MATHEMATICS HIGH SCHOOL

Find the equation of the line that is parallel to y = -7x + 2 and contains the point (-5,32)

Answers

Answer 1

Answer:

Y=-7x-3

Step-by-step explanation:

Answer 2

Answer:

Answer:

y = - 7x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 7x + 2 ← is in slope- intercept form

with slope m = - 7

Parallel lines have equal slopes, thus

y = - 7x + c ← is the partial equation

To find c substitute (- 5, 32) into the partial equation

32 = 35 + c ⇒ c = 32 - 35 = - 3

y = - 7x - 3 ← equation of parallel line

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Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The three pens are to have the same area. Express the area function for the three pens in terms of x. Determine the domain and range for the area function

Answers

Answer:

The area function is

$A=(135)/(2)x-(9)/(2)x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-(3x)/(2)$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-(3x)/(2)\right)$

$\Rightarrow A=(135)/(2)x-(9)/(2)x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-(2y)/(3)$

$\Rightarrow x<15 m$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=(135)/(2)-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow (135)/(2)-9x=0$

$\Rightarrow x=(15)/(2)$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}<0$ , so, point $x=(15)/(2)$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=(135)/(2)* \frac {15}{2}-(9)/(2)* \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

Final answer:

The area of each pen can be expressed as A(x) = x * (90 - 2x) / 3. The domain of this function is 0 < x < 45, and the range is 0 < A(x) < 300

Explanation:

In this problem, since Pam has to divide the petting zoo into three parts, we can consider the width of each pet pen to be x and the total length of the three pens to be (90 - 2x)/3, given that the total fence is 90m and we have two fences that are x meters long separating the pens. So, the area, A of each pen can be expressed as a function of x: A(x) = x * (90 - 2x) / 3. The domain of this function, or the possible values of x, would be all the values that make the area positive, which are 0 < x < 45. For the range of the function, we analyze the quadratic function which will have a maximum value at x = 15, as the area will be largest when the space is divided evenly, so the maximum area is A(15)= 15 * (60) / 3 = 300. Therefore, the range of the function is 0 < A(x) < 300.

Learn more about Area and Functions here:

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36x^2-21x-30 factor

Answers

Easy...

to even begin to factor..you must factor out a 3, to simplify your answer.

3(12 $x^(2)$ -7x-10)

Now, you can factor.

$3(12 x^(2) -7x-10)$

So..to find the answer...

12*-10=-120x
and
you would use -7x

What multiplies to -120..but adds to -7?

-15*8=-120
and
-15+8=-7

To find the answer, plug in what you know..

3(3x+2)(4x-5)

Thus, your answer.

Ebony walked at a rate of 3 1/2 miles per hour for 1 1/3 hours. how far did she walk?

Answers

Answer:

She walked $4(2)/(3)$ miles

Step-by-step explanation:

Speed of ebony = $3(1)/(2)$ miles/hour

= $(7)/(2)$ miles/hour

Time Taken = $1(1)/(3)$ hours.

= $(4)/(3)$ hours.

We are supposed to find how far did she walk i.e. Distance

Formula : $Distance = Speed * Time$

$Distance = (7)/(2) * (4)/(3)$

$Distance = (14)/(3)$

$Distance = 4(2)/(3)$

Hence she walked $4(2)/(3)$ miles

im wondering the same thing i have this question to

Simplify each equation, then solve. 1) log 2 128=x

Answers

$\log _( 2 ){ 128 } =x\n \n \log _( 2 ){ \left( { 2 }^( 7 ) \right) } =x\n \n 7\cdot \log _( 2 ){ 2 } =x$

$\n \n 7\cdot 1=x\n \n \therefore \quad x=7$

$l[tex]log_(2)128=x\n\n Formula\ for\ log:\nlog_(a)c=b\ \ \ =>\ a^b=c\n\n2^x=128\n\n 2^x=2^7\n\n x=7\n\nSolution\ is\ x=7.$ [/tex]