IM GIVING BRAINIEST TO THE FIRST CORRECT ANSWER !!! HURRY.

What would X is less than or equal to negative 7 look like as a graph

Anastaziya [24]

Answer:

Place a dot on 7 and do < underlined

8 0

2 years ago

The curve

kherson [118]

Answer:

Point N(4, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \sqrt{x - 3}$

$\displaystyle y' = \frac{1}{2}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

Step 3: Solve

Find coordinates

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$

y-coordinate

Substitute in x [Function]: $\displaystyle y = \sqrt{4 - 3}$
[√Radical] Subtract: $\displaystyle y = \sqrt{1}$
[√Radical] Evaluate: $\displaystyle y = 1$

∴ Coordinates of Point N is (4, 1).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

4 0

2 years ago

Derivation of f(x) = x^4 - 8x^2 + 3

weeeeeb [17]

The answer is F(0)=-3

7 0

2 years ago

A kitchen drawer has a Volume 1,125 cubic inches. The drawer is 15 inches long and 5 inches deep. What is the width of the drawe

Temka [501]

Answer:

The width of the drawer is $15\ in$

Step-by-step explanation:

we know that

The volume of the drawer is equal to

$V=LWH$

we have

$L=15\ in$

$H=5\ in$ -----> the deep of the drawer

$V=1,125\ in^{3}$

substitute the given values in the formula and solve for W

$1,125=(15)(W)(5)$

$1,125=(75)(W)$

$W=1,125/(75)$

$W=15\ in$

7 0

3 years ago

The Martin family's truck gets an average of 25 miles per gallon. Predict how many milrs they can drive using 7 gallons of gas.

Hunter-Best [27]

Okay so on average if they can go 25 miles per gallon that would mean you could just multiply 25 and 7 to get 175. So on average they could go 175 miles on 7 gallons of gas. Keep in mind that the answer can and will change depending on traffic, how fast or slow they are going, and if they are traveling behind a big-rig that moves more air that would normally be putting pressure on the car to push out of the way but the big-rig helps save gas but it can also waste more gas if they are driving slower then normal.
Sorry for the extra information once I start it's hard to stop. Any way I hope this helps.

8 0

2 years ago