Use inductive reasoning to predict the next three numbers in the pattern (or sequence).
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The height of the ramp is 9 meter
<u>Solution:</u>
It is given that a skateboard ramp is 15 meters long and it extends 12 meters from the base of the starting point.
If we look at the sum, closely we understand that the ramp is a right angled triangle.
Which has a base length of 12 metres and a hypotenuse of 15 metres.
We need to find its height.
To do so we can use the Pythagoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
By above definition, we get
Since we already know the lengths of the hypotenuse and base we can substitute them in the formula and solve for the height.
Let height of the ramp be denoted by ‘h’
Therefore, the height of the ramp is 9 meter
Short answer: (-8)^2 + 8 x -8 = 0
Use PEMDAS
"Evaluate the expression" just means solve until you can't simplify anymore. You must solve it in a certain order according to PEMDAS: Parentheses, Exponents, Multiply, Divide, Add, Subtract.
What does the beginning of the expression look like? It is
.
According to PEMDAS, you must solve what is in the parentheses *first*. But, since there is only a number (-8), there is nothing to solve for and you can move on to exponents.
The squared symbol, the little 2, means you have to square what is *inside* the parentheses. = 64, because -8 times itself is 64.
Next comes multiplication. Remember, we are not working from left to right. We must multiply the values on the far right before we do any adding, because multiplication comes *before* addition.
(64) + (8 times -8)
(64) + (-64)
Finally, we can add. In this case, because we are adding a negative number, we are really subtracting. 64 + -64 equals 0.
Use PEMDAS
"Evaluate the expression" just means solve until you can't simplify anymore. You must solve it in a certain order according to PEMDAS: Parentheses, Exponents, Multiply, Divide, Add, Subtract.
What does the beginning of the expression look like? It is
According to PEMDAS, you must solve what is in the parentheses *first*. But, since there is only a number (-8), there is nothing to solve for and you can move on to exponents.
The squared symbol, the little 2, means you have to square what is *inside* the parentheses.
Next comes multiplication. Remember, we are not working from left to right. We must multiply the values on the far right before we do any adding, because multiplication comes *before* addition.
(64) + (8 times -8)
(64) + (-64)
Finally, we can add. In this case, because we are adding a negative number, we are really subtracting. 64 + -64 equals 0.