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ella [17]
4 years ago
10

Solve for c. 3abc + b = 5 c = (5 - b)/(3ab) c = -5/3ab c = 2 - ab

Mathematics
2 answers:
ra1l [238]4 years ago
4 0

Answer:

the first one is correct

Step-by-step explanation:

i took the test and it was correct

nadezda [96]4 years ago
3 0

Answer:

The answer to your question is: the first option

Step-by-step explanation:

          Equation                     3abc + b = 5                 solve for c

                                              3abc = 5 - b                  pass b subtracting

                                              3ac = (5 - b)/b              pass b dividing

                                              3c  = (5 - b) / ab            pass a dividing

                                              c = (5 - b) / 3ab            pass 3 dividing

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Classify the expression: 5x^2 + 2x - 6
svp [43]

Answer:

A second degree polynomial or a positive quadratic.

Step-by-step explanation:

4 0
3 years ago
Find cot and cos <br> If sec = -3 and sin 0 &gt; 0
Natali5045456 [20]

Answer:

Second answer

Step-by-step explanation:

We are given \displaystyle \large{\sec \theta = -3} and \displaystyle \large{\sin \theta > 0}. What we have to find are \displaystyle \large{\cot \theta} and \displaystyle \large{\cos \theta}.

First, convert \displaystyle \large{\sec \theta} to \displaystyle \large{\frac{1}{\cos \theta}} via trigonometric identity. That gives us a new equation in form of \displaystyle \large{\cos \theta}:

\displaystyle \large{\frac{1}{\cos \theta} = -3}

Multiply \displaystyle \large{\cos \theta} both sides to get rid of the denominator.

\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}

Then divide both sides by -3 to get \displaystyle \large{\cos \theta}.

Hence, \displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}

__________________________________________________________

Next, to find \displaystyle \large{\cot \theta}, convert it to \displaystyle \large{\frac{1}{\tan \theta}} via trigonometric identity. Then we have to convert \displaystyle \large{\tan \theta} to \displaystyle \large{\frac{\sin \theta}{\cos \theta}} via another trigonometric identity. That gives us:

\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}

It seems that we do not know what \displaystyle \large{\sin \theta} is but we can find it by using the identity \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}  for \displaystyle \large{\sin \theta > 0}.

From \displaystyle \large{\cos \theta = -\frac{1}{3}} then \displaystyle \large{\cos ^2 \theta = \frac{1}{9}}.

Therefore:

\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}

Then use the surd property to evaluate the square root.

Hence, \displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}

Now that we know what \displaystyle \large{\sin \theta} is. We can evaluate \displaystyle \large{\frac{\cos \theta}{\sin \theta}} which is another form or identity of \displaystyle \large{\cot \theta}.

From the boxed values of \displaystyle \large{\cos \theta} and \displaystyle \large{\sin \theta}:-

\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}

Then rationalize the value by multiplying both numerator and denominator with the denominator.

\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}

Hence, \displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}

Therefore, the second choice is the answer.

__________________________________________________________

Summary

  • Trigonometric Identity

\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}

  • Surd Property

\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}

Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.

5 0
2 years ago
37.67 x 70.71 (please show the work) ​
Aliun [14]

Answer:

2663.6457

Step-by-step explanation:

37.67 *70.71

Multiply without the decimal points then put the decimal point in the answer :

3767*7071

37.67 has 2 decimal places :

70.71 has 2 decimal places :

Therefore , the answer has 4 decimal places :

=2663.6457

Hope it Helps :) !!!

6 0
3 years ago
I need help with #5
hoa [83]

Answer:

<1 = 50

<2 = 130

Step-by-step explanation:

<1 and 130 are supplementary angles

<1 + 130 = 180

<1 =180-130

<1 = 50

130 and <2 are corresponding angles and corresponding angles are equal when the lines are parallel

<2 = 130

3 0
3 years ago
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3 years ago
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