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3 years ago

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Which of the following describes graphing y ≥ |x| - 4? Translate y = |x| down 4 units and shade inside the V. Translate y = |x|

up 4 units and shade inside the V. Translate y = |x| left 4 units and shade inside the V. Translate y = |x| right 4 units and shade inside the V.

1 answer:

Andru [333]3 years ago

6 0

Answer:

Translate y = |x| down 4 units and shade inside the V.

Step-by-step explanation:

We want to graph the inequality

$y \geqslant |x| - 4$

We first need to graph the corresponding absolute value equation.

$y = |x| - 4$

We graph the parent absolute value function,

$y = |x|$

and shift 4 units down.

We then test the origin:

$0 \geqslant |0| - 4 \\ 0 \geqslant - 4$

This is true.

Therefore we shade inside the V shape.

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Last digit (unit digit) of 2^2014

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Answer:

4

Step-by-step explanation:

Let's find a pattern.

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So starting after power of 0, the pattern begins at power=1. The pattern is 2,4,8,6 for the units digit. Since the pattern repeats in 4, then we shall divide the power in question by 4 seeking it's remainder.

Remainder=1 implies unit digit is 2 (see 2^1=2)

Remainder=2 implies unit digit is 4 (see 2^2=4)

Remainder=3 implies unit digit is 8 (see 2^3=8)

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A 3-column table with 6 rows. Column 1 is labeled Number Rolled with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Observed Freq

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Given

$A = (-1,-2)$

$B = (2,4)$

$AP:BP = 1 : 2$

Required

The locus of P

$AP:BP = 1 : 2$

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Cross multiply

$2AP = BP$

Calculate AP and BP using the following distance formula:

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Take square of both sides

$4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2$

Evaluate all squares

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Collect and evaluate like terms

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Open brackets

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Collect like terms

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$3x^2 + 12x + 3y^2 +24y = 0$

Divide through by 3

$x^2 + 4x + y^2 +8y = 0$

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