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4 years ago

−5|x + 1| = 10 what is the answer to that

Mathematics

1 answer:

Dmitriy789 [7]4 years ago

6 0

Answer:

x = -3

Step-by-step explanation:

-5(x+1) = 10

Distribute

-5x - 5 = 10

get rid of the -5 by making it positive and adding it to the other side

-5x = 15

divide 15 by -5

x = -3

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A positive integer is 5more than 23 times another. Their product is 6732. Find the two integers

aliina [53]

One integer is m.

The other integer is n.

n = 23m + 5

mn = 6732

m = 6732/n

n = 23 * 6732/n + 5

n = 154,836/n + 5

n^2 = 154,836 + 5n

n^2 - 5n - 154,836 = 0

n = [5 +- sqrt(25 + 4 * 154,836)]/2

n = (5 +- 787)/2

n = 396 or n = -391

We discard -391 because the problem is looking for positive integers.

mn = 6732

m = 6732/n = 6732/396

m = 17

Answer: The integers are 17 and 396.

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3 years ago

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3 years ago

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3 years ago

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The point (- square-root 2/2, square-root2/2 is the point at which the terminal ray of angle theta intersects the unit circle. W

Rufina [12.5K]

Answer: The value of cosine is $\frac{-\sqrt{2}} {2}$ and the value of cotangent is -1.

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The given point is $(\frac{-\sqrt{2}} {2}},\frac{\sqrt{2}} {2})$ .

Since the x coordinate is negative and y coordinate is positive so the point must be lies in second quadrant.

The distance of the point from the origin is,

$r=\sqrt{(\frac{-\sqrt{2}} {2}-0)^2+(\frac{\sqrt{2}} {2}-0)^2}$

$r=\sqrt{ \frac{2}{4}+\frac{2}{4}}$

$r=1$

The given point is in the form of (a,b). So we get,

$a=\frac{-\sqrt{2}} {2}$

$b=\frac{\sqrt{2}} {2}$

The formula for cosine,

$\cos \theta =\frac{a}{r}$

$\cos \theta =\frac{\frac{-\sqrt{2}} {2}}{1}}$

$\cos \theta =\frac{-\sqrt{2}} {2}}$

The formula for cotangent,

$\cot \theta =\frac{a}{b}$

$\cos \theta=\frac{\frac{-\sqrt{2}} {2}}{\frac{\sqrt{2}} {2}}$

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Therefore, the value of cosine is $\frac{-\sqrt{2}} {2}$ and the value of cotangent is -1.

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3 years ago

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