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ArbitrLikvidat [17]

4 years ago

11

Determine the standard form of the equation of the line that passes through (-6, 6) and (3, -2). A. -8x + 9y = -6 C. -8x -9y = 6

B. 8x + 9y = 6 D. 9x - 8y = 6

1 answer:

d1i1m1o1n [39]4 years ago

5 0

Answer:

B. 8x + 9y = 6

Step-by-step explanation:

You can eliminate answer choices A and C because their leading coefficient is negative. In standard form, the leading coefficient is positive.

For the remaining two equations, you can check to see if the given points are on the line

B: for point (-6, 6), we want 8(-6) +9(6) = 6 . . . true

for point (3, -2), we want 8(3) +9(-2) = 6 . . . . true

The appropriate equation is 8x +9y = 6.

D: (we don't need to check to know it won't work after the above)

__

The equation in standard form, can be written from ...

(Δy)(x -a) = (Δx)(y -b) . . . . . for some point (a, b)

The values of Δx and Δy are the differences between corresponding coordinates.

Δy = 6 -(-2) = 8

Δx = -6 -3 = -9

For point (-6, 6), the above equation becomes ...

8(x +6) = -9(y -6)

8x +48 = -9y +54 . . . . eliminate parentheses

8x +9y = 6 . . . . . . . . . . add 9y-48

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andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

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:

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

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

Now, from equation (i)

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

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

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

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

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [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 $x$ .

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

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

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

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

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

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

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

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

$\Rightarrow A=253.125 m^2$

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

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4 years ago

Under a microscope, ms. kapinski studies a culture with bacteria. as the number of hours progresses, ms. kapinski sees that the

velikii [3]

Answer:

Study 1 Answers:

1) 0.76 represents the multiplier of the bacteria, in this case it is decreasing by 24% because the formula for exponential decay is 1 - r.

2) 1290 represents the initial value, or before the study began.

Study 2 Answers:

1) 1180 is the initial value, or before the study began.

2) Study 1 started with more bacteria

3) Study 1 is experiencing exponential decay, while study 2 is experiencing exponential growth

Step-by-step explanation:

Exponential functions are in the form $y=a(b)^x$ , where a is the initial value, b is the multiplier, and x represents inputs, such as hours after a bacteria study.

Any multiplier above 1.00 is experiencing exponential growth, meaning it grows gradually over time, and any multiplier below 1.00 is experiencing exponential decay, meaning it decreases in population over time.

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Answer:

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Step-by-step explanation:

pa brainlest na lang po ty po

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Sonia finished the 200-meter dash in 26.12 seconds. Gladys finished the 200-meter dash 1.08 seconds

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Answer:

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Step-by-step explanation:

26.12-1.08

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3 years ago

Read 2 more answers

The area of the square, the

const2013 [10]

Answer:

B.

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.

Please have a look at the attached photo.

My answer:

As given in the question, we know that:

The ratio of the area of the circle to the area of the square is π/4

The formula to find the volume of the cone is:

V = 1/3*the height*the base area

<=> V1 = 1/3*h*π $r^{2}$

The formula to find the volume of the pyramid is:

V2 = 1/3*the height*the base area

<=> V = 1/3*h*4 $r^{2}$

=> the ratio of volume of the cone to the pyramid is:

= $\frac{V1}{V2}$

= (1/3*h*π $r^{2}$ ) / ( 1/3*h*4 $r^{2}$ )

= π/4

S we can conclude that the volume of the cone equals π/4 the volume of the pyramid

Hope it will find you well.

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3 years ago