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3 years ago

Solve the inequality. Enter any fractions as reduced improper fractions. 4x ≤ -2/5(6x + 6) The solution is _____

Mathematics

1 answer:

Deffense [45]3 years ago

6 0

Answer:

x≤ -3/8

Step-by-step explanation:

$4x\le \:-\frac{2}{5}\left(6x+6\right)\\$

Expand ;

$\mathrm{Expand\:}-\frac{2}{5}\left(6x+6\right):\quad -\frac{12}{5}x-\frac{12}{5}$

$4x\le \:-\frac{12}{5}x-\frac{12}{5}\\\\\mathrm{Add\:}\frac{12}{5}x\mathrm{\:to\:both\:sides}\\\\4x+\frac{12}{5}x\le \:-\frac{12}{5}x-\frac{12}{5}+\frac{12}{5}x$

Simplify

$\frac{32}{5}x\le \:-\frac{12}{5}\\\\Multiply \:both\:sides\:by\:5\\5\times\frac{32}{5}x\le \:5\left(-\frac{12}{5}\right)\\\\Simplify\\32x\le \:-12\\\\Divide \:both\:sides\:by\:32\\\frac{32x}{32}\le \frac{-12}{32}\\\\Simplify\\x\le \:-\frac{3}{8}$

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3 years ago

The graph of 15x + 7y = 15 is shown on the grid. Which ordered pair is in the solution set of 15x + 7y ≥ 15?

elena55 [62]

Answer:

The correct option is c.

Step-by-step explanation:

The given equation is

$15x+7y=15$

The given inequality is

$15x+7y\geq 15$

A point will contained in solution set if the above inequality satisfied by that point.

Check the point (0,-3),

$15(0)+7(-3)\geq 15$

$-21\geq 15$

This statement is false, therefore option a is incorrect.

Check the point (-3,0),

$15(-3)+7(0)\geq 15$

$-45\geq 15$

This statement is false, therefore option b is incorrect.

Check the point (3,3),

$15(3)+7(3)\geq 15$

$66\geq 15$

This statement is true, therefore option c is correct.

Check the point (-3,-3),

$15(-3)+7(-3)\geq 15$

$-66\geq 15$

This statement is false, therefore option d is incorrect.

7 0

3 years ago

I don’t know how to do this. Can you help please help me ?

N76 [4]

Answer:

sin = -√3/2
cos = -1/2
tan = √3
sec = -2
csc = (-2/3)√3
cot = (√3)/3

Step-by-step explanation:

See the attached picture for a drawing of the angle and its terminal point coordinates. Those are (cos(4π/3), sin(4π/3)), so we have the following trig function values:

sin(4π/3) = -√3/2

cos(4π/3) = -1/2

tan(4π/3) = sin/cos = √3

sec(4π/3) = 1/cos = -2

csc(4π/3) = 1/sin = -(2√3)/3

cot(4π/3) = 1/tan = (√3)/3

_____

<em>Additional comment</em>

It helps to know that 1/√a = (√a)/a. This lets you write the ratios with a rational denominator in each case.