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3 years ago

So i need reasons for each of these i legit have no idea how to do proofs

Mathematics

2 answers:

VashaNatasha [74]3 years ago

5 0

Yes they are in order

9966 [12]3 years ago

4 0

$\begin {array}{l|l||l}\underline{\quad Statement\quad&\underline{\qquad Reason\qquad}&\underline{\qquad Side\ Note\qquad}\\ 3x-4=2(x+8)&\text{Given}&\\3x-4=2x+16&\text{Distributive Property}&\text{multiplied 2 into x+8}\\3x=2x+20&\text{Addition Property}&\text{added 4 to both sides}}\\x=20&\text{Subtraction Property}&\text{subtracted x from both sides}\\\end{array}$

NOTE:

The Statement is what was provided, Reason is the justification (proof), Side Note is JUST FOR YOU so you understand why the answer for the Reason was chosen.

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9.a )Explain why plane JKL is not an appropriate

VLD [36.1K]

Answer:

I will attach the missing drawing with the answer.

9.b)

Plane JKM

Plane JLM

Plane KLM

Step-by-step explanation:

The drawing for this question is missing. I will attach it with the answer.

9.a) Plane JKL is not an appropriate name for the plane because all of three points lie in the same line.

Through a line pass infinite planes. The plane JKL doesn't define a unique plane. That's why plane JKL isn't an appropriate name for the plane.

9.b) We can name the plane using three points that don't lie in the same line.

Three possible names for the plane are :

Plane JKM

Plane JLM

Plane KLM

6 0

3 years ago

Find the smallest 4 digit number such that when divided by 35, 42 or 63 remainder is always 5

alex41 [277]

The smallest such number is 1055.

We want to find $x$ such that

$\begin{cases}x\equiv5\pmod{35}\\x\equiv5\pmod{42}\\x\equiv5\pmod{63}\end{cases}$

The moduli are not coprime, so we expand the system as follows in preparation for using the Chinese remainder theorem.

$x\equiv5\pmod{35}\implies\begin{cases}x\equiv5\equiv0\pmod5\\x\equiv5\pmod7\end{cases}$

$x\equiv5\pmod{42}\implies\begin{cases}x\equiv5\equiv1\pmod2\\x\equiv5\equiv2\pmod3\\x\equiv5\pmod7\end{cases}$

$x\equiv5\pmod{63}\implies\begin{cases}x\equiv5\equiv2\pmod 3\\x\equiv5\pmod7\end{cases}$

Taking everything together, we end up with the system

$\begin{cases}x\equiv1\pmod2\\x\equiv2\pmod3\\x\equiv0\pmod5\\x\equiv5\pmod7\end{cases}$

Now the moduli are coprime and we can apply the CRT.

We start with

$x=3\cdot5\cdot7+2\cdot5\cdot7+2\cdot3\cdot7+2\cdot3\cdot5$

Then taken modulo 2, 3, 5, and 7, all but the first, second, third, or last (respectively) terms will vanish.

Taken modulo 2, we end up with

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod2$

which means the first term is fine and doesn't require adjustment.

Taken modulo 3, we have

$x\equiv2\cdot5\cdot7\equiv70\equiv1\pmod3$

We want a remainder of 2, so we just need to multiply the second term by 2.

Taken modulo 5, we have

$x\equiv2\cdot3\cdot7\equiv42\equiv2\pmod5$

We want a remainder of 0, so we can just multiply this term by 0.

Taken modulo 7, we have

$x\equiv2\cdot3\cdot5\equiv30\equiv2\pmod7$

We want a remainder of 5, so we multiply by the inverse of 2 modulo 7, then by 5. Since $2\cdot4\equiv8\equiv1\pmod7$ , the inverse of 2 is 4.

So, we have to adjust $x$ to

$x=3\cdot5\cdot7+2^2\cdot5\cdot7+0+2^3\cdot3\cdot5^2=845$

and from the CRT we find

$x\equiv845\pmod2\cdot3\cdot5\cdot7\implies x\equiv5\pmod{210}$

so that the general solution $x=210n+5$ for all integers $n$ .

We want a 4 digit solution, so we want

$210n+5\ge1000\implies210n\ge995\implies n\ge\dfrac{995}{210}\approx4.7\implies n=5$

which gives $x=210\cdot5+5=1055$ .

5 0

3 years ago

Ezekiel wants to use a one-sample z interval to estimate the proportion of seniors at his school who have a smartphone. He takes

Snezhnost [94]

Answer:

answer is A

Step-by-step explanation:

"The data is a random sample from the population of interest.

This condition is met since he took an SRS (simple random sample) from the population of interest."

khan academy (trust me i try to find the answer might as well just give it, it was the only green one)

8 0

3 years ago

Read 2 more answers

Plz help will mark brainliest

levacccp [35]

Answer:

-2

Step-by-step explanation:

$-2^{2}-3(-2)-10 \\4+6-10\\10-10\\0$

$5^{2} -3(5)-10\\25-15-10\\10-10\\0$

7 0

3 years ago

Read 2 more answers

Any one please need help

fiasKO [112]

The answer to the question is right

6 0

3 years ago