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3 years ago

Solve the equation. 5x−7=4x−1

Mathematics

1 answer:

balandron [24]3 years ago

7 0

5x-7=4x-1

5x-4x=1x

1x-7=1

7+1= 8

1x=8 then divide 1 and 8 which shows x=8

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MATCH THE NUMBER ( WORD) TO THE CORRECT DEFINITION (LETTER)

Shtirlitz [24]

1. c
2. e
3. c
4. a
5. b

6 0

3 years ago

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

Someone please help.

frutty [35]

Answer:

Step-by-step explanation:

8 0

3 years ago

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The length, in millimeters of each side of a square shaped electronic chip is a rational number. What statement is true about th

AVprozaik [17]

Answer:

The diagonal is irrational because it is a product of a rational and an irrational number

Step-by-step explanation:

The options are not given. However, the question is still answerable.

Given

Shape: Square

Length: Rational

Since the side length is said to be rational, I'll answer the question based on whether the diagonal is rational or not.

Having said that:

The diagonal (d) of a square with side length (l) is calculated using Pythagoras theorem.

$d^2 = l^2 + l^2$

$d^2 = 2l^2$

Take positive square root of both sides

$d = \sqrt{2l^2}$

Split:

$d = \sqrt{2} * \sqrt{l^2}$

$d = \sqrt{2} *l$

Recall that the side length (l) is rational.

However, $\sqrt 2$ is irrational.

So, the product of l and $\sqrt 2$ will be irrational

Hence:

The diagonal is irrational

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3 years ago

In each box, 20% of the total candies are grape flavored. In a box of 45 candies, how many are grape flavored?

Debora [2.8K]

Answer:

20% of 45 would be 9. That means 9 candies, will be grape flavored.

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2 years ago

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