If one leg of a right triangle is 18 units and the other leg is 24 units, what is the length of the hypotenuse (in units)?
To find the length of the hypotenuse, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of one leg is 18 units and the length of the other leg is 24 units.
So, using the Pythagorean theorem:
hypotenuse^2 = 18^2 + 24^2
hypotenuse^2 = 324 + 576
hypotenuse^2 = 900
Taking the square root of both sides, we find the length of the hypotenuse:
hypotenuse = sqrt(900)
hypotenuse = 30 units
Therefore, the length of the hypotenuse is 30 units.
9.
You are converting the numbers shown below into scientific notation. Which of the options will be a number times
1
0
3
10
3
Select all that apply
191.77
1589
2415.81
9884
To convert a number into scientific notation, we need to write it as a product of a number between 1 and 10, multiplied by a power of 10.
The options that can be written in scientific notation are:
191.77 = 1.9177 × 10^2
1589 = 1.589 × 10^3
2415.81 = 2.41581 × 10^3
9884 = 9.884 × 10^3
So, all four options can be written in scientific notation.
10.
>
Drag the numbers into the inequality above to show which is larger.
Drag and drop the correct choice into the blank spaces above
I apologize, but I am unable to see or interact with any visual representation or options for you to drag and drop the correct choice. Could you please provide the numbers you would like me to compare?
12.
Solve for x
�
2
=
256
x
2
=256
±
18
±18
±
12
±12
±
14
±14
±
16
±16
To solve for x in the equation 2^x = 256, we need to determine the value of x that satisfies the equation.
To find x, we can use logarithms. Taking the logarithm (base 2) of both sides of the equation:
log2(2^x) = log2(256)
Using the property of logarithms, where log_b(b^x) = x:
x = log2(256)
Calculating the value of log2(256):
x = 8
Therefore, the value of x that satisfies the equation is 8.
Gerald bought 5 tomato plants for $16.20. What is the cost if he bought 8 tomato plants? Write your answer as a decimal.
To find the cost of 8 tomato plants, we can set up a proportion using the number of plants and the cost.
We know that 5 tomato plants cost $16.20.
So, we can set up the proportion:
5 plants / $16.20 = 8 plants / x
To solve for x, we can cross-multiply:
5x = 8 * $16.20
5x = $129.60
Dividing both sides of the equation by 5:
x = $129.60 / 5
x ≈ $25.92
Therefore, if Gerald bought 8 tomato plants, the cost would be approximately $25.92.
To solve this problem, we can use the Pythagorean Theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's label the given legs as side A and side B. In this case, side A has a length of 18 units, and side B has a length of 24 units. Let's label the hypotenuse as side C.
We can use the Pythagorean Theorem equation: A^2 + B^2 = C^2.
Plugging in the values: 18^2 + 24^2 = C^2.
Simplifying the equation: 324 + 576 = C^2.
Adding the numbers: 900 = C^2.
To find the length of the hypotenuse, we take the square root of both sides of the equation: √900 = √C^2.
Simplifying the equation: 30 = C.
Therefore, the length of the hypotenuse is 30 units.