Suppose a-b=0 which one of these expressions equals ab

X+y+z=3<br> x-y+z=2<br> x+y-z=1

Dima020 [189]

Answer:

Step-by-step explanation:

I'm assuming you are solving this system for x, y, and z. Do it this way:

Combine the first 2 equations and the second 2 equations and eliminate the y's. The first 2 equations:

x + y + z = 3

x - y + z = 2

which solves to

2x + 2z = 5

The second 2 equations:

x - y + z = 2

x + y - z = 1

which solves to

2x = 3 so

x = 3/2 or 1.5

Now sub that x value into the bold equation above to get:

2(1.5) + 2z = 5 and

3 + 2z = 5 and

2z = 2 so

z = 1

Now we plug back in to solve for y:

1.5 + y + 1 = 3 and

2.5 + y = 3 so

y = .5

The solution set then is (1.5, .5, 1) or in fraction form:

$(\frac{3}{2},\frac{1}{2},1)$

6 0

3 years ago

If l=10 b=5 and h=2, find the values of 2(lb+bh+lh)

miss Akunina [59]

Answer:

160

Step-by-step explanation:

$2((10)(5)+(5)(2)+(10)(2))\\2(50+10+20)\\2(80)\\160$

8 0

3 years ago

Read 2 more answers

Solve:<br> 5y+34 = -2(-7y+1)

Blizzard [7]

Answer:

Slope = 1.200/2.000 = 0.600

x-intercept = 34/3 = 11.33333

y-intercept = 34/-5 = -6.80000

Step-by-step explanation:

1.1 Solve 3x-5y-34 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x-5y-34 = 0 and calculate its properties

Geometric figure: Straight Line

Slope = 1.200/2.000 = 0.600

x-intercept = 34/3 = 11.33333

y-intercept = 34/-5 = -6.80000

6 0

3 years ago

Read 2 more answers

Convert 6:16 a.m. in military time

Paraphin [41]

Answer: It remains 6:16 am

Step-by-step explanation:

5 0

3 years ago

A study was made comparing the cost of a one-bedroom apartment in philadelphia with the cost of similar apartments in Baltimore.

mars1129 [50]

Answer:

$t=\frac{(950 -915)-(0)}{\sqrt{\frac{50^2}{30}}+\frac{45^2}{25}}=2.73$

$p_v =2*P(t_{53}>2.73) =0.0086$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (Philadelphia) is significantly different than the mean for the group 2 (Baltimore).

Step-by-step explanation:

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2\neq 0$

Our notation on this case :

$n_1 =30$ represent the sample size for group 1 (Philadelphia)

$n_2 =25$ represent the sample size for group 2 (Baltimore)

$\bar X_1 =950$ represent the sample mean for the group 1

$\bar X_2 =915$ represent the sample mean for the group 2

$s_1=50$ represent the sample standard deviation for group 1

$s_2=45$ represent the sample standard deviation for group 2

If we see the alternative hypothesis we see that we are conducting a bilateral test or two tail.

Critical values

On this case since the significance level is 0.05 and we are conducting a bilateral test we have two critical values, and we need on each tail of the distribution $\alpha/2 = 0.025$ of the area.

The distribution on this case since we don't know the population deviation for both samples is the t distribution with $df=n_1+n_2 -2= 30+25-2=53$ degrees of freedom.

We can use the following excel codes in order to find the critical values:

"=T.INV(0.025,53)", "=T.INV(1-0.025,53)"

And we got: (-2.01, 2.01)

Calculate th statistic

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}$

And now we can calculate the statistic:

$t=\frac{(950 -915)-(0)}{\sqrt{\frac{50^2}{30}}+\frac{45^2}{25}}=2.73$

The degrees of freedom are given by:

$df=30+25-2=53$

P value

And now we can calculate the p value using the altenative hypothesis:

$p_v =2*P(t_{53}>2.73) =0.0086$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (Philadelphia) is significantly different than the mean for the group 2 (Baltimore).

4 0

4 years ago