Simplify the expression: -2(2c-4)-9c

If 3y+2 is equal to -2+y then what is y

garik1379 [7]

Answer:

y=-2

Step-by-step explanation:

3y+2=-2+y

subtract the 1y from both sides leaving you with 2y+2=-2

Then subtract 2 from both sides leaving you with 2y=-4

Then divide by 2 on both sides leaving you with y=-2

5 0

3 years ago

The set notation of [-5,16) is?

valentina_108 [34]

Answer: $\left\{x | x \in \mathbb{R}, \ -5 \le x < 16\right\}$

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Explanation:

We have some number x such that x is a real number, so we write that as $x \in \mathbb{R}$ which is saying "x is in the real number set".

The portion $-5 \le x < 16$ is how x is restricted. This means x can be -5 or larger, but also must be smaller than 16.

This is from the interval notation [-5, 16). The square bracket means we include -5 as part of the interval, but we exclude 16 because of the curved parenthesis.

The curly braces surrounding everything indicates that we have a set of values.

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Side note:

If x is an integer, then we can get this roster set {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} showing all of the integers between -5 and 16, including -5 but excluding 16.

Though chances are your teacher will want you to stick to real numbers rather than just integers.

4 0

4 years ago

What is the function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, a

MariettaO [177]

Given:

The parent function is $f(x)=x^2$

We need to determine the function g(x) created from the function f(x) by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units.

Shift left 9 units:

The rule to shift the graph c units to the left is given by

$y=f(x+c)$

where c is the positive real number.

Hence, to shift the graph 9 units to the left is given by

$f(x)=(x+9)^2$

Vertical stretch by a factor of 4:

The rule to stretch the graph vertically by a factor of c is given by

$y=cf(x)$

where $c>1$

Hence, to stretch the graph vertically by a factor of 4, we have;

$f(x)=4(x+9)^2$

Shifting 5 units up:

The rule to shift the graph c units upward is given by

$y=f(x)+c$

where c is the positive real number.

Hence, to shift the graph 5 units upward is given by

$f(x)=4(x+9)^2+5$

Therefore, the function $g(x)=4(x+9)^2+5$ is created from the graph $f(x)=x^2$ by moving the graph left 9 units, vertically stretching it by a factor of 4 and shifting up 5 units.