Answer:
14 and 16.
Step-by-step explanation:
We know that two consecutive even numbers is 30.
Let's let n be <em>any number</em>.
Then the first <em>even</em> number must be 2n.
This is because n can be any number, either even or odd. However, if we multiply it by 2, this <em>ensures</em> that 2n is even. Remember that any number multiplied by 2 yields an even number.
Therefore, the consecutive even number will be (2n+2). Not (2n+1), because that gives an odd number.
We know that they sum to 30. So, we can write the following equation.
And we solve from there:
So, the value of n is 7.
Therefore, the first even number is 7(2)=14.
And the consecutive even number is 16.
Edit: Typo
Answer:
These triangles cannot be proved congruent
Step-by-step explanation:
The theorems for congruence are SSS SAS ASA AAS. Here, there is only one common side and one common angle marked, therefore you cannot prove congruency.
Answer: 9 inches
Step-by-step explanation:
Answer:
8 inches.
Step-by-step explanation:
From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.
Ab = s ^ 2 = 100
Therefore each side would be:
s = (100) ^ (1/2)
s = 10
So, side of the square base = 10 inches
Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:
Ap = 520/2 = 260
For an area of the square pyramid we have the following equation:
Ap = 2 * x * s + s ^ 2
Where x is the height of each triangular surface and s is the side of the square base
Replacing we have:
260 = 2 * x * 10 + 10 ^ 2
20 * x + 100 = 260
20 * x = 160
x = 160/20
x = 8
Therefore, the value of x is 8 inches.
