If p(x) = b² - 16b +32 and q(x) = -32b-32 what values of x does p(x)=q(x)?

The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is given by

y' = -1/[(1 + x)²× √[(1 - x)/(1 + x)]].

To find the derivative, we use the chain rule. The derivative of the outermost function, arctan, is

1/[1 + (√[(1 - x)/(1 + x)])²], and the derivative of the innermost function, the square root, is

-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]. Multiplying these two derivatives together gives us the final result.

1/[1 + (√[(1 - x)/(1 + x)])²]×-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]

=-1/[(1 + x)²× √[(1 - x)/(1 + x)]].

When we take the derivative of a function, we are essentially finding the slope of the tangent line of a function at a given point. This derivative will tell us the rate at which y changes with respect to x. The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is a negative value, which means that as x increases, y decreases. Therefore, this function has a negative slope.

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Answer:

3014.4

Step-by-step explanation:

Answer:

business plan proposal

Answer:

we have to make the denominator of both the fraction same so that we can compare.

We have to multiplybboth nominator and denominator by 6.then,

7×6/4×6=28/16

Now, comparing 28/6 and 28/6 we get to know that both the fraction are proportional.i.e.28/16=7/4

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Answer:

Ok ill find the slope for this graphhhhh

Step-by-step explanation:

-3/4

Answer:

x = -4

y = 29

Step-by-step explanation:

Let's take our two equations and turn the decimals into fractions for simplicity's sake. We get:

x/4 + 5y/100 = 9    x + y = 25

Simplifying a bit gives us:

x/4 + y/20 = 9       x + y = 25

Now, we will take the first equation and multiply it by 20 to get rid of the fractions. We get:

5x + y = 9

We will rearrange numbers to give us an answer to y that we can substitute in. we get:

y = 9 - 5x

Then, we will plug this into our second equation giving us:

x + 9 - 5x = 25

Combining like terms and subtracting 9 from both sides gives us:

-4x = 16

Dividing by -4 gives us:

x = -4

Then, we can substitute this into our second equation giving us:

-4 + y = 25

We will add 4 to both sides giving us:

y = 29

Hope this helped!

Answer:

b

Step-by-step explanation:

The range of the function g(x) = 3|x-1| - 1 by evaluation is; [-1,00].

From the taks content, the function given is;

Hence, it follows that the lowest possible value of y is -1 by means of the absolute value sign in the equation.

The range is therefore; [-1, 00].

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Answer:

c=2,25

Step-by-step explanation:

c4=5+4

c4=9

c=9:4

c=2,25

Answer:

c=4

Step-by-step explanation:

4c-5=4

/4         /4

c-5=1

+5    +5

c=6

In this case I believe you would add 25 to both sides. The -25 +25 would cancel out and then +25 would be on the right.

For the curve [tex]x^{2} +xy+y^{2} = 27[/tex] , the line tangents to the curve at the x intercepts of the curve are parallel .

The Slope of tangent line to a function at any point is denoted by [tex]\frac{dy}{dx}[/tex] .

The Curve is given as ⇒[tex]x^{2} +xy+y^{2} = 27[/tex] ;

On differentiating both sides of the curve with respect to "x"  ,

we get ;

the slope of the line as ⇒ [tex]Slope = \frac{dy}{dx} = -\frac{2x+y}{x+2y}[/tex] ;

Now for the  x- intercepts , the value [tex]y = 0 ,[/tex]

On substituting [tex]y=0[/tex] in the curve [tex]x^{2} +xy+y^{2} = 27[/tex] ,

we get ;

[tex]x^{2} +x(0)+0^{2} =27[/tex]

On simplifying further ,

we get ;

[tex]x=\pm 3\sqrt{3}[/tex] ;

So , the two x intercepts of the curve are [tex](3\sqrt{3},0)[/tex] and [tex](-3\sqrt{3},0)[/tex] ;

to find the slopes , we substitute the values in the slope equation .

On substituting the values in the slope equation ,

we get ;

[tex]Slope_{(3\sqrt{3} ,0)} = -\frac{2(3\sqrt{3}) +9}{3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex]  and

[tex]Slope_{(-3\sqrt{3} ,0)} = -\frac{2(-3\sqrt{3}) +9}{-3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex].

we see that the slope at both the intercepts is same ,

Therefore , the lines tangents of the curve at the x intercepts are parallel .

The given question is incomplete , the complete question is

Consider the curve defined by [tex]x^{2} +xy+y^{2} = 27[/tex] . Determine whether the lines tangent to the curve at the x - intercept of the curve are parallel .

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Answer:

-1764

Step-by-step explanation:

use BODMAS rule

⇒7{-7+8[5-3(4+6)]-9(9-4)}

solve round brackets

⇒7{-7+8[5-3(10)]-9()}

multiply 3 by 10 within the square bracket

⇒7{-7+8[5-30]-9(5)}

solve square bracket

⇒7{-7+8[-25]-9(5)}

move to curly brackets and multiply first

⇒{-7-200-45}

subtract

⇒7{-252}

multiply

⇒-1764 Answer

hope that helps...

The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.

a = 10

The common difference r = 60/10 = 6

As we know the general formula of the nth term of a geometric series is

aₙ = a × [tex]r^{n-1}[/tex]

Now, put the values of a = 10, r = 6 and n in the general formula,

aₙ = 10 × [tex]6^{n-1}[/tex]

Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

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Answer:

where the image??

Step-by-step explanation:

Answer:

the formula is

Step-by-step explanation:

a + b + c = P  ( P= perimeter )

The fifth term of the given arithmetic sequence is 36.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d

Given that, in a sequence the first term of 4 and the common difference is 8.

Here, a=4 and d=8

Now, the fifth term is

a₅=4+(5-1)×8

= 4+32

= 36

Therefore, the fifth term of the given arithmetic sequence is 36.

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Answer:

see image

Step-by-step explanation:

Right at the point (1,2) there's a nice point. Going up and right along the line there's another nice point at (5,5)

To get from one point to the next, you can draw a stair-step line that goes up3 and over4. The slope is up3/over4.

m = 3/4

The slope is 3/4. See image.

Answer:

x + y = 180

y + 6 = x

The total number of students on the honor roll increased by 20%.

Given that, 75 boys and 50 girls on the honor roll

=> boys increased by 24% =  75*24/100  = 18

So, the number of boys is increased by 18.

=> girls increased by 14% =  50*14/100  = 7

So, the number of girls is increased by 7.

After the increment, the number of boys and girls on the honor roll is 93 and 57, respectively.

Thus, the total number of students increased = 18+7 = 25

Therefore, the percentage increment in total = 25 / 125 * 100 = 20%

Hence, The total number of students on the honor roll increased by 20%.

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Answer:

24.36m²

Step-by-step explanation:

area = ½×(8.9+2.7)×4.2= ½×48.72=24.36m²

Answer:

-17h-36 is your answer

Step-by-step explanation:

3(-7h-4) +4 (h-6)

-21h-12+4h-24

-17h-36

a) The data on the y-axis: the numbers of people in each salary category.

b) The data on the x-axis: salaries

c) The distribution of salaries is skewed to the right.

We know that a histogram is a graph in which the x-axis is a quantitative variable split into bins, and the y-axis is the frequency.

For given distribution of salaries for individuals, the Y-axis would have the frequency i.e., the numbers of people in each salary category.

And x-axis would have income, because this is out quantitative variable of interest.

consider the following histogram.

We can observe that the graph of distribution of salaries is skewed to the right, because most income data are positively skewed. There would be a substantial number of individuals at or near the lowest salary level, but some people make a tremendously high salary.

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this is a question of set of equations and solution is as follows,

Williamston Daily newspaper started printing newspaper.

Three years ago they had 5900 subscribers.

every month there is an increase of 66 new subscribers.

n is the number of months the paper has been printed.

so, the linear model will be  

B= early subscriber + number of month × increments

B= 5900 + n × 66

B= 66 n + 5900

Example - subscribers after 3 months,

n = 3

= 66 x 3 +5900

= 198 + 5900

= 6000

set of equations

A system of equations is a set or collection of equations that you deal with all together at once. Linear equations are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.

Linear equations

Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

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Answer:

C

Step-by-step explanation:

The volume is (6*12*5 1/4). Since 6*12 is 72, this is equal to 72*(5 1/4).

Answer:

625

Step-by-step explanation:

1.25.625

125 = 5³

625 = 5⁴

prime factor 5 , number 125 is 3 number 625 is 4 LCM is 4

LCM = 5⁴

so the LCM is 625

Answer:

94 inches

Step-by-step explanation:

first calculate the surface area of the side of the container by multiplying 20.5 by 12, then take that number and divied 23124 by it to see how many inches of sides you need to make 23124

another way to explain it, multiply 20.5 by 12 to get the surface area of a plane, then divide 23124 by the surface area fo the plane to get how many inches of planes you have to have in order to have 23124 inches of total space

if you have any questions, leave them in the comments and i will try to answer them, if this helped, pls give brainliest

The two lines are neither parallel nor perpendicular to each other.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the two equations of the lines are y= -1/3x+2 and 5y+15x=-40.

y= -1/3x+2

5y+15x=-40.

5y = -15x - 40

y =-3x - 40/3

Here the slopes of the lines are,

m₁= -1 / 3

m₂ = -3

For the lines to be parallel the slopes should be equal and for the lines to be perpendicular the slopes should be inverse and reciprocal.

Here the slopes are neither equal nor have the inverse reciprocal.

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Answer:

I believe the correct answer is D

= (7⁵ × 7ⁿ)⁴ = (7¹⁶/7ⁿ)³

= (7²⁰ × 7⁴ⁿ) = (7¹⁶ × 7-ⁿ)³

= 7²⁰⁺ ⁴ⁿ = 7⁴⁸ ⁻ ³ⁿ

= 20 + 4n = 48 - 3n

= 20 - 48 = -3n - 4n

= -28 = -7n

= -28/-7 = n

= 4 = n

_____________

If you have any doubt,let me know in comments :D

Answer:

(x + 2)² + (y - 4)² = 16

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (- 2, 4 ) and r = 4 , then

(x - (- 2))² + (y - 4)² = 4² , that is

(x + 2)² + (y - 4)² = 16

Answer:

7.5

Step-by-step explanation: