What is the slope of a line with the points of (4,7) & (6,7)

The given rational expression is 4y + 16 y + 4. To find the restricted values of y, we need to identify any values of y that would make the expression undefined.

In this case, the expression is in the form of a sum, so we don't have any denominators that could lead to division by zero. Therefore, there are no restricted values of y for this rational expression.

The expression 4y + 16 y + 4 is defined for all real numbers. We can evaluate it for any value of y without encountering any restrictions.

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Answer:

point-slope form:  \(y-3=-\frac{1}{3}(x - 3)\)

slope-intercept form: \(y=-\frac{1}{3}x+4\)

Step-by-step explanation:

point-slope form is: y - y1 = m(x - x1)

slope-intercept form is: y = mx + b

The formula used to find the slope(m): \(\frac{y2-y1}{x2-x1}\)

(x1, y1) = (3, 3)

(x2, y2) = (-6, 6)

The first thing we need to do to write the equations is to find the slope. We can do this by inputting the given points into the slope formula:

\(\frac{6-3}{-6-3}\)

Simplify:

6 - 3 = 3

-6 - 3 = -9

\(\frac{3}{-9} =-\frac{1}{3}\)

The slope is \(-\frac{1}{3}\). We can now write the equation in point-slope form:

\(y-3=-\frac{1}{3}(x - 3)\)

To write the equation in slope-intercept form, we need to find the value of b. To find its value, input the value of the slope and one point into the equation for slope-intercept form:

y = mx + b

3 = \(-\frac{1}{3}\)(3) + b

Now you can solve for b:

3 = \(-\frac{1}{3}\)(3) + b

3 = -1 + b

4 = b

Now that we know the value of b, we can write the equation in slope-intercept form:

\(y=-\frac{1}{3}x+4\)

I hope this helps. :)

Equation in point-slope form of the line that passes through the given points (-6,6) and (3,3) is y=-1/3x+4.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

The given two points are (-6,6) and (3,3)

x1=-6, y1=6, y1=3 and y2=3

m=y2-y1/x2-xq

m=3-6/3-(-6)

m=-3/9

m=-1/3

Hence slope of line is m=-1/3

To write the equation in slope-intercept form, we need to find the value of b. To find its value, input the value of the slope and one point into the equation for slope-intercept form:

y = mx + b

3=-1/3(3)+b

4=b

Now that we know the value of b, we can write the equation in slope-intercept form:

y=-1/3x+4

Hence equation in point-slope form of the line that passes through the given points (-6,6) and (3,3) is y=-1/3x+4.

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Answer:

C

Step-by-step explanation:

Answer:

x=90°

Step-by-step explanation:

The inside angles in a triangle always add up to 180°.

So:

53°+37°=90°

180°-90°=90°

x=90°

Answer:

see below

Step-by-step explanation:

since the sum of angles in a triangle is 180 degrees

x + 53 + 37 = 180

x = 180 - 53 - 37

x = 90 degrees

hope this helps, please mark it brainliest

Picture 1: w = 14 units

Picture 2: The angles are 30°, 60° and 90°

Picture 3: p = 22√2 units

Picture 4: The distance is 42 ft

Picture 5: The perimeter of the equilateral triangle is 30√3 m

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

Picture 1

cos 30° = 7√3 / w

w cos 30° = 7√3

w  = 7√3 /(cos 30°)

w = 14 units

Picture 2

We have a right angle there already i.e. 90°. Let the two unknown angles be x and y.

sin x = (7√3) /(14√3)

sin x = 1/2

x = arcsin (1/2)

x = 30°

y = 90 - 30 = 60°

Thus, the angles are 30°, 60° and 90°

Picture 3

sin 45° = p/44

p = 44 * sin 45°

p = 44 * (√2)/2

p = 22√2 units

Picture 4

The distance from corner to corner is the length of the diagonal of the square.

Distance = √(30² + 30²) = 42 ft    (Pythagoras' theorem)

Picture 5

The perimeter of the equilateral triangle is the sum of all three sides.

Let's find the side x:

sin 60° = 15/x

x = 15/sin 60°

x = 10√3 m

perimeter = 3x = 3 * 10√3 = 30√3 m

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Answer:

C = 10π ft

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius )

to find r use the area formula, that is

A = πr² = 25π ( divide both sides by π )

r² = 25 ( take square root of both sides )

r = \(\sqrt{25}\) = 5

then

C = 2π × 5 = 10π ft

The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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$6.60 because 6.00 + 0.60 = 6.60

Answer:

A and C.

Step-by-step explanation:

A. 4/18 = 6/27     2/9 = 2/9 (Correct)

B. 4/6 = 16/36     2/3 = 4/9 (Unequal)

C. 3/4 = 9/12     3/4 = 3/4 (Correct)

D. 5/9 = 8/12     5/9 = 2/3 (Unequal)

The solution to the given system is (3,8).

Step-by-step explanation:

To draw a graph system for a linear equation,

Step 1: Consider two x values and draw a line joining the new points.

y = x + 5  ⇒1

y = 2x + 2  ⇒2

For both equations substitute two random values for x.

Let us Consider x=0 and x=10.

For equation 1,

y=x+5.                           y=x+5

y=0+5.                           y=10+5

y=5                                y=15

The new points for equation 1 are (0,5) and (10,15).

Draw a big straight line passing through these two points.

For equation 2,

y=2x+2.                         y=2x+2

y=0+2.                           y=20+2

y=2                                y=22.

The new points for equation 1 are (0,2) and (10,22).

Again, draw a big straight line passing through these two points.

Step 2: Mark the intercepting point and that will be the solution for the given system.

For this system, the solution is (3,8).

To check this answer equates both equations,

x+5=2x+2.

2x-x=5-2.

x=3.

Substitute the x value in any of the equations,

y=3+5.

y=8.

The angle of elevation of the sun is \(tan^{-1}\)(106/ 135).

The angle of elevation:

The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.

Here we have to find the angle of elevation of the sun.

Data given:

length of the tower = 106 feet

shadow form by the tower = 135 feet

The formula for the angle of elevation = height/base

tanФ = height/base

        = 106/ 135

Ф = \(tan^{-1}\)(106/135)

Therefore the angle of elevation is \(tan^{-1}\)( 106/ 135).

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Answer:

12 cm confirm ...................

From the concept of trigonometric ratios, we determine the length of the side  BC is 6.75 cm.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, The length of the side AC = 9cm.

The measure of tan∠ABC = 0.75.

We know tan = opposite/adjacent.

Here, the opposite is AC and adjacent is BC.

Therefore, 0.75 = 9/BC.

BC = 9×0.75.

BC = 6.75.

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The interval of convergence for both f(x) and g(x) is -1/3 < x < 1/3.

To express the function f(x) = (2x-4)/(x^2-4x+3) as a sum of a power series using partial fractions, we first factorize the denominator:

x^2 - 4x + 3 = (x-1)(x-3).

Now, we can express the function f(x) as a sum of partial fractions:

f(x) = A/(x-1) + B/(x-3).

To find the values of A and B, we can multiply both sides of the equation by (x-1)(x-3):

(2x-4) = A(x-3) + B(x-1).

Expanding the right side:

2x - 4 = (A+B)x - 3A - B.

By comparing the coefficients of x on both sides, we have:

2 = A + B,

-4 = -3A - B.

Solving these equations simultaneously, we find A = 2 and B = -4.

Therefore, f(x) can be expressed as:

f(x) = 2/(x-1) - 4/(x-3).

Now, let's find the power series representation for f(x) by expressing each term as a power series:

Using the geometric series formula, we have:

1/(1+3x) = 1 - 3x + 9x^2 - 27x^3 + ...

Now, let's differentiate term-by-term:

d/dx[1/(1+3x)] = d/dx[1 - 3x + 9x^2 - 27x^3 + ...].

Differentiating each term:

-3 + 18x - 81x^2 + ...

Multiplying by -3:

3 - 18x + 81x^2 - ...

Therefore, the power series representation for g(x) = -3/(1+3x)^2 is:

g(x) = -3 + 18x - 81x^2 + ...

The interval of convergence for both f(x) and g(x) will be determined by the interval of convergence of the power series for 1/(1+3x).

The geometric series converges when the absolute value of the common ratio, in this case 3x, is less than 1.

Thus, the interval of convergence is:

|3x| < 1,-1/3 < x < 1/3.

Therefore, the interval of convergence for both f(x) and g(x) is

-1/3 < x < 1/3.

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Erica works in a soda-bottling factory and earns 46¢ for each successfully capped bottle but loses 2¢ for each bottle she breaks. After capping some bottles, she has earned only 6¢ and has broken some bottles. To determine how many bottles Erica capped and how many she broke, a system of equations can be used.

   Let x be the number of bottles Erica capped and y be the number of bottles she broke. Then the following system of equations can be written:

46x - 2y = 6 (Equation 1)

x + y = 15 (Equation 2)

To solve the system of equations using substitution, we can isolate one of the variables in terms of the other from Equation 2, and substitute it in Equation 1. From Equation 2, y = 15 - x. Substituting this in Equation 1, we get 46x - 2(15 - x) = 6. Simplifying the equation, we get 48x - 30 = 6, which gives x = 9. Therefore, Erica has capped 9 bottles and broken 6 bottles.

To solve the system of equations using elimination, we can multiply Equation 2 by 46 to eliminate y. This gives us 46x + 46y = 690. Subtracting Equation 1 from this equation, we get 48y = 684, which gives y = 14.25. However, y cannot be a fractional value, so we can round it to the nearest whole number, which gives y = 14. Substituting y = 14 in Equation 2, we get x = 1. Therefore, Erica has capped 1 bottle and broken 14 bottles.

Both methods lead to different solutions, but this is because one of the solutions obtained is not feasible. Erica cannot cap a fraction of a bottle or break a fraction of a bottle. Therefore, the solution obtained using the elimination method needs to be rounded to the nearest whole number, which then gives the same solution as the substitution method, that Erica capped 9 bottles and broke 6 bottles.

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Erica works in a soda-bottling factory and earns 46¢ for each successfully capped bottle but loses 2¢ for each bottle she breaks. After capping some bottles, she has earned only 6¢ and has broken some bottles. To determine how many bottles Erica capped and how many she broke, a system of equations can be used.

  Let x be the number of bottles Erica capped and y be the number of bottles she broke. Then the following system of equations can be written:

46x - 2y = 6 (Equation 1)

x + y = 15 (Equation 2)

To solve the system of equations using substitution, we can isolate one of the variables in terms of the other from Equation 2, and substitute it in Equation 1. From Equation 2, y = 15 - x. Substituting this in Equation 1, we get 46x - 2(15 - x) = 6. Simplifying the equation, we get 48x - 30 = 6, which gives x = 9. Therefore, Erica has capped 9 bottles and broken 6 bottles.

To solve the system of equations using elimination, we can multiply Equation 2 by 46 to eliminate y. This gives us 46x + 46y = 690. Subtracting Equation 1 from this equation, we get 48y = 684, which gives y = 14.25. However, y cannot be a fractional value, so we can round it to the nearest whole number, which gives y = 14. Substituting y = 14 in Equation 2, we get x = 1. Therefore, Erica has capped 1 bottle and broken 14 bottles.

Both methods lead to different solutions, but this is because one of the solutions obtained is not feasible. Erica cannot cap a fraction of a bottle or break a fraction of a bottle. Therefore, the solution obtained using the elimination method needs to be rounded to the nearest whole number, which then gives the same solution as the substitution method, that Erica capped 9 bottles and broke 6 bottles.

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To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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Answer: B

\(f(x) = 7x-2\) and        \(g(x) = \frac{x+2}{7}\)

How to solve:

check if the composite functions of f(x) and g(x) are equal to x (this means they are inverses)

f[g(x)] = x

g[f(x)] = x

Step-by-step explanation:

Checking A.

\(f(x) = \frac{5}{x} -2\)

\(g(x) = \frac{x+2}{5}\)

\(f(g(x)) = f(\frac{x+2}{5} ) = \frac{5}{\frac{x+2}{5} } -2\)

This does not equal x, so we know these are not inverses

Checking B.

\(f(x) = 7x-2\)

\(g(x) = \frac{x+2}{7}\)

\(f(g(x)) = f(\frac{x+2}{7} ) = 7(\frac{x+2}{7}) - 2 = x+2-2 = x\)

\(g(f(x)) = g(7x-2) = \frac{7x-2 + 2}{7} = \frac{7x}{7} = x\)

since both f(g(x)) = x and g(f(x)) = x, we can determine that they are inverses of each other.

Answer:

D. \( 8 {m}^{ - 1} n\)

Step-by-step explanation:

\( \huge \frac{(4 {m}^{2} n)^{2} }{2 {m}^{5}n } \\ \\ \huge= \frac{16 {m}^{4} {n}^{2} }{2 {m}^{5}n } \\ \\ \huge = 8 {m}^{4 - 5} {n}^{2 - 1} \\ \\ \huge \purple{ \boxed{= 8 {m}^{ - 1} n}}\)

Answer:

8m^-1n

Step-by-step explanation:

The area of the window is 1440 square inches. Given that the ratio of the length of the base to the height will be 5 to 2 and the base will have a length of 60 inches. We are to determine the area of the window.

Solution:

Let's first calculate the height of the window.

If the ratio of the length of the base to the height will be 5 to 2,

Then we can assume the length of the base is 5x, where x is some constant of proportionality.

And we can also assume the height is 2x.

So we know,

Length of the base = 60 inches

5x = 60x

= 60/5

= 12 inches

Height of the window = 2x

= 2 × 12

= 24 inches

Now we can calculate the area of the window.

Area of the window = Length × Width

Area of the window = 60 × 24

Area of the window = 1440 square inches

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increase= 31° F

Explanation

Step 1

Graph

let x represent the increase in temperature,then

now, to find the increase, solve for x

so the increase is 31° F.

I hope this helps you

The reflection paper is about REHB 200. Each student is expected to use appropriate person-first language. The paper must be a minimum of 5 pages.

This reflection paper about REHB 200 requires a minimum of 5 pages from each student. The paper must include a summary of what will be discussed in the body of the paper. To write the reflection paper, the following points should be considered: three things not known about disability before taking this course, the favorite video clip(s) and why, laws designed to protect people with disabilities, thoughts associated with employment obstacles faced by people with disabilities, inclusion and normalizing disability in society, compare and contrast intellectual, physical, cognitive, and psychiatric disability, thoughts about the accessibility audit activity and discussion board questions, and biggest takeaway from the class.

In conclusion, this reflection paper about REHB 200 requires a minimum of 5 pages from each student. It is expected that each student will comply with appropriate person-first language. The reflection paper includes a summary of what will be discussed in the body of the paper and must cover several points including the comparison and contrast of intellectual, physical, cognitive, and psychiatric disability.

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Answer:

its the first option, y = -3/2x+6

Step-by-step explanation:

Answer:

pretty sure its D. 1.6 x 10^9

The train will take 3hour 7.5min to travel a distance of 250 km

Given that,

Distance of 250 km with a speed of 80 kmh

To find: Time taken by train to travel a distance of 250 km with a speed of 80 kmh

Distance = 250km

Speed of the train =80km/h

Speed is calculated as distance times speed. You need to be aware of the units for distance and time in order to calculate the units for speed. The units in this example will be metres per second (m/s), since the distance is measured in metres (m) and the time is measured in seconds (s).

Time = Distance /speed

=250km /80km/h

=25/8 h

= 3⅛h

= 3hour ⅛*60

= 3hour 7.5min.

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Answer:

3 hours 7.5 mim

Step-by-step explanation:

The train will take 3hour 7.5min to travel a distance of 250 km

Given that,

Distance of 250 km with a speed of 80 kmh

To find: Time taken by train to travel a distance of 250 km with a speed of 80 kmh

Distance = 250km

Speed of the train =80km/h

Speed is calculated as distance times speed. You need to be aware of the units for distance and time in order to calculate the units for speed. The units in this example will be metres per second (m/s), since the distance is measured in metres (m) and the time is measured in seconds (s).

Time = Distance /speed

=250km /80km/h

=25/8 h

= 3⅛h

= 3hour ⅛*60

= 3hour 7.5min.

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$932.34 amount left on June 8th.

Traditionally, an employer would issue a paper document known as a paycheck—also spelled paycheque, pay check, or pay cheque—to pay an employee for services rendered.

Given:

Your bank charges a $16-per-check overdraft fee.

At the end of the month, you had $36.92 in your account.

On June 1st, your monthly paycheck of $2, 100

On June 3rd, rent check of $667.35

On June 4th, cell phone bill of $127.37

On June 5th, internet bill of $60

On June 6th, Netflix premium bill $17.99

On June 7th, car payment of $331.87

So, on June 8th

= 2100 + 36.92 -667.35-127.37-60-17.99-331.87

= $932.34

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Answer: I believe the answer is: A(subscript)n = n^2 + 2n + 5

Step-by-step explanation:

There are 73,701 different 6-card hands (from a standard deck) with at least 3 kings.

To calculate the number of 6-card hands with at least 3 K's, the problem can be divided into:

Case 1:

Exactly 3 Kings

There are 4 ways to choose 3 kings to put in the hand, then there are 48 cards left to choose the remaining 3 cards (because we used 3 cards in a 52-card deck). Therefore, the number of 6-card hands with exactly 3 kings is:

4 * (48 choose 3) = 4 * 17,296 = 69,184

Case 2:

Exactly 4 Kings

There are 4 ways to choose 4 kings to put in the hand, then there are 48 cards left to choose the remaining 2 cards. Therefore, the number of 6-card hands with exactly 4 kings is:

4 * (48 choose 2) = 4 * 1.128 = 4.512

Case 3:

Exactly 5 kings

There are 4 ways to choose the 5 kings in the hand, then there is only one card left to choose from (because we used 5 of the 52 cards in the deck of cards). Therefore, the number of 6-card hands with exactly 5 kings is:

4*1=4

Case 4:

6 cards are king

There is only one way to choose all 6 cards as king.

Therefore, the total number of 6-card hands with at least 3 kings is:

69,184 + 4,512 + 4 + 1 = 73.701

So there are 73,701 different 6-card hands with at least 3 kings.  

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Answer:

4

Step-by-step explanation:

8x + 15 = 5.5x +25

so 2.5x =10

x=4

Answer: they both have four sides (quadrilateral)

Step-by-step explanation:

Answer:

Quarderlaterals with reflecting (or parrel) sides of the same length.

Step-by-step explanation:

Squares always have 4 equal sides

Parrallegrams always have two sides that are parrel to each other that are the same lenghth.

Answer:

sorry hindi ko maintindihan yong tanong