2. A square playground has a side which measures 40 metres. What is its area?​

A system that has no solution is classified as inconsistent.

A system that has one and only one solution is classified as  independent

The system of equation graphed is consistent and independent.

The equations given by the graph are expressed as;

3x - 4y = 32

3x + 5y = 24

Now, if we subtract eq 1 from eq 2, we will get;

5y - (-4y) = 24 - 32

9y = -8

y = -8/9

Put 8/9 for y in eq 2 to get;

3x + 5(8/9) = 24

3x = 24 - 40/9

3x = 176/9

x = 176/27

Now, to classify solution to equations, we say that;

1) When there is no solution, it is inconsistent.

2) When there is one and only one solution, it is independent

Since we have a solution and only one solution, then we can say that the system of equation graphed is consistent and independent.

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Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

p(x)=6x+2

for p(-2)

p(-2) = 6(-2) + 2

p(-2) = -12 + 2

p(-2) = -10

for p(4)

p(4) = 6(4) + 2

p(4) = 24 + 2

p(4) = 26

p(-2) < p(4)

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Answer:

(B) "The value of p(-2) is smaller then the value of p(4)" is True

Step-by-step explanation:

p(x)=6x+2

p(-2) = 6*(-2)+2

p(-2) = -12+2

p(-2) = -10

p(4) = 6*(4)+2

p(4) = 26

====

p(-2) = -10

p(4) = 26

===

(A) The value of p(-2) is larger then the value of p(4).   False

(B) The value of p(-2) is smaller then the value of p(4).  True

(C) The value of p(-2) is the same as the value of p(4).  False

(D) The values of p(-2) and p(4) cannot be compared.   False

Answer: 7/12

Step-by-step explanation:

Based on the given conditions, formulate: 3/4 - 1/4

Find the common denominator and write the numerators above the common denominator: 9/12 - 2/12

Calculate the product or quotient:

Write the numerators over the common denominator: 9-2                                          

                                                                                          12

Calculate the sum or difference: 7/12

Answer: 7/12

The value of x will be; x = 3

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that  the equation 5x+7=6x+4

Here, we need to solve for x;

5x+7=6x+4

combine the like terms;

5x - 6x = -7 +4

-x= - 3

x = 3

Therefore, the solution will be as;

x = 3

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198.5 is the answer

50X4-(3÷2)=198.5

Answer: 198.5

Step-by-step explanation:

= 50x4-(3 divided by 2)

= 50x4-(3/2)

= (50 x 4) - ( 3/2 )

= (200) - (3/2)

= 200 - 1.5

= 198.5

Answer:

81/100 is the answer I believe if I'm wrong my bad

Answer:

81/100

Step-by-step explanation:

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Table A is a function.

Table B is not a function.

Table C is a function.

Table D is not a function.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is a function if it is one-to-one or many-to-one.

But a relation is not a function if it is one to many.

Table A is a function and it is a many-to-one function.

Table B is not a function as input 1 leads to two different outputs 1, - 1.

Table C is a function and it is a one-to-many function.

Table D is not a function as one input leads to 3 different outputs.

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The perimeter of ΔABE is 70 units.

The  perimeter of ΔCDF​ is 35 units.

A triangle is a polygon with threes sides. The sum of angles in a triangle is 180 degrees.

Therefore, the perimeter of a triangle is the sum of the whole sides.

Triangle mid point theorem is used to find the perimeter of the triangles.

It states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Let's find the perimeter of triangle ABE.

Hence,

perimeter of triangle ABE = AB + BE + AE

BE = 24

AE = 13 + 13 = 26

AB = 10 + 10 = 20

perimeter of triangle ABE = 24 + 26 + 20 = 70 units

perimeter of triangle CDF = DF + CD + CF

perimeter of triangle CDF = 10 + 13 + 12

perimeter of triangle CDF = 35 units

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The 10 represent in the function f(x) = 10(1. 015)* shows the balance in a savings account as time increases is the starting balance of the savings account.

Therefore the answer is D) The starting balance of the savings account.

The compound interest formula is used to calculate the total interest earned on a principal amount over a period of time, where the interest is compounded at regular intervals. The formula is:

A = P(1 + r)^(t)

Where:

A is the final amount (principal + interest)

P is the principal (initial) amount

r is the annual interest rate (expressed as a decimal)

t is the number of years the money is invested or borrowed

The function f(x) = 10(1. 015)* shows the balance in a savings account as time increases.

So 10 represents the principal (initial) amount

0.014 represents the annual interest rate (expressed as a decimal)

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An imaginary number is produced when we square a negative number.

The value of I is -1.

This article's introduction included a proposition. The specific measure or value of what I stands for was the subject of the statement. It is discussed in this section of the article along with an explanation of its value.

Iota is the term used to describe the imaginary portion of a complex number. The symbol "iota" or I is used to represent an imaginary number's value. An imaginary number is produced when we square a negative number.

The value of I is -1.

The concept of complex numbers is understood using this value of i.

x2 plus 1 equals zero in a quadratic equation.

x2 = -1

x = √-1

The imaginary portion is shown as -1.

I = √-1

i2 = -1

An imaginary number can be squared to get a negative value, as was previously discussed.

I = √-1

both sides being square

i2 = -1

An imaginary number plus a real number are combined to get any complex number. Iota, sometimes known as I stands for all non-real quantities.

Real numbers include 10, -20, 3, and other like values.

The integers 2i, -5, -i, etc. are examples of imaginary numbers.

Complex numbers take the form of a + ib, where I denotes the imaginary component. In addition, the number zero is complicated. Only the imaginary component of a complex number can be added to or subtracted from the imaginary part, and vice versa for the real part of the complex number.

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The true statement about the function in the list of options is (d) none of these

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

p c

0.25 1.69

0.45 3.04

0.75 5.06

1.25 11.81

Where

The values in the p column represent the domain

In this case, the domain is

Domain = [0.25, 1.25]

The values in the c column represent the range

In this case, the range is

Range = [1.69, 11.81]

This means that the options (a), (b) and (e) are false

For option (c), we have

c = 6.75p

This means that

c = 6.75 * 0.25 = 1.69

c = 6.75 * 0.45 = 3.04

c = 6.75 * 0.75 = 5.06

c = 6.75 * 1.25 = 8.43 -- false

This means that the option (d) is false

Hence, none of the options is true

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This is a coordinate pair of a point. 2 and 3 denotes X and Y coordinate respectively.

The system that is used to represent the location of points in the space is termed as coordinate system. There are two types of coordinate system such as polar and cartesian. In case system there are two reference axes which are perpendicular to each other.

In the cartesian system points are represented with respect to a vertical axis named Y axis and a horizontal axis named X axis.

We stated earlier that in the cartesian system a location of a point is identified by a pair of numerical terms.

So, 2, 3 indicates a pair of numerical terms. 2 denotes the X coordinate of the point and 3 denotes the Y coordinate of that point.

In the next, the distance of the point from X axis is 3 unit and distance from Y axis is 2 unit.

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Complete question is: In the point (2,3) which point denotes the y-coordinate.

The area of the given shape is 46 cm²

Formulas used:

Area of the triangle = (1/2) × Base × Height

Area of rectangle = Base × Width

Here we have  

The composite figure with a right-angled triangle and a rectangle

In a right-angled triangle,

The base of the triangle = 3 cm

Height of the triangle = 4 cm

Area of the triangle

= (1/2) × base × height

= (1/2) × 3 × 4

=  (1) × 3 cm × 2 cm

=  6 cm²  

In rectangle,

Length of the rectangle = 10 cm

Width of the rectangle = 4 cm

Area of the rectangle

= Length × Width

= 10 cm × 4 cm

= 40 cm²

By the above calculations,

Area of the given figure = Area of triangle + Area of rectangle

= 6 cm² + 40 cm² = 46 cm²

Therefore,

The area of the given shape is 46 cm²

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Consequently, the answer to the above fraction problem comes out to be 1/2 .

An element of a fraction or ratio is a piece of a whole. The number of equally sized pieces into which the whole has been divided is represented by the denominator b, and the number of parts that are included is represented by the numerator a. The LCM of two fractions' denominators is the least common multiple (LCD) of those denominators.

Here,

Given here is: (4√(2) - √(2)) × √(2) /  (2) (2) × √(18) (18)

The radical is then simplified in order to determine its value.

=> 3√(2) × √(2) / 2√(2) × 3√(2)

=> 3(2) / 6(2)

=> 3/6

=> 1/2 or 0.5

so,

after simplification, the answer is 1/2.

Consequently, the answer to the above fractional problem comes out to be 1/2 .

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A rectangular prism has dimensions of 8cm by 9cm by 10cm therefore the volume is 720cm³.

This is referred to as the measure of the space occupied within the boundaries of any three-dimensional solid.

Volume of rectangular prism = l × w × h where l is length, w is width and h is height.

Volume =  8cm × 9cm × 10cm = 720cm³.

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The multiplication of the algebraic expressions gives x⁴ + 1.5x³ - 2x²

An algebraic expression is an expression that consists of variables, constants, and a finite number of algebraic operations (such as addition, subtraction, multiplication, and division) e.g. 2x + 25

In order to perform the multiplication, you use expression outside the parenthesis to multiply the expressions inside the parenthesis one after the other. That is:

-0.5x²(-2x² - 3x + 4) = -2x²(-0.5x²) - 3x(-0.5x²) + 4(-0.5x²)

= 1x⁴ + 1.5x³ - 2x²

= x⁴ + 1.5x³ - 2x²

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The conclusion on if there is convincing evidence that the one detergent is better than the other is; Option D: No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.

We are told that, 25 pieces are randomly assigned to be cleaned with detergent A, while the remaining 25 pieces are cleaned with detergent B.

Therefore, we can say that the sample size for both detergent A and detergent B is same. We can also say that the sample is distributed randomly which means that the sample is unbiased (fair).

We are also told that the mean rating for detergent B is found to be significantly less than the mean rating for detergent A.  Since we know that the mean is the average of a set of given numbers, then we can conclude that there is No evidence that the one detergent is better than the other because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.

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Answer:  Part A:

To represent the cost per night x and cost per meal y in a system of equations, we can use the information provided in the question:

First Special:

3x + 4y = 233

Second Special:

3x + 3y = 226.50

Where x is the cost per night and y is the cost per meal.

Part B:

To find the cost per night and the cost per meal, we can use the information provided in the question and system of equations.

We can solve this system of equations using several methods: substitution or elimination method.

One common method to find the solution is by substitution method, where we find the value of x in terms of y from one of the equations and then substitute it into the other equation to solve for y.

x = (233 - 4y)/3

then substitute it into the other equation:

3(233 - 4y) + 3y = 226.50

now solve for y:

699 - 12y + 3y = 226.50

-9y = -472.50

y = 52.50

and we can substitute it back into the first equation:

3x + 4(52.50) = 233

3x = 80.50

x = 26.83

So the cost per night is $26.83 and the cost per meal is $52.50

Step-by-step explanation:

If William spends a winter day recording the temperature once every three hours for science class. If  the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. The temperature at 6pm is: -11.1°F

Between 9am and noon, the temperature rose 16.2°F, so the temperature at noon will be:

Temperature at noon  = -12.2 + 16.2

Temperature at noon  = 3.0°F

Between noon and 3pm, the temperature dropped 9.1°F, so the temperature at 3pm will be:

Temperature at 3pm = 3.0 - 9.1

Temperature at 3pm = -6.1°F

Between 3pm and 6pm, the temperature dropped 5°F, so the temperature at 6pm was:

Temperature at 6pm =-6.1 - 5

Temperature at 6pm = -11.1°F

Therefore the temperature at 6pm is  -11.1°F.

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Her painting rate in window frames per hour will be;

⇒ 1.6 frames per hour

Her painting rate in hours per window frame will be;

⇒ 0.25 hours per window frame

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Joyce painted 8 window frames in 5 hours while earning money for college.

Here, Joyce painted 8 window frames in 5 hours while earning money for college.

Hence, Her painting rate in window frames per hour is,

⇒ 8/5

⇒ 1.6 frames per hour

And, Her painting rate in hours per window frame is,

⇒ 5/8

⇒ 0.25 hours per window frame

Thus, Her painting rate in window frames per hour = 1.6 frames per hour

Her painting rate in hours per window frame = 0.25 hours per window frame

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To simplify the expression 5c−3d−12c+d−6, we can combine like terms:

5c − 12c + d − d − 6 = (-12c + d) + (-6)

Therefore, the expression 5c−3d−12c+d−6 can be simplified to -12c + d - 6.

a) Using the slope-intercept equation, after 4 years of working at the new company, Nachelle's salary will be $73,000 per annum.

b) After t years of working at the new company, Nachelle's salary will be $57,000 + $4,000(t).

The slope-intercept equation is in the form of y = mx + b.

The slope intercept describes the equation of a straight line, where m is the slope of the line, y and x are the y and x coordinates, and b is its y-intercept.

Initial starting salary per year = $57,000

Annual raise in salary = $4,000

Period = 4 years

Salary after 4 years = $73,000 [$57,000 + $4,000(4)]

Salary after t years = $57,000 + $4,000(t)

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Answer:

x = 11

Step-by-step explanation:

The two angles are consecutive interior angles so they add up to 180

13x -26 + 5x + 8 = 180

13x + 5x -26 + 8 = 180

18x - 18 = 180
18x = 180 + 18

18x = 198

x = 11

By plot in graph, we get Y=6 and x=-1 is perpendicular lines.

Parallel lines are lines in a plane that are always the same distance apart and never intersect. They are coplanar lines that do not intersect each other, and they have the same slope.

Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, they are lines that are at a 90-degree angle to each other. The slope of perpendicular lines are opposite reciprocals of each other, meaning that if one line has a slope of m, the other line will have a slope of -1/m.

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Yes, the rate 4.8 laps every 8 minutes; 3.6 laps every 6-minute form a proportion.

A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:

1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

4.8 lap every 8 minutes will be equal to (4.8/8) = 0.6 lap a minute.

3.6 lap every 6 minutes will be equal to (3.6/6) = 0.6 lap in a minute.

Here, as the value of the ratio of both the quantities are same so the given values are said to be in Proportion.

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The midpoint for zero is (0,0).

The midpoint can be zero. This is dependent on the value of the two points. For two points on a number line on points with values -4, and 4, the midpoint is 0. And for two points such as (-2, 5), and (2, -5), the midpoint is equal to (0, 0).

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.

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Answer:

g (x) = −7 x 2 + 26 x + 8

Step-by-step explanation: