5x+4+8x-3=79
13x=79-1
x=6
DBC=34
ABC=45
6x+20+2x+4 = 180
8x = 156
x=19.5
TQS=137
RQS=43
Answer:
There is no solution for C.
Step-by-step explanation:
Answer:
- -35/3, -140/3, - 560/3, -2240/3
- 7, -28, 112, - 448
Step-by-step explanation:
<u>The terms are:</u>
<u>Given:</u>
- a₁ = a₂ + 35
- a₃ = a₄ + 560
<u>Use the nth term formula:</u>
- a₂ = a₁r
- a₃ = a₁r²
- a₄ = a₁r³
<u>Substitute:</u>
- a₁ = a₁r + 35 ⇒ a₁(1 - r) = 35
- a₁r² = a₁r³ + 560 ⇒ a₁(1 - r)r² = 560
<u>Divide the second equation by the first:</u>
- r² = 560/35
- r² = 16
- r = √16
- r = ± 4
<u>Use the first equation to find the first term:</u>
- a₁( 1 ± 4) = 35
- 1. a₁ = 35/-3 = -35/3
- 2. a₁ = 35/5 = 7
<u>We have two sequences:</u>
r = 4
- -35/3, -140/3, - 560/3, -2240/3
r = -4
<span>Solution can be gained by using "Product of means = Product of extremes" concept. So the information we have is 23 miles on 1 gal and 135 mile on 'x' gal.
23 : 1 :: 135 : x
As per Product of means = Product of extremes,
23 multiplied x = 135 multiplied by 1.
And x will be 135 divided by 23 which is 5.86 gal
Now, we have to convert gal to liters, 1 gal = 3.78 liters,
so 5.86 gal = 5.86 multiplied by 3.78, which is 22.15 liters.
Hence, 22.15 liters of gasoline are needed for a 135 mile trip</span>
Answer: 172 boys.
Step-by-step explanation: The ratio of boys to girls is 4:5. We can say that the number of boys in the class is four multiplied by the common value that the ratio is based on. We can call this common value x and say that the number of boys in the class is 4x. Applying the same logic to the girls, we can say that there are 5x girls in the class. Thus, a total of 9x children. We divide the total value by 9 to get x, which equals 43. We can then retrieve the number of boys by calculating 4x, which equals 172.