then the curve will get shifted left side by four units.

Thus, the correct option is A.

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The solution of the system of equation is , x= -4 & y= -8.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

from the given graph we get,

one line is passing through the points (0,10) , ( 4,28)

so, the equation of the line can be,

4y= 18x + 40

and, second line is passing through the points (0,8) , (1,12)

so, the equation of the line can be,

y= 4x+8

solving the equations we get,

x= -4

y= -8

Hence, The solution of the system of equation is , x= -4 & y= -8.

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Answer:

There is no given price so lets say I need something that is 85$ and I have a 10% off coupon well I will be saving 8.50$ and only needing to pay 76.50.

4$ would not take that much off only would be paying 81$

Step-by-step explanation:

85 divided by 100 x10 = 8.50

85$-4=81

Answer:

Here you have

Step-by-step explanation:

8 x 7 x 6 = 336 cm²

The value of the variable, x is 45 degrees

We have that the polygon is one with eight sides, that is, it is a regular octagon.

To determine the interior angle, we have

(n - 2) 180

n is the number of sides

(8-2)180

1080 degrees

Now, divide it by the number of sides

1080/8 = 135 degrees

Note that angles on a straight line is equal to 180

Then,

x + 135 = 180

Collect like terms

x = 180 -135

subtract the values

x = 45 degrees

Hence, the value is 45 degrees

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The gross monthly pay for the given service is $1241.67

Monthly pay means the wages paid by an employer to an employee for the whole or part of the month during which the employee is employed by the employer.

Given that, the annual pay of some service is $14900, we need to calculate the monthly pay of same,

Therefore,

To find, monthly pay, we will divide annual pay by 12, because there are 12 months in a year,

Monthly pay = annual pay / 12

= 14900 / 12

= 1241.67

Hence, the gross monthly pay is $1241.67.

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Answer:right angles, two sets of parallel sides, and opposite sides equal.

Step-by-step explanation:

The commission earned on the sale of $1253.70 is $233.20

A fee paid to an agent or employee for transacting a piece of business or performing a service is called commission.

Given that, there is a commission of 18.6% on the sale of $1253.70

Therefore,

The commission earned = 1253.70 × 18.6%

= 1253.70 × 18.6 / 100

= 233.20

Hence, the commission earned on the sale of $1253.70 is $233.20

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Answer:

Step-by-step explanation:

OK YOU ARE GOOD OH AND IT

5/8

The probability that the car selected was a domestic car and older than 2 years is 0.63 or 63%.

Probability is a mathematical concept that quantifies the likelihood or chance of an event occurring. It is a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between, probabilities reflect the degree of certainty that an event will occur, with values closer to 1 indicating a higher likelihood of occurrence and values closer to 0 indicating a lower likelihood.

The probability of an event is calculated by taking the ratio of the number of favorable outcomes to the total number of possible outcomes.

domestic car older than 2 years/total domestic cars = (28 + 12 + 23)/100 = 63/100 = 0.63 = 63%

Therefore, the probability of selecting a car that is less than 2 year given that it is a domestic car is 0.63 or 63%.

*The problem seems incomplete, attached might be the complete version of it.

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The rate of diesel in the second case is less. Then the Shell cost is the cheapest per liter.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

50L of diesel from Sasol costs R 799.59. Then the rate is given as,

⇒ 799.59 / 50

⇒ R 15.9918 per liter

40L of diesel from Shell costs R 619.60. Then the rate is given as,

⇒ 619.60 / 40

⇒ R 15.49 per liter

The rate of diesel in the second case is less. Then the Shell cost is the cheapest per liter.

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It would cost R451.4 to buy an item that was priced at £37

During 2012, the article was priced at £15 to R183

Therefore the cost of the item in rand when the article is priced at £37 can be calculated as follows

£15= R183

£1= x

cross multiply both sides

15x= 183

x= 183/15

x= 12.2

£1= R12.2

£37= Y

Cross multiply both sides

y= 12.2 ×37

= 451.4

Hence the price of the item when it was priced at £37 is $451.4

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As per the linear equation the system has one solution, which is x = 1 and y = 1.

A linear equation is a mathematical expression that represents a straight line. A linear equation has a set of variables, and the coefficients (numbers in front of the variables) are constant.

The reason why most overdetermined linear systems are inconsistent is that there are more restrictions placed on the variables than what is required to find a solution.

It is possible for an overdetermined linear system to have one solution, but this is a rare occurrence.

When an overdetermined system has infinitely many solutions, this means that there are an infinite number of combinations of values that satisfy all of the equations simultaneously.

For example, consider the following system of linear equations:

2x + 3y = 6

4x + 6y = 12

This system is overdetermined because there are two equations and only one variable (x and y). In this case, the system has one solution, which is x = 1 and y = 1.

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Answer:

15√2

Step-by-step explanation:

3[tex]\sqrt{50}[/tex] = 3√25·2 = 3·5√2 = 15√2

The probability of randomly drawing a green marble form the bag would be = 12/25

Probability is defined as the expression that show the possible outcome of an event.

The number of red marbles = 5

The number of blue marbles = 8

The number of green marbles = 12

The total number of marbles = 5+12+8 = 25

Therefore the probability of randomly drawing a green marble = 12/25

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Answer:

5.83 x 10^13.

Step-by-step explanation:

5.3x10^6 x 1.1x10^7

= 5.3 x 1.1 x 10^(6+7)

= 5.83 x 10^13.

The required sum of the given partial sequence is 33525.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The sum of the partial sequence.
[tex]= \sum_{n=1}^{75}12n - 9[/tex]

[tex]= \sum_{n=1}^{75}12n - \sum_{n=1}^{75} 9\\= 34200-675\\=33525[/tex]

Thus, The required sum of the given partial sequence is 33525.

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5 triangles could be formed from the polygon pictured.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The given figure is an irregular heptagon (7 unequal sides).

Now,

Taking a common vertex A we can draw the triangles as given below.

We see that,

There are 5 triangles that can be drawn.

Thus,

5 triangles can be formed.

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The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

y = a (1 ± r)ˣ

The rate is 6% for 20 years semiannually. Then the rate is given as,

r = 0.06 / 2

r = 0.03

Then the time is given as,

x = 20 (2)

x = 40

Then the exponential function is given as,

A = $2000 × (1 + 0.03)⁴⁰

A = $2000 × (1.03)⁴⁰

A = $2000 × 3.262

A = $6524.1

The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.

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A new dog park is enclosed by a fence and shaped like a parallelogram. So, the area and perimeter of the dog park is 2125 m² and 202.5 m.

Pictures can be seen in the attachment.

These are the specified parameters:

Coordinate points in the image = (-8, 0), (5, 5), (9, 0), and (-4, -5).

1 unit = 5 m

The area of the parallelogram of the dog park

Triangular base (b) = (9 - (-8)) × 5 m = 85 m

Triangle height (h) = (0 + 5) × 5 = 25 m

A = 2 × 1/2 × b × h

  = 2 × 1/2 × 85 m × 25 m

  = 2125 m²

Perimeter of the dog park

The line a goes through the point (-8, 0) and (5, 5)

a² = (5 - (-8))² + (5 - 0)²

   = 13² + 5²

   = 169 + 25

   = 194

a = √192

a = 13.85

Length a = 13.85 × 5 m = 69.25 m

The line b goes through the point (5, 5) and (9, 0).

b² = (9 - 5)² + (0 - 5²

   = 4² + (-5)²

   = 16 + 25

   = 41

b = √41

b = 6.4

Length b = 6.4 × 5 m = 32 m

Perimeter = 2 × (a + b)

                = 2 × (69.25 m + 32 m)

                = 2 × 101.25 m

                = 202.5 m

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Answer:

-1/-3 s the slope

Step-by-step explanation:

(7,-1) and (6,-4)

-4-(-1)=-3

6-7=-1

so -1/-3 is the slope

Porosity calculated as ratio of pore to total vol. Plot of porosity vs averaging length scale (edge of square used for averaging). Rep. elemental vol = vol of square used for averaging.

The porosity as a function of the averaging length scale can be calculated as follows:

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When there are an even number of observations, and the observations are in order from smallest to largest, the median is:The average of the two middle observations.

The median is a measure of central tendency that is commonly used for data sets with an odd number of observations. When there are an even number of observations, the median is defined as the average of the two middle observations. This provides a representative value that splits the data set in half, with half of the observations having values lower than the median, and half having values higher.

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Answer:

see below

Step-by-step explanation:

Susan

4lbs of coffee

2lbs of nuts

Tom

2lbs of coffee

4lbs of nuts

6 hrs per day.

if only coffee x = (4+2)*6=36lbs

if only nuts y = (4+2)*6=36lbs