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2 years ago

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Suppose that gcd(a,b)=1. Prove that for every integer c, the equation ax+by=c has a solution in integers x and y. [Hint: Find a

solution to au+bv=1 and multiply by c] Find a solution to 37x + 47y = 103. Try to make x and y as small as possible

1 answer:

frosja888 [35]2 years ago

4 0

Answer:

okie

Step-by-step explanation:

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janelle wishes to finance a car for $33,000. the bank's annual interest rate is 3.5%, and she can choose between durations of fi

Harman [31]

Answer:

For a duration of 5 years, Monthly Payment =$600.42

For a duration of 6 years, Monthly Payment =$508.83

Step-by-step explanation:

$P=\dfrac{ar (1+r)^n}{(1+r)^n-1} \\$

where a= Amount to Finance=$33,000

Annual interest rate = 3.5%=0.035

r=Monthly Interest Rate= 0.035 ÷ 12 = $\frac{7}{2400}$

n=number of months to pay

For a duration of 5 years

n=5X12=60 months

$P=\dfrac{ar (1+r)^n}{(1+r)^n-1} \\\\P=\dfrac{33000 X\frac{7}{2400} (1+\frac{7}{2400} )^{60}}{(1+\frac{7}{2400})^{60}-1} \\=\dfrac{96.25 (1.1909)}{1.1909-1}\\=\dfrac{96.25 (1.1909)}{0.1909}\\=\dfrac{114.62}{0.1909}=\$600.42$

For a duration of 6 years

n=6X12=72 months

$P=\dfrac{ar (1+r)^n}{(1+r)^n-1} \\\\P=\dfrac{33000 X\frac{7}{2400} (1+\frac{7}{2400} )^{72}}{(1+\frac{7}{2400})^{72}-1} \\=\dfrac{96.25 (1.2333)}{1.2333-1}\\=\dfrac{96.25 (1.2333)}{0.2333}\\=\dfrac{118.71}{0.2333}=\$508.83$

4 0

2 years ago

Uhh help lol<br> 5.3x + y = 28.5 <br> 4.2x + 3.1y = 27.2<br> find x and y

navik [9.2K]

Answer:

x = 5, y = 2

Step-by-step explanation:

First, isolate y in the top equation.

$y = -5.3x+28.5$

Next, substitute y in the bottom equation.

$4.2x + 3.1(-5.3x + 28.5) = 27.2$

$5.3x + y = 28.5$

Simplify.

$4.2x + -16.43x + 88.35 = 27.2$

Combine like terms.

$-12.23x + 88.35 = 27.2$

Isolate x on one side.

$-12.23x = -61.15$

Isolate x.

$x = 5$

Substitute x into $5.3x + y = 28.5$

$5.3(5) + y = 28.5$

Simplify.

$26.5 + y = 28.5$

Isolate y.

$y = 2$

$x = 5 \\y = 2$

6 0

3 years ago

the length of a diagonal of a square field is 220 metres find the length of a side in metres and the area of the field in hectar

andre [41]

Answer:

Step-by-step explanation:

h^2=x^2+y^2, since this is a square x=y=s so

220^2=2s^2

2s^2=48400

s^2=24200

s=24200^(1/2)m (exact)

s=155.56m (rounded to nearest hundredth of a meter)

One hectare is equal to 10000m^2

A=24200m^2(h/10000m^2)

A=2.42 hectares

7 0

2 years ago

Can someone explain this to me I need help T_T

vaieri [72.5K]

Answer: 6,800,000 people

Step-by-step explanation:

We are looking for the number of people, not the percentage of wealth that has been made up by the people.

2% of the people are the richest in the United States, and there are 340,000,000 people in total in the United States.

2% = 0.02

340,000,000 * 0.02 = 6,800,000

I hope this was helpful! :)

4 0

3 years ago

Simplify the difference quotient f(x) − f(a) / x − a if x ≠ a. f(x) = x^3 − 36

Annette [7]

Fx - fa÷x - ( aif x ÷ n (2.178282)) (a) = -2.718282a² fix²+ fnx² - afn ÷ nx

7 0

3 years ago