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PSYCHO15rus [73]
1 year ago
8

1. Solve each system of linear equations below, then check your work.

Mathematics
1 answer:
Brut [27]1 year ago
5 0

Answer:

a)  \: x =  - 3 \: and \: y = 2 \\ b) \: x = 1 \: and \: y =  -  \frac{5}{4}  \\ c) \: \: x = 25 \: and \: y = 0 \\ d ) \: x = 10 \: and \: y =  - 12

Step-by-step explanation:

question (a)  \: \: \: 3x - y =  - 11 \\ \: \: \: - x + y = 5 \\ \\ 2x =  - 6 \\  \frac{2}{2} x =  \frac{ - 6}{2}   \\ x =  - 3

\\ since \: x =  - 3 \: then \: y = \\ \\ - x + y = 5 \\  - ( - 3) + y = 5 \\ y = 5  - 3 \\ y = 2

\\ (check) \\ recall \: that \: x =  - 3 \: and \: y = 2 \\ \\ - x + y = 5 \\  - ( - 3) + 2 = 5 \\ 3 + 2 = 5 \\ 5 = 5

question (b)  \: \: \: -2y + 3 = 4x + 2 \\ 6x + 4y =   1 \\ \\ ( - 4x - 2y =  - 1) \times 2 \\\: \: \: 6x + 4y = 1 \\ \\ - 8x - 4y =  - 2 \\ 6x + 4y = 1 \\ \\ - 2x =  - 2

\frac{ - 2}{ - 2} x =  \frac{ - 2}{ - 2}  \\ x =  1 \\ \\ since \: x = 1 \: then \: y =  \\ \\ 6x + 4y = 1 \\ 6(1) + 4y = 1

4y =  - 6 + 1 \\  \frac{4}{4} y =   - \frac{ 5}{4}  \\ y = -   \frac{ 5}{4}  \\ \\ (check) \\  - 2y + 3 = 4x + 2

- 2( -  \frac{5}{4} ) + 3 = 4(1) + 2 \\  \frac{5}{2}  + 3 = 6\\  6 = 6

question (c) \: \: \: 32y - x =  - 25 \\ \: \: \:  5x = 100 + x - 8y \\ \\ 32y - x =  - 25 \\ 8y + 5x  -  x = 100 \\ \\ (32y - x =  - 25) \times 4 \\ 8y + 4x = 100

128y - 4x =  - 100 \\ 8y + 4x = 100 \\ 136y = 0 \\ y = 0 \\ \\ since \: y = 0 \: then \: x = \\ \\ 32y - x =  - 25 \\ 32(0) - x =  - 25 \\  - x =  - 25 - 0 \\  \frac{ - 1}{ - 1} x =  \frac{ - 25}{ - 1}  \\ x = 25 \\

(check) \\ 5x = 100 + x - 8y \\ 5(25) = 100 + (25) - 8(0) \\ 125 = 125 - 0 \\ 125 = 125

question (d) \:  \:  \: 2y + 3x = 6 \\ \: \: \:  4x + 5y + 20 = 0 \\ \\ ( 2y + 3x = 6) \times 4 \\ (5y + 4x =  - 20) \times  - 3 \\ \\ 8y + 12x = 24 \\  - 15y - 12x = 60

- 7y = 84 \\  \frac{ - 7}{ - 7} y =  \frac{84}{ - 7}  \\ y =  - 12 \\ \\ since \: y =  - 12 \: then \: x =  \\ \\ 2y + 3x = 6 \\ 2( - 12) + 3x = 6 \\  - 24 + 3x = 6 \\ 3x = 6 + 24 \\ x = 10 \\ \\ (check) \\ 4x + 5y + 20 = 0 \\

4(10) + 5( - 12)  + 20 = 0 \\ 40 - 60 + 20 = 0 \\  - 20 + 20 = 0 \\ 0 = 0

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Solve equation by using the quadratic formula.
Sati [7]

Answer: 1:  x=3, x=1

2:  x= -5

3:  There are 2 real solutions.

4:  There are 2 real solutions.

5:  There are no real solutions.

6.  There is 1 real solution.

7.  

8.  x= -6, x = -2

9.  x = -1/6, x=1

10.  

Explanation:

1.  The quadratic formula is

Substituting our known information we have:

2.  Rewriting the quadratic in standard form we have x²+10x-25=0. Substituting this into the quadratic formula gives us:

3.  The discriminant is b²-4ac.  For this problem, that is 20²-4(-4)(25)=400--400=800.  Since this is greater than 0, there are 2 real solutions.

4.  The discriminant in this problem is 7²-4(2)(-15)=49--120=49+120=169.  This is greater than 0, so there are 2 real solutions.

5.  The discriminant in this problem is 1²-4(-2)(-28)=1-224=-223.  Since this is less than 0, there are no real solutions.

6.  If the discriminant of a quadratic is 0, then by definition there is 1 real solution.

7.  Rewriting the quadratic we have 3x²-4x-2=0.  Using the quadratic formula we have:

8.  Factoring this trinomial we want factors of 12 that sum to 8.  6*2 = 12 and 6+2=8, so those are our factors.  This gives us:

(x+6)(x+2)=0

Using the zero product property we know that either x+6=0 or x+2=0.  Solving these equations we get x= -6 or x= -2.

9.  Factoring this trinomial we want factors of 6(-1)=-6 that sum to -5.  (-6)(1)=-6 and -6+1=-5, so this is how we "split up" the x term:

6x²-6x+1x-1=0

We group together the first two and the last two terms:

(6x²-6x)+(1x-1)=0

Factor the GCF out of each group.  In the first group, that is 6x:

6x(x-1)+(1x-1)=0

In the second group, the GCF is 1:

6x(x-1)+1(x-1)=0

Both terms have a factor of (x-1), so we can factor it out:

(x-1)(6x+1)=0

Using the zero product property, we know either x-1=0 or 6x+1=0.  Solving these equations we get x=1 or x=-1/6.

10.  Substituting our information into the quadratic formula we get:

Step-by-step explanation:

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2 years ago
How do you do inverse operation on a fraction ( y/3 ) = -6
NemiM [27]

\frac{-1}{18}

Solution:

Given expression is \frac{y}{3}=-6

To find the inverse of y.

⇒ \frac{y}{3}=-6

Do cross multiplication.

⇒ y = –6 × 3

⇒ y = –18

Inverse of y means reverse the function.

We know that inverse of y is \frac{1}{y}.

⇒ \frac{1}{y}= \frac{-1}{18}

Hence, inverse of y is \frac{-1}{18}.

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3 years ago
What is the Surface area for a rectangular prism that has the measurements of 2, 12, and 6?
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Answer:

216

Step-by-step explanation:

A=2(wl+hl+hw)=2·(12·2+6·2+6·12)=216

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Answer:

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Step-by-step explanation:

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