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What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

(t₁......t₆) = (5, 1, 44, 10, 90, 20) is the solution of the given matrix.

(A) An augmented matrix for a system of equations is a matrix of numbers where each column represents all the coefficients for a single variable and each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign).

The system's augmented matrix is shown here:

[tex]\left[\begin{array}{cccccc|c}1 & 1 & 1 & -\frac{1}{2} & -\frac{1}{2} & 0 & 0 \\0 & 1 & 1 & 1 & -\frac{1}{2} & -\frac{1}{2} & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & 0 & 0 & 10\end{array}\right][/tex]

(B) Use these row operations to convert this augmented matrix to a reduced echelon form.

Here is the augmented matrix's reduced echelon form:

[tex]\left[\begin{array}{ccccccc}1 & 0 & 0 & 0 & 0 & \frac{1}{2} & 15 \\0 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & -\frac{1}{2} & -\frac{1}{2} & -11 \\0 & 0 & 0 & 1 & 0 & 0 & 10\end{array}\right][/tex]

(C) There are more rows:

[tex]\begin{array}{lllllll}0 & 0 & 0 & 0 & 0 & 1 & 20\end{array},\\\begin{array}{lllllll}1 & 1 & 1 & 0 & 0 & 0 & 50\end{array}[/tex]

Augmented matrix:

[tex]\left[\begin{array}{ccccccc}1 & 0 & 0 & 0 & 0 & \frac{1}{2} & 15 \\0 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & -\frac{1}{2} & -\frac{1}{2} & -11 \\0 & 0 & 0 & 1 & 0 & 0 & 10 \\0 & 0 & 0 & 0 & 0 & 1 & 20 \\1 & 1 & 1 & 0 & 0 & 0 & 50\end{array}\right][/tex]

(D) You must employ these row operations in order to solve the system.

[tex]\left[\begin{array}{lllllll}1 & 0 & 0 & 0 & 0 & 0 & 5 \\0 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 & 44 \\0 & 0 & 0 & 1 & 0 & 0 & 10 \\0 & 0 & 0 & 0 & 1 & 0 & 90 \\0 & 0 & 0 & 0 & 0 & 1 & 20\end{array}\right][/tex]

Therefore, (t₁......t₆) = (5, 1, 44, 10, 90, 20) is the solution of the given matrix.

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Answer:

y = 3

Step-by-step explanation:

given y is inversely proportional to x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion

to find k use the condition x = 3, y = 8

8 = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 )

24 = k

y = [tex]\frac{24}{x}[/tex] ← equation of proportion

when x = 8 , then

y = [tex]\frac{24}{8}[/tex] = 3

Answer

3

Step-by-step explanation:

when one is increasing the other one should decrease.since 3 has increased by 5 ,then y should decrease by 5.

Answer:

49.2F

Step-by-step explanation:

To find the difference you can see how far they both are from 0 and add them together. So for this, it would be 36.6+12.6=49.2

John is putting 10 books in a row on his bookshelf. he would arrange it in

40,320 ways.

Generally, A permutation is a rearrangement of a set of elements. In other words, it is a way to arrange a set of items in a specific order. For example, the permutations of the set {1, 2, 3} are {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}. The number of possible permutations of a set of n elements is n!.

John is placing 8 books on the shelf in between Pride and Prejudice and Little Women.

The number of ways to arrange these 8 books is 8! (8 factorial).

since the order of the books in the first and last spots is predetermined,

The final answer is 8! = 40320ways

= 40,320 ways.

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The mean of the sample means will be 25

As Sample mean is an estimate of the population mean. If we increment the number of observations the precision of the sample means will be improved to get closer to the population mean and according to Central Limit Theorem, The sampling distribution of the sample statistic can be considered roughly if any of the below-mentioned criteria is satisfied :

We are provided with a sample size which is 100, a population mean which is 25, and a population standard deviation which is 20.

So , n =100

      μ= 25

      σ= 20

therefore, the mean of the sample means is

μₓ =μ

    =  25

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Answer:

A)

If you are driving many miles a day, Alpha Car Rental is cheaper. If you are driving fewer miles a day, then Amazing Car Rental is cheaper.

B)

You can find this out by graphing the 2.

Alpha: y = 0x + 72.

Amazing: y = 0.30x +22.9

Where y is cost, and x is miles.

When you graph the 2, Alpha is a straight line because it has no mileage charge. The 2 linear functions meet at point (163.6, 72). Meaning if you drive more than 163 miles, it is cheaper to use Alpha Car Rental over Amazing Car rental.

Hope that helps

All you do is divide:

3 ÷ 8 = 0.375 or 0.38 or 0.4

7 ÷ 5 = 1.4

21 ÷ 7 = 3

5 ÷ 3 = 1.66666666667 or 1.67 or 1.7

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Answer:

A line parallel to 3x+4y=12 must have a slope of -34

The cost of a rugby ball is $6.57

The cost of a golf ball is $1.75

Let x represent the cost of a rugby ball and y represent the cost of a golf ball

2x + 3y= 18.39.........equation 1

5x + 7y= 45.10.........equation 2

multiply equation 1 by 5 and equation 2 by 2

10x + 15y= 91.95

-

10x + 14y= 90.2

y= 1.75

Substitute 1.75 for y in equation 2

5x + 7(1.75)= 45.10

5x + 12.25= 45.10

5x= 45.10-12.25

5x= 32.85

x= 32.85/5

x= 6.57

Hence the cost of a rugby ball is $6.57 and the cost of a golf ball is $1.75

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Answer:

Step-by-step explanation:

The ratio of flour to honey is always 10/8 because she uses a constant ratio.

1. The missing values in the table would be the value of honey (1, 16, 30, h) times 10/8.

2. The equation would be f = (10*h)/8

3. Plug 15 and 17 into the equation above.

If 10 points are awarded for a good deed and (-5) for not attempting a good deed each day then, a) The score of Teena is equal to 105 b) The score of Tia is equal to 225

a) As Teena did a good deed for 17 days, she would receive 10 points for 17 days, and for the rest of the days, she would be deducted 5 points for each day for not attempting a good deed.

Number of days she did not attempt a good deed = 30 - 17 = 13

Points she got = 17 × 10 = 170

Points for not attempting a good deed = 13(-5) = 65

The final score of Teena can be calculated using subtraction;

Teena score = 170 - 65 = 105

b) If Tia did not attempt any good deed for 5 days this means she did a good deed for 25 days (30 - 5 = 25)

Points she got = 25 × 10 = 250

Points for not attempting a good deed = 5(-5) = -25

Tia score = 250 - 25 = 225

Hence the score of Teena and Tia were calculated to be 105 and 225 respectively.

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The correct rounding place for 438.612439000 is thousands as there are 3 zeros at end of the decimals which has no value.

To estimate a specific number in a context, rounding is a process. Look at the next digit in the correct position to determine how to round a number; if it is less than5, round down, and if it is 5 or more, round up.

The term "rounding decimals" describes the accurate rounding of decimal numbers. To the nearest whole, tenth, or hundredth, we can round decimals.

To quickly and easily estimate an answer, rounding decimals is helpful. Finding out the approximate average score of the students in a class is also helpful.

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Answer:

See below

Step-by-step explanation:

Comment

This is a good question. It makes you think about when you should round and maybe when you shouldn't.

You have a building side that is 38 square yards. You want to know how much paint to buy to cover the given side.

Let us say that each can of paint could cover 5 square yards. You cannot buy any can that might be smaller to take care of the 3 remaining square yards.

You have no choice. You have to round the answer from 7 R 3 to 8.

The two events are mutually exclusive if they cannot occur at the same time. A triangle is equiangular if it is equilateral. The two events are mutually exclusive if they cannot occur at the same time.

What pairs of occurrences can never coexist?

Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously.

A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.

What are some examples of mutually exclusive events?

Several instances of occurrences that can never occur simultaneously include:

The outcomes of receiving head or tail while flipping a coin are mutually exclusive.

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Answer: 15

Step-by-step explanation:

For them to both get 30 you have to get 15 because 15+15 equals 30!

Sense Virginia got twice as much just times 15 by 2 to get 30

Very simple ! Hope this helped ! Have a great day ! :D

The number of bottled drinks bought by Marisol is 10 in the student council party.

For the given linear equation;

The total budget of the party is $50.

The linear function function which represents the number of pizzas x and the number of bottled drinks y is;

15x + 2y = 50

Now, the number of pizza bought = 2.

To find the value of bottled drinks, put x = 2 in the linear function.

15×2 + 2y = 50

Simplify the equation;

30 + 2y = 50

2y = 50 - 30

2y = 20

y = 10

Thus, the total number of bottled drink bought by the Marisol is 10.

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Answer:

Step-by-step explanation:

rhombus formed by 4 right triangles, 51ft hypotenuse and 45ft cathetus (90: 2 = 45). we use pythagoras to find the missing side so that we can find the area of ​​a triangle and multiply it by 4

c = √(51²-45²)

c = √(2601 - 2025)

c = √576

c = 24ft

Area triangle= (½)×b×h

(½)45 * 24 =

(½)1080=

540ft²

multiply by 4

540 * 4 =

2160ft² (Area of the rhombus)

or

Rhombus Area Using Diagonals:

A = ½ × d1 × d2

A = ½ * 90 * 48

A = 2160ft² (Area of the rhombus)

Based on the anchor points for the trend line, the equation of the line can be found to be y = 6x + (-2)

To find the equation of a trend line, you first need to find the difference between the anchor points:

= Change in y / Change in x

= (28 - (-38)) / (5 - (-6)

= (28 + 38) / (5 + 6)

= 66 / 11

= 6

The y intercept is:

y = mx + c

28 = 6(5) + c

c = 28 - 30

c = - 2

The equation of the line is:

y = 6x + (-2)

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The price of one ticket is $150 without the discount.

Discounts are defined as lowered prices or the sale of an item for less than it would typically cost. A pocketbook offered at 50% off the regular price or a shop that specializes in selling designer goods at below-market pricing are two examples of things that might be considered discounts.

Given Data

$30 discount on each world-series baseball game ticket.

They spent $840 for the seven tickets.

7 tickets = $840

1 ticket = [tex]\frac{840}{7}[/tex]

1 ticket = $120

Price of 1 ticket = $120 + $30

Price of 1 ticket = $150

The price of one ticket is $150 without the discount.

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Solving a system of equations we can see that:

Let's define the variables:

With the given information we can write the system of equations:

y = 2*x

x*45 + y*80 = 1435

To solve the system, we can replace the first equation into the second one.

x*45 + (2*x)*80 = 1435

x*45 + x*160 = 1435

x*205 = 1435

x = 1435/205 = 7

x = 7

So we conclude that 7 small boxes were shipped, and then:

y = 2*x = 2*7 = 14

14 large boxes were shipped.

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Answer:

$3.25

Step-by-step explanation:

This question tests on the concept of conversion.

Given from the question,

8.5 pounds = $27.63

(8.5 ÷ 8.5) pounds = $27.63 ÷ 8.5

1 pound = $3.25 (Rounded off to 2 decimal places)

Answer:

Sum of angles in a triangle add up to 180°.

x = 180 - 76 - 44 = 60°

The cost of one small box is $10 and the cost of one large box of grapefruit is equal to $16.

This type of problem can be solved using linear equations.

If we consider x to be the cost of one small box and y to be the cost of one large box of fruit, the linear equations can be given as;

12x + 5y = 200

4x + 10y = 200

Multiplying the second equation by 3

12x + 5y = 200

12x + 30y = 600

Now by subtracting both equations we get;

-25y = -400

y = -400 / -25

y = 16

Now adding this value of y = 16 in the first equation;

12x + 5y = 200

12x + 5(16) = 200

12x + 80 = 200

12x = 200 - 80

12x = 120

x = 120 / 12

x = 10

Therefore, $10 is the cost of one small box and $16 is the cost of one large box of grapefruit.

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chaperones/students; 1/7 = x/45

7x = 45

x = 6.43

the min amount would be 7, as there can not be .43 of a chaperone. It cannot also be 6 because 6 x 7 would be 42 < 45.

The ships and the port form a right triangle and hence, their distance is 72.1 nautical miles

Knot is a velocity unit equals to nautical miles per hour.

The situation can be depicted in the attached picture.

The distance travelled by the 1st ship after 2.5 hours is:

s1 = 16 knots x 2.5 hours = 40 nautical miles.

The distance travelled by the 2nd ship id:

s2 = 24 knots x 2.5 hours = 60 nautical miles.

Since the angle difference between those 2 ships is 90⁰, the distance between the ships can be obtained using the Pythagorean Theorem.

Referring to the attached picture,

d² = 40² + 60²

d² = 1600 + 3600

d² = 40² + 60²

d² = 5200

d = 72.1 nautical miles

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Answer:

8p+32

Step-by-step explanation:

Answer: 9,875

Step-by-step explanation: 125 x 79 = 9,875

Answer: x=17

Step-by-step explanation:

1.Identify relationship

Since both the angles are on the inside of both parallel lines and on the same side of the transversal you know that you have a same side interior relationship that makes them supplementary

2. set up equation

because they are supplementary you know that they are equal to 180 which gives the equation: 3x+6+123=180

3. solve the equation

3x+6+123=180

3x+129=180 | combine like terms

3x=51 | subtract 123 from both sides

x=17 | divide by 3 on both sides