Plot the image of point P under a translation by 4 units to the left and 3 units down.

Let,

B = the speed of the boat in still water

S = the speed of the stream

Use the equation for distance.

Rate * Time = Distance

Upstream:

(B-S)6 = 282

Downstream:

(B+S)6 = 402

Simply first:

(B-S)6 = 282

(B-S) = 282/6

B-S=47

(B+S)6 = 402

(B+S) = 402/6

B+S=67

Solve by elimination. Add the two equations.

B-S=47

+ B+S=67

2B = 114

B = 114/2

B = 57 km/hr (the speed of the boat in still water)

Substitute this into either equation and solve for S.

B+S=67

57 + S = 67

S = 67 - 57

S = 10 km/hr (the speed of the stream)

First number (x) = 88

Second number (9x) = 792

Third number (x + 100) = 188

Let x be the first number, so accordingly the second number will be 9 times x i.e., 9x and the third number will be 100 more than the first number i.e., x + 100

Now, put all the numbers into an equation of finding their sum,

First no. + Second no. + Third no. = SUM, i.e.,

x + 9x + (x+100) = 1068

Simplify,

x + 9x + (x+100) = 1068

x + 9x + x +100 = 1068

11x + 100 = 1068

11x = 1068 - 100

11x = 968

x = 968/11

First number (x) = 88

Second number (9x) = 792

Third number (x + 100) = 188

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If Connor edits 34 pages in 8 hours. Using the equivalent ratios, the table has been completed.

The equivalent ratios are the ratios that has same value when we compare them. We can check two or more ratios and check whether they are equivalent or not.

Connor edits 34 pages in 8 hours

Number of pages he edits in 8 hours = 34 pages

Number of pages he edits in 1 hour = 34/8 = 17/4 pages

Number of pages he edits in 12 hours = (17/4)×12

= 51 pages

Complete the table

Hence, if Connor edits 34 pages in 8 hours, using the equivalent ratios, the table has been completed

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Step-by-step explanation:

plug in y=(⅓)x+1 to a graphing calculator and it gives you the answer

Answer: x values make sure they don't repeat if they do its not a function.

Using linear functions, it is found that:

A. The costs will be the same when 250 shirts are bought.

B. The Tees-4-U Company would charge them less.

C. They are saving $350 by going with the more economical company.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

For the cost functions in the context of this problem, we have that:

Hence the functions for the cost of buying x shirts are given as follows:

The costs will be the same when:

C(x) = T(x)

Hence:

6.5x = 250 + 5.5x

x = 250

For item b, the costs are given as follows:

The amount saved in item c is:

3900 - 3550 = 350.

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The input value x when the output value f( x ) = 4 in the function f( x ) = 5x - 7 is 11/5.

A function is simply a relationship that maps one input to one output, each x-value can only have one y-value.

Given the data in the question;

To determine the input value x when the output value f( x ) = 4, replace f( x ) by 4 in the function and solve for x.

f( x ) = 5x - 7

4 = 5x - 7

Collect like terms

4 + 7 = 5x

5x = 11

Divide both sides by 5

5x/5 = 11/5

x = 11/5

Therefore, the input value x is 11/5, this forms an ordered pair of ( 11/5, 4 ).

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Consider the relation,

Let the distance between Trent and Austin is 'd' kilometers.

Then the time taken by Trent to reach Austin is given by,

Similarly, the time taken by Trent on his return trip is given by,

Given that the trip to Austin was 1 hour less than the return trip,

Solve for the total time of the trip as,

Thus, the total time required for complete trip is 5 hours.

Using the Fundamental Counting Theorem, it is found that there are 27 possible outcomes.

It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each trial independent of other trials, the number of possible outcomes is given as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, the trials are represented as follows:

For each trial, there are 3 possible outcomes, from the table, hence the parameters are given as follows:

[tex]n_1 = 3, n_2 = 3, n_3 = 3[/tex]

Hence the total number of possible outcomes is given as follows, from the Theorem:

N = 3 x 3 x 3 = 27.

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The value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k. Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

Given Data

X 5 6 7 8

Y 1 2/3 2 2 1/3 2 2/3

Yes, the table shows proportional relationship.

Value of Y when X will be 10 is

x = 10

= 3[tex]\frac{1}{3}[/tex]

the value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].

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Answer:

y = -3x + 11

Step-by-step explanation:

(4, -1) m = -3

y = -3x + b

y + 1 = -3(x-4)

-3(x-4) = -3x + 12 - 1

y = -3x + 11

The statement which is true about Function A and Function B is that: C. The initial value for Function A is greater than the initial value of Function B.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope A = (0 - 2)/8 - 0)

Slope A = -2/8

Slope A = -1/4 or -0.25.

Note: The slope of any straight line also represents its rate of change.

Rate of change of Function A = -0.25.

Rate of change of Function B = 4.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁)

At point (0, 2), we have:

y - 2 = -1/4(x - 0)

y - 2 = -x/4

y = -x/4 + 2.

Therefore, the intercept (initial value) of Function A is greater than the intercept (initial value) of Function B.

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the monthly deposit that will be required will be equal to $ 1214 by compound interest.

We are given the information that:

Amount (A) = $ 30,000

Time = 18 years

Compound interest rate = 4.1 %

Now, let the principal amount be x.

So, by using the formula for compound interest, we get that:

30,000 = x ( 1+ 0.041)¹⁸

30,000 = x (1.041)¹⁸

30,000 = x × 2.06

x = 30,000 / 2.06

x = 14563 ( approx.)

Monthly deposit = 14563 / 12 = 1214 (approx.)

Therefore, the monthly deposit that will be required will be equal to $ 1214 by compound interest.

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Answer:

TRUE

Step-by-step explanation:

an integer is a whole number from the set of negative, non-negative, positive and 0 numbers.

ex : -1, -2, -3, -4, -5, 0, 1, 2, 3, 4, 5

-17 is a negative whole number

so yes, -17 is an integer

a) the two angles are supplementary, then:

(3x - 45) + (2x + 25) = 180

(3x + 2x) + (-45 + 25) = 180

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 200/5

x = 40

Then, the measure of the angles are:

3x - 45 = 3*40 - 45 = 75°

2x + 25 = 2*40 + 25 = 105°

b) the two angles are complementary, then:

(2y) + (6y - 30) = 90

(2y + 6y) - 30 = 90

8y = 90 + 30

8y = 120

y = 120/8

y = 15

Then, the measure of the angles are:

2y = 2*15 = 30°

6y - 30 = 6*15 - 30 = 60°

c) the two angles are vertical angles, then they are congruent, that is,

2z + 7 = 5z - 23

7 + 23 = 5z - 2z

30 = 3z

30/3 = z

10 = z

Then, the measure of the angles are:

2z + 7 = 2*10 + 7 = 27°

5z - 23 = 5*10 - 23 = 27°

d) the two angles are alternative exterior angles, then they are congruent, that is,

4x - 5 = 3x + 15

4x - 3x = 15 + 5

x = 20

Then, the measure of the angles are:

4x - 5 = 4*20 - 5 = 75°

3x + 15 = 3*20 + 15 = 75°

Simone, these are the steps to calculate Q1, Q2, and Q3.

Step 1: You need to put all the values in order from the lowest to the greatest.

Step 2: The tenth value from left to right is the median or Q2.

Step 3: The

Answer:

D

Step-by-step explanation:

RISE/RUN = slope

This slope will be POSITIVE because it rises in quadrant 1.

Rise=2, run=3

Slope= 2/3

Hope that helps

The equation of the blue line is y = 2(2 - x).

Equation of A(1,0) and B(0, -2)

Use y = mx + c,

m = change of x axis ÷ change of y axis

The difference in x-coordinates equals the difference in y-coordinates, and the difference in y-coordinates equals the difference in y-coordinates.

m = (y2 - y1) ÷ (x2 - x1)

To get the slope, plug in the parameters of both x and y into to the equation.

m = (2 - 0) ÷ (0 - 1)

m = -2

The value of b calculated using the expression of a line formula.

b = 2

Now that you have the measurements of m (slope) and b (y-intercept), plug them into y = m x + b to determine the equation of the line.

y = −2x+2

Because the line is two primary components to the left, the parallel line's equation is,

y = -2x + 2 + 2

y = -2x + 4

y = 2(2 - x)

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

6 ===> 15%

Step 02:

Percentage:

percentage = part / whole * 100

percentage = 15

part = 6

whole = number = x

The answer is:

The number is 40

In linear equation, 4 is the Simplify your answer .

What is a linear equation example?

2y-9 ............1

-3y-2=4 .............2

From equation  (2)

                  - 3y = 4 + 2

                  - 3y = 6

                     y = 6/-3  ⇒ -2

value of y put in equation 2

                         -3y-2=4

                       - 3 * -2 - 2 = 4 ⇒ 6 - 2 ⇒ 4

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Using proportional relationships, it is found that:

Brown 12 10 14 30

Green 20 25 35 75

Total 32 35 49 105

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

For the first question, we have that out of a total distance of 8 miles, they:

Hence the proportional relationships for the distances are given as follows:

For a total distance of 32 miles, the distances walked and ran are given as follows:

For the second question, we have that the table has to following the given ratios of the first row to the second row, with the third row being the sum of the first two rows, hence the third table is correct.

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The number of three digit number formed are-

For the given question;

The three digit number is to be formed.

The digits are given as-  1,2,6,7,8

Case 1: Repetition allowed

The number of combination will be;

= 5×5×5

= 125

Thus, the number of three digit number formed with repetition is 125.

Case 2: Repetition not allowed

The number of combination will be;

= 5×4×3

= 60

Thus, the number of three digit number formed with without repetition is 125.

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The net decimal equivalent is 0.48, 0.27, and 0.12 when a series of discounts of 48%, 27%, and 12% are applied respectively.

The percentage is defined as a ratio expressed as a fraction of 100.

By multiplying the complement of the discounts collectively, one can determine the net decimal equivalent which is given in the question.

To determine the net decimal equivalent when a series of discounts of 48%, 27%, and 12% is applied.

The value of compliment (%) = 1/100

As per the given condition, the required discounts would be as:

discount of 48% = 48/100 = 0.48

discount of 27% = 27/100 = 0.27

discount of 12% = 12/100 = 0.12

Therefore, the net decimal equivalent is 0.48, 0.27, and 0.12 when a series of discounts of 48%, 27%, and 12% are applied respectively.

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2(x) + 2(x+7)= 62

4x+14=62

4x=58

x=14.5

width= 14.5

length=21.5

The number that has a greater value in the thousands place is 16,918.

Given numbers are sixteen thousand, nine hundred eighteen,(16,918), and 64,704 on the board.

The thousand places in both numbers contain the digits 6 and 4.

The place value of 6 in 16,918 is expressed as 6 thousand or 6,000.

The place value of 4 in 64,704 is expressed as 4 thousand or 4,000.

As 6000 > 4000, the number that has a greater value in the thousands place is 16,918.

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iven:: △TVX is equilateral.

To prove: △TUV≅△XWV

The given proof is completed and attached below:

he proogf is complete.

The area of the irregular shape is found as 50 sq. cm.

For the given question;

The irregular shape is composed of two rectangles.

The formula for finding the area is;

Area =  length x breadth

The area of the top rectangle is;

Top area = 4 x (3 + 5 + 2)

Top area = 4 x 10

Top area = 40 sq. cm.

The area of the bottom rectangle is;

Bottom area = 5 x 2

Bottom area = 10 sq. cm.

Total area = Top area + Bottom area

Total area = 40 + 10

Total area = 50 sq. cm.

Thus, the area of the irregular shape is found as 50 sq. cm.

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The value of the numbers that are given will be:

1. 6

2. 12

3. 42

It should be noted that based on the information given, PEDMAS is important. This implies that multiplication will come first before addition. This will be illustrated thus:

1. 2 + 2 × 2

= 2 + 4

= 6.

2. 3 + 3 × 3

= 3 + 9

= 12

3. 6 + 6 × 6

= 6 + 36

= 42..

Therefore, it should be noted that we multiplied first before adding.

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