Choosing "r" things from a set of "n" can be done in this many ways:
combinations = n! / [r! * (n-r)!]
combinations = 7! / [3! * 4!]
combinations = 7 * 6 * 5 / 6
combinations = 35
Source:http://www.1728.org/combinat.htm
Question 2. :
8^2 = 64 and 9^2 = 81, therefore the square root of 65 falls between these two values, 8 and 9, 64<65<81
Question 3. :
13^2 = 169 and 14^2 = 196, the correct answer is square root of 175, because 169<175<196
Hope this helps, you only need to know the squared values and square roots.
Based on the distance travelled and the time taken, the speed of the train was <u>150 km/h</u>
Speed can be calculated by the formula:
<em>= Distance / Time </em>
Distance = 600 km
Time = 4 hours
Solving will give:
= 600 / 4
= 150 km/ h
In conclusion, the train was going at 150 km/h
<em>Find out more on speed at brainly.com/question/3004254</em>
Answer:
- 6. See solution
- 7. k = 2, k = -6
Step-by-step explanation:
6.
<u>Given equation:</u>
- The sum of the roots is q1 and the product of the roots is q2
Need to show that q1+q2 = 0
<h3>Solution</h3>
<u>Bringing the equation into standard form of ax² + bx + c = 0:</u>
- 2(x + 2)² + p(x + 1) = 0
- 2x² + 8x + 8 + px + p = 0
- 2x² + (p + 8)x + (p + 8) = 0
<u>Sum of the roots: </u>
<u>Product of the roots:</u>
<u>We see that q1 and q2 are opposite numbers, therefore their sum equals zero:</u>
- q1 + q2 = -(p + 8)/2 + (p + 8)/2 = 0
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7.
<u>Given quadratic equation:</u>
Need to find the possible values of k
<h3>Solution</h3>
<u>When the quadratic equation has equal roots, then its discriminant is equal to zero:</u>
- D = 0
- √b² - 4ac = 0
- √(-k -2)² - 4*1*4 = 0
- √k² + 4k + 4 - 16 = 0
- √k² + 4k - 12 = 0
- k² + 4k - 12 = 0
- k = {-4 ± √4² -4*1*(-12)}/2
- k = (-4 ± √16 + 48)/2
- k = (-4±√64)/2
- k = -2 ± 4
- k = 2, k = -6
