Mathematics, 24.06.2019 19:30 saltytaetae

Awalking path across a park is represented by the equation y= -4x - 6 . a new path will be built perpendicular to this path. the path will intersect at the point (-4 , 10) . identify the equation that represents the new path .

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Answer from: ScardeySpider

y=1/4 x +11

Step-by-step explanation:

So this is a word problem but it isn't too bad to figure what they want: They are looking for a line that is perpendicular to y=-4x-6 and goes through (-4,10).

So we are looking for an equation whose slope is the opposite reciprocal of the given equation's slope.

The given equation has a slope of -4

The opposite reciprocal of -4 is 1/4 so that is the slope of our new line.

So we know our equation is in the form of y=1/4 x+b

Now we are given that this line should go through (-4,10) so plug it in to find b.

10=1/4 * (-4)+b

10=-1+b

11=b

So the equation is y=1/4 x+11

Answer from: 23ricorvan

$y=\frac{1}{4}x+11$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

Given the equation of the line y= -4x - 6 , you can identify that the slope is:

m=-4

By definition, the slopes of perpendicular lines are negative reciprocals, then the slope of equation of the line that represents the new path which will be built perpendicular to other path, is:

$m=\frac{1}{4}$

Knowing that the path will intersect at the point (-4 ,10), you need to substitute the slope and this point into y=mx+b and solve for "b":

$10=\frac{1}{4}(-4)+b\\\\10+1=b\\\\b=11$

Therefore, the equation that represents the new path is:

$y=\frac{1}{4}x+11$

Answer from: Quest

answer: the answer is (b) amie should have multiplied

$54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

$v_s=\pi r^2h=\pi r^3,$

and the volume of the cylinder will be

$v_c=\dfrac{4}{3}\pi r^3=54~\textup{m}^3.$

therefore, we have

$v_c=\dfrac{4}{3}v_s=\dfrac{4}{3}\times 54=72~\textup{m}^3.$

thus, ammie should have multiplied the volume of the sphere $54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

Answer from: Quest

B. because the 7 represents "seven times", x represents "a number", 12 represents "plus twelve", and -4 represents "minus four"
Which of the following best describes an algebraic expression 7 (x+ 12) -4

Which of the following best describes an algebraic expression 7 (x+ 12) -4

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