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olga_2 [115]
3 years ago
13

Solve the equation. Check for extraneous solutions please help!!!

Mathematics
1 answer:
lozanna [386]3 years ago
4 0
!z!=a→z=a or z=-a; z=4x+3, a=9+2x

!4x+3!=9+2x
1) 4x+3=9+2x
Solving for x:
4x+3-3-2x=9+2x-3-2x
2x=6
2x/2=6/2
x=3

Checking for extraneous solution:
!4x+3!=9+2x
x=3→!4(3)+3!=9+2(3)
!12+3!=9+6
!15!=15
15=15 Ok, then x=3 is not a extraneous solution 

2) 4x+3=-(9+2x)
Solving for x:
4x+3=-9-2x
4x+3-3+2x=-9-2x-3+2x
6x=-12
6x/6=-12/6
x=-2

Checking for extraneous solution:
!4x+3!=9+2x
x=-2→!4(-2)+3!=9+2(-2)
!-8+3!=9-4
!-5!=5
5=5 Ok, then x=-2 is not a extraneous solution

Answer:
x = -2 or 3 
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Answer:

Mean track length for this rock specimen is between 10.463 and 13.537

Step-by-step explanation:

99% confidence interval for the mean track length for rock specimen can be calculated using the formula:

M±\frac{t*s}{\sqrt{N}} where

  • M is the average track length (12 μm) in the report
  • t is the two tailed t-score in 99% confidence interval (2.977)
  • s is the standard deviation of track lengths in the report (2 μm)
  • N is the total number of tracks (15)

putting these numbers in the formula, we get confidence interval in 99% confidence as:

12±\frac{2.977*2}{\sqrt{15}} =12±1.537

Therefore, mean track length for this rock specimen is between 10.463 and 13.537

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3 years ago
Please help and and explain
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Answer:

Step-by-step explanation:

6 0
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At a grocery store, the price of a watermelon is determined by how many pounds the watermelon weighs. The price of a watermelon
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P = w * .6

Explanation: First, we must determine the price per pound of watermelon. To do this, we take the cost of the watermelons, and divide it by the number of pounds. 4.38 / 7.3, which is .6. This tells us each pound costs 60 cents, or $.6. We’re trying to say “The total price of watermelon would be the amount of watermelon bought times .6.” Plug in the variables you’re given, and you get p = w * 6.
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Suppose restaurant​ A's chicken salad contains 6more grams of fat than restaurant​ B's chicken salad. Find the number of grams o
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Answer:

Restaurant A: 31 grams of fat

Restaurant B: 25 grams of fat

Step-by-step explanation:

x + (x + 6) = 56\\2x + 6 = 56\\2x = 50\\x = 25

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Find the values of a and b such that
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Answer:

a = 1.5

b = 1.75

Step-by-step explanation:

First, we need to solve (x+a)^2 and replace the result in the initial equation as:

x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b

Then, this equality apply only if the coefficient of x is equal in both sides and the constant is equal in both sides.

It means that we have two equations:

3x=2ax\\4=a^2+b

So, using the first equation and solving for a, we get:

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Finally, replacing the value of a in the second equation and solving for b, we get:

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