X=11,-1 is the right answer
Answer:
Step-by-step explanation
x1 = 2, y1 = -2 and m = 3/4
y - y1 = m(x - x1)
y - (-2) = 3/4(x - 2)
y + 2 = 3/4(x - 2)
Multiply each term by 4
4y + 8 = 3(x - 2)
4y + 8 = 3x - 6
4y = 3x - 6 - 8
4y = 3x - 14
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 !
Volume of a ball = (4/3)πr³
When r = 18cm, V = (4/3)×3.14×18³ =24416.64 cm³
When r = 12cm, V = (4/3)×3.14×12³ =7234.56 cm³
Difference = 24416.64 - 7234.56 = 17182.08 cm³
the volume of air in the larger ball is <span>17182.08 cm³ greater than smaller ball </span>
50 (1/3) mph
47 (1/2) = 47.5 mph
47.5 / 50 (1/3) =
<span>
<span>
<span>
0.943708609271523
</span>
</span>
</span>
hours
times 60 =
<span>
<span>
<span>
56.6225165563
</span>
</span>
</span>
minutes =
56 minutes <span><span><span>37.3509933775
</span>
seconds
</span></span>
