Directions: Solve each problem using the correct algebraic rules. 1. Write an expression for each of the following: a. the sum of 6 and z b. the difference between 20 and x c. 8 less than the quotient of x divided by 6 d. x increased by 5 divided by 4

Answer:

Step-by-step explanation:

0 886 pennies no np

Yes, m∠ABC and m∠XYZ are congruent

No, lines FG and DE are not congruent

Yes, OR and OS are congruent

Yes, 2∠ and ∠4 are congruent.

Congruent angles are angles that have the same measure, in degrees and are often represented by the symbol "≅". While congruent line segments are two or more line segments that have the same length.

m∠XYZ = 180° - 140° {supplementary angles}

m∠XYZ = 40°

so;

m∠ABC and m∠XYZ are congruent

line FG = and line DE =

so;

FG and DE are not congruent

OR = 2in and OS = 2in

so;

OR and OS are congruent

∠2 and ∠4 are vertical angles and are equal so;

2∠ and ∠4 are congruent

Therefore, (m∠ABC and m∠XYZ), (2∠ and ∠4), and (OR and OS), are two pairs of angles and line segments respectively which are congruent, while the lines segments FG and DE are not congruent.

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The packaging that uses more material is the packaging 2

The given parameters that can be used in our computation are:

For a packaging to use more material, it must have a higher perimeter value

The perimeter is then calculated as

Perimeter = 2 * (Rows + Column)

When the values are substituted, we have the following equations

Material 1 Perimeter = 2 * (3 + 4)

Material 1 Perimeter = 14

Material 2 Perimeter = 2 * (6 + 2)

Material 2 Perimeter = 16

This implies that the packaging 2 uses more material

This is so because 16 is greater than 14

Also, the company can choose to package 12 cans one way instead of another because one package can use more material than the other and they need to save cost

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A proper fraction is a fraction where the numerator is less than the denominator. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. A mixed fraction is a combination of a whole number and a fraction.

There are three main types of fractions: proper fractions, improper fractions, and mixed fractions.

1. Proper fraction: A proper fraction is a fraction where the numerator is less than the denominator. An example of a proper fraction is 2/3.

2. Improper fraction: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. An example of an improper fraction is 5/4.

3. Mixed fraction: A mixed fraction is a combination of a whole number and a fraction. An example of a mixed fraction is 3 1/2.

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The three primary categories of fractions are proper fractions, improper fractions, and mixed fractions.

The fraction is deemed accurate when the numerator is less than the denominator. It is considered unacceptable to use a fraction where the numerator is more than or equal to the denominator. A mixed fraction is produced by combining a whole number and a fraction.

The three primary categories of fractions are proper fractions, improper fractions, and mixed fractions.

1. Proper Fraction: A fraction that has a larger numerator than denominator is said to be inappropriate. Somewhere about 2/3 would be a reasonable fraction.

2. Improper fraction: A fraction that has a numerator that is more than or equal to the denominator is referred to as being improper. A bad fraction is demonstrated with the number 5/4.

3. Mixed Fraction: Mixture of a whole number and a fraction: A mixture fraction is one that combines the two. 3 1/2 is an illustration of a mixed fraction.

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the range of the graph is simply the region that it covers vertically, well, from the picture we can see the graph goes down down down to -2 vertically, makes an U-turn and goes back up, the arrowheads mean it keeps on going to infinity, so vertically the graph never goes below -2, so its range is just from -2 up to infinity, or in interval notation [ -2 , +∞ ).

The measure of the angle B is 55 degrees

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

A triangle

On the triangle, we have the following readings:

Angle A = 53 degrees

Side AC = 13 units

Side AB = 15 units

To calculate the angle B, we start by calculating the measure of the length BC

This is represented using the following cosine law

BC = √(AC² + AB² - 2 * AC * AB * cos(A))

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

BC = √(13² + 15² - 2 * 13 * 15 * cos(53 degrees))

Evaluate

BC = 12.6

Using the sine law, we have

AC/sin(B) = BC/sin(A)

This gives

sin(B) = AC * sin(A)/BC

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

sin(B) = 13 * sin(53)/12.6

Evaluate

sin(B) = 0.8239890183

Take the arc sin

B = 55 degrees

Hence, the angle is 55 degrees

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Answer: -4

Step-by-step explanation:

-2+3-5=-4

I HOPE THIS HELPS!!!!

Answer:

No- se p-ero quiero pun-tos

Step-by-step explanation:

por -favor :D

Answer:

y = 2.5x + 22

Step-by-step explanation:

the two points are (4,32) and (8,42)

The slope would be

[tex]\frac{42 - 32}{8-4}[/tex] = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5

This is the slope.  She saves $2.50 per week.

the y-intercept is how much money she started with

Use one point.  I will us (4,32) and the slope (2.5)

y = 32

m = 2.5

x = 4

y = mx + b

32 = 2.5(4) + b

32 = 10 + b   Subtract 10 from both sides

22 = b

This is the y-intercept.  This is how much money she had in the beginning.

y =mx + b

y = 2.5x + 22

Answer:

[tex]-16[/tex]

Step-by-step explanation:

[tex]f(5)=4(5)-1=19 \\ \\ g(5)=2^5+3=35 \\ \\ (f-g)(5)=f(5)-g(5)=19-35=-16[/tex]

The value of a digit in a number depends on its place value. The digit 4 will have a value of 40 if it is located in the tens place. The correct answer is option B: 17,524.

In the context of place value in mathematics, the value of a digit depends on its position in the number. The digit 4 would have a value of 40 if it is located in the tens place. Therefore, the correct answer to this question would be option B: 17,524, where the digit 4 is in the tens place, giving it a value of 40.

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The graph on the right depicts the linear function y=2x.

Linear function graph is a straight line that depicts linear function y = f(x) = mx + k. It tells the dependent variable y changes by a constant amount as the independent variable x also changes by a constant amount. Whilst variable k is the y-intercept.

The slope of the graph, m, is determined by:

m = (y₂-y₁) / (x₂-x₁)

We are given two graphs. The left graph depicts the line y=x. We want to know what the right graph depicts.

Firstly, we pick two random points on the left graph to find the slope of the graph. Let's say we pick (1,2) and (5,10).

m = (y₂-y₁) / (x₂-x₁)

   = (10-2) / (5-1)

   = 8 / 4

   = 2

Then we find the y-intercept (k), the point where the graph intersects the y-axis. Its value is 0.

Now we put the value of m and k into the linear function:

y = f(x) = mx + k

           = 2x + 0

           = 2x

Thus, the graph on the right shows the line y=2x

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The true statements are the equation of the function is y=4x+4, the relation is a function, the graph is linear.

The equation of the function start by calculating the slope (m)

The slope formula is used to calculate the inclination or steepness of a line. It finds application in determining the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis. The slope of a line is defined as the change in the "y" coordinate with respect to the change in the "x" coordinate of that line.

The formula to calculate slope is given as,

where, m is the slope of the line, x1, x2 are the coordinates of the x-axis, and y1, y2 are the coordinates of the y-axis.

m=[tex]\frac{12-8}{2-1}=4[/tex]

m=4

The equation is then calculated as:

So, we have

y=4(x-1)+8

y=4x-4+8

y=4x+4

Therefore, the equation is 4x+4. Hence the statement is true.

(b) The graph is nonlinear.

Because of (a) above, the graph is linear.

(c) The relation is a function

A linear relation is a relationship or connection between two variables that will produce a straight line when graphed. There will be times when the data points are scattered and do not form an absolutely straight line. When it appears that the scattered points resemble a straight line,

Hence, the given relation is function then the statement is true.

Therefore, the equation of the function is y=4x+4, the relation is a function, the graph is linear.

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Number of squares(x)        Perimeter(y)

1                                             8

2                                            12

3                                            16

4                                            20

Complete Question: What is the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form?

Answer: The relationship between the number of squares, x, and the perimeter of the rectangles  can be expressed as a  y = 5.1%x. This equation states that for every one square, the perimeter will increase by 5.1%.

To calculate the perimeter of a rectangle with x number of squares, the following calculation can be used: y = 5.1%x = 0.051x. This equation can be rearranged to solve for x: x = y/0.051.

For example, if the perimeter of the rectangle is 10, the number of squares, x, can be calculated as follows: x = 10/0.051 = 196.08. This indicates that the rectangle will have 196 squares.

Therefore, the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form can be expressed as y = 5.1%x, or x = y/0.051.

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Answer:

[tex]\huge\boxed{\sf p = -33}[/tex]

Step-by-step explanation:

p - 15 = -48

p = -48 + 15

[tex]\rule[225]{225}{2}[/tex]

Therefore , the solution of the given problem of inequality comes out to be m = 3 and b=4.

An inequality in mathematics is a link between two equations or values when there is no equal sign. Therefore, imbalance comes before inequality. An inequality creates a relationship between two numerical values that are not equal. Inequality and equality are different. have utilized the most typical sign for when variables are not comparable, not equal (). No matter how little or large the values, different inequalities are used to contrast them. A number of fundamental inequalities can be resolved by changing the two sides until the variables are all that is left. Numerous things can lead to unevenness, such as: The addition or division of low numbers from both sides. You switch the left and side.

Here,

Given  :  0-3x < 4 y = 12

=> Linear : Solid or Dashed

=>  m = 3

and

b =4

thus,

Therefore , the solution of the given problem of inequality comes out to be

m = 3 and b=4.

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Answer:

L C M

-9/8 will be your answer

correct if I'm wrong

Answer:

Step-by-step explanation:

part A Is 1600 because 80x20 is 1600

part b. Yes rick has enough because  each bag covers 1000ft so 8 bags is enough.

                    Hope this helped.

Answer: 75x^2-3 can be factored as (25x)^2 - 3 . The expression can be factored by taking the square root of the constant term and then using difference of squares.

In this case, the square root of -3 is not a real number, so it's not possible to factor it further.

So the final factored form of 75x^2-3 is (25x)^2 - 3.

Answer:

Step-by-step explanation:

75x^2-3 cannot be factored using integer numbers since it's a difference of squares. The expression 75x^2-3 is a binomial, not a trinomial. The difference of squares is a factoring pattern where you have a squared binomial subtracted from a constant.

75x^2-3 = 75x^2 -3x^2 = 72x^2 -3x^2 = (75-3)x^2 = 72x^2

So the factorization of 75x^2-3 is just 72x^2

There is only one way to paint such a cube, as each face must be a different color. So, the answer is one.

When it comes to creating art, there is no denying the importance of color. It is one of the most powerful tools an artist has at their disposal, as it can be used to convey a wide range of emotions, ideas, and messages. Even a simple object such as a cube can be transformed into a work of art with the right colors. This essay will explore the potential of painting a cube with a variety of colors, and why it's important to use a variety of colors in artwork.

When it comes to painting a cube, one must choose colors that will create a harmonious yet interesting look. The colors should be chosen carefully because they will be the focus of the piece. A cube painted with only one color would be too dull and boring, while a cube painted with an array of colors will make it more visually appealing. To create a successful painting of a cube, one should use colors that contrast and complement each other. For example, a cube can be painted so that one face is blue, two faces are red, and three faces are green.

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The solution to the given system of equations (x,y) is

(-3.5,-6.5)

Linear equation is an equation in which the highest power of the variable(s) is 1.Linear equations can have one or more variables, and can be written in the form “ax + by = c,” where a, b, and c are constants and x and y are variables. They always produce a straight line when plotted on a graph, hence the name “linear.”

To solve this substitution method can be used

In the first equation -3x+y=4

y=4+3x

substituting the value of y in second equation -9x+5y=-1

-9x+5(4+3x)=-1

-9x+20+15x=-1

6x=-1-20

x=(-21)/6=-3.5

y=4+3(-3.5)=4-10.5=-6.5

(-3.5,-6.5) is the solution to the given system of equations.

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Write the solution set of the equation:

x = [tex]\frac{-7}{2}[/tex]

y = [tex]\frac{-13}{2}[/tex]

Now, According to the question:

Given the system of equations:

−3x + y = 4 ----1

−9x + 5y = −1-----2

Multiply both sides of the equation by a coefficient:

3( −3x + y) = 4 × 3

−9x + 5y = −1

Apply Multiplicative Distribution Law:

-9x + 3y = 12

-9x + 5y = -1

Subtract the two equations:

-9x + 3y -(-9x + 5y) = 12 -(-1)

Remove parentheses = -9x + 3y + 9x - 5y = 12 + 1

Cancel the unknown variables:

3y - 5y = 12 + 1

Combine like terms:

-2y = 12+1

-2y = 13

Divide both sides of the equation by the coefficient of variable :

y = 13 ÷ (-2)

y = -6.5

Express the number in fractions: y = -13/2

Substitute one unknown quantity into the elimination:

-9x + 3 × ([tex]\frac{-13}{2}[/tex]) = 12

Write as a single fraction:

-9x - [tex]\frac{1}{2}[/tex](3 × 13)= 12

Calculate the product or quotient:

-9x - [tex]\frac{39}{2}[/tex] = 12

Rearrange the unknown terms to the left side of the equation:

-9x = 12 + [tex]\frac{39}{2}[/tex]

Find common denominator and write the numerator above common denominator :

-9x = [tex]\frac{24+39}{2}[/tex]

= -9x = [tex]\frac{63}{2}[/tex]

x = [tex]\frac{63}{2}[/tex]÷( -9)

x = -[tex]\frac{63}{2}[/tex] × 9

x = [tex]\frac{-7}{2}[/tex]

Write the solution set of the equation:

x = [tex]\frac{-7}{2}[/tex]

y = [tex]\frac{-13}{2}[/tex]

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The ratio of prime numbers to composite numbers in the lowest term is 4:5.

A number with precisely two factors, "1" and the number itself, is referred to as a prime number. A composite number can be divided by at least one positive integer in addition to being divisible by 1 and the number itself since it contains more than two elements. The number 1 is neither a prime nor a composite. In addition to these two, coprime numbers fall into a similar category of numbers.

From the set of whole numbers from 1 to 9, there are 4 prime numbers (2, 3, 5, 7) and 5 composite numbers (4, 6, 8, 9). The ratio of prime numbers to composite numbers in the lowest term is 4:5, which can also be expressed as 4/5.

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There are 3 cases to consider when determining horizontal asymptotes:

1) Case 1: if: degree of numerator < degree of denominator. then: horizontal asymptote: y = 0 (x-axis)

2) Case 2: if: degree of numerator = degree of denominator.

3) Case 3: if: degree of numerator > degree of denominator.

The measure of each base angle of the isosceles triangle is given as follows:

80º.

An isosceles triangle is an angle that has two equal side lengths, meaning that the base angles also have the same measure.

For the top angle of the isosceles triangle ABC, we have that the semicircle, which has an arc length of 180º, is divided into 9 regions, hence it's measure is calculated as follows:

Top angle = 180º/9 = 20º.

For the base angles, each of them have the same measure, which we are going to call x.

The sum of the measures of the internal angles is of 180º, hence the value of x can be found as follows:

20 + 2x = 180

2x = 160

x = 160/2

x = 80º.

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Answer:

Here you go. I hope this helps. Don't forget that when graphing, the x-axis (horizontal) number is written before the y-axis (vertical).

The number of months, m, given the number of years, y is 12 years.

The Calendar in use today has 12 months every year. The length of the months is either 28, 29, 30, or 31 days. The 12 months of the Calender each have a length of 28 to 31 days. In a typical year, which has 365 days, each month has either 28, 30, or 31 days.

Months to Years Conversion. Divide the time by the conversion ratio to change the measurement from a month to a year. The months are equal to the years when split by 12.

12 months = 1 years

24 months = 2 years

36 months = 3 years

The number of months greater than the number of years

m= 12y

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Answer: -10v

Step-by-step explanation:

**in the attached file** :)

The tables that show a proportional relationship is are :

If every pair of data values is related in the same way, by multiplying by a factor, then the relationship is proportional. A proportionate relationship can be identified by looking at data, an equation, or a graph.

In Table 1, we can see a proportional relationship because the values of x are increasing by 1 while the values of y are increasing by 3.

Table 3 also shows a proportional relationship because the values of p are increasing by 2 while the values of q are also increasing by 2 at the same time.

For this same reason, Table 4 shows a proportional relationship with r increasing by 5 while s is increasing by 1.

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The work done in lifting a bag of mulch was 504 Joules.

To find the amount of work done in this scenario, you can use the formula for work, which is work = force x distance x cos(theta), where force is measured in newtons (N), distance is measured in meters (m), and theta is the angle between the force and the displacement.

In this case, first, you lifted the bag of mulch 1.2 meters against gravity and the force applied is 45N and the displacement is 1.2m, the formula becomes:

work = force x distance x cos(theta) = 45 N x 1.2 m = 54 J

After, you carry the bag of mulch 10 meters, and the force applied is still 45N and the displacement is 10m, so the formula becomes:

work = force x distance x cos(theta) = 45 N x 10 m = 450 J

Therefore, the total amount of work done in lifting the bag of mulch 1.2 meters and carrying it at a distance of 10 meters is 54 J + 450 J = 504 J.

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dont take my word for it but,

The volume of a cylinder can be calculated using the formula:

V = x * r^2 * h

Where:

V is the volume of the cylinder

x is the value of pi (3.14 in this case)

r is the radius of the cylinder (half the diameter, so 2 feet in this case)

h is the height of the cylinder

Plugging in the values from the problem, we get:

V = 3.14 * 2^2 * 6

= 3.14 * 4 * 6

= 75.36 cubic feet

So the volume of the rainwater collection tank is 75.36 cubic feet. The answer is therefore 75.36 cubic feet (Option B).

Answer:

75. 36 ft²

Step-by-step explanation:

The volume of the cylinder can be calculated as:

base * height

the formula of base is:

πr²

find the radius by finding half the diameter: 4 ÷ 2 = 2 ft

π* 2² = 12.56 ft²

Then we calculate for the volume

12.56 * 6 = 75. 36 ft²

The quadratic equation y = x² - 4x - 5 have ordered points at (0, -5), (4, -5), (-2, 7) and (6, 7)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The standard form of a quadratic equation is:

y = ax² + bx + c

where a, b and c are constants

The degree of a quadratic equation is 2.

Given that:

y = x² - 4x - 5

When x = 0; y = (0)² - 4(0) - 5 = -5

When x = 4; y = (4)² - 4(4) - 5 = -5

When x = -2; y = (-2)² - 4(-2) - 5 = 7

When x = 6; y = (6)² - 4(6) - 5 = 7

The quadratic equation y = x² - 4x - 5 have a vertex at (2, -9)

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