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3 years ago

-\left(3\right)^2-(3)2is this the same as \left(-3\right)^2(-3)2

Mathematics

1 answer:

vovikov84 [41]3 years ago

4 0

recall that minus * minus = positive, so (-3)² is really (-3)(-3), which gives us a positive 3*3 or 9.

$\bf -(3)^2-(3)^2~~ = ~~ (-3)^2(-3)^2~\hspace{5em} \begin{array}{|ccc|ll} \cline{1-3} &&\\-(3)^2-(3)^2 &=& (-3)^2(-3)^2\\&&\\ -9-9&&(9)(9)\\&&\\ -18&\ne&81\\ &&\\ \cline{1-3} \end{array}$

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A rectangle has an area of 12 feet and a length of 5 feet .what is its width

Reil [10]

Area= l * b

12= 5 * b

b = 12/ 5

b= 2.4 ft

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4 years ago

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If the length of side a is 12 centimeters, m∠B = 36°, and m∠C = 75°, what is the length of side b? Round your response to two de

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3 years ago

I’m Really lost if I could get a answer it would be greatly appreciated

Nataly [62]

<h3>Answers:</h3>

$f(g(x)) = \sqrt{x^2+5}+5\\\\g(f(x)) = x+30+10\sqrt{x-1}$

================================================

Work Shown:

Part 1

$f(x) = \sqrt{x-1}+5\\\\f(g(x)) = \sqrt{g(x)-1}+5\\\\f(g(x)) = \sqrt{x^2+6-1}+5\\\\f(g(x)) = \sqrt{x^2+5}+5\\\\$

Notice how I replaced every x with g(x) in step 2. Then I plugged in g(x) = x^2+6 and simplified.

------------------

Part 2

$g(x) = x^2+6\\\\g(f(x)) = \left(f(x)\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}+5\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}\right)^2+2*5*\sqrt{x-1}+\left(5\right)^2+6\\\\g(f(x)) = x-1+10\sqrt{x-1}+25+6\\\\g(f(x)) = x+30+10\sqrt{x-1}\\\\$

In step 4, I used the rule (a+b)^2 = a^2+2ab+b^2

In this case, a = sqrt(x-1) and b = 5.

You could also use the box method as a visual way to expand out $\left(\sqrt{x-1}+5\right)^2$

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3 years ago

Line GJ is tangent to point A at point G.<br><br> If AI = 5 and IF = 12, find A F.

Drupady [299]

I believe this is how you do it...
AI=5, 5 squared=25
IF=12, 12 squared=144
144+25 (only because line A F is bigger than AI or IF does it add)
A F=169

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3 years ago

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zheka24 [161]

Answer:

The circumference of the smaller circle is:

C = 2*pi*x/3

Step-by-step explanation:

We know that for a circle of radius R the circumference is given by:

C = 2*pi*R

where pi = 3.14...

Here we have two circles, A and B, where B is the larger circle and A is the smaller circle.

We know that:

The circumference of B is 3 times the circumference of A.

The radius of circle B is: OB = x

The radius of circle A is: OA

We want to find an expression of OA.

The circumference of circle B will be:

C(B) = 2*pi*OB = 2*pi*x

The circumference of circle A will be:

C(A) = 2*pi*OA

And we know that the circumference of circle B is 3 times the circumference of circle A, then:

C(B) = 3*C(A)

replacing the equations for the circumferences, we get:

2*pi*x = 3*(2*pi*OA)

dividing both sides by 2*pi, we get:

x = 3*OA

Now we want to solve this for OA, then we need to isolate it,

x/3 = OA

We can conclude that the radius of the smaller circle is equal to x/3.

Then the circumference of circle A is:

C(A) = 2*pi*x/3

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3 years ago