Answer:
242
Step-by-step explanation:
Simplify the following:
11 ((9^2 - 5^2)/2^2 + 8)
Hint: | Evaluate 2^2.
2^2 = 4:
11 ((9^2 - 5^2)/4 + 8)
Hint: | Evaluate 5^2.
5^2 = 25:
11 ((9^2 - 25)/4 + 8)
Hint: | Evaluate 9^2.
9^2 = 81:
11 ((81 - 25)/4 + 8)
Hint: | Subtract 25 from 81.
| 7 | 11
| 8 | 1
- | 2 | 5
| 5 | 6:
11 (56/4 + 8)
Hint: | Reduce 56/4 to lowest terms. Start by finding the GCD of 56 and 4.
The gcd of 56 and 4 is 4, so 56/4 = (4×14)/(4×1) = 4/4×14 = 14:
11 (14 + 8)
Hint: | Evaluate 14 + 8 using long addition.
| 1 |
| 1 | 4
+ | | 8
| 2 | 2:
11×22
Hint: | Multiply 11 and 22 together.
| 2 | 2
× | 1 | 1
| 2 | 2
2 | 2 | 0
2 | 4 | 2:
Answer: 242
Answer:
The street light is 20 feet tall.
Step-by-step explanation:
This question depends on a proportion. Keep your height of the object in one ratio and the length of the shadow in the other.
25/x = 75/60 Notice the height of the structure is on the left. The length of the shadow is on the right. Cross multiply
75x = 60 * 25 Combine the right
75x = 1500 Divide by 75
x = 1500/75
x = 20
The street light is 20 feet tall.
Answer:
Step-by-step explanation:
We want to find the equation of a circle with a center at (7, 2) and a point on the circle at (2, 5).
First, recall that the equation of a circle is given by:
Where (<em>h, k</em>) is the center and <em>r</em> is the radius.
Since our center is at (7, 2), <em>h</em> = 7 and <em>k</em> = 2. Substitute:
Next, the since a point on the circle is (2, 5), <em>y</em> = 5 when <em>x</em> = 2. Substitute:
Solve for <em>r: </em>
<em />
<em />
Simplify. Thus:
Finally, add:
We don't need to take the square root of both sides, as we will have the square it again anyways.
Therefore, our equation is:
Answer:
Step-by-step explanation: This is five-fold proportion
The first ratio gives solution namely
We will write general proportion
a:b= c:d= e:f = g:h= i:j = k
According to this the first ratio gives coefficient k
When we divide 24/2 =12 our coefficient k=12
In the second ratio we will multiply 3 with 12 and get 36.
In the third ratio we will multiplu 5.5 with 12 and get 66.
In the fourth we will divide 108 with 12 and get 9.
In the fifth we will multiply 15 with 12 and get 180.
Finally the ratio is 24:2=36:3=66:5.5=108:9=180:15
Given expression in exponential form : 
.
We need to convert it into radical form.
<em>Please note: When we convert an exponential to radical form, the top number goes in the exponent of the term and bottom number of the fraction goes in the radical sign to make it nth radical.</em>
We can apply following rule:
![(a)^{\frac{m}{n}}= \sqrt[n]{x^m}](https://tex.z-dn.net/?f=%28a%29%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%3D%20%5Csqrt%5Bn%5D%7Bx%5Em%7D)
.
Therefore,
![a^{\frac{4}{9} }= \sqrt[9]{a^4}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B4%7D%7B9%7D%20%7D%3D%20%5Csqrt%5B9%5D%7Ba%5E4%7D)
.
Therefore, correct option is : D. ninth root of a to the fourth power.
