Question Find the equation of a line that contains the points (-7, 6) and (3, 8). Write the equation in slope-intercept form. ​

Taking into account the definition of a system of linear equations, the speed of the first train is 363 mph and the speed of the second train is 356.8 mph.

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 other words, 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:

So, the system of equations to be solved is

[tex]\left \{ {{F+S=719.8} \atop {F=S+6.2}} \right.[/tex]

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, substituting the second equation in the first one you get:

S + 6.2 + S= 719.8

Solving:

2S + 6.2= 719.8

2S= 719.8 - 6.2

2S= 713.6

S= 713.6÷ 2

S= 356.8

Remembering that F= S+ 6.2, then:

F= 356.8 + 6.2

F= 363

In summary, the speed of the first train is 363 mph and the speed of the second train is 356.8 mph.

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Yes,  the relation is a function.

What does the term "relation function" mean?

What is a relation simple definition?

H={(6, - 2), (5,- 2), (4, -2), (3, - 2), (2, - 2)}

In a function, an x value can never repeat.

This is basically the only rule (that I know of), so, the given values can represent a function.

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The number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812

Proportion can be defined as the mathematical comparison of two numbers.

It is also said to be an equation defining two given ratios as equivalent to each other.

From the information, we have that;

By recycling 1 ton of paper, 6, 953 gallons of water was saved

To determine the gallons of water that would be saved after recycling 4 tons of paper, we have to;

If 1 ton of paper = 6, 953 gallons of water

Then 4 tons of paper = x

cross multiply

x × 1 = 6953 × 4

multiply through

x = 27, 812 gallons

The number of gallons that would be saved after the recycling would be

27, 812 gallons

Thus, the number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812

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The solutions after rounding the numbers are;

a. 80

b. 190

c.780

d. 90

What is Rounding number?

Rounding means making a number simpler but keeping its value close to what it was.

The questions are given as;

a. -28 - 53

b. 514 + -321

c. -888 - - 111.

d. -61.1 + -29.3

Now, solve and rounding the numbers as;

a. -28 - 53 = 81

After rounding it we get;

81 ≈ 80

Hence, -28 - 53 = - 80

b. 514 + -321 = 514 - 321

                   = 193

After rounding it we get;

⇒ 193 ≈ 190

Hence, 514 + -321 ≈ 190

c. -888- - 111 = - 888 + 111

                  = - 777 ≈

After rounding it we get;

- 777 ≈ - 780

d. -61.1 + -29.3 = -61.1 - 29.3

                      = - 90.4

After rounding it we get;

- 90.4 ≈ - 90

So, The solutions are;

a. 80

b. 190

c.780

d. 90

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I think they're for posting questions

If a man drove 14 miles directly east from his home made a left turn at an intersection and then traveled 7 miles due north to his place of work. If a road was made directly from his home, to his place of work what would its distance be is: 15.65 miles.

            (Work)

                                      A

                                    /   ║

                             /          ║                              

                      /                 ║ 7 miles

                 /                      ║  

(Home) B /___________║C

                    14 miles

Using Pythagorean theorem formula to determine the what the distance will be:

Hypotenuse²=√Perpendicular² +Base²

Let plug in the formula

Hypotenuse²=√7²+14²

Hypotenuse²=√49+196

Hypotenuse²=√245

=15.65 miles

Therefore If a man drove 14 miles directly east from his home made a left turn at an intersection and then traveled 7 miles due north to his place of work. If a road was made directly from his home, to his place of work what would its distance be is: 15.65 miles.

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On a number line, 3 + (-4) is -1 units from 3 in the left direction.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values (integers) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to represent all negative numerical values (integers) to the left of 0 and all positive numerical values (integers) to the right of 0

Evaluating, we have:

3 + (-4) = 3 - 4 = -1.

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The monthly payment become $852. Thus , option C is correct option.

According to the statement

We have to find that the monthly repayment.

So, For this purpose, we know that the

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan.

From the given information:

You have decided to buy a new home and the bank offers you a 30 year fixed loan at 5.5% on a balance of $150,000.

Then

we know that the:

Monthly payment = Amount / discount factor

And discount factor = 1-(1+i)^-n / i

Then

M = A*i/1-(1+i)^-n

Where, A=$150000

r=5.5%=0.055

i = 0.555/12

i = 0.004

And t = 30 year

n = 30*12

n = 360

Substitute all the values,

M = 150000*0.004/ 1-(1+0.004)^-360

M = 687.5 / 1-0.192

M = 687.5 / 0.80722

M = 851.7

Approximately, Monthly payment is $852.

So, The monthly payment become $852. Thus , option C is correct option.

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The range of a function y = x² + 9 is y ≥ 9

A function is a mathematical expression rule or law that defines the relationship between one variable (dependent variable) and another (independent variable)

The range of a function is the set of output values of that function.

Given the function y = x² + 9, to find the range of the function, we need to find the values of y for which the function is valid.

Making y subject of the formula, we have

x = √(y - 9)

So, the function is valid for √(y - 9) ≥ 0

⇒ y - 9 ≥ 0

⇒ y ≥ 9

So, the range of a function is y ≥ 9

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Answer:4

5

÷

10

Rewrite the division as a fraction.

4

5

10

Multiply the numerator by the reciprocal of the denominator.

4

5

⋅

1

10

Cancel the common factor of

2

.

Tap for more steps...

2

5

⋅

1

5

Multiply

2

5

by

1

5

.

2

5

⋅

5

Multiply

5

by

5

.

2

25

The result can be shown in multiple forms.

Exact Form:

2

25

Decimal Form:

0.08

Step-by-step explanation:

It should be noted that writing 762,508 in expanded form using exponents will be 762,508 = 700000 + 60000 + 2000 + 500 + 8.

It should be noted that exponents simply means expanded notation. It's the way of writing to see the individual digits.

Therefore, writing 762,508 in expanded form using exponents will be:

762,508 = 700000 + 60000 + 2000 + 500 + 8

Therefore, it should be noted that writing 762,508 in expanded form using exponents will be 762,508 = 700000 + 60000 + 2000 + 500 + 8

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Answer:

The slope is 1

Step-by-step explanation:

(3-0)/(3-0) = 3/3 = 1

Based on the results, the below  list shows a comparison of the overall performance of the portfolios, from best to worst:

Portfolio 2, Portfolio 3, Portfolio 1

What is weighted average ROR?

The weighted average ROR is the sum of rate of returns of the assets in the portfolio multiplied by the portion of the portfolio invested in each security

Portfolio 1:

total investment=$700+$2,575+$220+$1,000+$1,430

total investment=$5925

weighted average ROR=(-3.8%*$700/$5925+2.1%*$2575/$5925+11.3%*$220/$5925+5.8%*$1000/$5925+1.6%*$1430/$5925)

weighted average ROR=2.25%(third)

Portfolio 2:

total investment=$1,250+$1,700+$1,515 +$1,345+$1,675

total investment=$7485

weighted average ROR=(-3.8%*$1,250/$7485+2.1%*$1,700/$7485+11.3%*$1,515 /$7485+5.8%*$1,345/$7485+1.6%*$1,675/$7485)

weighted average ROR=3.53%(first)

Portfolio 3:

total investment=$1,025+$500+$790+$250+$2,500

total investment=$5065

weighted average ROR=(-3.8%*$1025/$5065+2.1%*$500/$5065+11.3%*$790/$5065+5.8%*$250/$5065+1.6%*$2,500/$5065)

weighted average ROR=2.28%(second)

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The probability of getting no. less than 11  after 1 spin is  0.833 .

An experiment is a situation involving chance or probability that leads to results called outcomes.

An outcome is the result of a single trial of an experiment.

An event is one or more outcomes of an experiment.

Probability is the measure of how likely an event is.

P(A) = The Number Of Ways Event A Can Occur /(The total number Of Possible Outcomes).

The probability of an event depends on the number of favorable (occurrence of the desired event) outcomes in comparison to the total number of outcomes.

We define the probability of an event by dividing the favorable outcomes by the total number of outcomes, as shown below.

P = n(E) / n(S)

Where,

n(E) = The favorable number of outcomes

n(S) = The total outcomes

Given Data:

The spinner rotates 1 time

find the probability of getting P(number> 11) from numbers 1 to 12.

n(E) =  10

n(S) = 12

P(A) = 10 /12

p(A) = 5/6

p(A) = 0.8333..

Thus, the probability of getting no. less than 11  after 1 spin is  0.833

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Answer:

Step-by-step explanation: the coat was reduced by 12 dollars for 3 months so take 12x3= 36. So the coat was reduced by 36 dollars.

Two ways to do this! There are some more but these are the most intuitive.

Way 1:  Factoring

You can factor this equation into one with parentheses. A way I like thinking of doing this is by seeing if you can split the coefficient of the middle term into the sum of two numbers, which, when multiplied with each other, equal the third term.  To see what I mean, look at the equation you gave.

[tex]x^2 - 18x + 77 = 0[/tex]

[tex]x^2 - 7x - 11x + 77 = 0[/tex]

We notice that when -7 and -11 are multiplied, they equal 77. This means we can factor the equation! As follows:

[tex](x-7)(x-11)=0[/tex]

If you want to see why this works, cross-multiply out [tex](x-7)(x-11)[/tex]. You should see that it is equal to [tex]x^2 - 7x - 11x + 77[/tex].

From here, you should be able to see the solutions are [tex]x = 7, 11[/tex].

Way 2:  Complete the Square

We can do something like this:

[tex]x^2 - 18x + 77 = 0\\x^2 - 18x + 81 = 4\\(x-9)^2 = 4\\x-9 = \pm\sqrt{4}\\x = 9\pm 2\\x = 7, 11[/tex]

Essentially, what we are doing is we are adding / subtracting from both sides of the equation so the left side becomes a perfect square of some term [tex](x-a)[/tex].  From there, we can just solve for [tex]x[/tex].

Hope this helps you, please let me know if anything confuses you.

The dimensions of the rectangle are 8 ft by 5.5 ft.

According to the statement,We have to find that the dimensions of the rectangles.

So, For this purpose, we know that the

A Rectangle may be a four sided-polygon, having all the interior angles adequate 90 degrees.

From the given information:The length of a rectangle is 3 ft but double the width, and therefore the area of the rectangle is 44.

Then

The formula for the world of a rectangle may well be a = L(length) × W(width)A = L × W

Plug in the information:A = 44, L = 2W - 3

b/c but means switch the order before subtracting, W = W

44 = (2W - 3)×W

44 = 2W² - 3W

And then

2W² - 3W - 44 = 0

so,

Factoring: (2W - 11)(W + 4) = 0

2W - 11 = 0 solves to W = 5.5

W + 4 = 0 solves to W = -4

So W = 5.5 and L = 2(5.5) - 3 = 8.

So, The dimensions of the rectangle are 8 ft by 5.5 ft.

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Answer:

If the debt of 24 trillion was equally divided by 300 million people, it's not really an estimation. You have an exact answer.

You would just divide it so each person owes $80,000

The width of the rectangle, w, is: 19 inches.

The perimeter of a rectangle is the sum of all its four sides which is calculated using the formula:

Perimeter = 2(length + width).

Given:

Perimeter = 144 inches

Width = w inches

Length = 3w - 4 inches

Thus:

2(3w - 4 + w) = 144

2(4w - 4) = 144

8w - 8 = 144

8w = 144 + 8

8w = 152

8w/8 = 152/8

w = 19

Thus, the width of the rectangle, w, is: 19 inches.

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Based on the area of T, the area of U can be calculated to be 272 cm²

When you have an object that is enlarged and have the area of the object before it was enlarged, the area of the enlarged object is:

= Area of original object x Scale factor of enlargement ²

The scale factor is:

= Side of U / Corresponding side of T

= 12 / 3

= 4

The scale factor is 4.

The area of U is therefore:

= 17 x 4²

= 272 cm²

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The relationships represent proportional relationships and the constant of proportionalities are 5/7 and 12

Does it represent a proportional relationship?

Yes, the graph represents a proportional relationship

This is so because the graph is a linear equation and it passes through the origin

How to find the constant of proportionality (K=Y/X)

On the graph, we have the following point

(X, Y) = (28, 20)

So, we have

K = 20/28

Evaluate

K = 5/7

Here, we have

Y = K * X

This gives

Y = 5/7X

Does it represent a proportional relationship?

Yes, the table represents a proportional relationship

This is so because the table is a linear equation and it has a value (0, 0)

How to find the constant of proportionality (K=Y/X)

On the graph, we have the following point

(X, Y) = (5, 60)

So, we have

K = 60/5

Evaluate

K = 12

Here, we have

Y = K * X

This gives

Y = 12X

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Answer:

2/3 < 14/6

3/8 < 8/3

2 1/6 > 5/9

Answer:

y=x+6

Step-by-step explanation:

First, write out the slope intercept equation.

y=mx+b

Ok, the first step for finding a linear equation is finding the y-intercept. The line crosses the y-axis at 6, so the y-intercept is 6. Plug that into the slope-intercept Equation:

y=mx+6

Then, slope is rise over run, and the line goes up 1 and right 1 to get to the next point, so divide those numbers.

1/1=1

Then plug that into your slope intercept equation:

y=1x+6

Since the one won't do anything, it will just be this:

y=x+6

The equations of each line are:

a. y = -3x + 3

b. y = -2/3x - 3

In slope-intercept form, the equation of a line is written as, y = mx + b, given that:

Note: the slope values of parallel lines are the same.

a. The slope of y = -3x - 1 is, -3. The line that is parallel to it will have the same slope (m) of -3.

Substitute m = -3 and (x, y) = (2, -3) into y = mx + b to find b:

-3 = -3(2) + b

-3 = -6 + b

-3 + 6 = b

3 = b

b = 3

Substitute b = 3 and m = -3 into y = mx + b

y = -3x + 3

b. Rewrite 2x + 3y = 6 in the slope-intercept form

3y = -2x + 6

y = -2/3y + 2

The slope of y = -2/3y + 2 is, -2/3. The line that is parallel to it will have the same slope (m) of -2/3.

Substitute m = -2/3 and (x, y) = (0, 5) into y = mx + b to find b:

5 = -2/3(0) + b

-3 = 0 + b

-3 = b

b = -3

Substitute b = -3 and m = -2/3 into y = mx + b

y = -2/3x - 3

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James defines that an angle is a figure consisting of two rays.

The statement of James is not precise enough because he should specify that the rays must be collinear.

The two rays coming from the same point will form collinear rays which will form an angle at the end point. The common end point is the vertex of the angle. And each ray will known as an arm of an angle.

From the figure, we can see that the vertex is the corner of the angle, i.e.,  O is the vertex in the given figure.

OA and OB are the two arms of the angle. The line OB is also known as reference line which is the line where an angle is drawn.

Also, the line OA will be considered as terminal line. Terminal line is the side up to which an angle measurement done.

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The selling price of the bicycle in discuss upon addition of the mark-up which is 33.3% as described in the task content is; $131.63.

The wholesale cost price of the bicycle in discuss is $98.75 as described in the task content while the markup for the bicycle is as given in the task content.

On this note, it follows that the selling price of the bicycle is the sum of its cost price and it's mark-up. Hence, we have;

Selling price = $98.75 + (33.3% of $98.75)

= $98.75 + (0.333 × $98.75)

= 98.75 + 32.88

= $131.63.

Ultimately, selling price of the bicycle in discuss upon addition of the mark-up which is 33.3% as described in the task content is; $131.63.

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Answer: We have m = −3/2 as the slope and b = 150 as the y-intercept.

Step-by-step explanation:

Given data,

The slope of the following line 3x+2y=300

Define Slope :

Slope = (Change in height)/(Change in width) Or: Slope = rise/run. If y represents the vertical direction on a graph, and x represents the horizontal direction, then this formula becomes: Slope = (Change in y)/(Change in x)

The equation of a line presents the relationship between the components of a line in a certain coordinate system. To construct the equation of the line, we must take note of the parameters such as the slope, a point at which the line passes through, and the intercepts.

We solve for the slope, m, and the y-intercept, b, for the given line. We do this by rewriting the expression into the slope-intercept form,

                                y = mx + b

We proceed with isolating y in the given equation.

                                3x + 2y = 300

                                 2y = - 3x + 300

                                  y = (-3x + 300) / 2

                                  y = (-3/2) x + 300/2

                                  y = (-3/2) x + 150

Therefore, we have m = −3/2 as the slope and b = 150 as the y-intercept.

So, slope = -3/2

      b = 150

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The figure 0.12 as given in the task content based on the given data can be interpreted as; the fraction of the books in the library that are how-to books on electronics.

It follows from the task content that the best interpretation of 0.12 is to be determined.

On this note, since three-tenths of the books in the school library are how-to books, and of those, 0.4 deal with electronics;

The statement above therefore means that the fraction of books which are how-to books and deal with carpentry can be evaluated as;

= (3/10) × 0.4

= 0.3 × 0.4

= 0.12.

Ultimately, The figure 0.12 as given in the task content based on the given data can be interpreted as; the fraction of the books in the library that are how-to books on electronics.

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Answer:

6 trips

Step-by-step explanation:

divide by 3

17/3

5.66666666

now round it off and say 6