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ollegr [7]
3 years ago
14

Solve the equation using a method other than factoring. Show all your work. x² - 7x + 3 = 0

Mathematics
1 answer:
natka813 [3]3 years ago
5 0
Completing the square

7/2=3.5
3.5^2=12.25
add that to both sides
x<span>²-7x+12.25+3=12.25
factor perfect square
(x-3.5)</span><span>²+3=12.25
minus 3 both sides
(x-3.5)</span><span>²=9.25
square root both sides
x-3.5=+/-√9.25
add 3.5 to both sides
x=3.5+/-√9.25

x=3.5+√9.25 or 3.5-√9.25</span>
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Indicate the equation of the given line in standard form.
Ganezh [65]
Since the slope stays the same as it's parallel, we have y=(3/4)x+b. Plugging (2,-1) in, we get -1=3*2/4+b=6/4+b=1.5+b. Subtracting 1.5 from both sides, we get -2.5=b and our equation being y=(3/4)x-2.5 (since in y=mx+b, y and x remain as variables)
8 0
3 years ago
[Quick Answer Needed] Which of the following shows the extraneous solution to the logarithmic equation?
Nitella [24]

Answer:

C

Step-by-step explanation:

Given the logarithmic equation

\log_4x+\log_4(x-3)=\log_4(-7x+21)

First, notice that

x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

\log_4x+\log_4(x-3)=\log_4x(x-3),

then

\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3

Hence, x=3 and x=-7 are extraneous solutions

6 0
2 years ago
suppose you got 8 mangoes and 3 apples for $18 and 3 mangoes and 5 apples for $14.50. how mush does each mango and each apple co
Zanzabum
Suppose a mango cost x dollar and a apple cost y dollar

there will be an binary system of equation

8*x+3*y=18
3*x+5*y=14.5

so soultions have to x=48/31     y=16/31

6 0
3 years ago
Read 2 more answers
Of the 10 people attending a seminar, 2 have red hair.
kari74 [83]

Answer:

20%

Step-by-step explanation:

6 0
3 years ago
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A 90% confidence interval for the mean height of students
Westkost [7]

Answer:

ME= \frac{69.397-60.128}{2}= 4.6345 \approx 4.635

And the best answer on this case would be:

b) m = 4.635

Step-by-step explanation:

Let X the random variable of interest and we know that the confidence interval for the population mean \mu is given by this formula:

\bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}

The confidence level on this case is 0.9 and the significance \alpha=1-0.9=0.1

The confidence interval calculated on this case is 60.128 \leq \mu \leq 69.397

The margin of error for this confidence interval is given by:

ME =t_{\alpha/2} \frac{s}{\sqrt{n}}

Since the confidence interval is symmetrical we can estimate the margin of error with the following formula:

ME = \frac{Upper -Lower}{2}

Where Upper and Lower represent the bounds for the confidence interval calculated and replacing we got:

ME= \frac{69.397-60.128}{2}= 4.6345 \approx 4.635

And the best answer on this case would be:

b) m = 4.635

4 0
3 years ago
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