All categories

3 years ago

Y=2x y=7x + 15 substitution

Mathematics

2 answers:

sergejj [24]3 years ago

7 0

$y = 2x \\ y = 7x + 15$

Substitute the given value of y into the equation y=7x+15

$2x = 7x + 15$

Move the variable to the left-hand side and change its sign

$2x - 7x = 15$

Collect like terms

$- 5x = 15$

Divide both sides of the equation by -5

$x = - 3$

Substitute the given value of x into the equation y=2x

$y = 2 \times ( - 3)$

Solve the equation for y

$y = - 6$

The possible solution of the system is the ordered pair (x,y)

$(x,y) = ( - 3, - 6)$

hodyreva [135]3 years ago

5 0

Answer:

y = -6 and x = -3

Step-by-step explanation:

Data :

Eq 1 : y = 2x

Eq 2 : y = 7x + 15

Take eq 1 and solve for x

⇒ x = y/2 eq 3

Put eq 3 in eq 2

y =7 (y/2) + 15

y - 7y/2 = 15

( 2y-7y )/2 = 15

-5y/2 = 15

-5y =30

y = -6

And put value of y in eq 3 to find x

x = -6/2

x =-3

You might be interested in

How many times does 1/14 go into 6 7/10

vovikov84 [41]

1/14 goes into 6 7/10, 93.8 times

8 0

3 years ago

Read 2 more answers

Hi, can someone plz help me with this question?

just olya [345]

Answer: All of them accept h. guarantee that m || n

Step-by-step explanation:

8 0

3 years ago

A magazine reports that women trust recommendations from a particular social networking site more than recommendations from any

Misha Larkins [42]

Answer:

a) $p_A$ represent the real population proportion for women

$\hat p_A =\frac{123}{150}=0.82$ represent the estimated proportion for women

$n_A=150$ is the sample size selected for women

b) $p_B$ represent the real population proportion for male

$\hat p_B =\frac{102}{170}=0.6$ represent the estimated proportion for male

$n_B=170$ is the sample size selected for male

c) $(0.82-0.6) - 1.96 \sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.124$

$(0.82-0.6) + 1.96 \sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.316$

And the 95% confidence interval would be given (0.124;0.316).

We are confident at 95% that the difference between the two proportions is between $0.124 \leq p_A -p_B \leq 0.316$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

$p_A$ represent the real population proportion for women

$\hat p_A =\frac{123}{150}=0.82$ represent the estimated proportion for women

$n_A=150$ is the sample size selected for women

Part b

$p_B$ represent the real population proportion for male

$\hat p_B =\frac{102}{170}=0.6$ represent the estimated proportion for male

$n_B=170$ is the sample size elected for male

$z$ represent the critical value for the margin of error

Part c

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.