All categories

3 years ago

Solve the system of equations. x+2y=6; 3x-14y=8 please help

1 answer:

8 0

Let x = 6 = 2y so
3(6 - 2y) + 14y = 8 so
18 - 6y + 14y = 8 so
8y = -10 and
$y = \frac{ - 10}{8} = - \frac{5}{4} \\ \\ since \: x = 6 - 2y \\ 6 - 2( \frac{ - 5}{4}) = x \: so \\ x = 6 + \frac{10}{4} = \frac{24}{4} + \frac{10}{4} = \frac{34}{4} = \frac{17}{2}$

You might be interested in

(08.01 MC)

Colt1911 [192]

Part A:

We see that this pair of equations has 1 solution. On a graph, the solutions of 2 (or more) lines is where the lines intersect. In this case, since these lines intersect 1 time, they have 1 solution.

Part B:

As previously mentioned, the solutions of multiple lines is where the lines intersect. In this case, since they intersect at (4,4), that is the solution.

6 0

3 years ago

Find each product. (2x+4)(2x-4)

trasher [3.6K]

The answer to your question is 4x^2 - 16

Hope this helped

3 0

3 years ago

Read 2 more answers

The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a na

lorasvet [3.4K]

Answer:

a. 95% confidence interval estimate for the population mean amount of paint included in a 1-gallon can is 0.998±0.0055

b. No, because a 1-gallon paint can containing exactly 1-gallon of paint lies within the 95% confidence interval.

c. Yes. The population amount of paint per can is assumed normally distributed, because confidence interval calculations assume normal distribution of the parameter.

d. 90% confidence interval is 0.998±0.0046. The answer in b. didn't change; 1-gallon paint can containing exactly 1-gallon of paint lies within the 90% confidence interval. The manager doesn't have a right to complain to the manufacturer.

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

M is the sample mean amount of paint per 1-gallon can (0.998 gallon)

ME is the margin of error from the mean

And margin of error (ME) can be calculated using the equation

ME= $\frac{z*s}{\sqrt{N} }$ where

z is the corresponding statistic in the 95% confidence level (1.96)

s is the sample standard deviation (0.02 gallon)

N is the sample size (50)

Then ME= $\frac{1.96*0.02}{\sqrt{50} }$ ≈0.0055

95% confidence interval is 0.998±0.0055

90% confidence interval can be calculated similary, only z statistic is 1.64.

ME= $\frac{1.64*0.02}{\sqrt{50} }$ ≈0.0046

90% confidence interval is 0.998±0.0046

8 0

3 years ago

If there are 36 performers in a dance recital. The ratio of men to women is 2:7. How many men are in the dance recital ?

MrRissso [65]

$\frac{m}{w}= \frac{2}{7} \\ \\ \frac{m}{2}=\frac{w}{7}=k \\ \\ m=2k\\ w=7k \\ \\ m+w=36 \\ 2k+7k=36 \\ 9k=36 \\ \\ \boxed{k=\frac{36}{9}=4} \\ \\ m=2*4=8 \ men \\ \\ w=7*4=28 \ women$

6 0

3 years ago

Combine terms: 12a + 26b -4b – 16a.

noname [10]

Answer:

The answer is -4a + 22b

Step-by-step explanation:

12a + 26b -4b -16a

12a - 16a + 26b - 4b

-4a + 22b

Thus, The answer is -4a + 22b

-TheUnknownScientist

3 0

3 years ago

Read 2 more answers