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3 years ago

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Need help with all 3 pleaseeee

2 answers:

lozanna [386]3 years ago

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xxTIMURxx [149]3 years ago

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Solve the following system

scZoUnD [109]

Answer:

{x = -4 , y = 2 , z = 1

Step-by-step explanation:

Solve the following system:

{-2 x + y + 2 z = 12 | (equation 1)

2 x - 4 y + z = -15 | (equation 2)

y + 4 z = 6 | (equation 3)

Add equation 1 to equation 2:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - 3 y + 3 z = -3 | (equation 2)

0 x+y + 4 z = 6 | (equation 3)

Divide equation 2 by 3:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y + z = -1 | (equation 2)

0 x+y + 4 z = 6 | (equation 3)

Add equation 2 to equation 3:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y + z = -1 | (equation 2)

0 x+0 y+5 z = 5 | (equation 3)

Divide equation 3 by 5:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y + z = -1 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract equation 3 from equation 2:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y+0 z = -2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Multiply equation 2 by -1:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract equation 2 from equation 1:

{-(2 x) + 0 y+2 z = 10 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract 2 × (equation 3) from equation 1:

{-(2 x)+0 y+0 z = 8 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Divide equation 1 by -2:

{x+0 y+0 z = -4 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Collect results:

Answer: {x = -4 , y = 2 , z = 1

4 0

3 years ago

Thirty-three college freshmen were randomly selected for an on-campus survey at their university. The participants' mean GPA was

Ivan

Answer: $\pm0.1706$

Step-by-step explanation:

Given : Sample size : n= 33

Critical value for significance level of $\alpha:0.05$ : $z_{\alpha/2}= 1.96$

Sample mean : $\overline{x}=2.5$

Standard deviation : $\sigma= 0.5$

We assume that this is a normal distribution.

Margin of error : $E=\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

i.e. $E=\pm (1.96)\dfrac{0.5}{\sqrt{33}}=\pm0.170596102837\approx\pm0.1706$

Hence, the margin of error is $\pm0.1706$

7 0

3 years ago

Find the cost of 20 grams of lead at 60$ per kilogram

ASHA 777 [7]

Answer:

$1.20

Step-by-step explanation:

Ratio:

Grams : Kilograms

1 : .001

Multiply both sides by 20 to convert grams to kilograms:

Grams : Kilograms

1 : .001

x20 x20

20 : .02

This means that 20 grams of lead = .02 kilograms of lead

Price:

Cost : Kilogram

$60 : 1

Multiply both sides by .02 to find the price of the lead:

Cost : Kilogram

$60 : 1

x.02 x.02

$1.20 : .02

Therefore, .02 kg of lead costs $1.20.

6 0

2 years ago

Which sequence of similar transformations could map △ABC onto △A'B'C'?

nadya68 [22]

Answer: A sequence of similar transformations of dilation and translation could map △ABC onto △A'B'C'.

Step-by-step explanation:

Similar transformations: If one figure can be mapped onto the other figure using a dilation and a congruent rigid transformation or a rigid transformation followed by dilation then the two figures are said to be similar.

In the attachment △ABC mapped onto △A'B'C' by a sequence of dilation from origin and scalar factor k followed by translation.

7 0

3 years ago

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the planet jupiter has an average distance of about 0.00008 LIght years from the sun. What is this distance in scientific notati

LuckyWell [14K]

Answer :The planet Jupiter

Step-by-step explanation: It has an average distance from the sun of about

4.837

×

10

8

. The planet Venus average distance from the sun of about

6.72

×

10

7

On average, how much farther from the sun is Jupiter than Venus?

8 0

3 years ago

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