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lawyer [7]
4 years ago
5

Solve the quadratic equation by completing the square. (Enter your answers as a comma-separated list.)x2 − 6x − 27 = 0

Mathematics
1 answer:
Alexus [3.1K]4 years ago
8 0
x^2 - 6x - 27 = 0 \\ \\a=1, \ b=-6 , \ c= -27 \\ \\ \Delta =b^2-4ac = (-6)^2 -4\cdot1\cdot (-27) = 36+108 =144 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{6-\sqrt{144}}{2 }=\frac{ 6-12}{2}=\frac{-6}{2}=-3 \\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}= \frac{6+\sqrt{144}}{2 }=\frac{ 6+12}{2}= \frac{18}{2}=9 \\ \\ \\ Answer : \ x= -3 \ \ or \ \ x= 9
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cellular phone companies often package their products to make them more attractive to potential users. if you average 356 minute
Lemur [1.5K]

Answer: package B is the better deal.

Step-by-step explanation:

package A offers free phone and 300 minutes. it will cost 0.12 per minute for each minute over the plan time. Also, package A has a base rate of $39.95. This means that if you average 356 minutes per month in talk time, the cost using package A would be

0.12(356 - 300) + 39.95 = $46.67

package B : phone costs $10 and has 350 minutes of time and 0.08 per minute for each minute over the plan time. Also, package B has a base rate of 35.95 not including the phone. This means that if you average 356 minutes per month in talk time, the cost using package B would be

10 + 0.08(356 - 350) + 35.95 = $46.43

Therefore, package B is the better deal since it is cheaper.

5 0
3 years ago
Which ordered pair needs needs to be removed in order for the mapping to represent a function?
Fed [463]

Answer:

b - (-2,-1)

Step-by-step explanation:

A function is a mapping in which each element of the domain, or input, is mapped to one element of the range, or output.

In this mapping, the input value -2 is mapped to both 2 and -1; this makes the points (-2, 2) and (-2, -1).  If one of these two was removed, the mapping becomes a function.

The only one of these listed in the values given is (-2, -1).

4 0
3 years ago
Read 2 more answers
Change 32/6 to a mixed number in lowest terms .
timama [110]

Answer:

5 1/3

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
For a certain​ candy, 15​% of the pieces are​ yellow, 1010​% are​ red, 2020​% are​ blue, 55​% are​ green, and the rest are brown
MatroZZZ [7]
A) the probability it is brown would be 50%; the probability it is yellow or blue would be 35%; the probability it is not green is 95%; the probability it is striped is 0%.
B) the probability of all brown would be 12.5%; the probability that the third one is the first red one drawn is 8.1%; the probability that none are yellow is 61.4%; the probability that at least one is green is 14.3%.

Explanation:
A) The probability that it is brown is the percentage of brown we have.  Brown is not listed, so we subtract what we are given from 100%:
100-(15+10+20+5) = 100-(50) = 50%.  The probability that one drawn is yellow or blue would be the two percentages added together:  15+20 = 35%.  The probability that it is not green would be the percentage of green subtracted from 100:  100-5=95%.  Since there are no striped candies listed, the probability is 0%.
B) Since we have an infinite supply of candy, we will treat these as independent events.  All 3 being brown is found by taking the probability that one is brown and multiplying it 3 times:
0.5*0.5*0.5 = 0.125 = 12.5%.  
To find the probability that the first one that is red is the third one drawn, we take the probability that it is NOT red, 100-10 = 90% = 0.9, for the first two, and the probability that it IS red, 10% = 0.1, for the last:
0.9*0.9*0.1 = 0.081 = 8.1%.

The probability that none are yellow is found by raising the probability that the first one is not yellow, 100-15=85%=0.85, to the third power:

0.85^3 = 0.614 = 61.4%.

The probability that at least one is green is computed by subtracting 1-(probability of no green).  We first find the probability that all three are NOT green:
0.95^3 = 0.857375
1-0.857375 = 0.143 = 14.3%.
3 0
3 years ago
-4x + 3y = 29<br> 5x + y = -3<br> solve by substitution
Anna35 [415]

Step-by-step explanation:

please mark me as brainlest

5 0
2 years ago
Read 2 more answers
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