Ok, I am horrible at math so I am going to need someone's help.....
1. Solve.
|x+3|<5
a. -8<x<2 ****
b. -2<x<8
c.3<x<5
d.-3<x<5
2. Solve.
|-3n| - 2 = 4
a. 2 or -2 ****
b. 3 or -3
c. 4 or -4
d. 6 or -6
3. Solve.
|f| - 2/3=5/6
a. 5/6 or -5/6
b. 2/3 or -2/3
c. 1 1/2 or -1 1/2
d. no solution
4. Solve.
-2 |x - 5|≤ -10
a. x ≤ -5 or x ≥ 5
b. -5 ≤ x ≤ 5
c. x ≤ 0 or x ≥ 10
d. -10 ≤ x ≤ 10
5. The ideal circumference of a woman's basketball is 28.75 in. The actual circumference may vary from the ideal by at most 0.25 in. What are the acceptable circumferences for a woman's basketball? Let the variable,c, represent circumference.
a. c ≤ 28.5 in. or c ≥ 29 in.
b. c < 28.5 in. or c > 29 in.
c. 28.5 in. ≤ c ≤ 29 in.
d. 28.5 < c < 29 in.
Please help!!
Answer:
1: A
2: A
3: C
4: C
5: C
playfun is correct i got a 100 !
playfun is 100% correct.
playfun is right, i was on here to check and all the answers were right
1. agree
2. agree
3. hint f - 4/6 = 5/6 and -f - 4/6 = 5/6
-2 |x - 5|≤ -10
|x-5| >= 5
That is, x must be at least 5 away from 5
x ≤ 0 or x ≥ 10
or, algebraically,
(x-5)^2 >= 25
x^2 - 10x + 25 >= 25
x^2-10x >= 0
x(x-10) >= 0
so, either both are positive (x >= 10)
or both are negative (x <= 0)
28.75 - 0.25 <= c <= 28.75 + 0.25
28.5 <= c <= 29.0
4.
-2 |x - 5|≤ -10
|x-5| >/= 5
ends
(x-5) = 5 is x = 10
-(x-5) = 5 is -x = 0
c
circumference between AND including the end points
Sure! I'd be happy to help you solve these math problems. Let's go through each of them step by step:
1. Solve |x + 3| < 5:
To solve this absolute value inequality, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
When x + 3 is positive:
In this case, the inequality becomes x + 3 < 5. Solving for x, we have x < 2.
When x + 3 is negative:
In this case, we have -(x + 3) < 5. Simplifying, we get -x - 3 < 5. Adding x and 3 to both sides, we get -x < 8. Multiplying both sides by -1 (since we are dividing by a negative number), we have x > -8.
Combining both cases, we have -8 < x < 2.
Therefore, the correct answer is a. -8 < x < 2.
2. Solve |-3n| - 2 = 4:
First, let's isolate the absolute value by adding 2 to both sides of the equation:
|-3n| = 6.
Now, we need to consider two cases: when -3n is positive and when it is negative.
When -3n is positive:
In this case, the equation becomes -3n = 6. Solving for n, we have n = -2.
When -3n is negative:
In this case, we have -(-3n) = 6. Simplifying, we get 3n = 6. Dividing both sides by 3, we have n = 2.
Combining both cases, we have n = -2 or n = 2.
Therefore, the correct answer is a. 2 or -2.
3. Solve |f| - 2/3 = 5/6:
To solve this equation, we isolate the absolute value term by adding 2/3 to both sides:
|f| = 5/6 + 2/3 = 5/6 + 4/6 = 9/6 = 3/2.
Once again, we consider two cases: when f is positive and when it is negative.
When f is positive:
In this case, the equation becomes f = 3/2.
When f is negative:
In this case, we have -f = 3/2. Multiplying both sides by -1 (since we are dividing by a negative number), we get f = -3/2.
Combining both cases, we have f = 3/2 or f = -3/2.
Therefore, the correct answer is c. 1 1/2 or -1 1/2.
4. Solve -2|x - 5| ≤ -10:
We start by dividing both sides of the inequality by -2. Remember to reverse the inequality when dividing by a negative number:
|x - 5| ≥ 5.
Now, we consider two cases: when x - 5 is positive and when it is negative.
When x - 5 is positive:
In this case, the inequality becomes x - 5 ≥ 5. Solving for x, we have x ≥ 10.
When x - 5 is negative:
In this case, we have -(x - 5) ≥ 5. Simplifying, we get -x + 5 ≥ 5. Subtracting 5 from both sides, we have -x ≥ 0. Multiplying both sides by -1, we get x ≤ 0.
Combining both cases, we have x ≤ 0 or x ≥ 10.
Therefore, the correct answer is c. x ≤ 0 or x ≥ 10.
5. The acceptable circumferences for a woman's basketball can be found by adding and subtracting the maximum allowable variation (0.25 inches) from the ideal circumference (28.75 inches).
The acceptable circumferences are:
c ≤ 28.75 + 0.25 = 29 inches, and
c ≥ 28.75 - 0.25 = 28.5 inches.
Therefore, the correct answer is a. c ≤ 28.5 in. or c ≥ 29 in.
I hope this explanation helps you understand how to solve these problems. If you have any further questions, feel free to ask!