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3 years ago

How many solutions does the system of equations below have? y= 3x + 4 2y -8 = 6x

Mathematics

1 answer:

Cerrena [4.2K]3 years ago

3 0

Answer:

infinitely many solutions (infinite solutions)

Step-by-step explanation:

2y - 8 = 6x

+8 +8

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

2y = 6x + 8

$\frac{2y}{2}$ = $\frac{6x}{2}$ + $\frac{8}{2}$

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

y = 3x + 4

Because 3x + 4 = 3x + 4, there are infinitely many solutions to this system of equations. This is because they're the exact same equations. Any substitution for x will give you a true statement to y when compared to the other equation.

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Is (0,0) a solution to this system y> x2+x-4 y <x2+2x+1

Aliun [14]

Answer:

Yes, the ordered pair (0,0) is a solution of the system

Step-by-step explanation:

we have

$y\geq x^{2}+x-4$ ----> inequality A

$y < x^{2} +2x+1$ ----> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify

For x=0,y=0

Inequality A

$0\geq (0)^{2}+0-4$

$0\geq -4$ ----> is true

The ordered pair satisfy inequality A

Inequality B

$0 < (0)^{2} +2(0)+1$

$0 < 1$ ----> is true

The ordered pair satisfy inequality B

therefore

The ordered pair (0,0) is a solution of the system

7 0

3 years ago

Read 2 more answers

4p2-p=0 how do you solve this

VladimirAG [237]

combine you like terms

4p and -p = 3p

3p+2=0

subtracts 2 from itself and 0

3p=-2

divide 3p from itself and -2

p=-2/3

6 0

3 years ago

In Triangle MNP, what Is sinN?

Alchen [17]

Step-by-step explanation:

Sin N = Opposite/Hypotenuse = 15/17

Hope it helps

5 0

3 years ago

The length of country and western songs is normally distributed and has a mean of 170 seconds and a standard deviation of 40 sec

Serga [27]

Answer: 0.1210

Step-by-step explanation:

Given : The length of country and western songs is normally distributed with $\mu=170 \text{ seconds}$

$\sigma=40\text{ seconds}$

Sample size : $n=16$

Let x be the length of randomly selected country song.

z-score : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$z=\dfrac{158.30-170}{\dfrac{40}{\sqrt{16}}}\approx-1.17$

The probability that a random selection of 16 songs will have mean length of 158.30 seconds or less by using the standard normal distribution table will be

= $P(x\leq158.30)=P(z\leq-1.17)$