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gulaghasi [49]
3 years ago
10

Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state thi

s.
15x + 9y = 240
6x + 3y = 90 ...?
Mathematics
1 answer:
vladimir2022 [97]3 years ago
6 0
The answer is x = 10, y = 10.

Step 1: rearrange the second equation for y.
Step 2: substitute y from the second equation into the first equation.
Step 3. Calculate y.

Step 1.
<span>The second equation is: 6x + 3y = 90
Divide both sides of the equation by 3:
(6x + 3y)/3 = 90/3
6x/3 + 3y/3 = 30
2x + y = 30
Rearrange the equation:
y = 30 - 2x

Step 2.
</span>Substitute y from the second equation (y = 30 - 2x) into the first equation:
<span>15x + 9y = 240
15x + 9(30 - 2x) = 240
15x + 270 - 18x = 240
15x - 18x = 240 - 270
-3x = -30
x = -30/-3
x = 10

Step 3.
Since </span>y = 30 - 2x and x = 10, then:
y = 30 - 2 * 10
y = 30 - 20
y = 10
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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago
Graph y = 3(x + 2)3 - 3 and describe the end behavior.
-BARSIC- [3]
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3) Since the polynomial is of odd degree you can predict that the ends head off in opposite direction. The limits confirm that.

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5) The limit when x approaches positive infinity is positivie infinity, then the right end of the function heads off upward (toward + ∞).

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- y-intercepts
- critical points: local maxima, local minima, and inflection points.


7) x-intercepts ⇒ y = 0

⇒ <span>3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0
</span>

<span>⇒ (x + 2)³ = -1 ⇒ x + 2 =  1 ⇒ x = - 1
</span>

8) y-intercepts ⇒ x = 0

y = <span>3(x + 2)³ - 3 = 3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 = 21
</span><span>
</span><span>
</span><span>9) Critical points ⇒ first derivative = 0
</span><span>
</span><span>
</span><span>i) dy / dx = 9(x + 2)² = 0
</span><span>
</span><span>
</span><span>⇒ x + 2 = 0 ⇒ x = - 2
</span><span>
</span><span>
</span><span>ii) second derivative: to determine where x = - 2  is a local maximum, a local  minimum, or an inflection point.
</span><span>
</span><span>
</span><span>y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.
</span><span>
</span><span>
</span><span>Then the function does not have local minimum nor maximum, but an inflection point at x =  -2.
</span><span>
</span><span>
</span><span>Using all that information you can graph the function, and I attache the figure with the graph.
</span>


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3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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