All categories

3 years ago

Solve the system by substitution -x-y-z= -8 -4x+4y+5z= 7 2x+2z= 4

Mathematics

2 answers:

o-na [289]3 years ago

8 0

Answer: x=3, y=6, z=-1

Step-by-step explanation:

2x+2z=4

2x=4-2z

X=2-z

-(2-z)-y-z=-8

-2+z-y-z=-8

-2-y=-8

-2+y=-8+y

-2+8=y

6=y

-4 (2-z)+4 (6)+5z=7

-8+4z+24+5z=7

9z=8-24+7

9z=-9

Z=-1

2x+2z=4

2x+2 (-1)=4

2x-2=4+2

2x=6

X=3

x=3 y=6 z=-1

Gennadij [26K]3 years ago

4 0

- x - y - z = - 8 ------- (1)
- 4x + 4y + 5z = 7 -------- (2)
2x + 2z = 4 --------- (3)

From (3): x + z = 2
x = 2 - z --------- (4)

Substitute (4) into (1),
- x - y - z = - 8
- (2-z) - y - z = - 8
- 2 + z - y - z = -8
- 2 - y = - 8
2 + y = 8
Therefore, y = 6

Substitute y = 6 and (4) into (2),
- 4x + 4y + 5z = 7
- 4(2 - z) + 4(6) + 5z = 7
- 8 + 4z + 24 + 5z = 7
9z + 16 = 7
9z = - 9
Therefore, z = - 9

Substitute z = - 9 into (4),
x = 2 - z
x = 2 - (-9)
x = 2 + 9
Therefore x = 11

Solution:
x = 11
y = 6
z = -9

You might be interested in

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 340 babies were born, a

Bas_tet [7]

Answer:

The 99% confidence interval estimate of the percentage of girls born is (0.8, 0.9).

b)Yes, the proportion of girls is significantly different from 0.5.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

In the study 340 babies were born, and 289 of them were girls. This means that $n = 340, \pi = \frac{289}{340} = 0.85$

Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born.

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{340}} = 0.85 - 2.575\sqrt{\frac{0.85*0.15}{400}} = 0.80$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{340}} = 0.85 + 2.575\sqrt{\frac{0.85*0.15}{400}} = 0.90$

The 99% confidence interval estimate of the percentage of girls born is (0.8, 0.9).

Does the method appear to be effective?

b)Yes, the proportion of girls is significantly different from 0.5.

4 0

3 years ago

Arlene is showing her work in simplifying −7.9 + 8.2 − 3.4 + 2.1. Identify any errors in her work or in her reasoning. Write fee

kodGreya [7K]

The answer is correct but i do not know what ARLENE did wrong

7 0

3 years ago

Read 2 more answers

I need some Help please

djverab [1.8K]

Answer:

a) f(2) = 4

b) g(3) = 3

c) g(1/3) = -1

d) f(3) = 1/2

e) g(-2) = 2

f) f(π) = 3

Step-by-step explanation:

We are given:

f={(2,4),(-4,3),(3,1/2),(π,3)} and g={(3,3),(-2,2),(1/3,-1)}

We need to find the following values of f and g

a) f(2)

f(2) means when x=2, we need to find the value of y.

Looking at the given f={(2,4),(-4,3),(3,1/2),(π,3)} , when x =2 then y=4

So, f(2) = 4

b) g(3)

g(3) means when x=3, we need to find the value of y.

Looking at the given g={(3,3),(-2,2),(1/3,-1)}, when x =3 then y=3

So, g(3) = 3

c) g(1/3)

g(1/3) means when x=1/3, we need to find the value of y.

Looking at the given g={(3,3),(-2,2),(1/3,-1)}, when x =1/3 then y=-1

So, g(3) = -1

d) f(3)

f(3) means when x=3, we need to find the value of y.

Looking at the given f={(2,4),(-4,3),(3,1/2),(π,3)} , when x =3 then y=1/2

So, f(3) = 1/2

e) g(-2)

g(-2) means when x=-2, we need to find the value of y.

Looking at the given g={(3,3),(-2,2),(1/3,-1)}, when x =-2 then y=2

So, g(-2) = 2

f) f(π)

f(π) means when x=π, we need to find the value of y.

Looking at the given f={(2,4),(-4,3),(3,1/2),(π,3)} , when x =π then y=3

So, f(π) = 3

6 0

3 years ago

19 pint is equal to how many pints

Ludmilka [50]

Not sure what your asking here

5 0

3 years ago

What is the factored form of y = x² - 12x + 36

djverab [1.8K]

Answer: y = (x - 6)^2

work:

y = x^2 - 12x + 36

y = (x - 6) (x - 6)

y = (x - 6)^2

7 0

3 years ago