MATHEMATICS HIGH SCHOOL

Simplify (b^(9))/(b^(11)) and write answer using only positive exponents

Answers

Answer 1

Answer:

Answer:

1/(b^2)

Step-by-step explanation:

using exponential rules, we know that the problem can be simplfied by subtracting the exponents

b^(11-9)

b^(-2)

which then just simplifies to

1/(b^2)

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2(1/2q+1)=−3(2q−1)+8q+4 .

Answers

Answer:the answer is 7

Step-by-step explanation: 7d9wid9

I need help pls, i would appreciate it !!

Answers

Answer:

a. x = 1.2, b. A = 32.1°

Step-by-step explanation:

1.41²-.75²=x²

a. x = 1.2

sin A = 0.75/1.41

b. A = 32.1°

The endpoints of GE are located at G(–6, –4) and E(4, 8). Using slope-intercept form, write the equation of GE.

Answers

The equation of the line in slope-intercept form is:

Where,

m: slope of the line

b: cutting point with the y axis.

For the slope of the line we have:

$m=(y2-y1)/(x2-x1)$

Substituting values we have:

$m=(-4-8)/(-6-4)$

Rewriting we have:

$m=(-12)/(-10)$

$m=(6)/(5)$

Then, we choose an ordered pair:

Substituting values in the generic equation of the line we have:

$y-8 = (6)/(5) (x-4)$

Rewriting we have:

$y = (6)/(5)x -(24)/(5) + 8$

$y = (6)/(5)x -(24)/(5) + (40)/(5)$

$y = (6)/(5)x + (16)/(5)$

Answer:

The equation of the line in slope-intercept form is:

$y = (6)/(5)x + (16)/(5)$

Answer:

y = $(6)/(5) x + (16)/(5)$

Step-by-step explanation:

The slope-intercept form is y = mx + b, where "m" is the slope and 'b" is the y-intercept.

Given: G(-6, -4) and E(4, 8)

Now we can use these points G(-6, -4) and E(4, 8) and find the slope.

Slope (m) = $(y2 - y1)/(x2 - x1)$

Here x1 = -6, y1 = -4, x2 = 4 and y2 = 8

Plug in these values in the above formula, we get

slope(m) = $(8 - (-4))/(4 -(-6))$

= $(12)/(10)$

Slope (m) = $(6)/(5)$

Now we can use the formula (y - y1) = m(x - x1) and find the required equation.

We can plug in m value and (x1, y1) value and find the equation.

y - (-4) = 6/5(x - (-6))

y + 4 = 6/5(x + 6)

Using the distributive property a(b + c) = ab + ac, we get

y + 4 = 6/5 x + 36/5

y = 6/5 x + 36/5 - 4

y =6/5 x +( $((36 - 20))/(5)$

y = $(6)/(5) x + (16)/(5)$

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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What is the value of x? 2/3(x-6)=6

Answers

Answer: x=15

Step-by-step explanation: THIS IS THE CORRECT ANSWER

5x^3+15x^2+10x please help with this I need to see how its worked out not just the answer I no the answer just don't no how to work out the problem

Answers

hi!

5x^3+15x^2+10x = 0

x(5x^2+15x+10) = 0

=> x=0

5x^2+15x+10=0

5(x^2+3x+2)=0

=> (x+1) (x+2) = 0

x= -1 , x= -2

it has three answers, hope im right :)

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