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2 years ago

How do you do this I really need some help!please

Mathematics

2 answers:

kow [346]2 years ago

7 0

Answer:

yes

Step-by-step explanation:

you plug in the 3 into the x, because x=3 so therefore 3+5>7 which becomes 8>7. Is 8 more than 7? yes! so its true. For the next, 7>12, thats not true. And for the last one, 10-7<5, so 3<5, which is true.

Rzqust [24]2 years ago

5 0

Answer:

It is correct for 5. Incorrect for 6. Lastly, correct for 7.

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Which of the following is parallel to the line 2x+4y=16

k0ka [10]

Answer:

Option C: y=-1/2x + 8

Step-by-step explanation:

So we have the options:

A) y=2x+5

B) y=-1/2x+4

C)y=-1/2x+8

D)y=-2x+5

But first let's define what parallel even is. When two lines are parallel it means that there slope is the same value and the same sign, while there y-intercepts are different, because if they were the same, then they wouldn't be parallel, they would just be the same exact line.

So we're given the equation in standard form. To find the slope we can change it so it's in the form of y=mx+b. This can be done by simply isolating y. The reason we want it in the slope-intercept form is because m represents the slope and b represents the y-intercept. m is the slope because as x increases by 1 the y-value will increase by m. So the "rise" will be m and the "run" will be 1, thus the slope will be m/1 or in other words m because the slope is defined as rise/run. So let's start the steps to isolating y

Original equation

2x+4y=16

Subtract 2x from both sides

4y=-2x+16

Divide both sides by 4

y = -1/2x + 4

Here we have it in slope-intercept form. In this case the slope, or m, is -1/2 and the y-intercept or b is 4. So now let's look at the other equations.

Option A: This equation has a slope of 2, which is not the same as -1/2 so it is not parallel

Option B: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. But look at the y-intercept it's 4, that's the same y-intercept as the original equation. This means the two equations are equal and not parallel

Option C: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. It has a y-intercept of 8 which is not the same as 4, so the two lines are parallel and not equal! This is the answer

6 0

2 years ago

Find the distance from the point (1,4) to the line y = 1/3x - 3

Troyanec [42]

Answer:

Step-by-step explanation:

If I'm not mistaken, and I very well could be, this is a calculus problem(?). In order to find the distance without calculus you'd need a point on the given line to use to find the distance in the distance formula. But you don't have a point on the given line, so we can find the shortest distance between the point (1, 4) and the given line using the derivative of the polynomial formed when using the distance formula.

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ and we have the x and y for x2 (or x1...it doesn't matter which you choose to fill in):

$d=\sqrt{(1-x)^2+(4-y)^2}$

but what we find is that we have too many unknowns here, namely, the distance, the x coordinate, and the y coordinate. So we can replace the y coordinate with what y is equal to in terms of the linear equation:

$d=\sqrt{(1-x)^2+(4-\frac{1}{3}x-3)^2 }$ and simplify:

$d=\sqrt{(1-x)^2+(7-\frac{1}{3}x)^2 }$

. No we'll expand each binomial by squaring:

$d=\sqrt{(1-2x+x^2)+(49-\frac{14}{3}x+\frac{1}{9}x^2) }$

. Combining like terms gives us

$d=\sqrt{\frac{10}{9}x^2-\frac{20}{3}x+50 }$

The distance between the point (1, 4) and the given line will be at a minimum when the polynomial above is at a minimum. We find the value of x for which the polynomial is at a minimum by finding its derivative, setting the derivative equal to 0, and then solving for x. The derivative of the polynomial is

$\frac{20}{9}x-\frac{20}{3}$

Setting equal to 0 and getting rid of the denominators gives us

20x - 60 = 0

Solving for x gives us

20x = 60 and x = 3.

That's the value of x that gives us the shortest distance between (1, 4) and the line y = 1/3x - 3. Sub into the distance formula that x value to find the distance:

$d=\sqrt{(\frac{10}{9})(3)^2-(\frac{20}{3})(3)+50 }$