One ordered pair (a,b) satisfies the two equations ab^4 = 12 and a^5 b^5 = 7776. What is the value of 'a' in this ordered pair?
1 answer:
Answer:
a = 4.762203156
Step-by-step explanation:
Given:
ab^4 = 12 and a^5b^5 = 7776
Making the equations a subject of a;
a = 12/b^4 and a^5 = 7776/b^5
Finding fifth root on both sides of equation two;
a = /b
You will get a = 6/b
Equating the two equations;
12/b^4 = 6/b
Multiplying both sides by b^4 gives:
b = = 1.25992105
We had that a = 12/b^4 so;
a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156
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Step-by-step explanation:
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Answer:
The length of WX is 31 units.(third option)
Step-by-step explanation:
Given that In trapezoid WXYZ, WX║ZY and S and T are the mid points of the sides WZ and XY. We have to find the length of WX.
By trapezoid mid-segment Property,
A mid-segment of a trapezoid join the midpoints of the two non-parallel sides of trapezoid. The length of the mid-segment is the average of the lengths of the two bases and is parallel to the bases of the trapezoid.
∴
⇒
⇒
⇒
The length of WX is 31 units.(third option)
Essentially, what we're looking at here are two alternate interior angles.
Wait. What? Alternate interior angles?
It sounds like some super fancy math jargon, but it's a fairly simple concept that I'll try my best to explain. First, let's look at lines L and M as two parallel lines, meaning that these two are lines with equal slopes, and will never intersect. See that line that goes in between the parallel lines L and M? That's called a transversal. It's basically a line that goes through two parallel lines.
Now we know that there's a transversal going through the parallel lines. So what? Well, there's a couple of special attributes to transversals. See the two angles, 7x-7 and 4x+14? As you can tell, these two angles alternate in the interior space between the transversal and the parallel lines.
Alternate interior angles are equal. There's a way to prove that they're equal, but I won't bore you with the specifics since that's not what the question's asking.
If the angles need to be equal for lines L and M to be parallel, we can make an equation that'll solve for x:
7x - 7 = 4x + 14
<u>Subtract 4x from both sides:</u>
7x - 4 x - 7 = 4x - 4x + 14
3x - 7 = 14
<u>Add 7 to both sides:</u>
3x - 7 + 7 = 14 + 7
3x = 21
<u>Divide both sides by 3 to completely isolate x:</u>
=
x = 7
And that's our answer! If you need me to explain anything any further, just ask!
- breezyツ