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3 years ago

Where is the location of the vertex of the parabola on a coordinate grid?

Mathematics

1 answer:

IrinaVladis [17]3 years ago

7 0

Answer:

below the x-axis

Step-by-step explanation:

y=x^2+2x-3

the vertex is located on the axis of symmetry

to find h ax^2 +bx+c

h= -b/2a = -2/2(1) = -1

the x coordinate of the vertex is -1

to find the y coordinate, substitute into the equation

y = (-1)^2 +2(-1) -3

= 1-2-3

= -4

(-1,-4)

the vertex is below the x axis

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What is the explicit formula for the sequence below? 4, -12, 36, -108 ...

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Answer:

This is a geometry sequence (I.e each term is found by multiplying the same value to the previous term).

T1 = 4

T2 = -12 = T1 X (-3) = 4 X (-3)

T3 = 36 = T2 X (-3) = 4 X (-3)^2

T4 = 108 = T3 X (-3) = 4 X (-3)^3

The general (explicit) formula for the n-th term of this sequence is:

S(n) = 4 X (-3)^(n-1)

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3 years ago

Solve the inequality for x 3^(6x+18)<27^(3x)

Lera25 [3.4K]

Answer:

$\displaystyle x > 6$

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

Terms/Coefficients
Factoring

Algebra II

Exponential Rule [Powering]: $\displaystyle (b^m)^n = b^{m \cdot n}$
Solving exponential equations

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle 3^{6x + 18} < 27^{3x}$

Step 2: Solve for x

Rewrite: $\displaystyle 3^{6x + 18} < 3^{3(3x)}$
Set: $\displaystyle 6x + 18 < 3(3x)$
Factor: $\displaystyle 3(2x + 6) < 3(3x)$
[Division Property of Equality] Divide 3 on both sides: $\displaystyle 2x + 6 < 3x$
[Subtraction Property of Equality] Subtract 3x on both sides: $\displaystyle -x + 6 < 0$
[Subtraction Property of Equality] Subtract 6 on both sides: $\displaystyle -x < -6$
[Division Property of Equality] Divide -1 on both sides: $\displaystyle x > 6$

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3 years ago

Read 2 more answers

Solve system by graphing 2x-6y=12 x+y=2

astraxan [27]

First get y by its self , then graph , find intersection point and plug in x and y to both equations, see if it makes sense , then the solution must be you intersection point

5 0

3 years ago