An elevator can carry 800 pounds of weight. A student weighing 95 pounds gets on the elevator. Write and solve an inequality to represent the remaining weight that can be added.

Answers

Answer 1

Answer: It would be 95x less than or equal to sign 800

Answer 2

Answer:

Final answer:

To represent the remaining weight that can be added to the elevator, write and solve the inequality 800 - 95 ≥ x. The remaining weight is 705 pounds or less.

Explanation:

To represent the remaining weight that can be added to the elevator, we can use an inequality. Let's assume that the remaining weight is represented by 'x' pounds. The total weight the elevator can carry is 800 pounds. So, the inequality can be written as:

800 - 95 ≥ x

To solve the inequality, we subtract 95 from both sides:

x ≤ 800 - 95

x ≤ 705

Therefore, the remaining weight that can be added to the elevator is 705 pounds or less.

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Three times a number s plus 4 times a number y is 1 more than 6 times the number s. solve for s

Answers

Three times a number s => 3s
4 times a number y => 4y
1 more than 6 times the number s => 6s + 1

The full equation would be:

3s + 4y = 6s + 1

Solve for s.
group same letter numbers and change its signs.
3s - 6s = -4y + 1
-3s = -4y + 1
solve for s. divide both sides by -3
-3s / -3 = (-4y + 1) / -3
s = (4y - 1) / 3

"Three times a number S" is 3s.
"Plus 4 times a number y" is + 4y
"is" =
"1 more than" is 1 +
"6 times the number S" is 6s.
The equation is:
3s+4y=1+6s
subtract 3s:
4y = 1 +3s
subtract 1:
4y - 1 = 3s
Divide everything by 3:
4y/3 - 1/3 = s

Which values are within the range of the piecewise-defined function?f(x) =
2 x + 2 x < - 3
X x = -3
- x - 2 X > -3
y = -6
y=-4
y=-3
y = 0
y = 1
y = 3

Answers

-6, -4, -3, and 0 are the values which are within the range of the piecewise-defined function.

Correct options: a) y = -6, b) y = -4, c) y = -3, d) y = 0

Here, we have, to determine which values are within the range of the piecewise-defined function, we need to evaluate the function for each given value of y.

Given piecewise-defined function:

f(x) =

2x, x < -3

x, x = -3

-x - 2, x > -3

Let's evaluate the function for each value of y:

a) y = -6

For y = -6, we need to find x such that f(x) = -6.

-6 is in the range of the function if there exists an x such that f(x) = -6.

For x < -3: f(x) = 2x

2x = -6

x = -3

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -6

x = 4

Since there is a value of x (-3) that satisfies f(x) = -6, option a) y = -6 is correct.

b) y = -4

For y = -4, we need to find x such that f(x) = -4.

-4 is in the range of the function if there exists an x such that f(x) = -4.

For x < -3: f(x) = 2x

2x = -4

x = -2

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -4

x = 2

Since there is a value of x (-3) that satisfies f(x) = -4, option b) y = -4 is correct.

c) y = -3

For y = -3, we need to find x such that f(x) = -3.

-3 is in the range of the function if there exists an x such that f(x) = -3.

For x < -3: f(x) = 2x

2x = -3

x = -1.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -3

x = 1

Since there is a value of x (-3) that satisfies f(x) = -3, option c) y = -3 is correct.

d) y = 0

For y = 0, we need to find x such that f(x) = 0.

0 is in the range of the function if there exists an x such that f(x) = 0.

For x < -3: f(x) = 2x

2x = 0

x = 0

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 0

x = -2

Since there is a value of x (-3) that satisfies f(x) = 0, option d) y = 0 is correct.

e) y = 1

For y = 1, we need to find x such that f(x) = 1.

1 is in the range of the function if there exists an x such that f(x) = 1.

For x < -3: f(x) = 2x

2x = 1

x = 0.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 1

x = -3

Since there is no value of x that satisfies f(x) = 1, option e) y = 1 is incorrect.

f) y = 3

For y = 3, we need to find x such that f(x) = 3.

3 is in the range of the function if there exists an x such that f(x) = 3.

For x < -3: f(x) = 2x

2x = 3

x = 1.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 3

x = -5

Since there is no value of x that satisfies f(x) = 3, option f) y = 3 is incorrect.

Correct options: a) y = -6, b) y = -4, c) y = -3, d) y = 0

The correct values within the range of the piecewise-defined function are -6, -4, -3, and 0.

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Answer:

-6, -4, -3, 0

Step-by-step explanation:

I just did this question and got it right.

A total of 60 children signed up for hockey. There were 3 boys for every 1 girl who signed up. How many of the children who signed up for hockey were girls?

Answers

Answer: The answer is 15.

Step-by-step explanation: Given that there are a total of 60 students who signed up for hockey, where there were 3 boys for every 1 girl who signed up. We are to find the number of girls who signed up.

The ratio of the number of boys to the number of girls will be 3 : 1.

Let '3x' and 'x' be the number of boys and number of girls respectively who signed up.

Therefore, we have

$3x+x=60\n\n\Rightarrow 4x=60\n\n\Rightarrow x=15.$