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4 years ago

6. Given: 9x^3 – 3x^2 + 2x^4 – 7x – 10

Mathematics

1 answer:

Alexandra [31]4 years ago

8 0

Answer:

a. 2, because it is the coefficient of the highest degree.

b. 4

c. 5 terms.

d. -10

e. 3, as it is the coefficient of x^2.

If you need more help don't hesitate to ask :)

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The sum of twice a number and 18 less than the number is the same as the difference between -10 and the number. What is the numb

Lera25 [3.4K]

Answer:

n=-14

Step-by-step explanation:

2n+18-n=-10-n

n+18=-10-n

+n +n

2n+18=-10

-18 -18

2n=-28

/2 /2

n=-14

4 0

4 years ago

Read 2 more answers

Could someone please help me

slava [35]

78
because 5 times 2 equals 10 so then u times 39 times 2 and get 78

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

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3 years ago

A rectangle is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse, and two other on th

Rufina [12.5K]

Answer:

Part 1) The base is $25\ in$ and the height is $10\ in$

Part 2) The base is $7.5\ in$ and the height is $18.75\ in$

Step-by-step explanation:

case 1) Right isosceles triangle of the left

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

$y+x+y=45$

$2y+x=45$ ----> equation A

$\frac{x}{y} =\frac{5}{2}$

$x=2.5y$ -----> equation B

substitute equation B in the equation A

$2y+2.5y=45$

$4.5y=45$

$y=10\ in$

Find the value of x

$x=2.5(10)=25\ in$

case 2) Right isosceles triangle of the right

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

$y+x+y=45$

$2y+x=45$ ----> equation A

$\frac{y}{x} =\frac{5}{2}$

$y=2.5x$ -----> equation B

substitute equation B in the equation A

$2(2.5x)+x=45$

$6x=45$

$x=7.5\ in$

Find the value of y

$y=2.5(7.5)=18.75\ in$

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3 years ago

How can you use the strategy make a table to solve problems by using equivalent fractions

RideAnS [48]

If you use a table you see all the fractions next to each other and you see what did I do the get from this fraction to this fraction.

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4 years ago