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3 years ago

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