All these equations are in the form of ax^2 + bx + c = 0, where a, b, and c are some numbers. the discriminants of equations like this are equal to b^2 - 4ac. if the discriminant is negative, there are two imaginary solutions. if the discriminant is positive, there are two real solutions. if the discriminant is 0, there is one real solution.
<span>x^2 + 4x + 5 = 0
</span>b^2 - 4ac
4^2 - 4(1)(5)
16-20
-4, two imaginary solutions.
<span>x^2 - 4x - 5 = 0
</span>b^2 - 4ac
(-4)^2 - 4(1)(-5)
16 + 20
36, two real solutions.
<span>4x^2 + 20x + 25 = 0
</span>b^2 - 4ac
20^2 - 4(4)(25)
400 - 400
0, one real solution.
Answer:
150,595
Step-by-step explanation:
First, convert miles to feet:
4.1 mi × (5280 ft/mi) = 21648 ft
The area that the crowd takes up is:
2 × 8 ft × 21648 ft = 346368 ft²
The number of people is:
346368 ft² × (1 person / 2.3 ft²) = 150594.8
Rounding to the nearest integer, there are approximately 150,595 people in the crowd.
He made his mistake in Step 2. Tom should have subtracted 4/8 instead of 1/8. The mistake is that he was not consistent when he multiplied Denominators (bottom number) must be the same when handling fractions so Tom must multiply both the numerator and denominator by the SAME number to balance it out. 1/2 x 4/4= 4/8. Subtract. 7/8 - 4/8= 3/8. Tom has 3/8 of a gallon of paint leftover.
Answer:
35.25
Step-by-step explanation:
Give the data set:
23 37 49 34 35 41 40 26 32 22 38 42
We are expected to calculate the midquartile of the given data set.
22 23 26 32 34 35 37 38 40 41 42 49
First step is to find the lower quartile which comprises of
22 23 26 32 34 35
Here the Q1 is (26+32)/2 = 58/2= 29
Second step to find the upper quartile which comprises of
37 38 40 41 42 49
Here the Q3 is (40+41) /2 = 81/2 = 41.5
Then to find the midquartile which is (Q1+Q3) /2 where Q1 is 29 and Q3 is 41.5
= (29+41.5)/2
= (70.5) /2 = 35.25
Answer:
x = -1
Step-by-step explanation:
Solve for x:
12 = 24 - 4 (-6 x - 3)
-4 (-6 x - 3) = 24 x + 12:
12 = 24 x + 12 + 24
Grouping like terms, 24 x + 12 + 24 = 24 x + (12 + 24):
12 = 24 x + (12 + 24)
12 + 24 = 36:
12 = 24 x + 36
12 = 24 x + 36 is equivalent to 24 x + 36 = 12:
24 x + 36 = 12
Subtract 36 from both sides:
24 x + (36 - 36) = 12 - 36
36 - 36 = 0:
24 x = 12 - 36
12 - 36 = -24:
24 x = -24
Divide both sides of 24 x = -24 by 24:
(24 x)/24 = (-24)/24
24/24 = 1:
x = (-24)/24
The gcd of -24 and 24 is 24, so (-24)/24 = (24 (-1))/(24×1) = 24/24×-1 = -1:
Answer: x = -1
