Choose the equations in which w = 100 makes the equation true.

Given the equation Square root of 8x plus 1 = 5, solve for x and identify if it is an extraneous solution.

Kisachek [45]

Do recall that squaring and the *radical sign* cancel each other out... like so:( $\sqrt{a}$ ) $^{2}$ = a

When you put it that way, it isn't enough :P
( $\sqrt{a}$ ) $^{2}$ = a
( $\sqrt{8x+1}$ ) $^{2}$ =?

so you start with
( $\sqrt{8x+1}$ ) $^{2}$ = $(5)^{2}$
8x+1=25 <-- subtract 1 to both sides
8x=24 <- divide 8 to both sides
x= 3

To find out if it's an extraneous solution ask yourself: It mustn't result in a radical that I like to call... 'illegal'. Plug it into the radicand 8x+1 and make sure you get something that is not a negative number.... so, DO you get a negative number when you plug in x = 3 into the radicand?

(extraneous solution is a invalid solution)

x=3 not extraneous

6 0

2 years ago

Read 2 more answers

Graph each equation<br> Y=-2|-3X+3|+4<br><br> NEED HELP ASAP!!

HACTEHA [7]

Graph the absolute value by using the vertex and a few selected points

Point One: X= -1, Y= -8

Point Two: X= 0, Y= -2

Point Three: X= 1, Y= 4

Point Four: X= 2, Y= -2

Point Five: X= 3, Y= -8

The graph should look something like a mountain or an upside down V

3 0

3 years ago

Can you help me i don’t know the answers

Advocard [28]

1)

An irrational number is a number that a) can't be written as a fraction of two whole numbers AND b) is an infinite decimal without any sort of pattern.

For the first answer choice, clearly $\frac{1}{3}$ does not pass the first criterion so we look at the second choice.

Let's come back to $\sqrt{2}$ and $\pi$ .

$\frac{2}{9}$ doesn't meet our first criterion, and let's skip $\sqrt{3}$ for now.

It is often easier to disprove an irrational number than to prove one. There are a few famous irrationals to know (although there is an infinite number of irrationals). The most common are $\sqrt{2}, \pi, e, \sqrt{3}$ . For now, it's just helpful to know these and recognize them.

So we can check off $\sqrt{2}, \pi$ and $\sqrt{3}$ .

2)

For this next question, we know that $\sqrt{64} = 8$ . Clearly this isn't irrational. Likewise, $\frac{1}{2}$ isn't irrational. $\frac{16}{4} = \frac{4}{4} = 1$ , which is rational, leaving only $\frac{ \sqrt{20}}{5} = \frac{2 \sqrt{5} }{5}$ . By process of elimination, this is the correct answer. Indeed, $\sqrt{5}$ is an irrational number.

3) This notation means that we have 0.3636363636... and so on, to an infinite number of digits. It is called a repeating decimal.

But it can be written as a fraction because its pattern repeats, unlike for an irrational number.

Let's say $x=0.36363636...$ . Would you agree that $100x=36.36363636...$ ? (We choose to multiply by 100 because there are two decimals that repeat. For 1, choose 10, for 3 choose 1,000, and so on.)

Now, let's subtract x from 100x and solve.

$100x=36.36363636\\-x \ \ \ \ \ \ \ -0.36363636\\99x=36\\\\x= \dfrac{36}{99}= \dfrac{4}{11}$

Voila!

4 0

3 years ago

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The graph of a linear equation contains the points (3,11) and (-2,1) . Which point also lies on the graph.

Ainat [17]

The answer for this is b

6 0

2 years ago

Does the order in which the two transformations in a composite transformation affect the final

kap26 [50]

The order in which the two transformations in a composite transformation affect the final answer

<h3>How to determine the composite transformation?</h3>

To determine if order matters or not, I will use the following example and illustration.

Let the coordinate of point A be:

A = (2, 5)

Perform the following transformations:

Translate by (x, y + 1)
Dilate by a scale factor of 2

First order: Translation before dilation

The translation by (x, y + 1) would give:

A' = (2, 5 + 1)

A' = (2,6)

The dilation by a scale factor of 2 would give

A" = 2 * (2,6)

A" = (4,12)

Second order: Dilation before translation

The dilation by a scale factor of 2 would give

A' = 2 * (2,5)

A' = (4,10)

The translation by (x, y + 1) would give:

A'' = (4, 10 + 1)

A'' = (4,11)

See that the final coordinates in both orders are not the same.

Hence, the order in which the two transformations in a composite transformation affect the final answer