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il63 [147K]
3 years ago
9

Write the equation of the line with a slope of 24 and a y-intercept of -5​

Mathematics
1 answer:
zmey [24]3 years ago
8 0

Answer:

y=24x-5

Step-by-step explanation:

General slope intercept form equation of straight line is given as

y=mx+b

where m is slope and b is y-intercept

here m=24 and b=-5

Therefore

y=mx+b=24x-5

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andrey2020 [161]

Answer:

the vertex of the parabola is at the point; (5, -1)

which agrees with answer "B" in the list of options

Step-by-step explanation:

Notice that this is the equation of a parabola with branches that open horizontally (not vertically), since the variable the goes squared is the y-variable instead of "x".

By analyzing it we can then write it by isolating the term in "x" on one side of the equation, and use at the same time the fact that it is being written in "vertex" form:

-8\,(x-5)=(y+1)^2\\(x-5)=-\frac{1}{8} (y+1)^2

Therefore, the "y-value" of the vertex must be that which renders zero in the expression squared, that is y = -1. On the other hand, the x-value of the vertex is that which renders zero for the variable "x":  x=5.

Then, the vertex of the parabola is at the point; (5, -1)

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3 years ago
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Step-by-step explanation:

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Step-by-step explanation:

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Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis
stealth61 [152]

Complete question is;

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.) y = 6 - x²

Answer:

height = 4 and base = 2√2

Step-by-step explanation:

Area of a rectangle is given by;

A = base(b) × height(h)

To start off, we will first have to consider half of the rectangle.

Due to the fact that it is bounded by a parabola which is symmetric over the y-axis, it means that the rectangle will have the same area on the right and left hand sides.

So if we maximize the area of the first quadrant, it means that we are also maximizing the area of the entire rectangle.

Now, since we are dealing with the base and other 2 vertices on the x-axis, it means that the base(b) of this half rectangle will be x.

The height of this rectangle is the y coordinate of the corner that is directly above the x coordinate, which is also on the rectangle.

Therefore, the coordinates of the upper corner will be (x, y), or (x, 6 - x²). Thus our half base is x and full height is 6 - x². Area will be;

A = x(6 - x²)

A = 6x - x³

We will maximize this area by finding the derivative and equating to zero.

Thus;

A' = 6 - 3x²

At A' = 0,we have;

6 - 3x² = 0

3x² = 6

x² = 6/3

x² = 2

x = √2

Thus, from y = 6 - x², we have;

y = 6 - (√2)²

y = 6 - 2

y = 4

Since x is half base, it means our full width is 2x = 2 × √2 = 2√2

So, height = 4 and base = 2√2

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3 years ago
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