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BlackZzzverrR [31]
3 years ago
12

Solve the quadratic equation by completing the square. x^2-14x+42=0 First, choose the appropriate form and fill in the blanks wi

th the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas.
Form: ______
Solution: _______
Mathematics
2 answers:
Tju [1.3M]3 years ago
6 0
X^2-14x+42=0  subtract 42 from both sides

x^2-14x=-42  halve the linear coefficient, square it, add it to both sides, in this case: (14/2)^2=7^2=49, add 49 to both sides

x^2-14x+49=7  now the left side is a perfect square...

(x-7)^2=7  take the square root of both sides

x-7=±√7   add 7 to both sides

x=7±√7

The above is the two solutions, 7+√7 and 7-√7

I am not sure what they mean by the proper form other than perhaps the point when you have a complete square as in the point in the process where you have a perfect square...

(x-7)^2=7
Tom [10]3 years ago
5 0
X^2 - 14x + 42 = 0
x^2 - 14x = -42
x^2 - 14x + 49 = 49 - 42
(x - 7)^2 = 7
x - 7 = (+-) sqrt 7
x = 7 (+-) sqrt 7

solutions are : x = 7 + sqrt 7 and x = 7 - sqrt 7

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The average of Shondra's test scores in physics is between 88 and 93 what is the inequality
kodGreya [7K]

Answer:

The inequality is

88<x<93

Step-by-step explanation:

The average of Shondra's test scores in physics is between 88 and 93.

Let me give out the meaning of some inequality symbols

<= Less than or equal to

>= Greater than or equal to

< Less than

> Greater than

Let the average score be x

In this case , the average score is between 88 and 93

The inequality is

88<x<93

3 0
3 years ago
3 plus the quotient of a number and 2 is 7. What is the number?​
Sidana [21]
3 + x/2 = 7
x = (7-3)*2 = 8 = the number
8 0
3 years ago
Read 2 more answers
I NEED HELPPP<br><br> Whats the length of LN?
andre [41]

Answer:

LN = 66 cm

Step-by-step explanation:

The 3 parallel lines divide the 2 sides they intersect in proportion, that is

\frac{DE}{EF} = \frac{LM}{MN} , substitute values

\frac{7}{15} = \frac{LM}{45} ( cross- multiply )

15LM = 315 ( divide both sides by 15 )

LM = 21

Hence

LN = LM + MN =  21 + 45 = 66 cm

3 0
3 years ago
The branch manager of an outlet (Store 1) of a nationwide
monitta

Answer:

1. ( 19.1416, 23.5384,)

2. (0.276348, 0.46651)

3. the sample size = 170.73 approximately 171

4. sample size = 334.07 approximately 334

5. sample of 334 should be taken by manager

Step-by-step explanation:

mean = bar x = 21.34 dollars

size of sample n = 70

standard deviation of sample = 9.22

we use t distribution as the population standard deviation is not known.

95% Confidence interval

1-α = 0.95

α = 0.05

degree of freedom = 70-1 = 69

α/2 = 0.025

using the t distribution tsble,

= 1.9949

confidence interval = 21.34+-1.9949*[\frac{9.22}{sqrt(70)}] \\

= 21.34 +- (1.9949*1.10200)

= 21.34 + 2.1984, 21.34 - 2.1984

= (23.5384, 19.1416)

the confidence interval of the mean amount spent at the supply store can be written as 19.1416<u<23.5384

2. sixe of those who only have a cat

p = 26/70 = 0.371429

at 90 % confidence interval,

1-α = 0.90

α = 0.10

we use the z table here

z(0.10/2) = Z(0.05)

= 1.645

0.371429+-1.645\sqrt} \frac{0.371429(1-0.371429)}{70}

= 0.371429 +-( 1.645 x 0.0578)

= 0.371429 + 0.095081, 0.371429 - 0.095081

= (0.276348, 0.46651)

3. sd = 10$

margin of erro,r e = 1.50$

α = 0.05

using z table

α/2 = Z0.025

= 1.96

sample size = 1.96² * 10² / 1.50²

= 3.8416 * 100/ 2.25

= 170.73

the sample size is approximately 171

d. we have 0.5 as sample proportion now

margin of error = 0.045

α = 0.10

Zα/2 = 0.05

= 1.645

sample size = 1.645²x0.5(1-0.5) / 0.045²

= 0.676506/0.002025

= 334. 07

sample size = 334

5.  sample of 334 should be taken by manager

3 0
3 years ago
If amir joins indian army, he is courageous.<br> convert this into contrapositive statement
Ronch [10]

If Amir is not courageous, then he will not join the indian army.

6 0
3 years ago
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