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strojnjashka [21]
3 years ago
6

Write eighteen hundredths as a decimal.

Mathematics
1 answer:
arsen [322]3 years ago
7 0
If you write eighteen hundredths as a decimal it will be .18
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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
3 years ago
Read 2 more answers
Spending on wars is essentially categorized as government purchases. How do increases in spending on the war in Afghanistan affe
DanielleElmas [232]

With the spending on wars, the aggregate demand falls and the curve will shift towards the left because the production of other goods will reduce in the economy.

<u>Explanation:</u>

When the government of a country spends on the war or the making of the weapons for the war, then the overall working of the economy is affected because the production of goods and services reduces compared to the normal production of goods and services.

With the fall in the production of the goods and the services, the demand also reduces because the overall income of the economy falls. The resources are used to produce war weapons and not consumer goods thus leading to fall in employment, income and so on. Thus the demand curve will shift to the left.

8 0
3 years ago
The base value is the <br><br> A. New value <br><br> B. Current value
Andrei [34K]
The base value is the current value

Good luck! I hope this helps!
6 0
3 years ago
Will give brainleist PLEASE HELP ASAP<br> Sorry if it’s a bit blurry
dangina [55]

Answer:

too blurry, I cant see the numbers

7 0
2 years ago
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What are factors of 30
Dennis_Churaev [7]
1,2,3,5,6,10,15,30 because by looking at the number at the ones place, when it is 0 or an odd number, it could be divided by 2. When the places are added together and when it is divisible by 3, it is the factor of 3. Also, when there are 2 and 3 as a factor, it is also divisible by 6.
8 0
3 years ago
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