Answer:
a = 
b = 12
c = 
Step-by-step explanation:
Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.
A 45-45-90 right triangle has side lengths 
.
A 30-60-90 right triangle has side lengths 
.
Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.
Side a corresponds to side length 
. Therefore, 
.
Side b corresponds to side length 2, b = 2*6 = 12.
The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to 
. This means was multiplied by 
. This means that side c is 
.
Your question is not well presented. See complete question below
Which expression is equivalent to 
?
A) –63
B) 36
C) ![\sqrt[3]{6}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B6%7D)
D) 
Answer:
The equivalent of 
is
Step-by-step explanation:
Given
Expression:
Required:
Find the Equivalent Expression
To find the equivalent of this expression, we make use of law of indices.
One of the laws of indices states that
If we apply this law to the expression above ()
By comparison a = 6 and b = 3.
So, becomes
= 
Simplifying further;
= 
This can also be written as
= 
By splitting the above expression; we have that
= 
Multiplication law of indices states that;
a * a * a = a³. (Because they have the same base of a)
So, can then be written as
Hence, =
So, the equivalent of is
To solve this problem, let's set up a proportion, letting x represent the unknown number of gallons the faucet loses in 48 hours.
5 gallons / 20 hours = x gallons / 48 hours
To solve this proportion, we are going to use cross-products. This is the products of numerator of one fraction and the denominator of the other fraction set equal to one another. It results in the equation:
5 * 48 = 20 * x
Next we simplify by performing the operations.
240 = 20x
Finally, we divide both sides by 20 to get x alone on the right side of the equation.
12=x
Therefore, 12 gallons of water will be lost in 48 hours.
Answer:
a = 60
2a = 120
Step-by-step explanation:
<u>360 = 2a + 2a + a + a </u>
360 = 6a
a = 360 / 6
a = 60
2a = 2(60)
2a = 120
You can use the equation to find the slope of a line given two points. This equation is y2 - y1 divided by x2 minus x1. The y2 is represented by the y coordinate of the second ordered pair, but it really doesn't matter, either way you get the same answer. The same way the x2 is represented by the x coordinate of the second ordered pair. For this problem, I will just use the normal coordinates. So the second y coordinate is 3. 3 -0 = 3. So your numerator is 3. The second x coordinate is 2. 2-0 = 2. So the denominator is 2. This is 3/2. So your slope would be 3/2. Hope this helps. :D Let me know if you didn't understand something in my explanation.
