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sineoko [7]
3 years ago
7

What is the solution set of 7x^2 + 3x = 0? A. {0, 3/7} B. {0, -3/7} C. {0, -4/7}

Mathematics
2 answers:
shtirl [24]3 years ago
6 0
To solve the solution set of the problem, we can factor the expression given into x* ( 7x + 3 ) = 0. This dissects the equation into two parts: 
x = 0 
and 
7x + 3 = 0x = -3/7 
Hence the answer to this problem must be B.  {0, -3/7} 
Oksana_A [137]3 years ago
3 0
7x² + 3x = 0

x(7x + 3) = 0 ⇔ x = 0 or 7x + 3 = 0    |subtract 3 from both sides

x = 0 or 7x = -3    |divide both sides by 7

x = 0 or x = - 3/7

Answer: B. {0; -3/7}
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Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβ
-Dominant- [34]

Answer:

\tan(\beta)

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something.  If you have options that you're building toward, aim toward one of them.

{\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}    and   {\sec(\theta)}={\dfrac{1}{\cos(\theta)}

Recall the following reciprocal identity:

\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}

So, the original expression can be written in terms of only sines and cosines:

\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)

\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }

\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}

\sin(\beta) *\dfrac{1 }{\cos(\beta) }

\dfrac{\sin(\beta)}{\cos(\beta) }

Working toward one of the answers provided, this is the tangent function.


The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero.  However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to \tan(\beta).

8 0
2 years ago
Jim
stealth61 [152]

yes i agree because if all the integers are positive, the answer stays positive which means if you know your integer rules: a positive divide by a positive it stays positive. its the same thing for all the other operations. hope this helps.

6 0
3 years ago
Read 2 more answers
Find the area of the trapezoid. points are (-5,-3)(4,-3)(6,-7)(-7,-7)​
Olegator [25]

Answer:

44 square units

Step-by-step explanation:

The area of a trapezoid with bases b₁ and b₂ and height h is given by the formula

A=\left(\dfrac{b_1+b_2}{2}\right)h

If you're wondering how we get this formula, check the attached illustration (remember the area of a parallelogram is its base multiplied by its height)! Moving on to our trapezoid, the pairs of points (-5,-3)(4,-3) and (6,-7)(-7,-7) form two horizontal segments, which form b₁ and b₂, and our height is the distance between the y-coordinates -3 and -7, which is 4. We can find b₁ and b₂ by finding the distance between the x coordinates in their pairs of points:

b_1=|-5-4|=|-9|=9\\b_2=|6-(-7)|=|6+7|=13

Putting it altogether:

A=\left(\dfrac{9+13}{2}\right)(4)=\left(\dfrac{22}{2}\right)(4)=(11)(4)=44

So the area of our trapezoid is 44.

4 0
3 years ago
Calculate the area of the figure. ____ ft^2
lapo4ka [179]
You need to divide it in 2 and solve separately
5 0
3 years ago
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3. A. Mr. Sullivan is organizing teams for the middle school’s annual field day. There are eight classes at the school and 21 st
ICE Princess25 [194]

Answer:

Step-by-step explanation:

A)Total number of students at the school= Number of classes * number of students in each class

= 8 *  21

= 168 students.

B) Number of teams=Total students÷ Number of students in each team

= 168/12

= 14

There will be 14 teams

3 0
3 years ago
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