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4 years ago

Solve the given system of equations using any method and then choose the correct ordered pair from the given choices:

Mathematics

1 answer:

Mnenie [13.5K]4 years ago

8 0

Answer:

Step-by-step explanation:

Given the 2 equations

x + y = 3 → (1)

3x - y = 1 → (2)

Adding the 2 equations term by term will eliminate the term in y

4x = 4 ( divide both sides by 4)

x = 1

Substitute x = 1 into either of the 2 equations and evaluate for y

Substituting into (1)

1 + y = 3 ( subtract 1 from both sides )

y = 2

Solution is (1, 2 ) → c

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I need help with this question, i am not exactly sure how to do it, help is veryy much appreciated

Jet001 [13]

Yeah i believe this question is a error!!if not it should be 88

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4 years ago

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.

Arisa [49]

Answer: $S_n=5(1-\dfrac{1}{n+1})$ ; 5

Step-by-step explanation:

Given series : $[\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]$

Sum of series = $S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]$

Consider $\dfrac{1}{n\cdot(n+1)}=\dfrac{n+1-n}{n(n+1)}$

$=\dfrac{1}{n}-\dfrac{1}{n+1}$

⇒ $S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]$

Put values of n= 1,2,3,4,5,.....n

⇒ $S_n=5(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+......-\dfrac{1}{n}+\dfrac{1}{n}-\dfrac{1}{n+1})$

All terms get cancel but First and last terms left behind.

⇒ $S_n=5(1-\dfrac{1}{n+1})$

Formula for the nth partial sum of the series :

$S_n=5(1-\dfrac{1}{n+1})$

Also, $\lim_{n \to \infty} S_n = 5(1-\dfrac{1}{n+1})$

$=5(1-\dfrac{1}{\infty})\\\\=5(1-0)=5$

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3 years ago

A restaurant had 5 pies each cut into eighths. By noon 3/4 of all the pieces were sold. How many pieces of the pie were sold by

Ad libitum [116K]

Answer:

Step-by-step explanation:

5 pies * 8 pieces = 40 total pieces

40 * 3/4 =

40/1 * 3/4 =

120/4 = 30

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3 years ago

a cake divided into 10 equal slices.kim ate 3/5 of 1/2 of cake. what part of the whole cake did kim ate?

joja [24]

Answer:

3/10 of the whole cake

Step-by-step explanation:

When you divide a cake in halve you get 5 pieces on each side, if Kim ate 3/5 of 1/2 of the cake, then she ate 3 pieces, so she ate 3/10 of the cake, and other way to figure this out is multiplying the two fractions, 3/5 x 1/2 = 3/10

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3 years ago

Pick the correct answer

umka2103 [35]

Answer:

I believe it is no solution i m so sorry if i am wrong!a

Step-by-step explanation:

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3 years ago