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lianna [129]
3 years ago
13

What is the solution to 3x -2y =1 and 4y = 7 + 3x

Mathematics
1 answer:
Delvig [45]3 years ago
8 0

Given.

3x-2y=1 (1)

4y=7+3x (2)

Re-arrange equation (2)

(4y=7+3x)-4y

0=-4y+3x+7

(0=-4y+3x+7)-7

-7=-4y+3x

Multiply equation (2) by -1

-1(3x-4y=-7)

-3x+4y=7(3)

Combine like terms and solve.

3x-3x-2y+4y=1+7

2y=8

Divide by (2y) and solve for (y).

\frac{2y}{2}=\frac{8}{2}

y=4

Substitute (y) for equation (1).

3x-2y=1

3x-2(4)=1

3x-8=1

Add (8) to both sides.

(3x-8)+8=(1)+8

3x=9

Divide by (3).

\frac{3x}{3}=\frac{9}{3}

x=3

Check your work.

3x-2y=1

3(3)-2(4)=1

9-8=1

1=1

4y=7+3x

4(4)=7+3(3)

16=7+9

16=16

Your answers is x=3 and y=4

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Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)
viktelen [127]
\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}

The first line segment can be parameterized by \mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle with 0\le t\le1. Denote this first segment by C_1. Then

\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt
=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt
=108

The second line segment (C_2) can be described by \mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle, again with 0\le t\le1. Then

\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt
=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt
=-\dfrac{229}3

Finally,

\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3
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3 years ago
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Dude that’s not an answer
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3 years ago
If the range of the function f(x) = 7x – 2.7 is {14.1, 30.9, 41.4, 58.9, 68}, what is its domain?
Drupady [299]

domain is {2.4, 4.8, 6.3, 8.8, 10.1 }

For domain, equate f(x) to each value in the range and solve for x

7x - 2.7 = 14.1 ⇒ x = \frac{x14.1 + 2.7}{7} = 2.4

7x - 2.7 = 30.9 ⇒ x = \frac{30.9 + 2.7}{7} = 4.8

7x - 2.7 = 41.4 ⇒ x = \frac{41.4 + 2.7}{7} = 6.3

7x - 2.7 = 58.9 ⇒ x = \frac{58.9 + 2.7}{7} = 8.8

7x - 2.7 = 68 ⇒ x = \frac{68 + 2.7}{7} = 10.1


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3 years ago
At your job, you are paid $50 per week plus $3 per sale. At least how many sales do you need to make in order to have over $250
julsineya [31]

<span>0+3⋅c>250</span>

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<span>3⋅c>200</span>

<span><span><span>3⋅c</span>3</span>><span>2003</span></span>

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<span><span>so 67 sales rouned</span></span>

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3 years ago
What is the answer for this please help -31=3w+9-8w simplify you answer as much as possible
ki77a [65]

-31=3w+9-8w\\\\-5w+9=-31 \ \ /-9\\\\-5w=-40 \ \ /:(-5)\\\\\huge\boxed{w=8}

3 0
3 years ago
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