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2 years ago

6x+4y=42 -3x+3y=-6 by elimination

Mathematics

2 answers:

creativ13 [48]2 years ago

6 0

Answer:

x=5, y=2

Step-by-step explanation:

To solve this system, we need to find x and y. First, let's find x. In the first equation (6x+4y=42), subtract 4y on both sides to isolate 6x. This will result in 6x=42-4y. Divide by 6 on both sides to isolate x and get x=7- $\frac{2}{3}$ y. Now we know what x equals. Go to the second equation ad plug this into it. So instead of -3x+3y=-6, you'll have -3(7- $\frac{2}{3}$ y)+3y=-6. Use the distributive property to get -21+2y+3y=-6. Add 2y and 3y to get -21+5y=-6. Add 21 to both sides to isolate 5y and get 5y=15. Divide by 5 on both sides to isolate y and get y=3. Now that we know that y=3, we can plug this back into the equation that was bolded above so that we can find x, so we'll have x=7- $\frac{2}{3}$ (3) since y=3, and we'll get x=7- $\frac{6}{3}$ , or x=7-2, or x=5.

x=5

y=2

N76 [4]2 years ago

6 0

Answer: (5, 3)

Step-by-step explanation:

Solve by Addition/Elimination

6x + 4y = 42 −3x + 3y = −6

Multiply each equation by the value that makes the coefficients of x opposite.

6x + 4y = 42

(2) ⋅ (−3x + 3y) = (2) (−6)

Simplify (2) ⋅ (−3x + 3y).

6x + 4y = 42

−6x + 6y = (2) (−6)

Multiply 2 by −6. 6x + 4y = 42

−6x + 6y = −12

Add the two equations together to e liminate x from the system.

6x + 4y = 42

±6x + 6y = −12

1 0y= 30

Divide each term in 10y = 30 by 10.

10y = 30

10 10

Cancel the common factor of 10.

y = 30/10

Divide 30 by 10.

y = 3

Substitute the value found for y into one of the original equations, then solve for x.

Substitute the value found for y into one of the original equations to solve for x. 6x + 4 (3) = 42

Multiply 4 by 3.

6x + 12 = 42

Move all terms not containing x to the right side of the equation.

6x = 30

Divide each term by 6 and simplify.

x = 5

The solution to the independent system of equations can be represented as a point.

(5, 3)

The result can be shown in multiple forms.

Point Form:

(5, 3)

Equation Form:

x = 5, y = 3

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SpyIntel [72]

Answer:

0.231

Step-by-step explanation:

Let the Probability of students that knew the correct answer be: P(A)

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P(B) = 15% =0.15

Let the Probability of the student that do not knew the correct answer Be P(C)

P(C) = 1 - P(A)

P(C) = 1 - 0.6

P(C) = 0.4

Let the Probability that the student does not know the right answer but guessed it correctly be: P(D)

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P(E) = 0.85

Probability that the student got the answer wrong = (0.60 X 0.15) + (0.40 X 0.75) = 0.39

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3 years ago

All the edges of a regular square pyramid have length 8. find the Volume of the pyramid, Lateral area of the pyramid and the Tot

RUDIKE [14]

Answer:

V = 120.6796

LA = 110.8513

SA = 174.8513

Step-by-step explanation:

Let me know if you need more of an explanation for any of these

First we need the height, one way to find that out is to use the diagonal of the and one of the diagonal edges of the pyramid. Specifically we will need half of the diagonal of the square. We will call the diagonal of the square d.

$8^2+8^2=d^2\\d=\sqrt{64+64} \\d=\sqrt{128}$

Gonna leave it like that for ease of writing. So then half of the diagonal is $\frac{\sqrt{128}}{2}$

The height, h, will be $(\frac{d}{2})^2+h^2 = 8^2$ . Plugging everything in gets us $h=\sqrt{32}$

last, we need to find slant height, which we will call s.

$(\frac{8}{2})^2+h^2 = s^2\\s=\sqrt{48}$

s is also the height of the triangles for purposes of finding area. Now for the volume and areas.

Volume is area of the base times height divided by 3, so $V=8^2\frac{\sqrt{32} }{3} = \frac{64\sqrt{48} }{3} = 120.6796$

Lateral area is the sum of the four areas of the triangles, and each of those are $\frac{8*h}{2}$ so the whole lateral area is 4 times that. So we get $4\frac{8\sqrt{32} }{2} =110.8513$