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2 years ago

Find the solution to the systems of equations using the elimination method. 3x + 5y = 2 5x + 8y = 4

Mathematics

1 answer:

Irina-Kira [14]2 years ago

6 0

Answer:

$\boxed{x = 4~~and~~y = -2}$

Step-by-step explanation:

3x + 5y = 2 (times 5) 15x + 25y = 10

5x + 8y = 4 (times 3) 15x + 24y = 12

15x + 25y = 10

y = -2

Substitute the value of y to one of equations

3x + 5y = 2

3x + 5(-2) = 2

3x - 10 = 2

3x = 2 + 10

3x = 12

$x = \frac{12}{3}$

x = 4

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2 years ago

Solve for x in the equation x²-12x+59=0

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2 years ago

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Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out 2/3 of the cho

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Answer:

9 packages of chocolate bars

Step-by-step explanation:

Let he bought c packages of chocolate bars and t packages of toffee bars,

Since, he bought 1 fewer package of chocolate bars than toffee bars.

⇒ c = t - 1 -----(1)

Also, he handed out out $\frac{2}{3}$ of the chocolate bars and $\frac{3}{5}$ of the toffee bars,

If he handed out the same number of each kind of candy bar.

$\implies \frac{2}{3}\times c=\frac{3}{5}\times t$

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$\implies t=\frac{10}{9}c$ ( Division property of equality )

From equation (1),

$c=\frac{10}{9}c-1$

$1=\frac{10}{9}c-c$

$1=\frac{10c-9c}{9}$

$1=\frac{c}{9}$

$\implies c = 9$

Hence, he bought 9 packages of chocolate bars.

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2 years ago

What is the value of the fourth term in a geometric sequence for which a1 = 30 and r = 1/2?

Pani-rosa [81]

Answer: The required fourth term of the geometric sequence is $\dfrac{10}{9}.$

Step-by-step explanation: We are given to find the value of the fourth term in a geometric sequence with first term and common ratio as follows :

$a(1)=30,~~~~~r=\dfrac{1}{2}.$

We know that

the n-th term of a geometric sequence with first term a1 and common ratio r given by

$a(n)=a(1)r^{n-1}.$

Therefore, the fourth term of the given geometric sequence will be

$a(4)=a(1)r^{4-1}=30\times r^3=30\times\left(\dfrac{1}{3}\right)^3=\dfrac{30}{27}=\dfrac{10}{9}.$

Thus, the required fourth term of the geometric sequence is $\dfrac{10}{9}.$

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2 years ago

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