Answer:
Aaron's bowling score is 30
David's bowling score is 54
Step-by-step explanation:
The variable representing Aaron's score is = a
The variable representing David's bowling score = d
The sum of their scores is 84.
= a + d = 84...... Equation 1
David's bowling score is 6 less than 2 times Aaron's score.
d = 2a - 6
Substituting 2a - 6 for d in Equation 1
a + 2a - 6 = 84
3a - 6 = 84
3a = 84 + 6
3a = 90
a = 90/3
a = 30
Hence, Aaron's bowling score is 30
d = 2a - 6
d = 2(30) - 6
d = 60 - 6
d = 54
David's bowling score is 54
Answer:
The consecutive odd integers are (15, 17, 19) or (-17, -15, -13).
Step-by-step explanation:
Let the three consecutive odd integers be: 
The condition given is:
![4[x-2+x+x+2]=3x(x+2)-765](https://tex.z-dn.net/?f=4%5Bx-2%2Bx%2Bx%2B2%5D%3D3x%28x%2B2%29-765)
Solve this for <em>x</em> as follows:
![4[x-2+x+x+2]=3x(x+2)-765\\4\times 3x=3x^{2}+6x-765\\3x^{2}-6x-765=0\\x^{2}-2x-255=0\\x^{2}-17x+15x-255=0\\x(x-17)+15(x-17)=0\\(x-17)(x+15)=0](https://tex.z-dn.net/?f=4%5Bx-2%2Bx%2Bx%2B2%5D%3D3x%28x%2B2%29-765%5C%5C4%5Ctimes%203x%3D3x%5E%7B2%7D%2B6x-765%5C%5C3x%5E%7B2%7D-6x-765%3D0%5C%5Cx%5E%7B2%7D-2x-255%3D0%5C%5Cx%5E%7B2%7D-17x%2B15x-255%3D0%5C%5Cx%28x-17%29%2B15%28x-17%29%3D0%5C%5C%28x-17%29%28x%2B15%29%3D0)
- If
then the value of <em>x</em> is 17.
The odd numbers are:
- If
then the value of <em>x</em> is -15.
The odd numbers are:
Thus, the consecutive odd integers are (15, 17, 19) or (-17, -15, -13).
Answer: No es posible (It is not possible)
Step-by-step explanation:
The question in english is as follows:
Is it possible to draw 9 line segments so that each segment crosses exactly 1 of the other segments?
A necessary condition for two lines to intersect is that they must be in the same plane (they must be coplanar), being their intersection a single point.
Now, if we want several lines to intersect only once, we need to have an <u>even number</u> of line segments. However, this is not the case because <u>9 is odd.
</u>
Therefore, it is not possible.
Answer:
b = 8√3 mm, a = 16 mm, x = 5 ft, y = 5√2 ft.
Step-by-step explanation:
With 30° 60° 90° triangles, one side will be a number, the other leg will be that number multiplied by √3, and the hypotenuse will be 2 times that original number.
So in this case:
The original leg's length is 8 mm. Side b will be that 8 times √3.
So, b = 8√3 mm.
Side a will be 8 times 2.
So, a = 16 mm.
With 45° 45° 90° triangles, the two legs will be the same length, and the hypotenuse will be that number times √2.
So in this case:
The original leg's length is 5 ft. Side x will be that same length.
So, x = 5 ft.
Side y will be 5 times √2.
So, y = 5√2 ft.
