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labwork [276]
3 years ago
10

Solve the system of equations. ​

Mathematics
1 answer:
vampirchik [111]3 years ago
8 0

Answer:

(0, 6 )

Step-by-step explanation:

Given the 2 equations

- 6y + 11x = - 36 → (1)

- 4y + 7x = - 24 → (2)

Multiplying (1) by 4 and (2) by - 6 and adding the result will eliminate y

- 24y + 44x = - 144 → (3)

24y - 42x = 144 → (4)

Add (3) and (4) term by term

2x = 0 ⇒ x = 0

Substitute x = 0 in either of the 2 equations and solve for y

Substituting in (1)

- 6y + 11(0) = - 36, that is

- 6y = - 36 ( divide both sides by - 6 )

y = 6

Solution is (0, 6 )

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what is the highest number in the world and what is the lowest number in the world explain your answer
artcher [175]
Positive infinity and negative infinity 

5 0
3 years ago
June has a total of 35 marbles. She has 4 times as many blue marbles as green marbles. She writes the following system of equati
Ganezh [65]

Answer:

June has 7 green and 28 blue marbles

Step-by-step explanation:

b + g = 35

b = 4g

Use substitution method to solve them simultaneously

4g + g = 35

5g = 35

g = 7

b = 4g = 4(7) = 28

b = 28, g = 7

She has 7 green and 28 blue marbles

8 0
3 years ago
A coin is tossed twice. Let H represents heads, T represents tails, and the combination of the two letters represent the outcome
denis23 [38]

Answer:

{HH, HT, TH, TT}

Step-by-step explanation:

The set of all possible outcomes in tossing a coin twice is;

{HH, HT, TH, TT}

In the first toss the coin may land Heads. In the second toss the coin may land Heads or Tails. This can be represented as;

HH, HT

Heads in the first and second tosses. Heads in the first toss followed by a Tail in the second toss.

In the first toss the coin is also likely to land Tails. In the second toss the coin may land Heads or Tails. This can be represented as;

TH, TT

Tails in the first toss followed by a Head in the second toss. Tails in the first and second tosses.

Combining these two possibilities will give us the set of all possible outcomes in tossing a coin twice is;

{HH, HT, TH, TT}

4 0
3 years ago
The age of the Hawaiian islands gets older as you move from east to west. If the half-life of K-40 is 1.3 billion years, approxi
Mumz [18]

Answer:

t \approx 750550.12\,yr

Step-by-step explanation:

The time constant of the isotope is:

\tau = \frac{1.3\times 10^{9}\,yr}{\ln 2}

\tau \approx 1.876 \times 10^{9}\,yr

The decay of the isotope is described by the following model:

\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }

Now, the time is cleared in the equation:

t = -\tau \cdot \ln \frac{m}{m_{o}}

t = - (1.876\times 10^{9}\,yr)\cdot \ln 0.9996

t \approx 750550.12\,yr

5 0
3 years ago
(cot^2x - 1)/(csc^2x) = cos2x​
Alex787 [66]

Answer:

Step-by-step explanation:

The idea here is to get the left side simplified down so it is the same as the right side. Consequently, there are 3 identities for cos(2x):

cos(2x)=cos^2x-sin^2x,

cos(2x)=1-2sin^2x, and

cos(2x)=2cos^2x-1

We begin by rewriting the left side in terms of sin and cos, since all the identities deal with sines and cosines and no cotangents or cosecants.  Rewriting gives you:

\frac{\frac{cos^2x}{sin^2x} -\frac{sin^2x}{sin^2x} }{\frac{1}{sin^2x} }

Notice I also wrote the 1 in terms of sin^2(x).

Now we will put the numerator of the bigger fraction over the common denominator:

\frac{\frac{cos^2x-sin^2x}{sin^2x} }{\frac{1}{sin^2x} }

The rule is bring up the lower fraction and flip it to multiply, so that will give us:

\frac{cos^2x-sin^2x}{sin^2x} *\frac{sin^2x}{1}

And canceling out the sin^2 x leaves us with just

cos^2x-sin^2x which is one of our identities.

5 0
3 years ago
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