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MrRa [10]
3 years ago
14

A rectangle has a height of 4x4x4, x and a width of 3x+13x+13, x, plus, 1. Express the area of the entire rectangle.

Mathematics
1 answer:
svetlana [45]3 years ago
4 0

<u>Given</u>:

The rectangle has a height of 4x and the width of 3x+1

We need to determine the area of the entire rectangle.

<u>Area of the rectangle:</u>

Let us determine the area of the rectangle.

The area of the rectangle can be determined using the formula,

A=length \times width

Substituting the value length = 4x and width = 3x+1 in the above formula, we get;

A=4x(3x+1)

Let us remove the parenthesis by multiplying the term 4x within the bracket, we have;

A=12x^2+4x

Thus, the entire area of the rectangle is 12x^2+4x

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Jack drove to work in the morning at an average speed of 45 miles per hour. He returned home in the evening along the same route
Dmitry [639]

Answer:

Step-by-step explanation:

Let's say that the time it took him to get to work in the morning is  t hours. Then the time it took him to get home in the afternoon must be 1 - t hours. We know that for any trip, distance equals rate times time or d = rt . That means that the distance he drove to work is given by , but we also know that the distance he drove to get home must be the same distance, because he took the same route (and, presumably, no one picked up him house and moved it while he was at work) so for the trip home we can say  d = 30 × (1 - t) and since the distances are equal, we can say: 

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Find the radius of the congruent circles. Thanks and hope you have a good rest of your day!!
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How would you determine the axis of symmetry in order to graph x^2 = 8y^2.
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The picture illustrates the definition. The point P is a typical point on the parabola so that its distance from the directrix, PQ, is equal to its distance from F, PF. The point marked V is special. It is on the perpendicular line from F to the directix. This line is called the axis of symmetry of the parabola or simply the axis of the parabola and the point V is called the vertex of the parabola. The vertex is the point on the parabola closest to the directrix.

Finding the equation of a parabola is quite difficult but under certain cicumstances we may easily find an equation. Let's place the focus and vertex along the y axis with the vertex at the origin. Suppose the focus is at (0,p). Then the directrix, being perpendicular to the axis, is a horizontal line and it must be p units away from V. The directrix then is the line y=-p. Consider a point P with coordinates (x,y) on the parabola and let Q be the point on the directrix such that the line through PQ is perpendicular to the directrix. The distance PF is equal to the distance PQ. Rather than use the distance formula (which involves square roots) we use the square of the distance formula since it is also true that PF2 = PQ2. We get

<span>(x-0)2+(y-p)2 = (y+p)2+(x-x)2. 
x2+(y-p)2 = (y+p)2.</span>If we expand all the terms and simplify, we obtain<span>x2 = 4py.</span>

Although we implied that p was positive in deriving the formula, things work exactly the same if p were negative. That is if the focus lies on the negative y axis and the directrix lies above the x axis the equation of the parabola is

<span>x2 = 4py.</span><span>The graph of the parabola would be the reflection, across the </span>x<span> axis of the parabola in the picture above. A way to describe this is if p > 0, the parabola "opens up" and if p < 0 the parabola "opens down".</span>

Another situation in which it is easy to find the equation of a parabola is when we place the focus on the x axis, the vertex at the origin and the directrix a vertical line parallel to the y axis. In this case, the equation of the parabola comes out to be

<span>y2 = 4px</span><span>where the directrix is the verical line </span>x=-p and the focus is at (p,0). If p > 0, the parabola "opens to the right" and if p < 0 the parabola "opens to the left". The equations we have just established are known as the standard equations of a parabola. A standard equation always implies the vertex is at the origin and the focus is on one of the axes. We refer to such a parabola as a parabola in standard position.

Parabolas in standard positionIn this demonstration we show how changing the value of p changes the shape of the parabola. We also show the focus and the directrix. Initially, we have put the focus on the y axis. You can select on which axis the focus should lie. Also you may select positive or negative values of p. Initially, the values of p are positive. 

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