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3 years ago

13

Solve each inequality. The variable should be on the left-hand side in your solution.

1 answer:

lara [203]3 years ago

5 0

Answer:

x≤ −96 /23

Step 1: Simplify both sides of the inequality.

Step 2: Subtract 1/8x from both sides.

Step 3: Subtract 12 from both sides.

Step 4: Multiply both sides by 8/23.

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kifflom [539]

$\\ \sf\longmapsto \dfrac{x^2-1}{x^2+5x+4}\leqslant 0$

Solving denominator

$\\ \sf\longmapsto x^2+5x+4>0$

$\\ \sf\longmapsto x^2+4x+x+4>0$

$\\ \sf\longmapsto x(x+4)+1(x+4)>0$

$\\ \sf\longmapsto (x+4)(x+1)>0$

$\\ \sf\longmapsto x>-4\:or x>-1$

Hence x $\neq$ -1
x can't be 0 as it makes function undefined

$\\ \sf\longmapsto -4$

5 0

3 years ago

I think of a number I multiply it by 2,add 50 and my answer is 74 what was my number

alisha [4.7K]

74-50 is 24. 24/2 is 12. your number was 12.

6 0

3 years ago

Read 2 more answers

Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)2 = 16 in the manner described. (En

ArbitrLikvidat [17]

Answer:

a) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ , b) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ , c) $x = 4\cdot \cos \left(t+\frac{\pi}{2} \right)$ , $y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right)$ .

Step-by-step explanation:

The equation of the circle is:

$x^{2} + (y-1)^{2} = 16$

After some algebraic and trigonometric handling:

$\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = 1$

$\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = \cos^{2} t + \sin^{2} t$

Where:

$\frac{x}{4} = \cos t$

$\frac{y-1}{4} = \sin t$

Finally,

$x = 4\cdot \cos t$

$y = 1 + 4\cdot \sin t$

a) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ .

b) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ .

c) $x = 4\cdot \cos t''$ , $y = 1 + 4\cdot \sin t''$

Where:

$4\cdot \cos t' = 0$

$1 + 4\cdot \sin t' = 5$

The solution is $t' = \frac{\pi}{2}$

The parametric equations are:

$x = 4\cdot \cos \left(t+\frac{\pi}{2} \right)$

$y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right)$

7 0

3 years ago

Identify the values of the variables. Give your answers in simplest radical form. HELP ASAP!!

kumpel [21]

Answer:

B

Step-by-step explanation:

Since the triangle is right use the sine/ tangent ratios to solve for x and y

note sin60° = $\frac{\sqrt{3} }{2}$ and tan60° = $\sqrt{3}$

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{3\sqrt{6} }{y}$

ysin60° = 3 $\sqrt{6}$

y × $\frac{\sqrt{3} }{2}$ = 3 $\sqrt{6}$

multiply both sides by 2 and divide by $\sqrt{3}$

y v= 6 $\sqrt{\frac{6}{3} }$ = 6 $\sqrt{2}$

tan60° = $\frac{opposite}{adjacent}$ = $\frac{3\sqrt{6} }{x}$

xtan60° = 3 $\sqrt{6}$

x × $\sqrt{3}$ = 3 $\sqrt{6}$

divide both sides by $\sqrt{3}$

x = 3 $\sqrt{\frac{6}{3} }$ = 3 $\sqrt{2}$

8 0

3 years ago

Read 2 more answers

Where can the denominator be found in a fraction?

Anuta_ua [19.1K]

Down on the bottom, under the fraction line.

5 0

3 years ago

Read 2 more answers