All categories

3 years ago

Find the solution set to each inequality. Express the solution in set notation.

Mathematics

1 answer:

daser333 [38]3 years ago

3 0

The solution to the inequality 6m + 2 > -27 is m > -4.33

The solution to the inequality 8(p-6)>4(p-4) is p > 8

The given inequality is:

6m + 2 > - 27

Subtract 2 to both sides of the inequality

6m + 2 - 2 > -27 - 2

6m > -29

Divide both sides by 6

$\frac{6m}{6}> \frac{-29}{6} \\m > \frac{-29}{6}\\m > -4.83$

For the inequality 8(p-6)>4(p-4)

Expand the inequality using the distributive rule

8p - 48 > 4p - 16

Collect like terms

8p - 4p > -16 + 48

4p > 32

Divide both sides of the inequality 4

$\frac{4p}{4} > \frac{32}{4}\\p > 8$

The solution to the inequality 6m + 2 > -27 is m > -4.33

The solution to the inequality 8(p-6)>4(p-4) is p > 8

Learn more here: brainly.com/question/15816805

You might be interested in

6. Let f(x)=x-2 and g(x) = x^2. Find the value of (fog)(-1).<br> A. -1<br> B.9<br> C.3<br> D.-3

inna [77]

Answer:

<h2>The answer is option A</h2>

Step-by-step explanation:

f(x) = x - 2

g(x) = x²

In order to find (fog)(-1) we must first find (fog)(x)

To find (fog)(x) substitute the g(x) into f(x) that's for every x in f (x) replace it with

g (x).

That's

(fog)(x) = x² - 2

To find (fog)(-1) substitute the value of x that's - 1 into (fog)(x)

We have

(fog)(-1) = (-1)² - 2 = 1 - 2 = - 1

Hope this helps you

8 0

3 years ago

6x squared plus 12x plus 13 equals 2x squared plus 4

Andrews [41]

$12x^2+12x+3=2x^2+4\\\\12x^2-2x^2+12x+3-4=0\\\\10x^2+12x-1=0\\\\a=10;\ b=12;\ c=-1\\\\\Delta=12^2-4\cdot10\cdot(-1)=144+40=184\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{184}=\sqrt{4\cdot46}=2\sqrt{46}\\\\x_1=\frac{-12-2\sqrt{46}}{2\cdot10}=\frac{-6-\sqrt{46}}{10};\ x_2=\frac{-12+2\sqrt{46}}{2\cdot10}=\frac{-6+\sqrt{46}}{10}$

6 0

3 years ago

What is the location of the asymptote of this exponential function? Answer with an equation.

zloy xaker [14]

Answer:

y=0

Step-by-step explanation:

The asymptote of exponential equations is where is plateaus/flattens out. it will never actually touch it. Here it flattens out on the y-axis.

5 0

3 years ago

I-Ready

STatiana [176]

Answer:

I believe that the answer would be 5 because a one moth pass is 20 and it's 4 times the day pass and 5 times 4 is 20

6 0

3 years ago

Solve x2 + 8x = 33 by completing the square. Which is the solution set of the equation? {–11, 3} {–3, 11} {–4, 4} {–7, 7}

HACTEHA [7]

ANSWER
$x = - 11\: or \: x = 3$

EXPLANATION

The quadratic equation given to us is

${x}^{2} + 8x = 33$

We add half the square of the coefficient of
$x$
to both sides of the equation to obtain,

${x}^{2} + 8x + {(4)}^{2} = 33 + {(4)}^{2}$

This implies that,
${x}^{2} + 8x + {(4)}^{2} = 33 + 16$

The right hand side simplifies to

${x}^{2} + 8x + {(4)}^{2} = 49$

The left hand side is a perfect square.

This gives us

${(x + 4)}^{2} = 49$

We take the square root of both sides

$x + 4 = \pm \sqrt{49}$

This evaluates to

$x + 4 = \pm 7$

We make x the subject.

$x = - 4\pm 7$

We now split the square root sign to get

.

$x = - 4 - 7 \: or \: x = - 4 + 7$

$x = - 11\: or \: x = 3$

The correct answer is A.

7 0

3 years ago