Answer:
8
Step-by-step explanation:
Two different approaches:
<u>Method 1</u>
Apply radical rule √(ab) = √a√b to simplify the radicals:
√98 = √(49 x 2) = √49√2 = 7√2
√50 = √(25 x 2) = √25√2 = 5√2
Therefore, (√98 - √50)² = (7√2 - 5√2)²
= (2√2)²
= 4 x 2
= 8
<u>Method 2</u>
Use the perfect square formula: (a - b)² = a² - 2ab + b²
where a = √98 and b = √50
So (√98 - √50)² = (√98)² - 2√98√50 + (√50)²
= 98 - 2√98√50 + 50
= 148 - 2√98√50
Apply radical rule √(ab) = √a√b to simplify radicals:
√98 = √(49 x 2) = √49√2 = 7√2
√50 = √(25 x 2) = √25√2 = 5√2
Therefore, 148 - 2√98√50 = 148 - (2 × 7√2 × 5√2)
= 148 - 140
= 8
Answer:
the answer is B. 45" I took the test
Answer:
About 131.95 (you may have to round up)
Step-by-step explanation:
Volume of a cone = pi(r^2)(h/3)
= pi(3^2)(14/3)
= pi(9)(4 & 4/5)
= pi(43.2)
If your teacher wants an exact number, you have to multiply 43.2 y whatever your teacher says to shorten pi to, usually 3.14. The about 131.95 is from 43.2*3.14 I think.
What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)
Three consecutive integers are . . . x, x+1, and x+2
The smallest two are . . . x and x+1
Their product is . . . . . x(x+1)
5 times the largest one is . . . 5(x+2)
5 less than that is . . . . . . 5(x+2)-5
Now, the conditions of the problem say that <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .
Eliminate parentheses: x² + x = 5x + 10 - 5
Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: <u>x² - 4x - 5 = 0</u>
You could solve that by factoring it, or use the quadratic equation.
Factored, it says that (x + 1) (x - 5) = 0
From which <em>x = -1</em>
and <em>x = +5</em>
We only want the positive results, so our three consecutive integers are
5, 6, and 7 .
To answer the question, the smallest one is <em><u>5 </u></em>.
<u>Check</u>:
5 x 6 ? = ? (7 x 5) - 5
30 ? = ? (35) - 5
30 = 30
yay !
