1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kow [346]
3 years ago
10

Solve x 2 - 4x - 7 = 0 by completing the square. What are the solutions?

Mathematics
1 answer:
Bingel [31]3 years ago
3 0

Answer:

x = 2±sqrt(11)

Step-by-step explanation:

x^2 -4x - 7 =0

Add 7 to each side

x^2 -4x -7+7 =0+7

x^2 -4x =7

To complete the square take the coefficient of the x term and  divide by 2 and then square it.  Add it to both sides

-4 /2 = -2 then square

(-2)^2 = 4

Add 4 to both sides

x^2 -4x+4 =7+4

x^2 -4x+4 = 11

Factor the left side into (x-b/2)^2

(x-2)^2 =11

Take the square root of each side

sqrt((x-2)^2) =±sqrt(11)

x-2 = ±sqrt(11)

Add to to each side

x-2+2 = 2±sqrt(11)

x = 2±sqrt(11)

You might be interested in
A jawbreaker candy machine has 25 red jawbreakers, 30 green jawbreakers, 15 yellow
MArishka [77]
<h3>Answer: Choice C, 2/3</h3>

============================================

Work Shown:

A = # of candies that are not green

A = (# of red)+(# of yellow)+(#  of blue)

A = 25+15+20

A = 60

B = # of candies total

B = (# of red)+(# of green)+(# of yellow)+(# of blue)

B = 25+30+15+20

B = 90

P(not green) = probability of selecting candy that is not green

P(not green) = (# of candies not green)/(# of candies total)

P(not green) = A/B

P(not green) = 60/90

P(not green) = (2*30)/(3*30)

P(not green) = 2/3

7 0
3 years ago
Heights of Women. Heights of adult women are distributed normally with a mean of 162 centimeters and a standard deviation of 8 c
Bogdan [553]

Answer:

a) 6.68% of heights less than 150 centimeters

b) 58.65% of heights between 160 centimeters and 180 centimeters

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 162, \sigma = 8

a) The percentage of heights less than 150 centimeters

We have to find the pvalue of Z when X = 150. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{150 - 162}{8}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

6.68% of heights less than 150 centimeters

b) The percentage of heights between 160 centimeters and 180 centimeters

We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.

X = 180

Z = \frac{X - \mu}{\sigma}

Z = \frac{180 - 162}{8}

Z = 2.25

Z = 2.25 has a pvalue of 0.9878

X = 160

Z = \frac{X - \mu}{\sigma}

Z = \frac{160 - 162}{8}

Z = -0.25

Z = -0.25 has a pvalue of 0.4013

0.9878 - 0.4013 = 0.5865

58.65% of heights between 160 centimeters and 180 centimeters

7 0
3 years ago
Help ASAP
horrorfan [7]

Answer:

p=\frac{181}{301}

Step-by-step explanation:

30100 have dogs, 18100 have cats.

The question simply asks for a union scenario thus the law of AND & OR is applicable.

Therefore:-Those who have both cats and dogs partially have cats.

P(X=both \ cat \ and \ dog)=\frac{18100}{30100}\\p=\frac{181}{301}

8 0
3 years ago
Read 2 more answers
What two number multiplies to get 15 and adds to get 6
OverLord2011 [107]
Asking the Math Gods...

The factors of 15 Answer : 1,3,5,15

so 3 and 5 are the only that would get 15

therefore this problem isnt correctly written.. You can't get 6 by adding any of the factored numbers



5 0
3 years ago
3<br> 50%<br> Draw angle ABC of size 65º.<br> A-<br> B<br> X+
Snowcat [4.5K]

65* It is drawn with a round ruller...

5 0
3 years ago
Other questions:
  • A tire shop had to fill 3 1/2 tires with air. It took a small air
    6·2 answers
  • Create an original rational function that has at least one asymptote (vertical, horizontal, and/or slant) and possibly a removab
    6·1 answer
  • What is the smallest number that is divisible by 1,2,3,4,5,6,7,8,9 and 10?
    12·1 answer
  • Why does the value of money in What would be the value of $100 after 10 years if you earn 11 percent interest per yeara savings
    11·2 answers
  • a worker in an assembly line takes 8 hours to produce 23 parts. At that rate, how many parts can she produce in 20 hours?
    12·1 answer
  • Bob just turned 66 years old and is considering retirement. His average annual salary over the last 35 years is $50,760. Assumin
    14·2 answers
  • Please answer this question only if you know the answer!!! :)
    9·1 answer
  • Points B, D, and F are midpoints if the sides of ACE. EC=38 and DF=16. Find AC
    8·1 answer
  • Plsssss help me......
    12·2 answers
  • A vase in the shape of a cylinder has a radius of 4.3 cm and a volume of 1330.2 cm³ what is the height of the base in centimeter
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!