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3 years ago

Solve for x in the equation x2 - 12x+36 = 90.

Mathematics

1 answer:

cupoosta [38]3 years ago

5 0

Answer:

The correct answer is A. x = 6 + 3 √10

Step-by-step explanation:

Let's solve for x:

x² - 12x + 36 = 90

Factoring this quadratic equation, we have:

(x - 6) (x - 6) = 90

(x - 6)² = 90

x - 6 = √90 (Square root to both sides of the equation)

x = 6 + √90 (Adding 6 to both sides of the equation)

x = 6 + √9 * 10

x = 6 + √3² * 10

x = 6 + 3 √10

The correct answer is A. x = 6 + 3 √10

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Given cos theta = - 2/5 and sin theta < 0, find the six trigonometric values. I need help with this

Lena [83]

Answer:

$\sin\,\theta =-\frac{\sqrt{21} }{5}$

$\tan\,\theta =\frac{\sqrt{21} }{2}$

$\sec\,\theta = \frac{-5}{2}$

$cosec\,\theta =\frac{-5}{\sqrt{21} }$

$\cot\,\theta =\frac{2}{\sqrt{21} }$

Step-by-step explanation:

$\cos\theta =\frac{-2}{5}$

As both $sin\,\theta$ ,

$\theta$ lies in the third quadrant.

In the third quadrant,

$\sin\theta$

$\sin\,\theta =-\sqrt{1-\cos^2\,\theta} \\=-\sqrt{1-(\frac{-2}{5})^2 } \\\\=-\sqrt{1-\frac{4}{25} }\\\\=-\sqrt{\frac{25-4}{25} }\\\\=-\frac{\sqrt{21} }{5}$

$\tan\,\theta = \frac{\sin\,\theta}{\cos\,\theta }\\\\=\frac{\frac{-\sqrt{21} }{5} }{\frac{-2}{5} }\\\\=\frac{\sqrt{21} }{2}$

$\sec\,\theta =\frac{1}{\cos\,\theta }\\\\=\frac{1}{\frac{-2}{5} }\\\\=\frac{-5}{2}$

$\ cosec \,\theta = \frac{1}{sin\,\theta }\\\\=\frac{1}{\frac{-\sqrt{21} }{5} }\\\\=\frac{-5}{\sqrt{21} }$

$\cot\,\theta =\frac{1}{\tan\,\theta}\\\\=\frac{1}{\frac{\sqrt{21} }{2} }\\\\=\frac{2}{\sqrt{21} }$

3 0

2 years ago

A random sample of the amounts for 22 purchases was taken. The mean was $42.97, the standard deviation was $22.82, and the m

Illusion [34]

Answer: a) 84 and b ) 2084

Step-by-step explanation:

Given : Sample standard deviation : s= $22.82

(Population standard deviation is unknown ) , so we use t-test.

Critical value or the 95% confidence intervals : $t_{n-1}*=2.0$

Formula to find the sample size :

$n=(\dfrac{t^*\cdot s}{E})^2$

a) E = 5

$n=(\dfrac{(2)\cdot 22.82}{5})^2$

$n=(9.128)^2=83.320384\approx84$

i.e. Required sample size : n= 84

b) E = 1

$n=(\dfrac{(2)\cdot 22.82}{1})^2$

$n=(45.64)^2=2083.0096\approx2084$

i.e. Required sample size : n= 2084

8 0

2 years ago

PLEEEEASE HELP!!!! QUICK

lana [24]

Answer:

By 25% :)

Step-by-step explanation:

5 0

3 years ago

Which is of the numbers is composite? 41,77,83,89,97

lora16 [44]

Answer:

77 is a composite number

Step-by-step explanation:

41 = 1 × 41

77 = 1 × 77 = 7 × 11

83 = 1 × 83

89 = 1 × 89

97 = 1 × 97

8 0

2 years ago

Read 2 more answers

Max was on vacation twice as long is Jared and half as long as Wesley. The boys were on vacation a total of three weeks. How man

nasty-shy [4]

To begin with, the question is asking for the answer in days, so let's change 3 weeks to days. There are 7 days in 1 week; 3 weeks times 7 days = 21 days.
21 total days of vacation.

Max + Jared + Wesley = 21 days
(Let's use the first letter of their name to represent their vacation time)

M + J + W = 21 [This is the equation we'll be coming back to]

Now, we can use the clues given in the question to have an equation for each variable/boy.

Max was on vacation twice as long as Jared. We can interpret this as M= 2J Max was on vacation only half as long as Wesley. We can interpret this as M = (1/2)W.

So far we have these three equations: M + J + W = 21M = 2J M = (1/2)W

To have an equation for each individual boy, we must rearrange the last two equations in the list.

First, M = 2J.
Divide both sides by 2
M/2 = 2J/2
(1/2)M = J

Second, M = (1/2)W
Multiply both sides by 2
2M = W

New equations:
M + J + W = 21 [From the old list]
J = (1/2)W
W = 2M

Now we can substitute the last two equations into the first one.
M + J + W = 21
M + (1/2)W + 2M = 21
[Combine Like Terms]
(7/2)M = 21

Then, solve for M (Max's vacation days):
Multiply both sides by 2/7
$(\frac{2}{7})* (\frac{7}{2}m)= (\frac{2}{7})*(21)$
M = 6

Now we know Max was on vacation for 6 days.

If Max was on vacation twice as long as Jared, that means Jared was on vacation HALF as long as Max.

So...
J = (1/2)M
J = (1/2) * 6
J = 3
Jared was on vacation for 3 days

Wesley was on vacation twice as long as Max so... W = 2M
W= 2*6
W = 12
Wesley was on vacation for 12 days.

Let's double check our answer:
M + J + W = 21 days6 + 3 + 12 = 21
The numbers work out so the math is correct. Hope this helps and makes sense!

6 0

3 years ago