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aleksklad [387]
2 years ago
10

If k(x) = x2 and p(x) = k(x) + n, what is the value of n?

Mathematics
1 answer:
Sauron [17]2 years ago
6 0

Answer: Value of n is -6

Step-by-step explanation:

If the function f(x) is translated k units up, then its image is g(x) = f(x) + k

If the function f(x) is translated k units down, then its image is g(x) = f(x) - k

The vertex form of the quadratic function is f(x) = a(x - h)² + k, where a is the coefficient of x² and (h, k) is the vertex

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Kevin wants to buy his mom a $35 necklace if the necklace is 40% off, how much will Kevin have to pay?
Sliva [168]

Answer:

21

Step-by-step explanation:

8 0
3 years ago
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At a grocery store 4.5 pounds of meat cost $14.67. What is the cost of the meat per pound?
Elan Coil [88]

Answer:

$3.26

Step-by-step explanation:

If 4.5 pounds cost $14.67

You divide 14.67 by 4.5 which gives you 3.26

8 0
2 years ago
A recipe for cake needs 3/4 if a cup of milk. you are making 1/2 of the recipe.his much milk do you need
r-ruslan [8.4K]
I would say it's 3/8 of a cup because if you multiply 3/4 by 2 it would be 6/8. It's the same amount but just a different measurement. Now just take 3 away from 6/8 and you have 3/8 which is half of 3/4.
4 0
3 years ago
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Morgan moves no more than 26 of her sheep and goats into another field. Fewer than 14 of her animals are sheep.Let s represent t
GenaCL600 [577]
Let
s-------> <span>represent the number of sheep
g-------> </span><span>represent the number of goats

we know that
1) </span><span>Morgan moves no more than 26 of her sheep and goats into another field
so
(s+g) </span><span>≤ 26------> inequality 1

2) </span><span>Fewer than 14 of her animals are sheep
so
s < 14-------> inequality 2

therefore

the answers are
</span><span>B.) s < 14 
</span><span>D.) s + g ≤ 26</span>
3 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
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