Question

Evaluate the following expression when a = 5 and b = 1. Then, plot the resulting value on the provided number line. 12+2 (4 a²) ÷ 7 + 8

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Answer 1

To evaluate the expression when `a=5` and `b=1`, we simply substitute these values into the expression and simplify using the order of operations (PEMDAS):
```
12 + 2(4a^2)÷7 + 8
= 12 + 2(4(5)^2)÷7 + 8 (substituting a=5)
= 12 + 2(4(25))÷7 + 8 (evaluating 5^2 = 25)
= 12 + 2(100)÷7 + 8
= 12 + 28.57 + 8 (evaluating 2(100)÷7 = 28.57)
= 48.57
```
So the value of the expression when `a=5` and `b=1` is `48.57`.

To plot this value on a number line, we first need to determine the appropriate scale for the number line. Since the value we obtained is between 40 and 50, we can use a scale of 1 unit per tick mark. We then draw a number line and label it with tick marks at appropriate intervals. Finally, we plot the value `48.57` on the number line:
```
|-------------------------------------------
40 50
x=48.57
```
Therefore, the value of the given expression when `a=5` and `b=1` is `48.57` and we have plotted it on the number line.

Answer 2

To evaluate the expression when a = 5 and b = 1, we substitute the values into the expression:

12 + 2(4(5)²) ÷ 7 + 8

= 12 + 2(4 * 25) ÷ 7 + 8 (Note: 5² means 5 raised to the power of 2)

= 12 + 2(100) ÷ 7 + 8 (Note: 4 * 25 = 100)

= 12 + 200 ÷ 7 + 8

= 12 + 28.57 + 8 (Note: ÷ means divide)

= 48.57

To plot the resulting value on the provided number line , we would need to know the scale and range of the number line. Without this information, we cannot accurately plot the value.

Explanation: