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3 years ago

The system shown has solution(s). y= 2x+1 X 2y-x = 6 No one Infinite

Mathematics

1 answer:

LenaWriter [7]3 years ago

7 0

9514 1404 393

Answer:

one solution; (x, y) = (4/3, 11/3)

Step-by-step explanation:

The two lines described by the equations have different slopes, so there will be exactly one solution to the system of equations.

The slope of the line will be the coefficient of x when you solve for y. In the first equation, the slope is 2. In the second equation, you can solve for y by adding x, and dividing by 2. Then the slope of that line is found to be 1/2.

Lines with different slopes must intersect somewhere. That point of intersection is the (one) solution to the system of equations.

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QUICKK EXPERTS/ACE/GENIUSES ( question #2 )

kiruha [24]

180 - 90 -18 = 72

Answer is D 72 degrees

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3 years ago

A recent survey based on a random sample of n=470 voters, predicted that independent candidate for the mayoral election will get

julsineya [31]

I have an expression

$\sigma = \sqrt{p(1-p)/n}$

floating around in my head; let's see if it makes sense.

The variance of binary valued random variable b that comes up 1 with probability p (so has mean p) is

$E( (b-p)^2 ) = (-p)^2(1-p) + (1-p)^2p = p(1-p)$

That's for an individual sample. For the observed average we divide by n, and for the standard deviation we take the square root:

$\sigma = \sqrt{p(1-p)/n}$

Plugging in the numbers,

$\sigma = \sqrt{.24(1-.24)/490} = 0.019 = 1.9\%$

One standard deviation of the average is almost 2% so a 27% outcome was 3/1.9 = 1.6 standard deviations from the mean, corresponding to a two sided probability of a bit bigger than 10% of happening by chance.

So this is borderline suspect; most surveys will include a two sigma margin of error, say plus or minus 4 percent here, and the results were within those bounds.

7 0

3 years ago

6 millimeters = yards

sertanlavr [38]

6 millimeters equals 0.00656168 yards.

7 0

3 years ago

What is the value of x?

Ksenya-84 [330]

Answer:

Step-by-step explanation:

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2x - x = 5 + 15

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5 0

2 years ago

Write the equation of each line using the given information.

Leni [432]

a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8

<h3>Solution:</h3>

a. The points (-4,1) and (2,4) both lie on the line

The general line equation on which (a, b) and (c, d) lies is:

$y-\mathrm{b}=\frac{d-b}{c-a}(x - a)$

Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)

Thus the required equation is:

$y-1=\frac{4-1}{2-(-4)}(x-(-4))$

On solving we get,

$\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}$

b.) m= -1 and the point (2, -1) lies on the line

The equation of line in point slope form is y – b = m(x – a)

where m is slope and (a, b) is a point on it

Here m = -1 and (a, b) = (2, -1)

Thus the required equation is:

y – (-1) = -1(x - 2)

y + 1 = -x + 2

y = -x + 2 -1

y = -x + 1

c. )It has the same slope as y = 5 and passes through (1, 1)

our line has same slope with y = 5, then our equation would be y = k and it passes through (x, y) = (1, 1) so, then by substitution

1 = k

k =1

Then our equation will be y = k

y = 1

d. ) m= -3 and it has a y-intercept of (0, 8)

line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.

Then, our equation will be y = -3x + 8

We took y- intercept = 8 as it is the value of y when x = 0

6 0

3 years ago