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3 years ago

Multiply negative 1 over 3 multiplied by 1 over 4 . Which of the following is correct? (5 points)

Mathematics

1 answer:

seropon [69]3 years ago

4 0

-0.0833333333 Should be the answer

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URGENT HELP PLEASE!

Vaselesa [24]

Answer:

(a) $x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}$

(b) $x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}$

Step-by-step explanation:

It is given that $0\leq x\leq 2\pi$ .

(a)

$\sqrt{2}\sin 2x=1$

$\sin 2x=\dfrac{1}{\sqrt{2}}$

$\sin 2x=\dfrac{\pi}{4}$

$2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}$ $[\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]$

$x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}$

(b)

$\csc^2 x-\csc x-2=0$

$\csc^2 x-2\csc x+\csc x-2=0$

$\csc x(\csc x-2)+1(\csc x-2)=0$

$(\csc x+1)(\csc x-2)=0$

$\csc x=-1\text{ or }\csc x=2$

$\sin x=-1\text{ or }\sin x=\dfrac{1}{2}$ $[\because \sin x=\dfrac{1}{\csc x}]$

$x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}$

Therefore, $x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}$ .

5 0

3 years ago

Find the greatest common divisor of 100 and 254, using • prime factorization- • euclidean algorithm-

larisa [96]

Via prime factorization:

$100=10^2=2^2\cdot5^2$
$254=2\cdot127$

of which the only common factor is a single power of 2, so $\mathrm{gcd}(100,254)=2$ .

Via the Euclidean algorithm:

$254=2\cdot100+54$
$100=1\cdot54+46$
$54=1\cdot46+8$
$46=5\cdot8+6$
$8=1\cdot6+2$
$6=3\cdot2+0$

which means $\mathrm{gcd}(100,254)=2$ , as expected.

4 0

3 years ago

Solve for X. 5.4 + 0.2x = 7.09 Enter your answer as a decimal or as a mixed number in simplest form in the box. x =

FromTheMoon [43]

Answer:

x = 8.45

Step-by-step explanation:

5.4 + 0.2x = 7.09

Subtract 5.4 from both sides to leave 0.2x alone

0.2x = 1.69

Divide by 0.2 on both sides to isolate x

x = 1.69/0.2

x = 8.45

3 0

2 years ago

What is the y-coordinate for the solution of the system of equations below? 7y+5x=19 3y+5x=7

RoseWind [281]

I would go about solving this by elimination because the x variables are already the same so all you would have to do is change one equation to the opposite signs and add them, so it would look like:

7y + 5x = 19
+ -3y - 5x = -7
-------------------
4y=12
y=3

7 0

3 years ago

Read 2 more answers

A 33 - m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 37 m . Find the len

ArbitrLikvidat [17]

This is Pythagorean theorem, a^2+b^2=c^2 , a = 33 and c = 37 so b^2 + 1089 = 1369 , b^2 = 280 , b = 16.73m

5 0

3 years ago