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3 years ago

When solving a linear system by substitution, how do you decide which variable to solve first?

Mathematics

1 answer:

rosijanka [135]3 years ago

7 0

Answer: whichever one is easiest to get by itself.

Step-by-step explanation:

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Jenny drew a figure in art class. Does it have rotational symmetry? If yes, what is the angle of rotation.

Andrews [41]

Answer:

60°

Step-by-step explanation:

Jenny drew a figure in art school and the figure is shown in the attached diagram.

The diagram is a regular hexagon and it has rotational symmetry.

Two of its sides is placed parallel to the x-axis.

Therefore, by rotating 60° the adjacent sides will become parallel to the x-axis and the figure remains the same and symmetric with respect to the coordinate axes. (Answer)

6 0

4 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csec%5Cleft%28x%5Cright%29%7D%7B%5Ccos%5Cleft%28x%5Cright%29%7D-%5Cfrac%7B%5Csin%5

DanielleElmas [232]

Answer:

Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that $csc(x)=1/sin(x)$ and $sec(x)=1/cos(x)$ .

Thus:

$\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}$

$=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }$

Let's do the first part first: (Recall how to divide fractions)

$\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}$

For the second term:

$\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}$

So, all together: (same denominator; combine terms)

$\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}$

Note the numerator; it can be derived from the Pythagorean Identity:

$sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)$

Thus, we can substitute the numerator:

$\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1$

Everything simplifies to 1.

7 0

3 years ago

Two spinners are spun. One has 5 sections labeled Red, Orange, Purple, Yellow, and Green. The other has three sections labeled 1

quester [9]

Answer:

$S = 15$ possible outcomes

Step-by-step explanation:

For any experiment, the sample space of this experiment is the set of all the possible results of the experiment.

In this case we have two spinners. The first has 5 colors, by spinning the spinner you can get up to 5 different results. Therefore the sample space is $S_1 = 5$