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GenaCL600 [577]
4 years ago
14

Use the distributive property to correctly solve 7(2 - x) = 28.

Mathematics
1 answer:
Lina20 [59]4 years ago
6 0

Answer:

x = -2

Step-by-step explanation:

7(2 - x) = 28

Distribute

14 -7x = 28

Subtract 14 from each side

14-7x-14 = 28-14

-7x = 14

Divide each side by -7

-7x/-7 = 14/-7

x = -2

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Calculate y as a function of x when dy/dx = 4x3 + 3x2 - 6x + 5
PtichkaEL [24]
Answer:
y = x⁴ + x³ - 3x² + 5x + C

======

Separable differential equations such as these ones can be solved by treating dy/dx as a ratio of differentials. Then move the dx with all the x terms and move the dy with all the y terms. After that, integrate both sides of the equation.

   \begin{aligned}
\dfrac{dy}{dx} &= 4x^3 + 3x^2 - 6x + 5 \\
dy &= (4x^3 + 3x^2 - 6x + 5) dx \\
\int dy &= \int (4x^3 + 3x^2 - 6x + 5) dx 
\end{aligned}

In general (understood that +C portions are still there), 

   \int x^{m} = \dfrac{x^{m+1}}{m+1}

Note that ∫dy = y  since it is ∫1·dy = ∫y⁰ dy = y¹/(0+1) = y
For the right-hand side, we use the sum/difference rule for integrals, which says that

   \int \big[f(x) \pm g(x)\big]\, dx = \int f(x)\,dx \pm \int g(x) \, dx

Applying these concepts:

   \begin{aligned} 
 \int dy &= \int (4x^3 + 3x^2 - 6x + 5) \, dx \\
y &= \int 4x^3\,dx + \int 3x^2 \, dx - \int 6x\, dx + \int 5\, dx \\
&= \frac{4x^4}{4} + \frac{3x^3}{3} - \frac{6x^2}{2} + 5x + C \qquad \text{(only one $C$ is needed)} \\
&= x^4 + x^3 - 3x^2 + 5x + C
\end{aligned}

The answer is y = x⁴ + x³ - 3x² + 5x + C
6 0
3 years ago
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8 0
4 years ago
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blsea [12.9K]
Answer is c
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6 0
4 years ago
pd-100 has a half-life of 3.6 days. if one had 6.02 x 1023 atoms at the start, how many atoms would be present after 20.0 days?
Irina18 [472]
<span>half-life means you divide by 2 
21.6 / 3.6 = 6 hf (hf = half-life) 
then you divide by 2^6 
6.02 x 10^23 / 2^6 = 9.40625 x 10^21 atoms 
-------------- 
26 
3hf ===> 2^3 
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answer : 10 - 1.25 = 8.75g 
------- 
27 
128 / 2^n = 2 
64 = 2^n 
n = 6 
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4 days is the half-live of the sample 
----------- 
28 
2.5/4.46 of 50% initial mass 
(2.5/4.46) x 0.5 x 2 = 0.5605 g 
answer: 2 - 0.5605 = 1.4395 g 
---------- 
29 
2^7 = 128 
so 7 half-lifes 
7* 8040 = 56200 days 
---------- 
30 
the time of 10 half-lifes 
= 10 x 0.334s = 3.34s </span><span>
</span>
3 0
4 years ago
The graph of the following systems of equations is ______.
nexus9112 [7]

Answer:

coinciding lines

Step-by-step explanation:

y=4-6x

6 0
3 years ago
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