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3 years ago

Which of the following is not a solution of the equation y=3x−4 ?

Mathematics

1 answer:

lisabon 2012 [21]3 years ago

6 0

Answer:

(-1, -1) is not a solution to the system

Step-by-step explanation:

Y = 3x - 4. Substitute the points for x and y

2 = 3(2) - 4

2 = 2 solution

y = 3x - 4

-4 = 3(0) - 4

-4 = -4 solution

y = 3x - 4

8 = 3(4) - 4

8 = 8 solution

y = 3x - 4

-1 = 3(-1) - 4

-1 = -7 not solution

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-3 + 4x = 41<br> What's x

marusya05 [52]

Move the -3 to the other side which makes it 41 + 3 = 44

So now the equation looks like 4x=44

Now divide 44 by 4, equals 11

x=11

3 0

3 years ago

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Soft drinks are sold in 1.5-liter bottles.

Olegator [25]

I think it’s 5 because if u do 1.5 / 3in it’s turn out to be 0.5

8 0

3 years ago

You're at a clothing store that dyes your clothes while you wait. You get to pick from

Art [367]

Answer:

The probability that you'll end up with socks that aren't blue is $\frac{1}{6}$ .

Step-by-step explanation:

The pieces of clothing available:

X = {shirt, pants, socks and hat}

The color options:

Y = {purple, blue and orange}

So, if a person picks a shirt he/she has 3 color options.

Similarly for pants, socks and hat there are 3 color options each.

That makes 12 possible pieces of clothing.

That is, there are 12 total options available.

Now, compute the probability of selecting a socks as follows:

$P(Socks)=\frac{1}{4}$

Compute the probability of selecting the color blue as follows:

$P(Blue)=\frac{1}{3}$

Compute the probability of selecting a socks that are not blue as follows:

$P(Socks\cap not\ Blue)=P(Socks)\times [1-P(Blue)]$

$=\frac{1}{4}\times [1-\frac{1}{3}]$

$=\frac{1}{4}\times \frac{2}{3}$

$=\frac{1}{6}$

Thus, the probability that you'll end up with socks that aren't blue is $\frac{1}{6}$ .

6 0

4 years ago

Read 2 more answers

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

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4 years ago

What is the factor 4x^2-9

disa [49]

Answer:Since both terms are perfect squares, factor using the difference of squares formula,

−

(

)

(

−

)

(

)

(

)

where

and

(

)

(

−

)

Step-by-step explanation:

6 0

3 years ago