The answer would be=22.9n
Solutions
1) <span>Add the whole numbers first ( 7 and 2 )
</span><span>9+<span>7/8</span>+<span>11/12
2) </span></span>Find the Least Common Denominator (LCD) of
<span><span>7 / 8</span>,<span>11 / 12
</span></span>
Start by Listing Multiples
List out all multiples of each denominator, and find the first common one.
8 : <span><span>8,16,24</span>
</span>
12 : <span>12,24
</span>
Therefore, the LCD is <span>24
</span>Method 2: By Prime Factors
List all prime factors of each denominator, and find the union of these primes.
8 : <span>2,2,2
</span>
12 : <span>2,2,3
</span>
Therefore, the LCD is <span>2×2×2×3=24
3) </span>Make the denominators the same as the LCD
<span>9+<span><span>7×3 / </span><span>8×3</span></span>+<span><span>11×2 / </span><span>12×2
</span></span></span>4) Simplify. Denominators are now the same
<span>9+<span>21 / 24</span>+<span>22 / 24
5) J</span></span>oin the denominators
<span>9+<span><span>21+22 / </span>24</span></span>
6) Simplify
<span>9+<span>43 / 24
7) </span></span>Convert 43 / 24 <span>to mixed fraction
</span><span>9+1 <span>19 / 24
8) </span></span>Simplify
<span><span>10 <span>19 / 24</span></span></span>
The correct answers are A, D, and E.
Answer:
4 = 22
Step-by-step explanation:
Factor 40 into its prime factors
40 = 23 • 5
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
4 = 22
Factors which will remain inside the root are :
10 = 2 • 5
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
2 = 2
At the end of this step the partly simplified SQRT looks like this:
2 • sqrt (10x4)
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt(x8)=x4
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) sqrt(x5)=x2•sqrt(x)
(4.2) sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(x4) = x2
sqrt (40x4) =
2 x2 • sqrt(10)
Simplified Root :
2 x2 • sqrt(10)
9514 1404 393
Answer:
Step-by-step explanation:
The rhombus has several relevant properties.
- The sides are all the same length
- Diagonals are perpendicular bisectors of each other
- Diagonals divide the rhombus into congruent triangles
The last of these relations can be used to find x:
7x° = 35°
x = 35°/7° = 5
The second of the relations can be used to find y:
3y° = 90°
y = 90°/3° = 30
The first of the relations can be used to find z:
10z -8 = 5z +32
5z = 40 . . . . . . . . . add 8-5z
z = 40/5 = 8
