Answer:
207
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
=
[ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 37 and d = 34 - 37 = - 3 , thus
=
[ (2 × 37) + (17 × - 3) ]
= 9( 74 - 51)
= 9 × 23
= 207
Answer: the correct answer is 43 hours
Step-by-step explanation:
40x15=600
15x2=30 because you get your 50% extra doing overtime
then 30x3=90
90+600=690
Answer:
would it not have been: m= - 7/3
Answer:
yd^2
Step-by-step explanation:
Formula: ![A = \frac{pq}{2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7Bpq%7D%7B2%7D)
p = 7.5 + 7.5 = 15
q = 13 + 13 = 26
![A = \frac{26*15}{2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B26%2A15%7D%7B2%7D)
A = 195
Answer:
D
Step-by-step explanation:
Consider all options:
A. False, because
![(a^2+b^2)(c^2+d^2)=a^2c^2+a^2d^2+b^2c^2+b^2d^2\\ \\(ab-cd)^2+(ac+bd)^2=a^2b^2-2abcd+c^2d^2+a^2c^2+2abcd+b^2d^2=\\ =a^2b^2+c^2d^2+a^2c^2+b^2d^2\\ \\a^2c^2+a^2d^2+b^2c^2+b^2d^2\neq a^2b^2+c^2d^2+a^2c^2+b^2d^2](https://tex.z-dn.net/?f=%28a%5E2%2Bb%5E2%29%28c%5E2%2Bd%5E2%29%3Da%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%5C%5C%20%5C%5C%28ab-cd%29%5E2%2B%28ac%2Bbd%29%5E2%3Da%5E2b%5E2-2abcd%2Bc%5E2d%5E2%2Ba%5E2c%5E2%2B2abcd%2Bb%5E2d%5E2%3D%5C%5C%20%3Da%5E2b%5E2%2Bc%5E2d%5E2%2Ba%5E2c%5E2%2Bb%5E2d%5E2%5C%5C%20%5C%5Ca%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%5Cneq%20a%5E2b%5E2%2Bc%5E2d%5E2%2Ba%5E2c%5E2%2Bb%5E2d%5E2)
B. False, because
![(a^2-b^2)(c^2+d^2)=a^2c^2+a^2d^2-b^2c^2-b^2d^2\\ \\(ac-bd)^2-(ad+bc)^2=a^2c^2-2abcd+b^2d^2+a^2d^2+2abcd+b^2c^2=\\=a^2c^2+b^2d^2+a^2d^2+b^2c^2\\ \\a^2c^2+a^2d^2-b^2c^2-b^2d^2\neq a^2c^2+b^2d^2+a^2d^2+b^2c^2](https://tex.z-dn.net/?f=%28a%5E2-b%5E2%29%28c%5E2%2Bd%5E2%29%3Da%5E2c%5E2%2Ba%5E2d%5E2-b%5E2c%5E2-b%5E2d%5E2%5C%5C%20%5C%5C%28ac-bd%29%5E2-%28ad%2Bbc%29%5E2%3Da%5E2c%5E2-2abcd%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2B2abcd%2Bb%5E2c%5E2%3D%5C%5C%3Da%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%5C%5C%20%5C%5Ca%5E2c%5E2%2Ba%5E2d%5E2-b%5E2c%5E2-b%5E2d%5E2%5Cneq%20a%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2)
C. False, because
![(a^2+b^2)(c^2-d^2)=a^2c^2-a^2d^2+b^2c^2-b^2d^2\\ \\(ac+bd)^2-(ad+bc)^2=a^2c^2+2abcd+b^2d^2-a^2d^2-2abcd-b^2c^2=\\=a^2c^2+b^2d^2-a^2d^2-b^2c^2\\ \\a^2c^2-a^2d^2+b^2c^2-b^2d^2\neq a^2c^2+b^2d^2-a^2d^2-b^2c^2](https://tex.z-dn.net/?f=%28a%5E2%2Bb%5E2%29%28c%5E2-d%5E2%29%3Da%5E2c%5E2-a%5E2d%5E2%2Bb%5E2c%5E2-b%5E2d%5E2%5C%5C%20%5C%5C%28ac%2Bbd%29%5E2-%28ad%2Bbc%29%5E2%3Da%5E2c%5E2%2B2abcd%2Bb%5E2d%5E2-a%5E2d%5E2-2abcd-b%5E2c%5E2%3D%5C%5C%3Da%5E2c%5E2%2Bb%5E2d%5E2-a%5E2d%5E2-b%5E2c%5E2%5C%5C%20%5C%5Ca%5E2c%5E2-a%5E2d%5E2%2Bb%5E2c%5E2-b%5E2d%5E2%5Cneq%20a%5E2c%5E2%2Bb%5E2d%5E2-a%5E2d%5E2-b%5E2c%5E2)
D. True, because
![(a^2+b^2)(c^2+d^2)=a^2c^2+a^2d^2+b^2c^2+b^2d^2\\ \\(ac-bd)^2-(ad+bc)^2=a^2c^2-2abcd+b^2d^2+a^2d^2+2abcd+b^2c^2=\\=a^2c^2+b^2d^2+a^2d^2+b^2c^2\\ \\a^2c^2+a^2d^2+b^2c^2+b^2d^2= a^2c^2+b^2d^2+a^2d^2+b^2c^2](https://tex.z-dn.net/?f=%28a%5E2%2Bb%5E2%29%28c%5E2%2Bd%5E2%29%3Da%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%5C%5C%20%5C%5C%28ac-bd%29%5E2-%28ad%2Bbc%29%5E2%3Da%5E2c%5E2-2abcd%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2B2abcd%2Bb%5E2c%5E2%3D%5C%5C%3Da%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%5C%5C%20%5C%5Ca%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%3D%20a%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2)