1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kvv77 [185]
3 years ago
14

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

Mathematics
2 answers:
Alexeev081 [22]3 years ago
8 0

|4r+8|\geq32\iff4r+8\geq32\ \vee\ 4r+8\leq-32\ \ \ |-8\\\\4r\geq24\ \vee\ 4r\leq-40\ \ \ |:4\\\\r\geq6\ \vee\ r\leq-10

Answer:\ r\geq6\ \vee\ r\leq-10\to r\in\left(-\infty;\ -10\right>\ \cup\ \left< 6;\ \infty\right)

S_A_V [24]3 years ago
7 0

|4r + 8| ≥ 32

Split this expression into two expressions:

First ⇒ 4r + 8 ≥ 32 and second ⇒ 4r + 8 ≤ - 32

---

First expression: 4r + 8 ≥ 32

Subtract 8 from both sides.

4r ≥ 24

Divide both sides by 4.

r ≥ 6

---

Second expression: 4r + 8 ≤ - 32

Subtract 8 from both sides.

4r ≤ -40

Divide both sides by 4.

r ≤ -10

---

Your answer is \boxed {r \geq 6~or~ r \leq  -10}

You might be interested in
A person runs 1/8 mile in 1/64 hour.<br> The person's speed is (BLANK) miles per hour.
snow_tiger [21]

Answer: The person's speed is 8 miles per hour.

Step-by-step explanation:

To solve we want to convert the \frac{1}{8} and \frac{1}{64} proportionally for the number of miles per hour. We know that multiplying a fraction by its reciprocal will equal 1. So let's do that for the value of the hour.

\frac{1}{64}×\frac{64}{1} =\frac{64}{64} =1

Since we multiplied that to the number of hours we must also do that for the number of miles.

\frac{1}{8}×\frac{64}{1} =\frac{64}{8} =8

7 0
2 years ago
What's the answer for this? Explain
alexandr402 [8]
Exterior angle is equal to sum of interior opposite angles hence,

req. angle = 80 + 62 = 142
6 0
3 years ago
Read 2 more answers
If f(x)= (3x+7)^2, then f(1) = ?
Crank
To find f(1), substitute 1 for x.

f(1) = (3(1)+7)²
f(1) = (3+7)²
f(1) = 10²
f(1) = 100
3 0
3 years ago
Read 2 more answers
ILL GIVE BRAINLIEST PLEASE HELP ASAP PLS
postnew [5]

Answer:

5/12 of rain came, or 10 inches

Step-by-step explanation:

complete rain be 1

then, =1-(1/4+1/3)

=1-(3+4/12) take lcm

=1-7/12

=12-7/12 again lcm

= 5/12

or

1/4 of 24 inches means 1/4×24= 6 inches

1/3 of 24 inches, then 1/3×24= 8 inches

therefore, rest of the months get

= 24-(6+8)

=24-14

=10 inches

7 0
3 years ago
QUESTION 1
Kitty [74]

It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.

Let <em>θ</em> be the angle between the force vector <em>F</em> and the displacement vector <em>r</em>. The work <em>W</em> done by <em>F</em> in the direction of <em>r</em> is

<em>W</em> = <em>F</em> • <em>r</em> cos(<em>θ</em>)

The cosine of the angle between the vectors can be obtained from the dot product identity,

<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>)   ==>   cos(<em>θ</em>) = (<em>a</em> • <em>b</em>) / (||<em>a</em>|| ||<em>b</em>||)

so that

<em>W</em> = (<em>F</em> • <em>r</em>)² / (||<em>F</em>|| ||<em>r</em>||)

For instance, if <em>F</em> = 3<em>i</em> + <em>j</em> + <em>k</em> and <em>r</em> = 7<em>i</em> - 7<em>j</em> - <em>k</em> (which is my closest guess to the given vectors' components), then the work done by <em>F</em> along <em>r</em> is

<em>W</em> = ((3<em>i</em> + <em>j</em> + <em>k</em>) • (7<em>i</em> - 7<em>j</em> - <em>k</em>))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))

==>   <em>W</em> ≈ 5.12 J

(assuming <em>F</em> and <em>r</em> are measured in Newtons (N) and meters (m), respectively).

3 0
3 years ago
Other questions:
  • What number is a factor of 16, and prime?
    9·2 answers
  • Jasmine is traveling at 45 miles per hour. At that same rate, how long will it take her to travel 135 miles?
    9·2 answers
  • The equation of a circle is given below. (x − 5) 2 + ( y + 2 ) 2 = 81 4 (x−5) 2 +(y+2) 2 = 4/81 What is its center? Radius?
    5·1 answer
  • Can someone helping me?
    8·2 answers
  • Please help :( I’ve been on this fit awhile
    11·1 answer
  • If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).
    6·1 answer
  • If you add Natalie's age and Fred's age, the result is 42. If you add Fred's age to 3 times
    15·1 answer
  • Can someone help me with this question I’m confused
    11·1 answer
  • 16) What is the percent of increase from 15 to 60?
    9·1 answer
  • In the general population, the mean IQ is 100 with a standard deviation of 15. Dr. Robbins wants to see if a class of statistics
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!