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borishaifa [10]
2 years ago
12

Solve for x in the equation x squared + 2 x + 1 = 17.

Mathematics
1 answer:
Papessa [141]2 years ago
3 0

Answer:

x = - 1 + \sqrt{17}\\and\\x = - 1 - \sqrt{17}\\

Step-by-step explanation:

given equation

x^2 +2x +1 = 17

subtracting 17 from both sides

x^2 +2x +1 = 17\\x^2 +2x +1 -17= 17-17\\x^2 +2x - 16 = 0\\

the solution for quadratic equation

ax^2 + bx + c = 0 is given by

x = x = -b + \sqrt{b^2 - 4ac} /2a \\\\and \ \\-b - \sqrt{b^2 - 4ac} /2a

________________________________

in our problem

a = 1

b = 2

c = -16

x =( -2 + \sqrt{2^2 - 4*1*-16}) /2*1 \\x =( -2 + \sqrt{4  + 64}) /2\\x =( -2 + \sqrt{68} )/2\\x = ( -2 + \sqrt{4*17} )/2\\x =  ( -2 + 2\sqrt{17} )/2\\x = - 1 + \sqrt{17}\\and\\\\x = - 1 - \sqrt{17}\\

thus value of x is

x = - 1 + \sqrt{17}\\and\\x = - 1 - \sqrt{17}\\

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Two mixed numbers with different denominators to get 4 1/3
nalin [4]

Answer:

1 2/3 and 2 4/6

7 0
2 years ago
You’ve bought a cylindrical thermos 8 in. high with a base 6 in. across. How much coffee can you put in the thermos?
lana66690 [7]

Answer:

3.706 liters

Step-by-step explanation:

Hello

assuming that these measures correspond to the internal measures of the thermos,

we can calculate the volume as, the volume of a cylinder, which is given by

V=\pi r^{2} h

where r is the radius of the base, and h the height

also

Diameter=2r

r=Diameter/2

Step 1

let

h=8 in

base = diameter = 6 inch

r=diameter/2

r=6/2 inch,r=3 inch

Step 2

Put the values into the equation

V=\pi r^{2} h\\V=\pi (3in)^{2} (8 in)\\V=\pi *72 \ in^{3} \\\\V=72\pi\ in^{3} \\\\

Step 3

Now, the unit (cubic inches) is not an usual unit for measuring coffee, let´s convert cubic inches into liters by knowing

1 inch = 2.54 cm

1 litro =  1000 cubic centimeters

if\ 1\ inch\ = 2.54\ cm\\(1\ inch)^{3} =(2.54\ cm)^{3}\\\\1\ inch^{3}=16.3870\ cm^{3}

1 cubic inch = 16.3870 cubic centimeters

1\ cubic\ inch\ = 16.3870\ cubic\ centimeters\\\\\\72\pi =x?\ cubic\ centimeters\\\\x=\frac{72\pi \cubic \ inch\ \*16.3870 }{1\ cubic\ inch} \\\\x=3706.65\ cubic\ centimeters

Step 4

Finally, convert cubic centimeters into liters1000\ cubic\ centimeters =1\ liter \\\\\\3706.65\ cubic\ centimeters = x?\ liters\ centimeters\\\\x=\frac{3706.65 \cubic \ centimeters\ \*1 liter}{1000 cubic centimeters} \\\\x=3706.65\ cubic\ centimeters\\x=3.706 Liters

I can put 3.706 liters in the thermos

Have a good day

4 0
3 years ago
. The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about slee
scoundrel [369]

Answer:

Yes the conclusion in the question  is a reasonable conclusion

Step-by-step explanation:

From the question we are told that

    The sample size is  n_1 = n_2 = n = 250

     The sample mean for USA is  \= x_1 =  391 \ minutes

     The sample mean for Mexico is \= x_2 = 426 \ minutes

     The sample standard deviation for USA is  s_1 =  25 \ minutes

    The sample standard deviation for Mexico is  s_2 =  49 \  minutes

     

The null hypothesis is  H_o  :  \mu_1 = \mu_2

The alternative hypothesis is  H_a  :  \mu_1  < \mu_2

Generally the test statistics is mathematically represented as

        z =  \frac{\= x_1 - \= x_2 }{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2 } } }

=>     z =  \frac{ 391  - 426  }{ \sqrt{ \frac{25^2}{250} + \frac{49^2}{250} } }

=>     z =  -10

From the z table  the area under the normal curve to the left corresponding to   -10  is

    p-value =  P(Z <  -10 ) =  0.00

Generally from the value obtained we see that

  The p-value is  <  \alpha  hence

The decision rule is

Reject the null hypothesis

The conclusion is  

 The is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico

Hence the conclusion in the question is a  reasonable conclusion

6 0
3 years ago
Help me please. Quick!
Elden [556K]
The length of one side is 5
7 0
2 years ago
Read 2 more answers
Determine which of the sets of vectors is linearly independent. A: The set where p 1(t) = 1, p 2(t) = t 2, p 3(t) = 1 + 5t B: Th
denis-greek [22]

Answer:

(A)A and C

Step-by-step explanation:

In each case, represent each of the p_i as a column vector where  each row corresponds to the constant term, coefficient of t and t^2 respectively.

A= The set where p_1(t)=1 p_2(t)=t^2 p_3(t)=1+5t

A=\left[\begin{array}{ccc}1&0&1\\0&0&5\\0&1&0\end{array}\right]

|A|=\left|\begin{array}{ccc}1&0&1\\0&0&5\\0&1&0\end{array}\right|=-5

B: The set where p_1(t)=t, p_2(t)=t^2, p_3(t)=2t+5t^2

B=\left[\begin{array}{ccc}0&0&0\\1&0&2\\0&1&5\end{array}\right]\\|B|=0

C: The set where p_1(t)=1, p_2(t)=t^2, p_3(t)=1+5t+t^2

C=\left[\begin{array}{ccc}1&0&1\\0&0&5\\0&1&1\end{array}\right]\\|C|=-5

Since the determinants of A and C are not 0, the set of vectors in A and C are linearly independent.



6 0
3 years ago
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