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ELEN [110]
2 years ago
13

PLEASE HELP I WILL GIVE BRAINLIEST TO RIGHT ANSWER

Mathematics
1 answer:
tigry1 [53]2 years ago
4 0
1: 19 (4x+25=6x -13, solve for x, 25+13=6x-13, 38=2x, x=19, 4(19)+25=101 6(19)-13+101)

2: 23 (3x-8=2x+15)

3: Madison has $59 and Saul has $31 (together they have $90 so divided by 2 and you get 45, Madison has 6 dollars more so subtract 6 from Saul and ad 6 to Madison, make sure that when you ad them you get $90)

4 : 5 weeks ($3 each week, so you multiply 3x5 and get 15. 15+57=72 but the problem says more then so maybe it’s 6 weeks cause that’s $75)

5: 10 weeks (he has 1,800 and needs 2,150, subtract 1,800 from 2,150 for how much he needs. You get 350. He needs that and he makes 35 a week so that would be 350 divided by 35, which is 10)

6:20 miles (it’s 2.25 for that’s first mile. He spent 6.05 so subtract 2.25 from 6.05 and you get 3.80, 3.80 divided by 0.20 is 19, then you need to add that first mile and it’s 20)

7: 6 figures in a complete set (Charlie starts out with 2 and Patrick starts out with 20 individual figures. Charlie has 6 sets and Patrick has 3, i multiplied the number of sets they had by 6 then added their individual figures until they numbers matched up)

8: an orange has 45 calories and an apple has 75 calories (5x-150=3x, 5x-3x= -2x, -2x divided by -150 = 75, 75-30 is 45. 75 is the apple and because it’s 30 more you subtract 30 for orange)

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Find the first term and the common ratio <br>third term =6 and seventh term= 96​
mamaluj [8]

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First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: a_n= a_1r^{n-1}

We are given: third term = 6 i,e

a_3=a_1r(3-1)\\6=a_1r^2----eq(1)

Seventh term = 96

a_7=a_1r(7-1)\\96=a_1r^6----eq(2)

Dividing eq(2) and eq(3)

\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}

So, Common Ratio r = 2

Finding First term using eq(1)

a_3=a_1r^2\\6=a_1(2)^2\\6=a_1(4)\\a_1= \frac{6}{4}\\a_1= \frac{3}{2}

So, First term a₁ = 3/2 and common ratio r = 2

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