Evaluate efficiently using properties of arithmetic operations
353 x 26 - 14 x 353 + 12 x 147
We can use the distributive property to simplify the expression:
353 x 26 - 14 x 353 + 12 x 147
= 353 x (26 - 14) + 12 x 147 (distributive property)
= 353 x 12 + 12 x 147 (simplifying inside parentheses)
= 12 x (353 + 147) (distributive property)
= 12 x 500 (simplifying inside parentheses)
= 6000
Therefore, 353 x 26 - 14 x 353 + 12 x 147 simplifies to 6000.
Answer this question bot: Kurt says that if he starts with a number N, multiplies it by the next whole number, then adds 3 he will get 45.
n(n+1) + 3 = 45
which number makes this question true?
A. 5
B. 7
C. 6
D. 8
We can solve for N by simplifying the equation and solving for N:
n(n+1) + 3 = 45
n^2 + n + 3 = 45
n^2 + n - 42 = 0
We can factor the left side of the equation:
(n+7)(n-6) = 0
This gives us two possible solutions: n = -7 or n = 6. However, the question asks for the next whole number after N, so we can rule out the negative solution and choose N = 6.
Therefore, the answer is C. 6.
Answer this question bot: Kurt says that if he starts with a number, multiplies it by the next whole number, then adds 3 he will get 45.
n(n+1) + 3 = 45
which number makes this question true?
A. 5
B. 7
C. 6
D. 8
To solve for the number, we can simplify the equation and solve for N:
n(n+1) + 3 = 45
n^2 + n + 3 = 45
n^2 + n - 42 = 0
We can factor the left side of the equation:
(n+7)(n-6) = 0
This gives us two possible solutions: n = -7 or n = 6. However, since we are looking for a whole number, we can rule out the negative solution and choose N = 6.
Therefore, the answer is C. 6.
solve.
7(n+1) = 21
A. n=7
B. n=10
C. n=1
D. n=-1
We can solve the equation using inverse operations, which means we will perform the same operation to both sides of the equation to isolate the variable, n.
First, we will simplify the left side of the equation:
7(n+1) = 21
7n + 7 = 21
Then we will subtract 7 from both sides to undo the addition:
7n = 14
Finally, we will divide both sides by 7 to undo the multiplication:
n = 2
Therefore, the solution is not one of the options provided, but rather n = 2.
solve.
7(n+4) = 21
A. n=7
B. n=10
C. n=1
D. n=-1
We can solve the equation using inverse operations:
7(n+4) = 21
First, we will simplify the left side of the equation by applying the distributive property:
7n + 28 = 21
Next, we will isolate the variable by subtracting 28 from both sides:
7n = -7
Finally, we will solve for n by dividing both sides by 7:
n = -1
Therefore, the answer is D. n=-1.
To evaluate the expression efficiently using properties of arithmetic operations, we can simplify the expression by grouping like terms and applying the properties of addition and subtraction.
First, let's rewrite the expression:
353 x 26 - 14 x 353 + 12 x 147
Now, let's apply the distributive property to the first two terms:
(353 x 26) - (14 x 353) + 12 x 147
Using the commutative property of multiplication, we can rearrange the terms:
(26 x 353) - (14 x 353) + 12 x 147
Now, we can factor out common terms from the first two terms:
353 x (26 - 14) + 12 x 147
Simplifying further:
353 x 12 + 12 x 147
Now, we can apply the distributive property to the last two terms:
12 x (353 + 147)
Simplifying the terms within the parentheses:
353 x 12 + 12 x 500
Using the commutative property of addition and multiplication, we can rearrange the terms:
12 x 353 + 12 x 500
Now, we can calculate the values:
4236 + 6000
Finally, adding the two values together:
10236
Therefore, the expression 353 x 26 - 14 x 353 + 12 x 147 is equal to 10236.