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3 years ago

7

How many solutions does 9x-18=3(3x-6)have?

1 answer:

Reptile [31]3 years ago

5 0

Answer:

0

Step-by-step explanation:

9x-18=3(3x-6)

3(3x-6)=9x-18

9x-18=9x-18

9x-9x=0

-18+18=0

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Multiply <br> (-3/4) x (-2/9)

xeze [42]

Answer:

$\frac{1}{6}$

Step-by-step explanation:

When multiplying fractions, you simply multiply numerator by numerator and denominator by denominator, and if possible, you later simplify the answer.

$\frac{-3}{4} * \frac{-2}{9} = \frac{6}{36}$

$\frac{6}{36} / 6 = \frac{1}{6}$

Hope it helped,

BiologiaMagister

3 0

3 years ago

Read 2 more answers

20 POINTS !!!!<br> The roots of the equation x^2+bx+c=0 are −4 and 2. Find b.

Irina18 [472]

first, love the killua profile picture ! i love hunterxhunter i am currently on season 5, episode 44 or 45 aka 119 or 120 but anyways,

answer:

b = 2

step-by-step explanation:

because its roots are -4 and 2,

and a = 1 [The coefficient of $x^2$ ] we know that $x^2 + bx + c = (x - (-4)) (x-2)=(x+4)(x-2) = 0.$

using the distributive property we get,

$x^2 + 2x - 8 = 0.$

by equating coefficients (common strategy for partial fractions and undetermined coefficient method of solving ODE), we get b = 2 and c = -8 ( solved c just for fun guess :) ) .

hope this helps :)

<em>-audrey <3</em>

5 0

3 years ago

What is the slope of the linear function shown in the graph? The options are in the picture!

frez [133]

Answer:

5/4

Step-by-step explanation:

start from 0,0 then go up 5 and right 4

5 0

3 years ago

Zaire is making granola bars. For one batch of bars, the recipe requires 1 2/3 cups of rolled oats and 1/2 cups raisins. What is

morpeh [17]

Answer:

2 1/6

Step-by-step explanation:

The combined amount in cups needed can be determined by adding the cups of rolled oats with the cups of raisins

$1\frac{2}{3} + \frac{1}{2}$

$1 \frac{4 +3}{6}$

= $1\frac{7}{6}$

Converting the improper fraction to mixed fraction gives

$1 + 1\frac{1}{6}$

$2\frac{1}{6}$

8 0

3 years ago

Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

<em>2.21 and 2.23 are proved by contrapositive</em>
<em>2.22 is proved by induction</em>

<u />

<u />

<u>2.21: If </u> $n^3$ <u> is even, then n is even (By contrapositive)</u>

The contrapositive of the above statement is that:

<em>If n is odd, then </em> $n^3$ <em> is odd</em>

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

<em>i.e. If n is odd, then </em> $n^3$ <em> is odd</em>

<u />

<u>2.22 </u> $3n + 4$ <u> is even, if and only if n is even</u>

We have: $3n + 4$ <u />

<u />

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

<em>Hence, </em> $3n + 4$ <em> is even, if and only if n is even </em>

<em />

<u />

<u>2.22: </u> $s \ne -1$ <u> and </u> $t \ne -1$ <u>, then </u> $s + t + st \ne -1$ <u />

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

Read more about proofs at:

brainly.com/question/19643658

7 0

3 years ago