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andreyandreev [35.5K]
2 years ago
11

Algebra 2 How many Real solutions does the equation have? X-1 squared = x-4

Mathematics
1 answer:
ElenaW [278]2 years ago
3 0

The solutions are where the lines cross each other.

The lines only cross each other once so there is 1 real solution.

Answer: 1

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How do I solve the system of equations x^2 +y=0 and x^2+y=0? I have to use substitution
Wittaler [7]
Equations
• x² + y = 0 ... (1)
• x² - 4x - y = 0 ... (2)

Answer -> (x, y) = (2, -4)

Step-by-step solution:

From equation 2,
-> y = x² - 4x ... (3)

• Substitute y into equation 1

-> x² + (x² - 4x) = 0
-> 2x² - 4x = 0
-> 2x² = 4x
-> x²/x = 4/2
-> x = 2

• Put x = 2 in equation 3

-> y = (2)² - 4(2)
-> y = 4 - 8
-> y = -4
5 0
3 years ago
John Calipari, head basketball coach for the 2012 national champion University of Kentucky Wildcats, is the highest paid coach i
MrRissso [65]

Answer:

A) sample mean = $1.36 million

B) standard deviation = $0.9189 million

C) confidence interval = ($1.93 million , $0.79 million)

*since the sample size is very small, the confidence interval is not valid.

Step-by-step explanation:

samples:

  1. $2.7 million
  2. $2.4 million
  3. $2.2 million
  4. $2 million
  5. $1.5 million
  6. $1.5 million
  7. $0.5 million
  8. $0.5 million
  9. $0.2 million
  10. $0.1 million

sample mean = $1.36 million

the standard deviation:

  • $2.7 million - $1.36 million = 1.34² = 1.7956
  • $2.4 million - $1.36 million = 1.04² = 1.0816
  • $2.2 million - $1.36 million = 0.84² = 0.7056
  • $2 million - $1.36 million = 0.64² = 0.4096
  • $1.5 million - $1.36 million = 0.14² = 0.0196
  • $1.5 million - $1.36 million = 0.14² = 0.0196
  • $0.5 million - $1.36 million = -0.86² = 0.7396
  • $0.5 million - $1.36 million = -0.86² = 0.7396
  • $0.2 million - $1.36 million = -1.16² = 1.3456
  • $0.1 million - $1.36 million = -1.26² = 1.5876
  • total $8.444 million / 10 = $0.8444 million

standard deviation = √0.8444 = 0.9189

95% confidence interval = mean +/- 1.96 standard deviations/√n:

$1.36 million + [(1.96 x $0.9189 million)/√10] = $1.36 million + $0.57 million = $1.93 million

$1.36 million - $0.57 million = $0.79 million

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Find the values of x and y that make these triangles congruent by the HL Theorem.
RideAnS [48]

According to HL theorem if one leg and hypotenuse of one right triangle are equal to one leg and hypotenuse of other right triangle, then the triangles are congruent.

By using this theorem we can set up the system of equations as follows:

x=y+1 ...(1)

2x+3= 3y + 3 ..(2)

By using equation (1) next step is to plug in y+1 for x in equation (2). So,

2 ( y + 1) + 3 = 3y + 3

2y + 2 + 3 = 3y + 3 By using distribution property.

2y + 5 = 3y + 3

2y + 5 - 5 = 3y + 3 - 5 Subtract 5 from each side.

2y = 3y - 2

2y - 3y = -2 Subtract 3y from each sides.

-y = -2

So, y=2

Next step is to plug in y=2 in equation (1) to get the value of x. Hence,

x= 2+1

=3

So, x=3 and y=2 make these triangles congruent.

So, the correct choice is 3. x = 3, y = 2.

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If you would like to know what is half one added to three quarters, you can calculate this using the following steps:

half one + three quarters = 1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4

The correct result would be five quarters (5/4).
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