The length of a rectangle is 2 in longer than its width.
If the perimeter of the rectangle is 68 in, find its length and width.

Use the Chain Rule:

[tex]\frac{d}{dx} [f(g(x))] = f'(g(x)) * g'(x)[/tex]

Given Information:

[tex]f(x) = x^5\\ g(x) = \frac{cos(x)}{1} +sin(x)\\ f(g(x)) = ( \frac{cos(x)}{1} +sin(x))^5\\ \\ f'(x)=5x^4\\ g'(x)=\frac{-sin(x)}{1} + cos(x)\\f'(g(x))*g'(x)=5(\frac{cosx)}{1} + sin(x))^4*(\frac{-sin(x)}{1} + cos(x))[/tex]

The answer is:

[tex]5(\frac{cosx)}{1} + sin(x))^4*(\frac{-sin(x)}{1} + cos(x))[/tex]

Answer:

m-4

Step-by-step explanation:

4 marbles taken away = -4 marbles

Answer:

The equation of a straight line is always

[tex]y=mx+b[/tex]

The constant m always refers to the slope, and the constant b always refers to the y-intercept.

Simply substitute the numbers in:

[tex]y=-\frac{1}{2}x+3[/tex]

There's your equation!

~quadratic equation

======================

2x² + 3x - 20 = 0

= a + b = 3

= ab = 2(-20) = -40

= a = -5

= b = 8

= (2x² - 5x) + (8x - 20)

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

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

= Solution 1 : x = 5/2 ✔️

Solution 2 : x = -4 ✔️

~ nice to help you ^^

[tex]2x^2 +3x -20 =0\\\\\\\implies x = \dfrac{-3 \pm \sqrt{(-3)^2 - 4 \cdot 2 \cdot (-20)}}{2 \cdot 2}\\\\\\\implies x = \dfrac{-3 \pm \sqrt{169}}{4}\\\\\\\implies x = \dfrac{-3\pm 13} 4 \\\\\\\text{Hence} \\\\x = \dfrac{-3+ 13}{4} = \dfrac{10} 4 = \dfrac{5}2\\\\\text{Or}\\\\x= \dfrac{-3-13}4 = -\dfrac{16}4 =-4[/tex]

Answer:

30 dinner rolls

Step-by-step explanation:

There are 5 dinner rolls per basket and there are 6 baskets

So there are 6 groups of 5:

5 + 5 + 5 + 5 + 5 + 5

In other words, multiply 5 and 6

5 dinner rolls x 6 = 30 dinner rolls

Answer:

y = mx + c ......( general form)

y = -1/5X - 3

Option D

step by step explanation:

[tex] \sf f(x) = \sqrt[3]{x + 10} \\ \sf y = \sqrt[3]{x + 10} \\ \sf y = \sqrt[3]{y + 10} \\ \sf y = {x}^{3} - 10 \\ \sf {f}^{ - 1} (x) = {x}^{3} - 10[/tex]

The inverse of the given function is represented as f' ( x ) = x³ - 10

A function is a mathematical object that takes an input (or several inputs) and produces an output. The rule of a function describes how the input is transformed to produce the output. It can be written using mathematical notation, words, or a combination of both.

Functions are used in many areas of mathematics, science, engineering, and other fields to model relationships between variables, make predictions, and solve problems.

Given data ,

Let the function be represented as A

Now , the value of A is

Now , the function is depicted as f ( x ) = ∛( x + 10 )    

Simplifying results in

The function's inverse is obtained by swapping the x and y variables.

So ,

y = ∛( x + 10 )

x = ∛( y + 10 )

On solving for y , we get

y = x³ - 10

And , the inverse is f' ( x ) = x³ - 10

The function is therefore f' (x) = x³ - 10.

Go here to read more about the function rule.

https://brainly.com/question/3760195

#SPJ7

Answer:

12

Step-by-step explanation:

20% is 20/100 = 0.2

60% is 60/100 = 0.6

So 20% of 60%= 0.2*0.6=0.12

0.12 in % = 0.12*100 = 12%

Yes i know… Math sucks

Anyways have a great day and if its correct please give brainliest

Stay Safe And Healthy

Thank you

Answer:

I will cryy because I only want to write 78 why it recorded as 98

Answer:

2

Step-by-step explanation:

7. The zeros of the quadratic function described by the graph below is

1

A. 2,1

B. -2,1

C. 2,-1

D. -2,-1

Answer:

Yes.

Step-by-step explanation:

Answer:

0.006%

Step-by-step explanation:

minused old price from the new one and then divided the answer by the old price

Answer:

[tex]x = \frac{70 + \sqrt{900} }{50}\\[/tex] or [tex]x = 2[/tex]

Or:

[tex]x = \frac{70 - \sqrt{900} }{50}\\[/tex] or [tex]x = \frac{4}{5}[/tex]

Step-by-step explanation:

Step 1 - Simplify by expanding the brackets:

[tex](5x - 7)^2\\(5x - 7)(5x - 7)\\25x^2 - 35x - 35x + 49\\25x^2 - 70x + 49 - 1\\25x^2 - 70x + 48 = 8[/tex]

Step 2 - Subtract 8 from both sides so the equation equals 0:

[tex]25x^2 - 70x + 48 - 8 = 8 - 8\\25x^2 - 70x + 40 = 0[/tex]

Step 3 - Use the quadratic formula:

[tex]x = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}\\a = 25\\b = -70\\c = 40[/tex]

Plug variables in:

[tex]\frac{-(-70) +- \sqrt{(-70)^2 - (4 * 25 * 40)} }{2 * 25}[/tex]

[tex]\frac{70 +- \sqrt{4900 - 4000} }{50}\\\\\frac{70 +- \sqrt{900} }{50}\\[/tex]

So x is either:

[tex]x = \frac{70 + \sqrt{900} }{50}\\[/tex]

[tex]x = 2[/tex]

Or:

[tex]x = \frac{70 - \sqrt{900} }{50}\\[/tex]

[tex]x = \frac{4}{5}[/tex]

Hope this helps!

Answer:

178

Step-by-step explanation:

All right!!

Line l is parellel to line m.

So if r is 91 then we can infer that s helps it make a 180 degree angle/straight line.

So 180 - 91 = 89

s = 89

If the two lines are parallel then s = u because of inner angles/outer angles stuff.

If s=u then u = 89 as well.

And because of vertical angles, t =u so t = 89.

Now the question asks to find t + u, so t + u = 89 + 89 = 178

Hope that helps!!

ATQ

[tex]\\ \tt\longmapsto 2(x+6x)=1190[/tex]

[tex]\\ \tt\longmapsto 2(7x)=1190[/tex]

[tex]\\ \tt\longmapsto 7x=595[/tex]

[tex]\\ \tt\longmapsto x=595/7[/tex]

[tex]\\ \tt\longmapsto x=85[/tex]

Answer:

The answer is A

Step-by-step explanation:

0.2% of 500 is 1 so in two year she would have 502$

Answer:

They are equal, so =

Step-by-step explanation:

We know that one-half is .50.  3/2 is an improper fraction and when we solve to a decimal, we get 1.5.  

Answer:

10 times for each number

Step-by-step explanation:

:)

Answer:

10

Step-by-step explanation:

if the dice is fair, the sides will land one time every 8, so if its rolled 80 time, and it was equal 10 would be your answer.

Answer:

They are not.

Step-by-step explanation:

Let's first calculate the vectors joining the first point to the second and the first to the third, they will be useful later.

[tex]\vec v_1_2 = \vec P_2 -\vec P_1 = <3; -7; -7>\\\vec v_1_3= \vec P_2 -\vec P_1 = <6; -14; -13>[/tex]

At this point we have at least three options:

Write down the line between P1 and P2 in vector form, and then see if we can fit the third point in there.

Calculate the cross product between the two, if it's non-zero the three point are not in a line.

Try to determine the plane passing for the 3 points: if we find one they are not in a line.

Option 1:

The vector form of the lne between the firs two points is [tex]<6+3t;9-7t;7-7t>[/tex]. Let's check the coordinates of the third point:

[tex]x_3:\ 6+3t= 12 \rightarrow t=2\\y_3:\ 9-7t = -5 \rightarrow t =2\\7z_3:\ 7-7t=-6 \rightarrow t = 13/7\ne 2[/tex]

So the three points are not in a line.

Option 2:

Let's calculate the cross product of the two vectors we found at the beginning.

[tex]\vec v_1_2 \times \vec v_1_3 = det \left[\begin{array}{ccc}\hat i&\hat j&\hat k\\3&-7&-7\\6&-14&-13\end{array}\right] = \hat i [-7(-13)-(-14)(-7)] - \hat j[3(-13)-6(-7)]+\hat k [3(-14)-6(-7)] = 7\hat i -3 \hat j + 0 \hat k \ne 0[/tex]

Since the result is not the null vector, the three points are not in a line.

Option 3:

Let's write the plane (in the [tex]z= ax+by+c[/tex] form that contain the three points. If the thre points are in a line, means that we can find only two of these parameters.

[tex]P1: 7= 6a+9b+c\\P2: 0= 9a+6b+c\\P3: -6= 12a-5b +c[/tex]

Since you can determine a, b and c ( I ended up with [tex]a=-\frac {10}3; b=-\frac18; c= \frac{123}8[/tex] but I probably messed something in there) the thre points are not in a line

alternate entireror angles are congurent by this rule you can find your answer by solving the equation

Jeremy is incorrect because a negative plus a negative will always be a negative.

Answer:

Step-by-step explanation:

Needs a picture to be solved, please put one.

Answer:

i know

Step-by-step explanation:

I know have a amazing day

Answer:

A, C, D

Step-by-step explanation:

All of the plot curves contain (0, -8) and (-2, 0)

B doe NOT contain (-3, 4), though the plot lines seem kind of fuzzy and other curves may miss, but not by much.

Answer:

Graph A , B, and D

Step by-step explanation:

All the points are one these three graphs.

Answer:

At the store the ratio of books sold to movies sold was 4:5.For every 4 books sold there were 5 movies sold.

Step-by-step explanation:

Answer:

Drayven has more

Step-by-step explanation:

If you look at the fractions through a drawing you would see that my claim is correct.

Answer:

The correct answer is "Option A".

Step-by-step explanation:

Hope this helps :)