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a_sh-v [17]
3 years ago
5

in germany, VAT is at 19% Jeremy buys a calculator in germny for €58.31 This price includes VAT Find the amount of VAT paid by

jeremy
Mathematics
2 answers:
Andreas93 [3]3 years ago
7 0
19 % = X/58.31 * 100%
X = ( 19*58.31 ) / 100
X = 11.08
(X) means > amount of paid
I hope it’s true ☺️
Len [333]3 years ago
4 0

We can use this equation to solve this problem:

<span>t=p+<span>(p⋅r)</span></span>

Where:

t is the total price paid: 58.31 for this problem

p is the price before taxes: What we are solving for in this problem.

r is the tax or VAT rate: 19% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 19% can be written as <span>19100</span> or 0.19.

Substituting and solving for p gives:

<span>58.31=p+<span>(p⋅0.19)</span></span>

<span>58.31=1p+0.19p</span>

<span>58.31=<span>(1+0.19)</span>p</span>

<span>58.31=1.19p</span>

<span><span>58.311.19</span>=<span><span>1.19p</span>1.19</span></span>

<span>49=<span><span>1.19p</span>1.19</span></span>

<span>49=p</span>

<span>p=49</span>

Now, we can find how much the VAT was by taking 19% of 49:

<span>19%×49=0.19×49=9.31</span>

Another was to solve this is to subtract the price without the tax or VAT from the total price giving:

<span>58.31−49=<span>9.31</span></span>

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Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)

\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]

Then shorten the fractions.

\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)

Distribute in all.

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We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.

x^2+x-4-2x-2=0\\x^2-x-6=0\\

We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)

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3 years ago
Calculate the effective annual interest rate if the annual interest rate, i, is 9%.
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Find the sum of the geometric sequence. three divided by two, three divided by eight, three divided by thirty two, three divided
Lynna [10]

Answer: we have that

[3/2,3/8,3/32,3/128,3/512]

the sum of the geometric sequence is [3/2+3/8+3/32+3/128+3/512]

=(1/512)*[256*3+64*3+16*3+4*3]

=(3/512)*[256+64+16+4]

=(3/512)*[340]

=(1020/512)

=255/128---------> 1.9922

the answer is

1.9922

another way to calculate it 

is through the following formula

∑=ao*[(1-r^n)/(1-r)]

where 

ao---------> is the first term

r----------> is the common ratio between terms

n----------> is the number of terms

ao=1.5

r=1/4-----> 0.25

n=5

so

∑=1.5*[(1-0.25^5)/(1-0.25)]-------------> 1.99

Step-by-step explanation: we have that

[3/2,3/8,3/32,3/128,3/512]

the sum of the geometric sequence is [3/2+3/8+3/32+3/128+3/512]

=(1/512)*[256*3+64*3+16*3+4*3]

=(3/512)*[256+64+16+4]

=(3/512)*[340]

=(1020/512)

=255/128---------> 1.9922

the answer is

1.9922

another way to calculate it 

is through the following formula

∑=ao*[(1-r^n)/(1-r)]

where 

ao---------> is the first term

r----------> is the common ratio between terms

n----------> is the number of terms

ao=1.5

r=1/4-----> 0.25

n=5

so

∑=1.5*[(1-0.25^5)/(1-0.25)]-------------> 1.99

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Since we know one of them (CBD) is 30, we can subtract 30 from 70 to find ABC. This is because the angle of ABC and CBD equal ABD.

30 + x = 70

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