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2 years ago

One-fourth of a number increased by thirteen is less than two.

Mathematics

1 answer:

finlep [7]2 years ago

3 0

Answer: x < -44

Step-by-step explanation:

alright my fellow dude gamer, i want you to know that "a number" is basically just x

so lets do this

$\frac{1}{4}x + 13 < 2$

ok now we are going to solve for x, no?

$\frac{1}{4}x < -11$

i just subtracted 13 from both sides

now we divide -11 by 1/4

$x < -44$

MAGIC! ABSOLUTELY FANTASTIC! OH MY GOODNESS AHHHHHHH

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I need the answer to this question

disa [49]

Answer:

y = 3/4x + 19/2

Step-by-step explanation:

m = 3/4. point (-6,5)

Point slope form:

y-5=3/4(x- -6)

y -5 = 3/4x + 18/4. 18/4 = 9/2

Y = 3/4x + 9/2 + 5. 5 times 2 plus 9 over 2 = 19/2

y = 3/4x + 19/2

6 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

(x+2)(x+6)=0

Mkey [24]

Here ya go.

Answer in picture

6 0

2 years ago

50 POINTS!!! Plz show work questions are in the addon

emmasim [6.3K]

1. Each term in this polynomial has a common factor of $3x^3$ :

$12x^6-9x^4+18x^3=3x^3(4x^3-3x+6)$

2. Not sure what the "vertical method" is, but I would guess it refers to some way of visualizing the distributive property.

$(3x-5)(2x^2+7x-3)=3x(2x^2+7x-3)-5(2x^2+7x-3)$

$(3x-5)(2x^2+7x-3)=(6x^3+21x^2-9x)+(-10x^2-35x+15)$

$(3x-5)(2x^2+7x-3)=6x^3+11x^2-44x+15$

3. You can use the same approach as in (2), or recall that $(a+b)^2=a^2+2ab+b^2$ :

$(5x-4y)^2=(5x)^2+2(5x)(-4y)+(-4y)^2$

$(5x-4y)^2=25x^2-40xy+16y^2$

4. Recall that a difference of squares can be factored as $a^2-b^2=(a-b)(a+b)$ . So

$(2x^2-7)(2x^2+7)=(2x^2)^2-7^2$

$(2x^2-7)(2x^2+7)=4x^4-49$

7 0

2 years ago

Please answer this question

Y_Kistochka [10]

$\bold{\huge{\underline{ Solution }}}$

Before answering the given question, you should know the difference between polygon and regular polygon. 

Polygon :- It is closed figure constitute of straight line having different measurements and also having varies angles.
Regular polygon :- It is also a closed figure constitute of straight lines which having equal measuresment and all the angles of the given polygon are equal .

There are different types of polygon based on the sides :-

A polygon having 3 sided called triangle ,having 4 sides called quadrilateral ,having 5 sides pentagon and so on.

<h3>Let's Begin :-</h3>

I have thought to make a 4 side polygon that is quadrilateral.

Steps of construction :-

Step - 1 :- Draw a 5 cm line AB horizontally
Step - 2 :- Then , From a point B, Draw a Vertical line of 5 cm and named it BC
Step - 3 :- Then, From a point C, Draw a horizontal line of 5 cm and named it CD
Step - 4 :- Now, join the line AD
Step - 5 :- Measure all the angles form by the 4 sides of the quadrilateral.