Find the values of the variables in the parallelogram. The diagram is not to scale.

Answer: This is a system of equations problem. We can set up the following equations:

x + y = 14 (where x is the number of hours Susie spent cutting grass and y is the number of hours Susie spent tutoring)

12x + 14y = 184 (where 12x represents the amount of money Susie made cutting grass and 14y represents the amount of money Susie made tutoring)

We can solve for x and y using different methods such as substitution or elimination.

By substitution:

x + y = 14

12x + 14y = 184

We know that y = 14-x.

so we can substitute it in second equation.

12x + 14(14-x) = 184

12x + 196 - 14x = 184

-2x = -12

x = 6

y = 14-x = 14-6 = 8

So Susie worked 6 hours cutting grass and 8 hours tutoring.

You can cross check by putting the values in the first equation x+y = 14.

Step-by-step explanation:

The value of x is 11.5.

Triangle ABC is a right-angle triangle.

We can apply the Pythagorean Theorem to get,

x² + 8² = 14²

We now solve for x to get,

⇒x² = 14² - 8²

The right-hand side is a difference of two squares, this factor gives us,

⇒x²  = (14 +8 )(14-8)         (using formula of a² -b²)

⇒x²  = 22 × 6

⇒ x² = 132

We take the positive square root of both sides to get,

x = [tex]\sqrt{132}[/tex]

⇒ x = 11.48

∴ x = 11.5 (  round to the nearest tenth)

So, the value of x is 11.5.

Read more about Pythagorean Theorem :

https://brainly.com/question/28981380

#SPJ4

The inverse of p v q →  p ∧ q is ~p v -q →-p ∧ ~q. hence option c is correct

What is mean by Inverse?

Opposite in order, nature or effect is called an Inverse.

Given that;

The statement is;

p → q

Now,

The inverse of p → q is written as;

~p → ~q

Thus, The inverse of p → q is ~p → ~q.

What is inverse in simple words?

something of a contrary nature or quality : opposite, reverse. : a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem. the inverse of "if A then B" is "if not-A then not-B"

Learn more about the inverse visit:

brainly.com/question/1210406

#SPJ4

Answer:

No solution.

Step-by-step explanation:

2y-8=6x

y=3x+2

--------------

2(3x+2)-8=6x

6x+4-8=6x

6x-4=6x

6x-6x=4

0=4

The solution of the given equations is x = 0, y=9. The value of x and y will satisfy the given equations.

What is an equation?

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Given a system of equations is

5y+30x=45  ........(i)

6y-x=54   .......(ii)

Applying the elimination method to solve the equations.

Multiply equation (ii) by 30 and with equation (i):

5y     + 30x=45

180y - 30x = 1620

_______________

185y           = 1665

Divide both sides by 185:

y = 1665/185

y = 9

Putting y = 9 in equation (ii)

6×9-x=54

54 - x = 54

-x = 54 - 54

x = 0

To learn more about the system of equations, click on the below link:

https://brainly.com/question/5601000

#SPJ1

A formula is an expression that instructs the computer how to mathematically process a given value. Some of the formulas for class 6 as explained.

Algebra, decimals, ratios, proportions, geometry, and mensuration are just a few of the crucial Math formulas for Class 6 that students must adhere to.

To know more about the formulas, here

https://brainly.com/question/657646

#SPJ4

On solving the system of linear equations 4x - 6y = 10 and 9x + 2y = 7, the value of x is x = 1 and y is y = -1.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The first linear equation is - 4x - 6y = 10

The second linear equation is - 9x + 2y = 7

Multiply equation (2) by 3 -

3(9x + 2y) = 7 × 3

27x + 6y = 21.....(3)

Add equation (1) and (3) -

4x - 6y + (27x + 6y) = 10 + 21

4x - 6y + 27x + 6y = 10 + 21

Combine the like terms -

31x = 31

x = 1

Substitute the value of x in equation (2) -

9(1) + 2y = 7

9 + 2y = 7

2y = 7 - 9

2y = -2

y = -1

Therefore, the values of x and y is x = 1 and y = -1 respectively.

To learn more about linear equation from the given link

https://brainly.com/question/2226590

#SPJ1

The factors of substitution are separating a polynomial into its component polynomials.

Factoring polynomials mean separating a polynomial into its constituent polynomials. Sometimes, when polynomials are particularly complicated, it is easiest to substitute a simple term and factor it down.

This is a quick technique to use with complicated polynomials, particularly if subsets of that polynomial repeat.

For example, we need to factorise (x − y)(x − y − 1) − 20

Let S = x − y. Then substituting S in for x − y for ease of computation, we get

(x − y)(x − y − 1) − 20​

= (S)(S − 1) − 20

= S² − S − 20

=(S − 5)(S + 4)

=(x − y − 5)(x − y + 4).

To know more about polynomials, here

https://brainly.com/question/29182596

#SPJ4

The null hypothesis is H0: u = 447, the alternative hypothesis is given as: H1: u ≠ 447

A null hypothesis is a statement that there is no significant difference between two groups or no relationship between two variables. The alternative hypothesis, on the other hand, is the statement that there is a significant difference or relationship between the groups or variables.

In statistical hypothesis testing, we test the null hypothesis against an alternative hypothesis. If the data provides enough evidence against the null hypothesis, we can reject it in favor of the alternative hypothesis.

Read more on hypothesis testing here:  brainly.com/question/4232174

#SPJ1

Answer:

88/24.       Mixed number: 3 16/24

Step-by-step explanation:

First, you want to find the LCM (Least Common Multiple) for the denominator. The LCM is 24. 24 divided by 4 is 6, so 6 x 5 is 30. 24 divided by 8 is 3, so 2 x 3 is 6. 24 divided by 6 is 4, so 4 x 13 is 52. All of the fractions’ denominators now have the same number, which makes it easier to add. So, 30/24 + 6/24 + 52/24 = 88/24. Your welcome :)

Answer:

this question has 3 answers according to decimal point your answer will be written as 3.67

According to mixed numbers your answer will be 3 written as whole number,2written as numerator and 3 written as denominator.

According to improper fraction your answer will be 11 written as numerator and 3 written as denominator

By using the fact that the sum of the interior angles must be equal to 180°, we will find that the value of x is 18.

I assume you need problem 4 solved.

There we can see the triangle JKL, such that the angles are:

K = (5x - 5)°

L = (3x)°

J = 41°

Remember that the sum of the interior angles of any triangle is always equal to 180°, then we can write the linear equation:

(5x - 5)° + (3x)° + 41° = 180°

We can solve that linear equation for x (i will remove the degree symbol so it is easier to follow it)

(5x - 5) + 3x + 41 = 180

(5x + 3x) + (41 - 5) = 180

8x + 36 = 180

8x = 180 - 36

8x = 144

x = 144/8 = 18

That is the value of x.

Learn more about triangles by reading:

https://brainly.com/question/2217700

#SPJ1

The mathematical mistake that Riley made is that She used the wrong common denominator.

A common denominator is a factor that all of the fractions in the set of equations have in common.

Thus, the appropriate response is:

(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))

See the steps in the proper order below:

Step 1: The expression is as follows:

(x/(x-3)(x-2)) + (3/(x+3))

Locate the common denominator in step 2 and rewrite the formula so that the numerators are higher than the common denominators.

Thus, we have:  (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)

Applying the Law of Multiplicative Distribution in Step 3

Thus, we have  (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)

Step 4: Gather Related Items

This results in:  (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)

Step 5: Group like coefficients together

This results in: ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)

Step 6: Determine the difference or sum

This results in:(4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)

To obtain, we factor and simplify the expression.

(2(2x²-6x+6)/(x-3)(x-2)(x+3).

Your question is incomplete but most probably your full question was

Riley makes a mistake in step 2 while doing her homework. What was her mistake? StartFraction x Over x squared minus 5 x + 6 EndFraction + StartFraction x Over x + 3 EndFraction Step 1: StartFraction x Over (x minus 2)(x minus 3) EndFraction + StartFraction 3 Over x + 3 EndFraction Step 2: StartFraction x Over (x minus 2) (x + 3) EndFraction + 3 (x minus 2) Over (x minus 2) (x + 3) EndFraction Step 3: StartFraction x + 3 x minus 6 Over (x minus 2) (x + 3) EndFraction Step 4: StartFraction 4 x minus 6 Over (x minus 2) (x + 3) EndFraction She added the two fractions incorrectly. She used the wrong common denominator. She did not distribute the negative correctly. She did not multiply the first fraction by a factor. Mark this and return

Learn more about Common Denominators at:

brainly.com/question/542317

#SPJ4

Answer:

Step-by-step explanation:

b<11.3/4.3

Answer:

9.8

Step-by-step explanation:

Answer: 98 Times.

[tex]2450/25=98[/tex]

The graph of linear equation y = 3x - 2 have a slope of 3 and y intercept of -2

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

The linear equation is in the form:

y = mx + b

where m is the rate of change and b is the y intercept.

Given that the graph of y = 3x - 2 is shown. It passes through the point (0, -2) and (1, 1)

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: b = 2 19/30  c = 3 13/30

Step-by-step explanation:

1 4/5 + 5/6

= 1 49/30

= 2 19/30

2 1/10 + 1 2/3

= 3 13/30

Answer:

b)

[tex]2 \times \frac{19}{30} [/tex]

c)

[tex]3 \times \frac{23}{30} [/tex]

Step-by-step explanation:

b)

x - 5/6 = 1 × 4/5

x - 5/6 = 9/5

x = 5/6 + 9/5

x = (25+54)/30

x = 79/30 (or 2×19/30)

c)

x - 2 × 1/10 = 1 × 2/3

x - 21/10 = 5/3

x = 21/10 + 5/3

x = (63+50)/30

x = 113/30 (or 3×23/30)

Note that the correct Two-way relative frequency table for the data is: (Option A) which is given as follows.

Movie Preference

Action                   Drama    Comedy    Row       Totals

High School        23.0%      13.2%         6.9%      43.1%

College                11.5%       29.3%         16.1%      56.9%

Column totals      34.5%     42.5%          23%      100%

See the tabularized format attached.

Tables of two-way relative frequency indicate percentages rather than counts. They are useful for determining whether or not two variables are related.

Thus, the first choice is the accurate depiction of a two-way frequency table since it shows the percentage of students in each group (high school and college) who picked each movie genre (action, drama, comedy), as well as row and column totals that sum up to 100%. The other three selections are incorrect because they lack percentages or column and row totals.

Learn more about Two-way relative frequency table:
https://brainly.com/question/20744563
#SPJ1

Answer:

Can't be answered, as written.

Step-by-step explanation:

Please check the equations.  As written, they are the same:

y=2x-4 and 6x-3y=12

The second, 6x-3y=12, can be rewritten:

-3y = -6x + 12

y = 2x - 4   is the same as the first equation.

========

I'll do an example based on a different first equation.  Let's try:

y = 4x-4 and 6x-3y=12

There are two equations and 2 unknowns.  We can solve this in either of two ways:  Mathematically and Graphically.  Let's try both.

Mathematically.

Pick either equation and isolate one of the variables (x or y)

I'll chose the first, since the variable y is already isolated.  (the efficient approach)

y = 4x-4

Take the second equation and use the definition of y provided by the first equation in place of y is the second:

6x-3y = 12

6x-3(4x-4) = 12  [Substituted the value of y given in the first equation]

6x - 12x + 12 = 12

-6x=0

  x= 0

Use x = 0 in either equation to find y:

y = 4x-4

y=4*(0)-4

y = -4

The solution (where the lines intersect) is (0,-4)

We can also solve this graphically.  

Plot the two lines and look for their intersection.  The attached graph shows that to be (0,-4).

The 8th term of the given sequence is [tex]a_8= \frac{78125}{243}[/tex].

A unique kind of sequence is a geometric sequence. Every term in the series (aside from the first term) is multiplied by a fixed amount to determine the following term.

The given sequence 9, 15, 25, . . . is a geometric progression series. The common ratio of the given GP is:

[tex]r= \frac{15}{9} =\frac{5}{3}[/tex]

Now, the nth term of the geometric sequence can be found out using the following formula, where a is the first term of the given series:

[tex]a_n= ar^{n-1}\\\\a_8= 9(\frac{5}{3} )^{8-1}\\[/tex]

[tex]a_8= \frac{78125}{243}[/tex]

Hence the 8th term of the given geometric sequence is [tex]a_8= \frac{78125}{243}[/tex].

Learn more about geometric sequence here:

https://brainly.com/question/11266123

#SPJ1

When a set of eight cards were labeled with A, D, D, I, T, I, O, N. The sample space for choosing a card is

A sample space is a set or collection of potential outcomes from a random experiment.

The letter "S" stands for the sample space in a symbol. The term "events" refers to a subset of probable experiment results.

Depending on the experiment, a sample area could include a variety of results.

For the given problem, the sample space is A, D, D, I, T, I, O, N which is rearranged to be S = {A, D, D, I, I, N, O, T}

Learn more on sample space at:

https://brainly.com/question/10558496

#SPJ1

For the given values the probability less than 3 equals 0.38.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12.

Given,

the probability of different scores

Probability of score less than 3 equals

= P(score 1) + P(score 2)

= 0.18 + 0.20

= 0.38

To learn more about probability from given link

https://brainly.com/question/13604758

#SPJ1

0.6×1.5=0.9 I know this answer come my home

The difference between total revenue and total costs is: gross profit.

Every element of production has a total cost that, depending on whether it has fixed costs or variable costs, includes the total opportunity cost (benefits from the next-best alternative) of each factor. Marginal cost is the added sum of the costs resulting from adding one more unit of output. Total cost is the collective term for all costs associated with manufacturing, including both fixed and variable costs. The total cost, as used in economics, is the sum of all expenses incurred in the production of a good.

Revenue is the entire sum of money that a business receives for items sold or services rendered during a specific period of time. The direct expenses incurred during the manufacture of the products a business sells are known as the cost of goods sold.

To know more about total revenue refer to:

https://brainly.com/question/21613450

#SPJ4

1. The graph that has a slope of -2/3 and a y-intercept of 2 is given as follows:

Graph of a line passing through the points (0,2) and (3,0).

2. The graph that represents the equation y = 0.5x - 1 is given as follows:

Graph of a line passing through the points (-2,-2) and (0,-1).

3. The graph that represents the relation is given as follows:

Graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point (0,58) and (1, 56).

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the graph that has a slope of -2/3 and a y-intercept of 2, we have that:

The y-intercept and the slope of the equation y = 0.5x - 1 is given as follows:

-1, meaning that the function passes through the point (0,-1).

When x = -2, the value of the function is given as follows:

y = 0.5(-2) - 1

y = -1 - 1

y = -2.

Hence the other point is (-2,-2).

For the relation in item 3, we have that when x increases by 3, y decays by 6, hence the slope m is given as follows:

m = -6/3

m = -2.

Hence:

y = -2x + b.

When x = 2, y = 54, hence the intercept b is given as follows:

54 = -2(2) + b

b = 58.

Hence the function is:

y = -2x + 58.

The points are:

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Therefore , the solution to the given problem of equation comes out to be $12 for a geranium and $11 for a square foot of grass.

When connecting two statements, a mathematical equation uses its equal sign (=) to denote equivalence. An equation in algebra is a claim that establishes the comparability of two equations. For instance, the formula 5x + 5 = 14 establishes a link between the two integers. The spaces seen between phrases with either front of a letter are used to form a mathematical connection. The lone variable so the only outcome are frequently the symbol. For instance, 8x - 4 = 2.

Here,

To start, you should underline and group pertinent information. Sort the products according to the individual who purchased them. We can give each of the two purchased things a constant or letter as there are only two of them:

Kim

5 feet by 2 feet (X for short) of grass

10 geraniums, designated as "Y" geraniums; total cost: $175

Matt

9 ft 2 of grass (let's call it grass X).

Four geraniums, designated as Y.

$147 in total

Now that the data has been split, you may create two equations: one for Matt and one for Kim.

Kim

5x + 10y = $175

Matt 9x plus 4y = $147

Observe how the numbers remained constant, but I eliminated the units and substituted X or Y depends on just what we assigned. We can start solving now.

I'll take the x out of Kim's equation. the following steps:

1) 5x + 10y = $175 Rewriting the equation

2) If you'd want to perform y first, 5x = $175 - 10y (again, you can still do y first as we're trying to isolate x). That's exactly how I did it.)

3) (5x)÷5 = ($175 - 10y)÷5 (divide both aspects of the equation by 5) 

4) 5x + 10y = $175

=>5x + 10($12) = $175 

5x + 10($12) = $175  

Add the value of y = $12 to Kim's equation to get 5x + $120 = $175.

5) 5x = $175 - $120

=> 5x = $55

=>  x = $11

x = $11

Therefore , the solution to the given problem of equation comes out to be $12 for a geranium and $11 for a square foot of grass.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

33!

Step-by-step explanation:

We can use the opposite of division (multiplication) to find what this number could be.

These are the multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, etc.

There are the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, etc.

As you can see, the lowest number that is both a multiple of 3 and 11 is 33.

A: you're finding the area where he needs carpet so you do 30x20 and 10x10 and then add those together B: you're seeing how much it would cost to carpet the bedroom so you take the answer from problem A and multiply it by 3

A single mathematical phrase is referred to as a term. It might be a single number (positive or negative), a single variable (a letter), or a combination of variables multiplied but never added or subtracted. A factor is a number that divides another number by itself and leaves no residue.

An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4m + 5 is an expression in which the words 4m and 5 are separated by the arithmetic sign + and m is the variable of the provided expression.

Here,

A term refers to a single mathematical phrase. It might be a single integer (positive or negative), a single variable (a letter), or a mixture of variables that have been multiplied but never added or subtracted. A factor is a number that divides another number by itself with no remainder.

To know more about algebraic expression,

https://brainly.com/question/953809

#SPJ4