Example 3. Find each measure.

After solving the provided question, The value for a in the system of equations below would yield no solutions for the system is [tex]= > a = 18 - 20\frac{y}{x}[/tex]

several equations at once, multiple equations In algebra, you must work together to solve two or more equations (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, there must be an equal number of equations and unknowns.

When there are two variables and you are given two pieces of information about how those variables are related, a system of equations is used. To address a number of typical problems, a system of equations can be employed.

[tex]3x-5y=15\\multiply with 6\\18x -30y = 90\\compare the equation with \\ax-10y=90\\then \\18x -30y = ax-10y\\ax = 18x + 10y -30y\\ax = 18x-20y\\a= (18x -20 y) / x\\[/tex]

[tex]= > a = 18 - 20\frac{y}{x}[/tex]

x≠o

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After checking Judi Imhoff's account statement her new balance is $1003.83

What is an account statement?

A statement of accounts is a document that lists all the transactions you have with a certain client during a specific time period. In order to inform their clients of the amount they owe for purchases made during that time period on credit, company owners typically issue statements of accounts to their clients. The manual explains the statement of accounts' contents and demonstrates how to file it for clients.

Your bank may send you a monthly or annual statement if you have a savings account.

account statement for the quarter. All deposits are reflected on the account statement,

withdrawals, as well as interest that is added to your account.

The new balance = Previous Balance + Interest + Deposits - Withdrawals

The new balance =  $717.52  + $4.36 + ($125.00 + $276.95) - $90.00

So, the new balance of Judi Imhoff is  $1003.83

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Answer: [tex]\displaystyle \frac{-1}{3}[/tex]

Step-by-step explanation:

       The slope of a perpendicular line will always be the reciprocal of the original line's slope. Here, the reciprocal of -3 is [tex]\frac{-1}{3}[/tex].

Zero is the slope of a line parallel to this line.

-1/9 is the slope of a line perpendicular to this line.

According to linguists, the Middle English adverb aslope, which meaning "at an angle," is where the term slope is said to have originated. A steep hill or the ramp in a parking garage are examples of things that are at an angle or on a slope and may be described using the word's noun form.

The ratio of the vertical change between two places is referred to as the slope. A line's slope is another indicator of how steep it is. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

The line becomes: y = 9x - 3

line is in the Slope-Intercept form : y = mx + c

Now comparing this two and we get slope, (m) = 9

So, The line perpendicular will have slope (m') = -1/m

or, m' = -1/9

The line parallel to this line will have slope (m'') = 0

because here the two lines are parallel, so they have no slope.

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Answer:

-38

Step-by-step explanation:

The sequence is decreasing by 7 everytime

-10 to -17 decrease of 7

-17 to -24 decrease of 7

-24 to -31 decrease of 7

Answer: A trend line is a line on a scatter plot, drawn near points, that approximates the association between the data sets.

Step-by-step explanation:

2. The linear trend in precipitation is the dominant trend type. The nonlinear trends occur much less frequently and more widely scattered over the globe. However, the nonlinear trends are credible patterns of change in precipitation.

3. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out. This component can be viewed as those variations with a period longer than a chosen threshold

4. The trend component represents changes in time-series data that are unpredictable and cannot be associated with a seasonal, cyclical, or random component. OB. The trend component is the long-term increase or decrease in a variable being measured over time.

5. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out.

6. The trend component is the long-term increase or decrease in a variable being measured over time.

a) The value of 8^1/3 is 2

b) The value of 8^2/3 is 4

c) The value of 16^3/4 is 8

Information given in the problem

a)   the value of 8^1/3

b)  the value of 8^2/3

c) the value of 16^3/4

This equation represents exponents in fraction form and the basics for the calculation is from

a^(b/c) =

[tex]\sqrt[c]{a}^{b}[/tex]

Rewriting the expression is done as below

8^1/3

=∛8

= 2

8^2/3

= ∛8²

= 2²

= 4

16^3/4

[tex]\sqrt[4]{16}^{3}[/tex]

= 2³

= 8

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Answer:

3

12

12

48

48

192

192

768

768

I hope I helped you

The equivalent expression by combining like terms is 1.10b and

If the cost increases by 10%, you can multiply the former cost by 110%

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

Expression of 10% raise = b + 0.10b

Evaluate the like terms in the above expression

So, we have the following representation

Expression of 10% raise = 1.10b

Hence, the expression is 1.10b

Recall that we have the mathematical statement to be

If the cost increases by 10%, you can multiply the former cost by %.

In this case, the factor is calculated as

factor = 1 + 10%

So, we have

Factor = 110%

So, the missing expression in the statement 110%

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Answer: 35%

Step-by-step explanation:

The total amount of candy is 20, and there is 7 green candy, so we got 7/20. Then we multiplied 20 and 7 by 5, so we got 100 and 35, so we got 35/100, which is 35%

Step-by-step explanation:

let the number be x

So,

(x - 6) × 2 = 22

2x - 12 = 22

2x = 34

x = 17

Thus, the answer is 17

Answer:

  400

Step-by-step explanation:

You want to know the number of foxes predicted after 42 years by y = 50·2^x, where x is measured in 14-year periods.

42 years is 42/14 = 3 14-year periods. Using x=3 in the equation, we predict ...

  y = 50·2^3 = 50·8 = 400

foxes.

After 42 years, there will be 400 foxes.

__

Additional comment

It is often convenient to use time measured in 1-year periods. In that case, the equation could be written ...

  y = 50·2^(t/14)

Then t/14 is the number of 14-year periods when t is in years.

Option (C) is the proper choice, both set A and B  

Describe a function.

It is described as a particular kind of relationship, and each value in the domain is associated to exactly one value in the range according to the function.

These are the ordered pairs:

Set A: (-1, 0), (-2, 1), (4, 3), (3, 4) (3, 4)

Set B: (1, 4), (2, 3), (3, 2), (4, 1) (4, 1)

Set C: (2, 1), (3, 2), (2, 3), (1, 4) (1, 4)

Sets A and B are both functions since they both have sets of x values that are all distinct. Set C is not a function because it repeats the x value of 2, while also providing two distinct y values.

As a result, the function option (C) is the proper choice and the set C: (2, 1), (3, 2), (2, 3), and (1, 4) does not represent the function.

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Answer:

5590-149,60

Step-by-step explanation:

sum completed

Answer: A.-20

Step-by-step explanation:

f(4)=-2(4)^2+12

f(4)=-2(16)+12

f(4)=-32+12

f(4)=-20

Answer:

a = 16

Step-by-step explanation:

6 = [tex]\frac{a}{4}[/tex] + 2 ( subtract 2 from both sides )

4 = [tex]\frac{a}{4}[/tex] ( multiply both sides by 4 to clear the fraction )

4 × 4 = a , that is

a = 16

Answer:

Step-by-step explanation:

for the first car  374/17 = 22 m per second

for bus  414/23 = 18  m per second

so the car is moving faster

car is moving faster than (22-18)=4 m per second from the bus

Answer: Car: 22 meters per second, Bus: 18 meters per second. The bus travels faster at 4 meters per second.

Step-by-step explanation: First, you should write a proportional relationship for meters per second so the car would be 374/17 and the bus would be written as 414/23. This is so you can know that you divide 374 by 17 to get 18, and 374 by 17 to get 22. So, you had it backward, the bus is faster by 4 meters per second, I hope this helped, for me (a 7th grader) this was review math, so I hoped this helped you.

The linear model representing the information is y = 600x + 1500.

To produce 12 solar heaters it cost $8,700.

The domain of the linear model is [1, 80].

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

10 solar heaters = $7500

20 solar heaters = $13,500

The linear model can be in the form of y = mx + c

m = (13,500 - 7500)/(20 - 10)

m = 6000/10

m = 600

Now,

(10, 7500) = (x, y)

7500 = 600 x 10 + c

c = 7500 - 6000

c = 1500

Now,

The linear model is y = 600x + 1500.

Where y is the cost of x solar heaters.

Now,

x = 12,

y = 600 x 12 + 1500

y = 7200 + 1500

y = 8700

Now,

y ≤ 50,000

We see that,

x = 81

y = 600 x 81 + 1500 = 48600 + 1500 = 50,100

x = 80

y = 600 x 80 + 1500 = 48000 + 1500 = 49,500

The domain is from x = 1 to x = 80.

Thus,

The linear model is y = 600x + 1500.

$8,700 is the cost to produce 12 solar heaters.

The domain is [1, 80].

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Answer:

x = -2/3; -20/9 so A

Step-by-step explanation:

im 100% percent sure:)

Answer:

m=-12/5

Step-by-step explanation:

yes

Isolate one of the two variables in one of the equations.

(- 2, - 4 )

- 4x + 4y = - 8 → (1)

4x - 6y = 16 → (2)

adding (1) and (2) term by term will eliminate x

0 - 2y = 8

- 2y = 8 ( divide both sides by - 2 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (2)

4x - 6(- 4) = 16

4x + 24 = 16 ( subtract 24 from both sides )

4x = - 8 ( divide both sides by 4 )

x = - 2

solution is (- 2, - 4 )

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Answer: 8.6

same side s C and B

Answer: 7.2

Step-by-step explanation:

Since this is a right triangle we can use the Pythagorean theorem to solve for side b.

Pythagorean theorem: a²+b²=c²

Since the side length opposite the right angle is the hypotenuse we plug 11.2 in for C

(8.6)² + b²=(11.2)²

73.96 + b² = 125.44

b²=51.48

b = 7.17495644586

b=7.2

The answer to this Question based on Thales Theorem is x = 8

What is Thales Theorem?

It says that when we join the mid points of two sides of a triangle the line is parallel to third side of triangle then the length of this joined line is half of length of third side

Here in Question given figure is like trapezium but we can extend it to make a triangle then by thales theorem we need to apply on other two sides hence joined line is parallel to third lines hence will be half of it

Solution:

1/2(x) = 2x - 12

x = 2(2x-12)

x = 4x - 24

24 = 3x

x = 8

Hence required value of x is 8

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Answer: [tex]y+3=-\frac{3}{5}(x+5)[/tex]

Step-by-step explanation:

The equation of the given line can be rearranged as follows:

[tex]3x+5y=15\\\\5y=-3x+15\\\\y=-\frac{3}{5}x+3[/tex]

Parallel lines have the same slope, so the slope of the line we need to find is -3/5.

Substituting into point-slope form, the equation of the line is [tex]y+3=-\frac{3}{5}(x+5)[/tex].

Answer:

$3.45

Step-by-step explanation:

To find the unit price, there must be one gallon of gas

24.82 : 7.2

?  : 1

Cross multiply: 24.85 = 7.2(?)

divide: 3.45138889 = ?

Round: 3.45

Answer:

I think it's repeating pattern

There are 990 ways to select 6 starters from a possible 14 using precisely two of the three triplets.

= C(3,2) = 3! / ( 2! x 1! ) = 3

To select the final 4 starters out of the 11 players ,

= C(11,4) = 11! / (4!7!)

= 330

There are a total of 6 ways to select starters.

= 3*330 = 990

Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method.

The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.

The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.

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The total bill if the student takes nine credit hours at the community college is T = $1415.

One or more variables can be present in a linear equation, but their maximal possible power is only one. The graph of a linear equation will thus always be a straight line. Y = mx + b, where m denotes the line's slope and b its y-intercept, or point of intersection with the y-axis, is how linear equations are expressed. Many real-world situations, such as the connection between two variables or the distance travelled at a constant pace, may be modelled using linear equations. In order to obtain the value of the variable(s) necessary to make the equation true, one must use algebraic methods.

How to solve?

The total bill, t, for a student carrying fewer than twelve credit hours is given by,

T = 155 n + 20, where n represents the hours taken for semester.

The total bill if the student takes nine credit hours is T = 155(9) + 20 = $1415.

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The arithmetic sequence has a 2nd term of -2 and a 7th term of 18 has the following answers.

What is arithmetic progression?

An progression or arithmetic sequence may be a sequence of numbers specified the difference between the consecutive terms is constant.

Main body:

General formula for arithmetic sequence

a + (n-1)d = aₙ

arithmetic sequence has a 2nd term of -2  , which means

a+d = -2    

a = -(d+2)      ---------(1)

7th term of 18 , which means

a+ 6d = 18

substituting value from equation 1,

-(d+2) +6d = 18

-d -2 +6d = 18

5d = 20

d = 5

using d= 5 in equation 1,

a = -(5+2)

a =-7

A) 10th term

=a +9d

= -7+9*5

= 38

B)  recursive formula for the sequence = aₙ+1=aₙ+d  .

Hence for the given sequence , it is

a₃ = a₂ +d

a₃ = -2+5

a₃ = 3

C) sum of first 10 terms

Sₙ =  n/2{2a+ (n-1)d}

S₁₀ = 5 {2*-7 + 9*5}

S₁₀ = 5[ -14 +45]

S₁₀ = 5*31

     = 105

Hence the sum of the first 10 terms is 105.\

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As the teacher-to-student ratio is equivalent in all schools, the number of students in school B is 506, the number of teachers in school C is 25 and  the number of students in school D is 792 respectively.

What are ratio and proportion?

An equation known as proportion shows that the two ratios presented are equal to one another. A ratio is the comparative or condensed form of two quantities of the same type. The majority of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. 

Given, the teacher-to-student ratio is equivalent for all schools.

For school A, ratio of teacher-to-student = 15/330 = 1:22

Then, for school B, the number of students = 23*22 = 506

For school C, the number of teachers = 550/22 = 25

For school D, the number of students = 36*22 = 792

Hence, these are the required number of students and teachers for the respective schools.

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