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3 years ago

The inequality 2x - 3y ≥ 5 is satisfied by point (1/2, 1/3). True False

Mathematics

2 answers:

True [87]3 years ago

8 0

Answer:

false

Step-by-step explanation:

Blizzard [7]3 years ago

4 0

The correct answer for this statement would be FALSE. Let us try to prove it by plugging in the values. So 2 (1/2) - 3 (1/3) ≥ 5.
So that would be 1 - 3 ≥ 5..
-2 ≥ 5, which makes the result false because -2 is not more than or equal to 5, but instead, it is less than. I hope this answer helps.

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If x varies directly with y and y is 10 when x is 8, what is x when y is 18?

swat32

Knowing that x varies directly with y, we know the basic skeleton of the equation is y = mx.

To find m, plug in the known coordinate (8,10), where the x-coordinate is 8 and the y-coordinate is 10.
$y=mx \\ 10=m8 \\ (10)/8=(8m)/8 \\ m= \frac{10}{8} = \frac{5}{4}$

Then, plug in m to the equation to get y = (5/4)x.

Finally, plug in the y-coordinate 18 to the equation and solve for x!
$y= \frac{5}{4}x \\ 18= \frac{5}{4}x \\ \frac{4}{5}(18)=( \frac{5}{4}x) \frac{4}{5} \\ x= \frac{4*18}{5} \\ x= \frac{72}{5}$

Your exact answer is x = 72/5. However, if your teacher prefers decimals, then x = 14.4

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Yuri [45]

Answer:

Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line $2x-3y=12$ is $3x+2y=34$

Step-by-step explanation:

Given:

$2x-3y=12$

To Find:

Equation of line passing through ( 16, -7) and is perpendicular to the line

$2x-3y=12$

Solution:

$2x-3y=12$ ...........Given

$\therefore y=\dfrac{2}{3}\times x-4$

Comparing with,

$y=mx+c$

Where m =slope

We get

$Slope = m1 = \dfrac{2}{3}$

We know that for Perpendicular lines have product slopes = -1.

$m1\times m2=-1$

Substituting m1 we get m2 as

$\dfrac{2}{3}\times m2=-1\\\\m2=-\dfrac{3}{2}$

Therefore the slope of the required line passing through (16 , -7) will have the slope,

$m2=-\dfrac{3}{2}$

Now the equation of line in slope point form given by

$(y-y_{1})=m(x-x_{1})$

Substituting the point (16 , -7) and slope m2 we will get the required equation of the line,

$(y-(-7))=-\dfrac{3}{2}\times (x-16)\\\\2y+14=-3x+48\\3x+2y=34......Equation\ of\ line$

Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line $2x-3y=12$ is

$3x+2y=34$

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