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Mrac [35]
3 years ago
8

Simplify: 3gh^2 x 4g^3h^3

Mathematics
1 answer:
katrin [286]3 years ago
7 0
\bf 3gh^2\times 4g^3h^3\implies 3\cdot 4\cdot g^1g^3h^2h^3\implies 12\cdot g^{1+3}h^{2+3}\implies 12g^4h^5
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Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)
Nitella [24]

The equation of a hyperbola is:

(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1

 

So what we have to do is to look for the values of the variables:

<span>For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9</span>

<span>
c = 7 (distance from center to vertices; given from the foci)
c^2 = 49</span>

 

<span>By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2 </span>

<span>b^2 =  49 – 9</span>

<span>b^2  = 40

</span>

Therefore the equation of the hyperbola is:

<span>(x^2 / 9) – (y^2 / 40) = 1</span>

5 0
3 years ago
Read 2 more answers
A triangle has two sides of length 4 and 15. What is the smallest possible whole-number length for the third side
Oduvanchick [21]

Answer:

The smallest whole number length is 12

Step-by-step explanation:

The sum of any two sides of any triangle must be greater than the length of the third side.

In this case, the two smallest sides of the triangle must be greater than the third side to satisfy the statement above.

Let "x" = the length of the third side.

Our two smaller sides are "x" and "4", and their sum must be greater than 15.

x + 4 > 15

x > 15 - 4

x > 11

5 0
3 years ago
That it cost eight dollars per adult and five dollars per child
tester [92]

Answer:

the answer is $31

Step-by-step explanation:

first you multiply 2 and 8 = 16

then multiply 3 and 5 =15

then add both and the answer will come out as 31

hope this is helpful =)

4 0
3 years ago
Read 2 more answers
4/5 equals how many 100th
victus00 [196]
80/100 also eighty out of a hundred.
7 0
3 years ago
Law of cosines <br><br> HELP MES
Lorico [155]

Answer:

70.52 degrees

Step-by-step explanation:

To find the angles, we must first find the lengths of each side of the triangle. Adding up the respective radii, we can see that

XY = 5+4 = 9 CM

XZ = 6+5 = 11 CM

ZY = 4+6 = 10 CM

Now we can apply the cosine rule

C\:=\:\sqrt{A^2+B^2-2ABcosx}

We need to rearrange the rule to solve for x, our missing angle

x\:=\:cos^{-1}\left(\frac{a^2+b^2-c^2}{2ab}\right)

solving for our unknown angle:

x\:=\:cos^{-1}\left(\frac{9^2+10^2-11^2}{2\cdot 9\cdot 10}\right)

x\:=\:70.52^{\circ }

Therefore angle YXZ is 70.52 degrees

7 0
3 years ago
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