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Olegator [25]
3 years ago
13

A = 6 - b (isolate b)

Mathematics
1 answer:
victus00 [196]3 years ago
7 0

Answer:

-a +6=b

Step-by-step explanation:

a= 6-b

a-6= -b

a- 6/-1 = -1b/-1

-a+6 =b

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In a G.P the 3rd term is 4 times the 1st term and the sum of the 2nd term and the 4th term is 30.find the common ratio,find the
STALIN [3.7K]

Answer:

the common ratio is either 2 or -2.

the sum of the first 7 terms is then either 765 or 255

Step-by-step explanation:

a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.

so,

a1

a2 = a1×f

a3 = a2×f = a1×f²

a4 = a3×f = a1×f³

the problem description here tells us

a3 = 4×a1

and from above we know a3 = a1×f².

so, f² = 4

and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).

again, the problem description tells us

a2 + a4 = 30

a1×f + a1×f³ = 30

for f = 2

a1×2 + a1×2³ = 30

2a1 + 8a1 = 30

10a1 = 30

a1 = 3

for f = -2

a1×-2 + a1×(-2)³ = 30

-10a1 = 30

a1 = -3

the sum of the first n terms of a geometric sequence is

sn = a1×(1 - f^(n+1))/(1-f) for f <>1

so, for f = 2

s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765

for f = -2

s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =

= -1×-255 = 255

4 0
2 years ago
If y=32, then 86y+25−78y =
FrozenT [24]

Answer:

281

Step-by-step explanation:

plug y value into expression

86(32) + 25 - 78(32)

pemdas says we must multiply first

2752 + 25 - 2496

2777 - 2496

281

4 0
3 years ago
Write an exponential expression: choose a number between 0 and 10 to be the base and another number between 0 and 10, different
lesya [120]

Answer:

2^4

2 * 2 * 2 * 2

Step-by-step explanation:

In the question above :

Write an exponential expression:

Base = number between 0 and 10

Exponent = number different from the base between 0 and 10

Let base = 2

Let exponent = 4

Hence, exponential expression will be

Base^exponent

2^4 (standard form)

Expanded form:

2 * 2 * 2 * 2 (multiply 2 in 4 places)

6 0
3 years ago
Evaluate a - b for a equals -62 and b equals 49.
Cloud [144]
<span>Simplify and you will get -111</span>
3 0
3 years ago
Geometric Probability
KiRa [710]

Answer:

Step-by-step explanation:

1) P= Area of Circle/ Area of large rectangle

Area of the circle = pi·r² = pi·2²=4 pi ft.²

Area of large rectangle=  l·w -12·10 =120 ft.²

P = 4pi/120 rewrite 120 as 4·30

P= 4 pi/4*30 = pi/30 = 3.14/40 ≈ .1047 ≈10% (because .1047·100 =10.47≅10)

2) P = Area of smaller rectangle/ Area of large rectangle

Area of smaller rectangle = l·w = 2·4 =8 ft.²

Area of large rectangle=l·w = 12·10=120 ft²

P= 8/120 ≅ .0666≅ 7% (because .0666·100 =6.66≅7)

3) P= Not the circle or smaller rectangle/ Area of large rectangle

Not the circle or smaller rectangle area

= Area of large rectangle - Area of circle -Area of smaller rectangle

= 120 -4·pi -8 = 120 - (4· 3.14) -8 = 99.4362939 ft²

Area of large rectangle = l·w = 12·10 =120 ft²

P = 99.4362939 /120 ≅ .8286 ≅83% (because .8286·100 =82.86≅83)

7 0
3 years ago
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