Find the slope that passed through the points (12,-10) (5,4)

Answer:

48

Step-by-step explanation:

24/32 = K/64

k = 48

Is this actually a college math problem

Answer:

\(\frac{t^2-16}{t^2-8t+16}\)

We can factorise the numerator which the difference of squares formula:

\(x^2-y^2=(x+y)(x-y)\)

---------------------------------

\(\frac{t^2-4^2}{t^2-8t+16} =\frac{(t+4)(t-4)}{t^2-8t+16}\)

Next, factorise the denominator:

\(\frac{t^2-4^2}{t^2-8t+16} =\frac{(t+4)(t-4)}{(t-4)^2}\)

\(\frac{(t+4)(t-4)}{(t-4)(t-4)}\)

Cancel out the common factor of (t-4):

\(\frac{t+4}{t-4}\)

To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.

We have,

The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

Now,

In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.

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complete question:

Applying the Pythagorean Theorem In this activity, you will explain your understanding of mathematical relationships and use the Pythagorean theorem to solve real-world problems. Question 1 In your own words, explain the relationship between the legs and the hypotenuse of a right triangle.

Answer:

193 1/3

Step-by-step explanation:

First, we need to convert \(\frac{145}{3}\) into a mixed number.

Now, we can add them together:

Therefore, the answer is \(193\frac{1}{3}\).

This equation has infinitely many solutions.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: 3x+4y = -10...(1),

y = -3/4x - 5/2....(2)

We solve this linear equation and we get

We multiply equation (2) by 4 and we get

4y + 3x = -5(2)

4y + 3x = -10

Hence, this equation has infinitely many solutions.

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In order to solve this exercise, you can use the Heron's formula for the area of a triangle:

Where "a", "b" and "c" are the lengths of the sides of the triangle and "p" is half the perimeter.

The value of "p" can be found with this formula:

Where "a", "b" and "c" are the lengths of the sides of the triangle.

In this case, you can set up that:

Then, you can find "p":

Then, substituting values into the Heron's formula and evaluating, you get:

The answer is:

Answer:

  (b)  40

Step-by-step explanation:

You want the value of the "whole" corresponding to a "part" of 25 in the given table.

Based on the relationships in the 2nd and 3rd columns, it appears that the parts on the second line are 5/8 of the whole.

This means that 25 is 5/8 of B, or ...

  B = 8/5 × 25 = 40

The value of B in the table is (b) 40.

__

Additional comment

The parts on the first line will be 3/5 of the value of the parts on the second line. The sum of the two parts in each column is equal to the whole.

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Answer:

A

Step-by-step explanation:

y - 3 = 4(x+5)

Let's convert the point-slope equation to y-intercept form: y = mx + b

Distribute the 4 to the equation inside the parenthesis

y - 3 = 4x + 20

Add 3 to both sides

y - 3 = 4x + 20

 + 3         + 3

y = 4x + 23

The slope of this equation is 4, meaning our equation's slope will have to be -1/4 to be perpendicular

y = -1/4x + b

Plug in the given x and y

-3 = -1/4(4) + b

-3 = -1 + b

Add 1 to both sides

-3 = -1 + b

+ 1   + 1

b = -2

y = -1/4x - 2

Math makes everything easier without math people would be sitting there all day wondering about simple things like money and how many eggs are in a carton

Answer:

The rock will reach to the canyon floor in 3.99 seconds.

Step-by-step explanation:

The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation

Where, h0 is the initial height of the object.

It can be written as

The height of the object is zero if it will reach to the canyon floor.

Quadratic formula:

Here a=-16, b=0 and c=255.

Time cannot be negative, therefore the rock will reach to the canyon floor in 3.99 seconds.

Answer:

Y=2x-5

Step-by-step explanation:

Answer:

5x + 3y = 12

Step-by-step explanation:

We are given the line 5x + 3y = 6 and are to find the equation of a new line that is parallel to this one and goes through (3, -1).

Parallel lines have the same slope.  The slope of the given line is determined by the coefficients 5 and 3 visible above.  Therefore, the form of the equation of the new line is 5x + 3y = C, where we must determine the value of C.

Substitute 3 for x and -1 for y in 5x + 3y = C, obtaining:  5(3) + 3(-1) = C.  Then 15 - 3 = 12 is the constant value, and the equation of the 'new line' is

5x + 3y = 12

The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60

(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.

Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200

Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments

Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]

Total amount paid = $1,300 + $13,200 + $14,041.60

Total amount paid = $28,541.60

Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.

(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.

Total interest paid = Total amount paid - Total amount borrowed - Down payment

Total interest paid = $28,541.60 - $13,200 - $1,300

Total interest paid = $14,041.60

Therefore, the amount of interest Debra paid on the loan was $14,041.60.

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Answer:

a = 18.6 ft ;  b = 16.7 ft ;  ∠B = 42° ;  ∠C = 90°

Step-by-step explanation:

            c = 25 ft

            ∠C = 90°

            ∠A = 48°

Using angle sum property of triangle, we can find ∠B.

      ∠B = 180 - 48 - 90

            = 180 - 138

            = 42°

We can find a and b using trigonometry ratio Sin and Cos.

     \(\sf Sin \ A = \dfrac{opposite \ side \ of \ \angle A }{hypotenuse}\\\\ Sin \ 48 = \dfrac{a}{c}\\\\ 0.7431 =\dfrac{a}{25}\\\\\\\)

0.7431*25 = a

             \(\boxed{\bf a = 18.6 \ ft }\)

To find the value of b, use Cosine ratio,

         \(\sf Cos \ A = \dfrac{adjacent \ side \ of \ \angle A}{hypotnuse}\\\\ Cos \ 48 = \dfrac{b}{25}\\\\\\0.6691= \dfrac{b}{25}\)

0.6691 * 25 = b

                    \(\boxed{b = 16.7 \ ft}\)

The required worth of all the boxes held in the warehouse is $6930.

Capacity implies the capacity to utilize and comprehend data to pursue a choice, and impart any choice made. An individual needs limit in the event that their brain is disabled or upset here and there, and that implies they're not able to pursue a choice around then.

We have,

Cost price of each box = $21

There are 330 boxes can be held in the warehouse.

On multiplying the the price of each box and the number of boxes, we get

$21 × 330

$6930

Thus, required worth of all the boxes is $6930.

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Answer:

9 is the answer

Step-by-step explanation:

got a delivery of 60ib...but dont have enough .thats why he or she sells 29..totally he or she have 38ib of carrots ...so when we subtract 38_29

its =9

Answer:

A

Step-by-step explanation:

After answering the given query, we can state that  the parabola equation expands upwards, and the apex is (4, 4.5).

Using the equals sign (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical formulas through a mathematical assertion. The equal symbol, for example, puts a space between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two lines that are printed on opposite sides of a letter. Most of the time, the emblem and the particular program match. e.g., 2x - 4 = 2 is an example.

P equals 1/2, meaning that the distance between the apex and the focus is equal to the distance between the directrix and the focus.

As a result, the parabola's equation is:

\((x - 4)^2 = 4(1/2)(y - 1.5)\\(x - 4)^2 = 2(y - 1.5)\)

The left half of the equation is expanded as follows: x2 - 8x + 16 = 2(y - \(1.5) x2 - 8x + 13 = 2y\\y = (1/2)x^2 - 4x + 13/2\)

The problem can also be expressed in vertex form by filling in the cube as follows:

\((x - 4)^2 = 2(y - 1.5)\\(x - 4)^2 = 2(y - 1.5) + 6\\(x - 4)^2 = 2(y - 4.5)\\(x - 4)^2/8 = (y - 4.5)\\\)

Therefore, the parabola expands upwards, and the apex is (4, 4.5).

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A graph of the inequality "y is less than negative one fourth times x minus 3" is: D. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.

In order to determine the ordered pair that is included in the solution to this linear inequality, we would first of all translate the word problem into an algebraic equation as follows;

y is less than negative one-fourth times x minus 3 ⇒ y < -x/4 - 3.

Next, we would use an online graphing calculator to graphically solve the linear inequality. Therefore, the required solution for the given linear inequality is the shaded area below the dashed line, which is given by the ordered pairs (−12, 0) and (0, -3).

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Answer:

it’s D dotted line with shading below

Step-by-step explanation:

i got it on my quiz

Answer:

4

Step-by-step explanation:

In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

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Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

Answer:

see below

Step-by-step explanation:

center of circle = (2,-1)

r = 6 -2 = 4

We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.

so the equation will be:

( x - 2 )^2 + ( y +1 )^2 =16

Answer: 1134

Step-by-step explanation:

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer: y = 18

Sentence: The value of y that makes T Parallel to U is 18.

Step-by-step explanation:

We are given 3 expressions:

We know that since the angle (7x) is on the same line as the angle (3x + 36), we can therefore determine that they correspond to each other. I referred an image to help demonstrate this concept. So since they correspond to each other, that means they have the same value (meaning they are equal to each other).

We can set both expressions equal to each other.

7x = 3x + 36

And solve:

7x = 3x + 36

-3x   -3x

4x = 36

/4     /4

x = 9

now we know the value of x, we can plug it into one of the equations. We  can plug it in to 3x + 36 to help with the process in solving y.

3(9) + 36 = 63 degrees

Since 6y + 9 and 3x + 36 (63 degrees) are supplementary angles, we can subtract 180 from 63.

180 - 63 = 117

now we know that 117 degrees = 6y + 9 BUT!, we need to solve for y, because that's what the question is asking for.

So lets solve for y:

117 = 6y + 9

-9            -9

108 = 6y

/6       /6

y = 18

Answer:

True

Step-by-step explanation:

4x8=32

4x8=3236-4=32

Hence, the equation is true.

Answer:

ST = 5

Step-by-step explanation:

Calculate ST using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with )x₁, y₁ ) = S(- 5, - 1) and (x₂, y₂ ) = T(- 2, 3)

ST = \(\sqrt{(-2+5)^2+(3+1)^2}\)

     = \(\sqrt{3^2+4^2}\)

    = \(\sqrt{9+16}\)

     = \(\sqrt{25}\)

      = 5

Answer:

3rd Option: -1

5th Option: 2

7th Option: i√6

8th Option: -i√6

Step-by-step explanation:

Graph the function first to find our real root factors.

When you find your real root factors, factor the equation down with x + 1 and x - 2 and then use Quadratic Formula to find complex roots.

Answer:

-2, 1. i\(\sqrt{6}\), and -i\(\sqrt{6}\)

Step-by-step explanation:

just took the test