Given y = f(u) and u=g(x), find =f(g(x))g'(x) for the following functions.
dx
y = cos u, u = 4x - 3
dy
dx = f'(g(x))g'(x) = 0

Answer:

The slope of the perpendicular line is 2/5.

Step-by-step explanation:

We want to find the slope of the line that is perpendicular to the line that passes through the points (-1, 6) and (3, -4).

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

Find the slope of the original line:

[tex]\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{(-4)-(6)}{(3)-(-1)}=\frac{-10}{4}=-\frac{5}{2}[/tex]

The slope of the perpendicular line will be its negative reciprocal.

Thus, the slope of the perpendicular line is 2/5.

The slope of the line perpendicular to the line through the points (-1,6) and (3,-4) is -5/2.

We have to find the slope of the line perpendicular to the line through the points (-1,6) and (3,-4).

using the formula;-

m = (y²-y¹) / (x²-x¹)

Where,

plug the value and simplify.

m = ( (-4 ) - 6)/(3 - (- 1)

m = - 10 / 4

m = - 5/2

Hence, The slope of the line perpendicular to the line through the points (-1,6) and (3,-4) is -5/2.

Step-by-step explanation:

X-1/X=3

X-1=3×X

X-1=3X

-3X+X=1

-2X=1

X=1/2 Answer

Answer:

Daylily: $9

Geranium: $2

Step-by-step explanation:

1 daylily costs x.

1 geranium costs y.

11x + 4y = 107

4x + 12y = 60

Multiply the first equation by 3 and subtract the second equation from it.

29x = 261

x = 9

4x + 12y = 60

4(9) + 12y = 60

12y = 24

y = 2

Answer:

Daylily: $9

Geranium: $2

Answer:

1) Set up a system of equations. Assign each plant a variable. I used X for Daylillies and Y for Geraniums. In this case:

11x + 4y = 107

4x + 12y = 60

2) Get one variable by itsef. You can choose to either get the X or the Y by itself. For the sake of ease, I'll go with achieving X.

3) Using the equation 4x + 12y = 60, isolate the 4x.

4x = -12y + 60

4) Divide both sides by 4.

x = -3y + 15

5) X is isolated. Now plug in that isolated X into another remaining equation in order to isolate Y. Don't forget to combine like terms.

11(-3y + 15) + 4y = 107

-33y + 165 + 4y = 107

-29y + 165 = 107

-29y = -58

y = 2

6) You have your Y, which means that each Geranium costs $2 each. Now, you need to find X. Plug in Y into any of the first two equations that we started with.

4x + 12(2) = 60

4x + 24 = 60

4x = 36

x = 9

7) You now have both X and Y. Daylillies cost $9 each, and Geraniums cost $2 each.

8) You can double-check your answers by plugging in your final X and Y values into any of the first equations you wrote. If it comes out equal, it works.

Answer:

29%

Step-by-step explanation:

First, let's fill in the table.

Male:

Freshmen: 4

Sophomore: 6

Juniors: 2

Seniors: 2

Total: 4 + 6 + 2 + 2

Total: 14

Female:

Freshmen: 3

Sophomore: 4

Juniors: 6

Seniors: 3

Total: 3 + 4 + 6 + 3

Total: 16

Now, to find the probability that a male would be a freshmen, we would do:

4/14

Convert it to a decimal:

.285

Convert to percentage:

29%

So, there is a 29% chance that a male is a freshmen.

Answer:

(x+5) (x^2+5)

Step-by-step explanation:

x^3+5x^2+3x+15

Using factoring by grouping

x^3+5x^2     +3x+15

x^2(x+5)   + 3(x+5)

Factor out (x+5)

(x+5) (x^2+5)

Answer:

( x + 5 ) (x² + 3)

Step-by-step explanation:

x³ + 5x² + 3x + 15

factor out x²

x² ( x + 5 ) + 3x + 15

factor out 3

x² ( x + 5 ) + 3 ( x + 5 )

factor out x + 5 from the expression

( x + 5 ) (x² + 3)

1.f(0) = 6

2.f(4)=5

3.f(-3)=-5

4. V(r) represent volume of basketball when radius is r

5.f(9) =5

Answer:

Step-by-step explanation:

1.

[In the attachment]

2.

again taking 4 as x and 5 as y.

since,

y = f(x)

5 = f(4)

that is option 3.

3.

x = -3

y = -5

y = f(x) = -5

f(-3) = -5

1st option

4.

V(r) = 4/3 pi r³

here the ou.tput is V(r) when the input is r.

and since V(r) denotes volume of air inside the basketball

V(r) is the volume of basketball when the radius is r.

that is option 2.

5.

given that:-

x = 9, f(x) = 5

•°• f(9) = 5

that is the 1st option

What is mean: A mean is the simple mathematical average of a set of two or more numbers. To solve for it add all numbers together then divide by how many numbers are there. (Its best to put them in order)

$40 + $40 $60 + $80 + $100= $320/5= $64 is the mean

what is median: The median is the value separating the higher half of a data sample

40,40,60,80,100 (i like to cross it out so 40 and 100 cancle each other, another 40 and 80 cancel each other) now that you are left with only 1 number which is 60 that is the median.

What is Mode: the number that repeats the most

Mode is 40 because 40 repeats twice

Given:

The minimum and maximum distance that the dog may be from the house can be found by using the equation:

[tex]|x-500|=8[/tex]

To find:

The minimum and maximum distance that the dog may be from the house.

Solution:

We have,

[tex]|x-500|=8[/tex]

It can be written as:

[tex]x-500=\pm 8[/tex]

Adding 500 on both sides, we get

[tex]x=500\pm 8[/tex]

Now,

[tex]x=500+8[/tex] and [tex]x=500-8[/tex]

[tex]x=508[/tex] and [tex]x=492[/tex]

The minimum distance is 492 meters and the maximum distance is 508 meters.

Therefore, the correct option is C.

Answer:

The answer is 32.

Step-by-step explanation:

Just multiply the height by the base length. 4*8=32

Answer:

1500

Step-by-step explanation:

The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,

[tex]\implies 360m^2 = 360 \times 10^4 \ cm^2 [/tex]

And , the number of tiles required will be ,

[tex]\implies n =\dfrac{Area \ of \ floor}{Area \ of \ a \ tile }\\\\\implies n =\dfrac{ 360 \times 10^4 \ cm^2}{240 cm^2} \\\\\implies \underline{\underline{ n = 1,500 }}[/tex]

Hence the required answer is 1500 .

Answer:

D

Step-by-step explanation:

(4ab)^2 = 4^2a^2b^2 = 16a^2b^2

Answer:

6 trials

Step-by-step explanation:

The number of rats that run the maze incorrectly after t trials ;

N(t) = 100e^-0.14t

Initial number of rats = 100

45% of rats to run the maze incorrectly ; 45% * 100 = 45 rats

N(t) = 45

N(t) = 100e^-0.14t

45 = 100e^-0.14t

45/100 = e^-0.14t

0.45 = e^-0.14t

Take the In of both sides :

In(0.45) = In(e^-0.14t)

- 0.798507 = - 0.14t

Divide both sides by -0.14

- 0.798507 / - 0.14 = - 0.14t / - 0.14

5.7036 = t

To the nearest whole number :

Number of trials, t = 6 trials

Answer:

100 degrees

Step-by-step explanation:

You can tell by just looking at the picture :)

Answer:

slope = [tex]\frac{6}{7}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (8, 8)

m = [tex]\frac{8-2}{8-1}[/tex] = [tex]\frac{6}{7}[/tex]

Answer:

5 in

Step-by-step explanation:

by doing a proportion of 2/4 for the known sides, you can find that the smaller triangle has sides that are half of the larger one. so 10/2 equals 5

Answer: X = 5

Step-by-step explanation:

4 divided by 2 = 2

So 10 divided by 2 = 5

Answer:

c = - 4

Step-by-step explanation:

Nothing else matters except that the number associated with the y value in equation one = 1 and the number in front of x is known in equation 1. Then we'll get around to looking at c

Add 2y to both sides of equation 1 (the top equation)

3x - 2y + 2y = 3 + 2y

3x = 2y + 3        

Now divide both sides of the equation by 2

3x/2 = y + 3/2

What's in front of x? It is (3/2)

So divide both sides of 6x + cy = 4       by c

6x/c + y = 4/c

Now put 6x/c on the right hand side so y is by itself.

y = -6x/c + 4/c

What do you have to do now?

You must equate -6x/c = 3/2x

Why?

The slopes have to be the same so the lines are parallel and never cross. That will give no solutions.

-6x/c = 3x / 2     Divide both sides by x

-6/c = 3/2           Cross multiply

3c = - 6 * 2        Combine

3c = - 12             Divide by 3

c = - 12/3

c = - 4

Answer:

x = π/4 and 5π/4

Step-by-step explanation:

Given the expression;

2cos²x - 1 = 0

2cos²x = 0+1

2cos²x = 1

cos²x = 1/2

cos x = ±√1/2

cos x = ±0.7071

x = arccos(±0.7071)

x = ±45 degrees

Convert to radians

Sence 180° = π rad

45°  = x

x = 45π/180

x = π/4

If x = -45°

Since cos is negative in the 3rd quadrant

x = 180 + 45

x = 225°

x = 225π/180

x = 45π/36

x = 5π/4

Answer:

45 x 56=

2520 and

5 x 7=35*8=280*9=2520

2520=2520

Hope This Helps!!!

Answer:

2402 people.

Step-by-step explanation:

Since a basketball court measures 998 inches on the sides while the baseline stretches 700 inches, and there is a circle in the middle of the court that has a diameter of 72 inches, and the team can fit 14 people in the circle at one time To determine how many people can fit on a court, the following calculation must be performed:

Area of a circle:

3.14 x (72/2) ^ 2 = X

3.14 x 36 ^ 2 = X

3.14 x 1.296 = X

4,069.44 = X

Area of a rectangle:

998 x 700 = X

698,600 = X

4,069.44 / 14 = 290.67

698,600 / 290.67 = 2,402

Answer:

11x + 8 = 12x - 4

x=12

∠ 4 = 180-140 = 40°

Step-by-step explanation:

Answer:

I think album is another name of CD.

When both sides of the equation are simplified, the coefficients are the same.

Step-by-step explanation:

An equation has infinite solutions when both sides of the equation are simplified, the coefficients are the same

Answer:

The answer is A.

Answer:

Step-by-step explanation:

Givens

Let the number in the Spanish Class = x

Then the number in the Geometry Class = (4/5) x

Equation

x + (4/5)x < 54

Solution

x + (4/5)x < 54

4/5 = 0.8

x + 0.8x < 54

1.8x < 54                    Divide both sides by 1.8

1.8x / 1.8 < 54/1.8

x < 30

The sign used in the equation is less than, not less than or equal to.

The number of students taking Spanish cannot equal 30. There must be 29 in the Spanish Class.

Note: There must be -4 instead of 4 otherwise all options are incorrect.

Given:

A polynomial function has a leading coefficient of 3 and roots -4, 1, and 2, all with multiplicity 1.

To find:

The polynomial function.

Solution:

The general polynomial function is defined as:

[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]

Where, a is the leading coefficient, [tex]c_1,c_2,...,c_n[/tex] are the zeros  with multiplicity [tex]m_1,m_2,...,m_n[/tex] respectively.

It is given that a polynomial function has a leading coefficient of 3 and roots 4, 1, and 2, all with multiplicity 1. So, the polynomial function is defined as:

[tex]P(x)=3(x-(-4))^1(x-1)^1(x-2)^1[/tex]

[tex]P(x)=3(x+4)(x-1)(x-2)[/tex]

Therefore, the correct option is A.

Answer:

The three Rational between 3 and 4

A rational number between 3 and 4 is 1/2 (3 + 4) = 7/2. Hence, 13/4, 7/2 and 15/4 are the three rational numbers lying between 3 and 4.

Step-by-step explanation:

Answer:

Multiplication property of the equality

7m + 12 = -4m + 78

7m + 4m = 78 - 12

11m = 66

m = 6

I hope you understand...

Mark me as brainliest...

Hello!

7x + 6x = 52 <=>

<=> 13x = 52 <=>

<=> x = 52 : 13 <=>

<=> x = 4 => 7 × 4 + 6 × 4 = 52

Good luck! :)

Answer:

[tex](2 {a}^{2} + 1)(1 {a}^{2} + 9)[/tex]

Step-by-step explanation:

[tex]2 {a}^{4} + 19 {a}^{2} + 9 \\ 2 {a}^{4} + {a}^{2} + 18{a}^{2} + 9 \\ {a}^{2} (2 {a}^{2} + 1) + 9(2 {a}^{2} + 1) \\ (2 {a}^{2} + 1)( {a}^{2} + 9) \\ [/tex]