The sentence 3+(5+2)=(5+2)+3 illustrates

Can someone please help me with this question, I have multiple of them and have no idea where to start. If you can help me with

Alika [10]

Answer:

x = 5

Explanation:

Well, there's a theorem about these triangles that helps you solve questions similar to this one.

The theorem states that the sum of the two angles of a triangle is equal to the magnitude of the angle exterior to them.

That is, 33° + (10x+1)° = (17x-1)°

17x - 10x = 33 + 1 + 1

7x = 35 => x = 5

Hope it helps you, mate! :)

6 0

2 years ago

Subtract fractions with different denominators

Tems11 [23]

Answer:

$\frac{10}{15}-\frac{2}{5}=\frac{4}{15}$

Step-by-step explanation:

We know that

A fraction consists of two integers—one on the top, and one on the bottom.
The top one is numerator, the bottom one is denominator, and
These two numbers are separated by a line.

Let us consider two different fractions with different denominators

$\frac{10}{15}$

$\frac{2}{5}$

Lets subtract the two fractions

$\frac{10}{15}-\frac{2}{5}\:\:\:\:$

$\mathrm{Cancel\:}\frac{10}{15}:\quad \frac{2}{3}$

$=\frac{2}{3}-\frac{2}{5}$

$\mathrm{Least\:Common\:Multiplier\:of\:}3,\:5:\quad 15$

$\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}$

$\mathrm{For}\:\frac{2}{3}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:5$

$\frac{2}{3}=\frac{2\cdot \:5}{3\cdot \:5}=\frac{10}{15}$

$\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:3$

$\frac{2}{5}=\frac{2\cdot \:3}{5\cdot \:3}=\frac{6}{15}$

so

$=\frac{10}{15}-\frac{6}{15}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{10-6}{15}$

$\mathrm{Subtract\:the\:numbers:}\:10-6=4$

$=\frac{4}{15}$

Therefore,

$\frac{10}{15}-\frac{2}{5}=\frac{4}{15}$

5 0

3 years ago

Can anyone explain those marked steps in case (iii)

Tema [17]

$\cos\dfrac{3x}2=\cos\left(\dfrac\pi2+\dfrac x2\right)$
$\implies \dfrac{3x}2=2n\pi+\dfrac\pi2+\dfrac x2$

follows from the fact that the cosine function is $2\pi$ -periodic, which means $\cos x=\cos(2\pi+x)$ . Roughly speaking, this is the same as saying that a point on a circle is the same as the point you get by completing a full revolution around the circle (i.e. add $2\pi$ to the original point's angle with respect to the horizontal axis).

If you make another complete revolution (so we're effectively adding $4\pi$ ) we get the same result: $\cos x=\cos(4\pi+x)$ . This is true for any number of complete revolutions, so that this pattern holds for any even multiple of $\pi$ added to the argument. Therefore $\cos x=\cos(2n\pi+x)$ for any integer $n$ .

Next, because $\cos(-x)=\cos x$ , it follows that $\cos x=\cos(2n\pi-x)$ is also true for any integer $n$ . So we have

$\implies \dfrac{3x}2=2n\pi\pm\left(\dfrac\pi2+\dfrac x2\right)$

The rest follows from considering either case and solving for $x$ .