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3 years ago

The y-intercept of (2,5) and (4,4)

Mathematics

2 answers:

DerKrebs [107]3 years ago

7 0

The Y intersept is 1

wolverine [178]3 years ago

4 0

First let's find the slope of line joining (2, 5) and (4, 4)

Assuming points (x₁, y₁) and (x₂, y₂)

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (4 - 5) / (4 -2) = -1/2 = -0.5

From equation of line: y = mx + c

y = -0.5x + c

Using the point (2 , 5) as passing through y = -0.5x + c

x = 2, y = 5

5 = -0.5*2 + c

5 = -1 + c

5 + 1 = c

6 = c

c = 6

Therefore the y-intercept which is c = 6

y-intercept = 6

Hope this explains it.

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The perimeter of triangle STU is 28.8 centimeters. Which is the perimeter of triangle JKL?

spayn [35]

Answer:

You forgot to add a picture and/or more context.

Step-by-step explanation:

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3 years ago

Suppose a rectangular pasture is to be constructed using 1 2 linear mile of fencing. The pasture will have one divider parallel

timama [110]

Answer:

$\displaystyle A=\frac{1}{192}$

Step-by-step explanation:

<u>Maximization With Derivatives</u>

Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.

We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.

The two divisions parallel to x have lengths y, thus the fencing will take 4x. The three dividers parallel to y have lengths x, thus the fencing will take 3y.

The amount of fence needed to enclose the external and the internal divisions is

$P=4x+3y$

We know the total fencing is 1/2 miles long, thus

$\displaystyle 4x+3y=\frac{1}{2}$

Solving for x

$\displaystyle x=\frac{\frac{1}{2}-3y}{4}$

The total area of the pasture is

$A=x.y$

Substituting x

$\displaystyle A=\frac{\frac{1}{2}-3y}{4}.y$

$\displaystyle A=\frac{\frac{1}{2}y-3y^2}{4}$

Differentiating with respect to y

$\displaystyle A'=\frac{\frac{1}{2}-6y}{4}$

Equate to 0

$\displaystyle \frac{\frac{1}{2}-6y}{4}=0$

Solving for y

$\displaystyle y=\frac{1}{12}$

And also

$\displaystyle x=\frac{\frac{1}{2}-3\cdot \frac{1}{12}}{4}=\frac{1}{16}$

Compute the second derivative

$\displaystyle A''=-\frac{3}{2}.$

Since it's always negative, the point is a maximum

Thus, the maximum area is

$\displaystyle A=\frac{1}{12}\cdot \frac{1}{16}=\frac{1}{192}$

6 0

3 years ago

Perform the indicated operation g(x)=-x-3 h(x) = x 2+X Find (goh) (x)

Klio2033 [76]

Answer:

$(g\circ h)(x)=-x^2-x-3$

Step-by-step explanation:

So we have the two functions:

$g(x)=-x-3\text{ and } h(x)=x^2+x$

And we want to find:

$(g\circ h)(x)$

This is the same thing as:

$=g(h(x))$

So, substitute h(x) into g(x):

$g(x)=-x-3\\g(h(x))=-(x^2+x)-3$

Distribute the negative:

$g(h(x))=-x^2-x-3$

And we're done!

So:

$(g\circ h)(x)=-x^2-x-3$

6 0

3 years ago

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The original loan amount is referred to as the______.

marishachu [46]

The answer is principal.
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5 0

3 years ago

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A math class is having a discussion on how to determine if the expressions 4x-x+5 and 8-3x-3 are equivalent using substitution.

bixtya [17]

Answer:

option (b) is correct.

Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.

Step-by-step explanation:

Given : A math class is having a discussion on how to determine if the expressions 4x - x + 5 and 8 - 3x - 3 are equivalent using substitution.

We have to choose the correct method from the given options that the class has suggested.

Since we have to show the given expressions 4x - x + 5 and 8 - 3x - 3 are equivalent using substitution.

We will choose a single value of x and then evaluate both the given expression at that single value and if the output of both expression comes out to be same then the two expressions must be equivalent.

For example lets take x = 2,

Then expression 4x - x + 5 becomes 4(2) - 2 +5 = 8 - 2 + 5 = 6 + 5 = 11

also, expression 8 - 3x - 3 becomes 8 - 3(2) - 3 = 8- 6 - 3 = 8 - 9 = -1

thus, the value is not equal hence, the two expression are not equivalent.

Thus, option (b) is correct.

Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.

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3 years ago

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