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-Dominant- [34]
3 years ago
11

What is the prime factorization of 81 m^2x^3 ?

Mathematics
1 answer:
kondaur [170]3 years ago
5 0
The prime factorisation of 81 is 3^4(because 3*3*3*3 four times =81)
do not change the rest 3^4 m^2 x^3
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The equation of a circle is ( x - 3) 2 + ( y + 2) 2 = 25. The point (8, -2) is on the circle.
Shtirlitz [24]

Answer:

x =8 is the equation of the tangent.

Step-by-step explanation:

Here the equation of the given circle is: (x-3)^{2}  + (y+2)^{2}  = 25

Now, comparing it with the general equation of circle: (x-h)^{2}  + (y -k)^{2}  = r^2

we get the central coordinates (h,k)  = (3,-2)

So, the slope of the line joining center and (8, -2) = \frac{-2 -(-2)}{8-3} = \frac{0}{5} = 0

Since the slope of line = 0, line is parallel to x axis.

Now, as tangent and the line is perpendicular to each other

⇒Slope of the tangent = -1/ slope of the line = \frac{-1}{0}

Now, by point slope formula: the equation of the tangent is

(y-y0)  = m (x-x0)

or, (y +2) = \frac{-1}{0} (x -8)

or x =8 is the equation of the tangent.

8 0
3 years ago
Five more than the product of two and a number,
never [62]

Answer:

It was difficult reading the question, as written.  Check my assumptions.

Step-by-step explanation:

"five more than the product of two and a number,

decreased by seven"

---

Let the "number" be a.

We are told "five more than . ." means +5,

"the product of two and a number" means 2a,

"decreased by seven" mean -7

Put the statements together to obtain:

+5+2a-7

Simplify to 2a-2

Evaluate when a = 8:

2a-2

2(8)-2

16-2

= 14

7 0
2 years ago
Help please!!! I really need it
jenyasd209 [6]

Answer:

140

Step-by-step explanation:

2000 divided by 7% will give you 140 hope it helps

6 0
3 years ago
identify a two-digit dividend that will result in a quotient with a remainder 1 when the divisor is 4
Afina-wow [57]
17, 21, 25, etc. because when you divided 4 by any of these numbers you will get your answer with a remainder of 1. For example, 17/4 is 4 R.1 because 4 times 4 is 16, then you will have one left over. (At my school you always go to a decimal not a remainder) 
3 0
3 years ago
If you buy six pens and one mechanical pencil, you'll get only $1 change from your $10 bill. but if you buy four pens and two me
xxTIMURxx [149]

Let p be the prize of a pen and m the prize of a mechanical pencils. If you buy six pens and one mechanical pencil, you spend 6p+m. We know that this equals 9, because you get 1$ change from a 10$ bill.

Similarly, if you buy four pens and two mechanical pencils, you spend 4p+2m, which is 8$, because now you get a $2 change. Put these equation together in a system:

\begin{cases} 6p+m=9\\4p+2m=8\end{cases}

Now, if you multiply the first equation by 2, the system becomes

\begin{cases} 12p+2m=18\\4p+2m=8\end{cases}

Subtract the second equation from the first:

12p+2m - (4p+2m) = 18-8 \iff 8p = 10 \iff p = \dfrac{10}{8} = 1.25

Plug this value into the first equation to get

6p+m=9 \iff 6\cdot 1.25 +m = 9 \iff 7.5 +m=9 \iff m = 9-7.5 = 1.5

7 0
3 years ago
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