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3 years ago

Solve the following system of equations using elimination: -x+5y=8 And 3x+7y=-2

Mathematics

1 answer:

djyliett [7]3 years ago

6 0

Answer:

x=-3, y=1. (-3, 1).

Step-by-step explanation:

-x+5y=8

3x+7y=-2

----------------

3(-x+5y)=3(8)

3x+7y=-2

--------------------

-3x+15y=24

3x+7y=-2

------------------

22y=22

y=22/22

y=1

-x+5(1)=8

-x+5=8

-x=8-5

-x=3

x=-3

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The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing

tester [92]

The length of pendulum is 2.485 feet

<h3><u><em>Solution:</em></u></h3>

Given that,

The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing back and forth

<u><em>Therefore, the given formula is:</em></u>

$T=2\pi \sqrt{\frac{L}{32} }$

We have to find the length of pendulum that makes one full swing in 1.75 seconds

So the modify the given equation to find "L"

$T=2\pi \sqrt{\frac{L}{32} }\\\\ \sqrt{\frac{L}{32} }=\frac{T}{2 \pi}\\\\\text{Taking square root on both sides }\\\\\frac{L}{32} = \frac{T^2}{4 \pi^2}\\\\L = \frac{T^2}{4 \pi^2} \times 32\\\\L = \frac{T^2}{\pi^2 } \times 8$

Substitute T = 1.75 seconds and $\pi = 3.14$

$L = \frac{1.75^2}{3.14 \times 3.14} \times 8\\\\L = \frac{3.0625}{9.8596} \times 8\\\\L = 2.485$

Thus length of pendulum is 2.485 feet approximately

7 0

4 years ago

If α , β are roots of x2 + 5x + a =0 and 2α + 5β = -1 then α is equal to _____?

ELEN [110]

9514 1404 393

Answer:

-8

Step-by-step explanation:

If α and β are roots of x^2 +5x +a = 0, then we must have ...

(x -α)(x -β) = x^2 +5x +a

x^2 -(α+b)x +αβ = x^2 +5x +a

Then ...

α + β = -5

Together with the other relation between the roots, we have a system of equations in α and β.

Using the above to write an expression for β, we get ...

β = -α -5

Substituting this into the given relation, we have an equation for α:

2α +5(-α -5) = -1

-3α -25 = -1 . . . . . . eliminate parentheses

-24 = 3α . . . . . . . . add 3α +1

-8 = α

The root α is equal to -8.

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4 years ago

A camel can drink 25 gallons of water in 10 minutes. How many cups of water can the camel drink in 10 minutes?

Alecsey [184]

Question:

A camel can drink 25 gallons of water in 10 minutes. How many cups of water can the camel drink in 10 minutes?

Solution:

1 cup = 0.25 quarts.

4 quarts= 1 gallon

Then, according to this information, we get the following table:

Note that 4 quarts= 1 gallon, then 1 gallon is equivalent to 16 cups.

Then, 25 gallons are equivalent to:

$25\text{ gallons(}\frac{16\text{ cups}}{1\text{ gallon}}\text{)}=\text{ 400 cups}$

D. According to the above information, we obtain that 25 gallons of water are 400 cups .

So that, we can conclude that the correct answer is:

The camel can drink 400 cups of water in 10 minutes

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