All categories

4 years ago

Solve the inequality. Show your work. |4r + 8| ≥ 32

Mathematics

3 answers:

saw5 [17]4 years ago

7 0

|4r + 8| ≥ 32

4r + 8 ≥ 32 or 4r + 8 ≤ -32 inside of absolute value could be + or -

4r ≥ 24 or 4r ≤ -40 subtracted 8 from both sides

r ≥ 6 or r ≤ -10 divided both sides by 4

Graph: ←---------------- -10 6 ------------------→

Interval Notation: (-∞, -10] U [6, ∞)

finlep [7]4 years ago

3 0

Okay here are the steps to solving this inequality:

First- Break down the problem into these 2 equations

4r + 8 ≥ 32 → - (4r + 8) ≥ 32

Second- Solve the 1st equation: 4r + 8 ≥ 32

r ≥ 6

Third- Solve the 2nd equation: - (4r + 8) ≥ 32

r ≤ -10

Lastly- Collect all solutions

lord [1]4 years ago

3 0

Okay here are the steps to solving this inequality:

First- Break down the problem into these 2 equations

4r + 8 ≥ 32 → - (4r + 8) ≥ 32

Second- Solve the 1st equation: 4r + 8 ≥ 32

r ≥ 6

Third- Solve the 2nd equation: - (4r + 8) ≥ 32

r ≤ -10

Lastly- Collect all solutions

You might be interested in

Given f(x)=5x-4, solve for x when f(x)=1

Sergio [31]

Answer:

X=1

Step-by-step explanation:

1=5x-4

5=5x

5/5=5/5x

X=1

8 0

3 years ago

The lines s and t intersect at point R. What is the value of y? y = ____

ozzi

Assuming that the angles are congruent, then y = 29.
4y - 8 = 79 + y
4y = 87 + y Add 8 to both sides
3y = 87 Subtract y from both sides
y = 29

7 0

3 years ago

Round 2.85 tons to the nearest hundredth

Dahasolnce [82]

Round up to get 2.90 because you have a 5 behind the decimal so you could round up

6 0

3 years ago

Given that f(x) = √(ax + 1) , with x ≥ -1/a and a > 0

padilas [110]

Answer:

$\displaystyle 7$

Step-by-step explanation:

first thing I assume by f~¹ you meant $f^{-1}$ however

we want to find a²+3x-3 for the given condition. with the composite function condition we can do so

Finding the inverse of f(x):

$\displaystyle f(x) = \sqrt{ax + 1}$

substitute y for f(x):

$\displaystyle y= \sqrt{ax + 1}$

interchange:

$\displaystyle x= \sqrt{ay + 1}$

square both sides:

$\displaystyle ay + 1 = {x}^{2}$

cancel 1 from both sides:

$\displaystyle ay = {x}^{2} - 1$

divide both sides by a:

$\displaystyle y = \frac{{x}^{2} - 1 }{a}$

substitute f^-1 for y:

$\displaystyle f ^{ - 1} (x) = \frac{{x}^{2} - 1 }{a}$

finding the inverse of g(x):

$\displaystyle g(x) = \frac{x + 1}{x}$

substitute y for g(x)

$\displaystyle y= \frac{x + 1}{x}$

interchange:

$\displaystyle \frac{y + 1}{y} =x$

cross multiplication

$\displaystyle y + 1= xy$

cancel 1 from both sides

$\displaystyle y - xy= - 1$

factor out y:

$\displaystyle y(1 - x)= - 1$

divide both sides by 1-x:

$\displaystyle y= - \frac{1}{ 1 - x}$

substitute g^-1 for y:

$\displaystyle g ^{ - 1} (x)= - \frac{1}{ 1 - x}$

remember that

$\displaystyle (f \circ g)x = f(g(x))$

therefore we obtain:

$\rm \displaystyle (f ^{ - 1} \circ g ^{ - 1} ) (3) = \frac{{ \bigg(- \dfrac{1}{1 - 3} } \bigg)^{2} - 1 }{a}$

since (f~¹•g~¹)(3)=-⅜ thus substitute:

$\rm \displaystyle \frac{{ \bigg(- \dfrac{1}{1 - 3} } \bigg)^{2} - 1 }{a} = - \frac{3}{8}$

simplify parentheses:

$\rm \displaystyle \frac{{ \bigg( \dfrac{1}{2} } \bigg)^{2} - 1 }{a} = - \frac{3}{8}$

simplify square:

$\rm \displaystyle \frac{{ \dfrac{1}{4} } - 1 }{a} = - \frac{3}{8}$

simplify substraction:

$\rm \displaystyle \frac{ - \dfrac{3}{4} }{ a}= - \frac{3}{8}$

simplify complex fraction:

$\rm \displaystyle - \dfrac{3}{4a} = - \frac{3}{8}$

get rid of - sign:

$\rm \displaystyle \dfrac{3}{4a} = \frac{3}{8}$

divide both sides by 3:

$\rm \displaystyle \dfrac{1}{4a} = \frac{1}{8}$

cross multiplication:

$\rm \displaystyle 4a= 8$

divide both sides by 4:

$\rm \displaystyle \boxed{ a= 2}$

as we want to find a²+3a-3 substitute the got value of a:

$\displaystyle {2}^{2} + 3.2 - 3$

simplify square:

$\displaystyle 4 + 3.2 - 3$

simplify multiplication:

$\displaystyle 4 +6 - 3$

simplify addition:

$\displaystyle 10 - 3$

simplify substraction:

$\displaystyle 7$

and we are done!

7 0

3 years ago

M(12, 1) is the midpoint of DG. If D is at (6, 5), then where is G?

sukhopar [10]

Answer:

18, -3

using the formula for midpoint M=(x1+x2)/2 ,(y1+y2)/2

4 0

3 years ago