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3 years ago

Solve for equation for ex in term of c 2/3(x+1/2) - 1/4=5/2

1 answer:

4 0

$\dfrac{2}{3}\left(x+\dfrac{1}{2}\right)-\dfrac{1}{4}=\dfrac{5}{2}\qquad|\text{use distributive property}\\\\\dfrac{2}{3}x+\dfrac{2}{3}\cdot\dfrac{1}{2}-\dfrac{1}{4}=\dfrac{5}{2}\\\\\dfrac{2}{3}x+\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{5}{2}\qquad|\text{multiply both sides by LCM(2,\ 3,\ 4)=12}\\\\12\cdot\dfrac{2}{3}x+12\cdot\dfrac{1}{3}-12\cdot\dfrac{1}{4}=12\cdot\dfrac{5}{2}\\\\4\cdot2x+4-3=6\cdot5\\\\8x+1=30\qquad|\text{subtract 1 from both sides}\\\\8x=29\qquad|\text{divide both sides by 8}\\\\x=\dfrac{29}{8}$

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A coordinate plane with a line passing through the points (negative 4, negative 5) and (1, negative 1).

Ksju [112]

Answer:

4x - 5y - 9 = 0

$\frac{9}{4}$

$\frac{-9}{5}$

Step-by-step explanation:

The equation of a straight line passing through the points (-4,-5) and (1,-1) is given by $\frac{y - (-5)}{-5-(-1)} =\frac{x-(-4)}{-4-1}$

⇒ $\frac{y+5}{-4} =\frac{x+4}{-5}$

⇒ 5y + 25 = 4x + 16

⇒ 4x - 5y - 9 = 0 ....(1) (Answer)

Now, this above equation can be represented as

$\frac{x}{\frac{9}{4} } + \frac{y}{\frac{-9}{5} } =1$

Therefore, the x-intercept is $\frac{9}{4}$ (Answer)

And the y-intercept is $\frac{-9}{5}$ . (Answer)

7 0

3 years ago

Read 2 more answers

5. The number −6 is 2 more than an unknown number. Find the unknown number.

Mariana [72]

Answer:

-4

Step-by-step explanation:

-6 - 2 = -4

3 0

2 years ago

Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil.

oksian1 [2.3K]

Answer:

0.36 = 36% probability that the land has oil and the test predicts it

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

45% chance that the land has oil.

This means that $P(A) = 0.45$

He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil.

This means that $P(B|A) = 0.8$

What is the probability that the land has oil and the test predicts it?

This is $P(A \cap B)$ . So

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$P(B \cap A) = P(B|A)*P(A) = 0.8*0.45 = 0.36$

0.36 = 36% probability that the land has oil and the test predicts it

5 0

2 years ago

Solve <br> 4x+6<-6<br><br> I could really use the help

aleksandr82 [10.1K]

Answer:

x < -3

Step-by-step explanation:

First subtract 6 from both sides of the inequality.

$4x+6-6$

$4x$

Divide 4 on both sides.

$\frac{4x}{4} < \frac{-12}{4}$

$x$

5 0

2 years ago

Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

4 0

3 years ago