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3 years ago

9

Determine whether the systems have one solution, no solution, or infinitely many solutions 5-y=2-y+3

1 answer:

tiny-mole [99]3 years ago

4 0

Answer:First system: no solution

Second system: one solution

Third system: one solution

Fourth system: infinite solutions

Fifth system: no solution

Step-by-step explanation:

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What is the answer to this equation |x−1|+5=2

barxatty [35]

Answer:

No solutions

Step-by-step explanation:

Isolate the absolute value:

|x−1| + 5 = 2

Subtract 5 from both sides:

|x-1| = -3

Since an absolute value can never be equal to a negative number, there are no solutions.

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3 years ago

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Round 685,135 to the nearest ten thousand.

garik1379 [7]

Answer:

690,000

Step-by-step explanation:

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Condense the expression log 2x + log(x² - 9) - log x +3

Rudik [331]

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2 years ago

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

A certain shampoo is available in two sizes. A 13.5 ounces bottle cost $2.98. A 29.2 ounce bottle cost $6.12. Find the Unit pric

Sladkaya [172]

Answer:

9.2 ounce bottle cost $6.12 is better buy with unit price of $0.22

Step-by-step explanation:

Unit price of any product is given by

unit price = weight of product/ price of product

Given sizes

A

13.5 ounces bottle cost $2.98

cost of 1 ounce of shampoo for this size = cost price/weight of shampoo

cost of 1 ounce of shampoo for this size =2.98/13.5 = $0.22

Unit price for this size is $.022

B

9.2 ounce bottle cost $6.12

cost of 1 ounce of shampoo for this size = cost price/weight of shampoo

cost of 1 ounce of shampoo for this size =6.12/9.2 = 0.66

Unit price for this size is $0.66

As $0.22 is less than $0.66 thus,

9.2 ounce bottle cost $6.12 is better buy.

6 0

4 years ago