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3 years ago

A. Describe how each student might have reached his or her conclusion. Is each student’s conclusion valid? Explain.

1 answer:

8 0

Answer: Conclusion validity is the degree to which conclusions we reach about relationships in our data are reasonable.

Step-by-step explanation:

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If 2(4x + 3)/(x - 3)(x + 7) = a/x - 3 + b/x + 7, find the values of a and b.

zmey [24]

Answer:

$a=3$ and $b=5$ .

Step-by-step explanation:

So I believe the problem is this:

$\frac{2(4x+3)}{x-3}(x+7)}=\frac{a}{x-3}+\frac{b}{x+7}$

where we are asked to find values for $a$ and $b$ such that the equation holds for any $x$ in the equation's domain.

So I'm actually going to get rid of any domain restrictions by multiplying both sides by (x-3)(x+7).

In other words this will clear the fractions.

$\frac{2(4x+3)}{x-3}(x+7)}\cdot(x-3)(x+7)=\frac{a}{x-3}\cdot(x-3)(x+7)+\frac{b}{x+7}(x-3)(x+7)$

$2(4x+3)=a(x+7)+b(x-3)$

As you can see there was some cancellation.

I'm going to plug in -7 for x because x+7 becomes 0 then.

$2(4\cdot -7+3)=a(-7+7)+b(-7-3)$

$2(-28+3)=a(0)+b(-10)$

$2(-25)=0-10b$

$-50=-10b$

Divide both sides by -10:

$\frac{-50}{-10}=b$

$5=b$

Now we have:

$2(4x+3)=a(x+7)+b(x-3)$ with $b=5$

I notice that x-3 is 0 when x=3. So I'm going to replace x with 3.

$2(4\cdot 3+3)=a(3+7)+b(3-3)$

$2(12+3)=a(10)+b(0)$

$2(15)=10a+0$

$30=10a$

Divide both sides by 10:

$\frac{30}{10}=a$

$3=a$

So $a=3$ and $b=5$ .

4 0

2 years ago

Read 2 more answers

Verify a x (b+c) = a x b + a x c for a = -1/6 b=4/7 c=-2/5

SVETLANKA909090 [29]

Step-by-step explanation:

✓(-1/6×4/7)+(-1/6×-2/5)

✓(-4/42)+(2/30)

✓(-2/21)+(1/15)

✓(-2/21+1/15)

=-1/35

3 0

2 years ago

Math 1125 – Unit 1 ~ Gunkelman Practice for Section 1.5 The Basics of Graphing Prep Skills The table represents the Seven Summit

marta [7]

According to the table, the highest mountain in Africa is Mt. Kilimanjaro with 19,340 feet in height. The highest mountain in Antarctica is Vinson Massif with 16,864 feet in height.

Then, we subtract

$19,340-16,864=2,476$ <h2>The difference between the heights of the highest mountain in Africa and the highest mountain in Antarctica is 2,476 feet.</h2>

7 0

1 year ago

3x+5=5x-3

madam [21]

answer= d Step-by-step explanation:

6 0

2 years ago

Describe the likelihood of an event as impossible, unlikely, equally likely, likely or certain. 21) There is a 0% chance of pick

Arturiano [62]

Answer:

21) There is a 0% chance of picking a 13 in a deck of cards. Impossible.

If there is a 0% chance that something will happen then it is impossible.

22) There is a 50% chance of picking a red card in a deck of cards. Equally likely.

If there is a 50% chance that something will happen, it is equally likely that it will happen.

23) There is an 80% chance of snow tomorrow. Likely or certain.

If there is an 80% chance of something happening, it means that the chances of that thing happening good and the event is likely to occur.

24) There is a 20% chance of rain tomorrow. Unlikely.

A low chance of 20% means that something is unlikely to occur.

7 0

2 years ago