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2 years ago

Convert the following measurements into

Mathematics

1 answer:

Andre45 [30]2 years ago

6 0

Answer:

1) 1076.4ft^2

2). 6561.68ft

3). 2.057kg

4). 1.25×10^-1

5). 6.58×10^1km

6). 278mg

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Brenda is cooking couscous. The recipe says she requires 480 grams of couscous for 4 people. How many will she need for 14?

Nimfa-mama [501]

Answer:

1,680 grams

Step-by-step explanation:

To solve this, we can create a proportion using this setup:

grams/people=grams/people

The recipe needs 480 grams for 4 people and x (unknown-what we are trying to find) grams for 14 people.

480 grams/4 people=x grams/14

480/4=x/14

Now, we have to solve for x-the grams needed for 14 people. To do this, we have to get x by itself. x is being divided by 14. To undo this, multiply both sides by 14, because multiplication is the opposite of division.

14(480/4)=(x/14)14

14(480/4)=x

14*120=x

1680=x

She needs 1,680 grams of couscous for 14 people.

8 0

3 years ago

If f(x) = 11x – 5, then f^-1(x)=

MAVERICK [17]

Answer: $f^-^1(x)=\frac{x+5}{11}$

Step-by-step explanation:

To find the inverse, you replace the x with y, and y with x.

$x=11y-5$ [add 5 on both sides]

$x+5=11y$ [divide both sides by 11]

$\frac{x+5}{11} =y$

$f^-^1(x)=\frac{x+5}{11}$

8 0

2 years ago

If the gradient of the tangent to

Marizza181 [45]

Answer:

Point A(9, 3)

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

Identify

$\displaystyle y = \sqrt{x}$

$\displaystyle y' = \frac{1}{6}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = x^{\frac{1}{2}}$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}$
Simplify: $\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x}}$

Step 3: Solve

Find coordinates of A.

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}$
[Multiplication Property of Equality] Cross-multiply: $\displaystyle \sqrt{x} = 3$
[Equality Property] Square both sides: $\displaystyle x = 9$