Latisha has $40 in her checking account. She makes a withdrawal of $20 and then writes a check for $40. Then she deposits $30.

The equation of the line perpendicular to the given line and passing through (-3, 7) is; y = (-2/3)x + 5

We are given the equation of a line as; y = (3/2)x - 1

Now, the general form of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, for our given equation we have;

Slope; m = 3/2

y-intercept; c = -1

Now, for a line perpendicular to this, will have a slope of -1/(3/2) = -2/3

Thus, equation of the line perpendicular to the given line and passing through (-3, 7) is;

y - 7 = (-2/3)(x - (-3))

y - 7 = (-2/3)(x + 3)

y = 7 - 2 - (2/3)x

y = (-2/3)x + 5

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Answer: 240,000

Step-by-step explanation: Ok so to get the answer we first do

10 x 20 which is 200 then you do 200 x 30 which is 6,000 then we times the last number which is 40 which would look like 6,000 x 40 which equals 240,000. Hope this helps but also a quicker way in your head could be lining them up straight and down in your head with all the numbers and with all the zeros you will no the answer will have 4 zeros on the end of the answer then do 1 x 2 = 2 x 3 = 6 x 4=24 so then add the four zeros on the end and there you go you get your final answer of 240,000.

[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ ~~ y^{\frac{3}{4}} ~~ }{y^{\frac{1}{2}}}\implies \cfrac{ ~~ y^{\frac{3}{4}}y^{-\frac{1}{2}} ~~ }{1}\implies y^{\frac{3}{4}-\frac{1}{2}}\implies y^{\frac{1}{4}}\implies \sqrt[4]{y^1}\implies {\Large \begin{array}{llll} \sqrt[4]{y} \end{array}}[/tex]

The time to travel one mile is 1636.4 times the time to travel one meter.

An equation is an expression that shows the relationship between two or more numbers and variables.Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent.

The amount of time light takes to travel one meter =  3.3 nanoseconds = 3.3 * 10⁻⁹ s

Time to travel one mile = 5.4 microseconds = 5.4 * 10⁻⁶ s

Ratio of time to travel one mile to time to travel:

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Answer:

10

Step-by-step explanation:

lol XD are you trolling?

Answer:

f

Step-by-step explanation:

find the difference using the number line 3-1

The most appropriate choice for area of rectangle will be given by:

Width of rectangle is 2 ft

What is area of rectangle?

Area of rectangle is the total space taken by the rectangle.

If the length of rectangle be [tex]l[/tex] ft and breadth of rectangle be [tex]b[/tex] ft, area of rectangle [tex]l \times b[/tex]  [tex]ft^2[/tex]

Here,

Let the width of the rectangle be w ft

Length = 7ft

Area  = 7 x w [tex]ft^2[/tex]

By the problem,

7 x w = 14

w = [tex]\frac{14}{7}[/tex]

w = 2 ft

Width of rectangle is 2 ft

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After a dilation with a scale factor of 2.5 and center of dilation (0, 0), the coordinates of the vertices of triangle A'B'C' are A' (-5, -2.5), B' (2.5, 5), and C' (5, -10).

Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as triangles.

For the given coordinates, the dilation with a scale factor of 2.5 and center of dilation (0, 0) should be calculated as follows:

Point A (-2, -1) → Point A' (-2 × 2.5, -1 × 2.5) = Point A' (-5, -2.5).

Point B (1, 2) → Point B' (1 × 2.5, 2 × 2.5) = Point B' (2.5, 5).

Point C (2, -4) → Point C' (2 × 2.5, -4 × 2.5) = Point C' (5, -10).

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Answer:

10.5

10.5x = 52.50

Step-by-step explanation:

To identify the constant of proportionality, divide money by hours.

52.50 ÷ 5 = 10.5

Use the constant of proportionality to write the equation.

10.5x = 52.50

[tex]\frac{3}{14}[/tex] is the straight section.

A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is 12. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.

Given Data

Length = 5[tex]\frac{5}{6}[/tex]

Length = [tex]\frac{35}{6}[/tex]

Straight section = 1[tex]\frac{1}{4}[/tex]

Straight section = [tex]\frac{5}{4}[/tex]

Dividing them:

= [tex]\frac{35}{6}[/tex] ÷ [tex]\frac{5}{4}[/tex]

= [tex]\frac{35}{6}[/tex] ×[tex]\frac{4}{5}[/tex]

= [tex]\frac{6}{28}[/tex]

= [tex]\frac{3}{14}[/tex]

[tex]\frac{3}{14}[/tex] is the straight section.

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Answer: 1122

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

The angles form a linear pair, and thus add to 180°.

[tex]3x+3+5x+1=180 \\ \\ 8x+4=180 \\ \\ 2x+1=45 \\ \\ 2x=44 \\ x=22[/tex]

The function rule for function g is g(x)=2x+3.

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Answer:

Step-by-step explanation:

Answer:

9x^6y√y

Step-by-step explanation:

√81x¹²y³ = √9*9* x^6* x^6 * y*y*y = 9x^6y√y

Answer:

This graph is not a function

Step-by-step explanation:

Because it fails the Vertical line test

Answer:

Step-by-step explanation:

3(x-2)+2x=1/2(10x-12)

3x - 6 + 2x = 5x - 6

5x - 6 = 5x -6

5x - 5x = 6 - 6

0 = 0

this equation is always true

Answer:

Infinitely many solutions

Step-by-step explanation:

[tex]\sf 3(x - 2) + 2x = \dfrac{1}{2}*(10x - 12)\\\\ 3x - 3*2 + 2x = \dfrac{1}{2}*10x - \dfrac{1}{2}*12 \ [\bf distributive \ property]\\\\ 3x - 6 + 2x = 5x - 6[/tex]

Combine like terms,

  3x + 2x - 6 = 5x - 6

         5x - 6  = 5x - 6

There are infinitely many solutions for this equation.

The tape diagram that could be used to represent the context is A.

It should be noted that a tape diagram is simply used to show number relationships. It so used to illustrate ratios, addition, etc.

In this case, the baseball team raised $1187.25 to go to a tournament and they rented a bus for $783.50 and budgeted $21.25 per player for meals.

Let x represents the number of players the team can bring to the tournament.

This will be illustrated as 783.50 + 21.25x = 1187.25. The tape diagram that illustrates this is A.

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Answer:

They are all incorrect except for C

Step-by-step explanation:

A. y = 4

B. y = -2x + 4

D. x = -4

Answer: [tex]\sqrt{82}[/tex]

Step-by-step explanation:

Points are (4,-4) and (3,5)

We find the difference between the numbers

5- - 4 = -9

3 - 4 = -1

Then find the length between them using a triangle [tex]c^{2} =a^{2} +b^{2}[/tex]

[tex]\sqrt{-9^{2} +-1^{2} } =\sqrt{82}[/tex]

Answer:

x=40 degrees

Step-by-step explanation:

adjacent angles add up to 180 degrees

First angle=x

second angles=x+20

third angle =x+40

add all and equate to 180 degrees i.e.

x+x+20+x+40=180

3x=180-60

x=40 degrees

x+20=40+20=60 degrees

x+40=40+40=80 degrees

g(x) = 2x² - 3x + 1 =

-2   = 2[tex](x+2)^{2}[/tex]+ 3(x+2) - 1

-2 = 2( [tex]x^{2}[/tex] + 4x + 4) + 3(x+2)  - 1

-2 = 2[tex]x^{2}[/tex] + 8x + 8 + 3x + 6 - 1

-2 = 2[tex]x^{2}[/tex] + 11x + 13

0 = 2[tex]x^{2}[/tex] + 11x + 15

0 = (  2x   +    5  )(kx  +   3   )

2x + 5 = 0 ---> kx= -5/2

x+3=0 ----> x = -3

Recognize that a function is a particular kind of relation where a rule states that every input must be paired with exactly one output.

one of them sums up a function the best?

Recognize that a function is a particular kind of relation where a rule states that every input must be paired with exactly one output. So, this is the best choice.

The function's type is f/x)= 2x 2 + 3x 1.

Explanation: Since the polynomial f(x)=2x33x+1 is continuous and contains continuous derivatives of all orders for all real x, it unquestionably meets the theorem's hypotheses.

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Answer: 2(2−x)(x−6)

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Vertical angles are congruent, so:

[tex]7x+7=112 \\ \\ 7x=105 \\ \\ x=15[/tex]

Using linear pairs,

[tex]112+4y=180 \\ \\ 4y=68 \\ \\ y=17[/tex]

An installation fee as well as a monthly service cost are charged by two Internet service providers the equation $y=45x+50$. Company A charges less per month then Company B.

Given that,

An installation fee as well as a monthly service cost are charged by two Internet service providers. The table displays the total expenses at Company A in USD for various lengths of time. The equation $y=45x+50$ represents the total cost of $y$ (in dollars) for $x$ months of work at Company B. 

We have to find which company has monthly fees that are lower.

Company A charges =220-180=40

Company A charges $40 per month.

Company B charges $45 per month

Because the slope is 45.

Therefore, Company A charges less per month then Company B.

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The values of the equations that are given will be:

17. b + 9 and -b + 7

18. c - 4 and c + 4

19. a + b - c and a + b + c

20. 5 + 2b and 5 - 2b

21. 4 - h - b and -b + h - 4

22. 2 - b - 2h and b - 2

Based on the information given, it should be noted that the equations will be expressed thus:

It should be noted that an equation is used to show the relationship between the variables. The equations will be:

17. |b + 1| + 8

= b + 1 + 8

= b + 9

and

|b + 1| + 8

= -b - 1 + 8

= -b + 7

18. 5 - |c + 1|

= 5 - c + 1

= - c + 4

= c - 4

and

5 - |c + 1|

5 + c - 1

= c + 4

19. |a + b|- c

= a + b - c

and

-a - b - c

Multiply through by -

= a + b + c

20. 5 + |2b|

= 5 + 2b

and

5 + |2b|

= 5 - 2b

21. |4 - h| - b

= 4 - h - b

and

-4 + h - b

= -b + h - 4

22. |2 - b - h| - h

= 2 - b - h - h

= 2 - b - 2h

and

-2 + b + h - h

= b - 2

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Answer:

10m/7n

Step-by-step explanation:

distribute the

7n-7m=3m

7n=

The set of constraints to model the problem include

The following is data given in the problem

The constraints to model the problem is as follows:

The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled.

Savanah will babysit at least 40 hours

The two constraints required is modelled using inequalities and represented as follows y < 5x and y ≥ 40 hours

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Taking into account the definition of a system of linear equations, Kevin and Randy Muise have 19 quarters and 50 nickels.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. In this way, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that

You know that:

The system of equations to be solved is

q + n= 69

0.25q + 0.05n= 7.25

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "q" from the first equation:

q= 69-n

Replacing this expression in the second equation:

0.25(69 - n) + 0.05n= 7.25

Solving:

0.25×69 - 0.25n + 0.05n= 7.25

17.25 - 0.25n + 0.05n= 7.25

- 0.25n + 0.05n= 7.25 - 17.25

-0.2n= -10

n= (-10)÷ (-0.2)

n= 50

Remembering that q= 69 -n, you get:

q=69 - 50

q= 19

Finally, there are 19 quarters and 50 nickels.

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Answer:

Step-by-step explanation:

5 3/4 - 2 1/4

whole numbers

5 - 2 = 3

fractions

3/4 - 1/4 = 2/4

so

3 2/4 is the answer