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3 years ago

5

Mentally determine the value of x that makes each equation true. 2(x−1)=10

1 answer:

alexdok [17]3 years ago

8 0

Answer:

Step-by-step explanation:

Divide both sides by 2

x - 1 = 5

Add 1 to both sides

x - 1 + 1 = 5 + 1

Combine

x = 6

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The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

3 years ago

Function h(x) = x + 4<br> If your input was 2, what is your output?

Natalka [10]

Answer:

h(2)=6

Step-by-step explanation:

just plug in 2 where you have an x, and you’d have 2 + 6, which equals 6

3 0

3 years ago

The number of cars at a dealership dropped from 64 to 48 after a weekend sale.

tigry1 [53]

Answer: B. 25%

Step-by-step explanation:

64-48 = 16

16/ 64= 0.25

0.25 x 100 = 25%

8 0

3 years ago

Jack is mixing a cleaning solution that is 12% bleach.After mixing the solution,jack has 150 ounces of cleaning solution.how man

marysya [2.9K]

To solve for the ounces of bleach that Jack used, we utilize the formula below

Bleach = (Percentage of bleach)*(Total ounces of cleaning solution)
Bleach = 0.12*150 ounces
Bleach = 18 ounces

<em>ANSWER: 18 ounces of bleach</em>

5 0

3 years ago

What are the side lengths of the equilateral triangle?

Alchen [17]

$5x + (6x - 5) + (3x + 10) = 360$

$5x + 6x - 5 + 3x + 10 = 360$

$11x - 5 + 3x + 10 = 360$

$14x + 5 = 360$

$14x = 360 - 5$

$14x = 355$

$x = 25.36$

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$x = 25.36$

$5x = 5 \times 25.36 = 126.8$

$6x - 5 = 6 \times 25.36 - 5 = 147.16$

$3x + 10 = 3 \times 25.36 + 10 = 86.08$

4 0

3 years ago