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Nadya [2.5K]
3 years ago
12

the line y=2x-4 and the parabola y=x^2- 4 intersect in the standard x,y coordinate plane if point a s,t is at an intersection of

the line and the parabola what is the greatest possible value of s?
Mathematics
1 answer:
mylen [45]3 years ago
7 0
2x-4=x^2-4 
-4=x^2-2x-4 (start moving everything to one side)
x^2-2x=0 (the 4 cancel out)
x(x-2)=0 (factor out an x)
x=0 & x=2 (solved for x)

y=2x-4 (pick one of the equations)
y=2(0)-4 (plug in x)
y=-4
(0,-4)

y=2(2)-4 (plug in the second point)
y=0
(2,0)

The greatest possible value of s is 2. (2,0)


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What is the y-intercept of the line y + 11 = -2(x +1.5)?<br> -<br> y-intercept = |<br> =<br> I
aleksandrvk [35]

Answer:

The y intercept of the line is (0, -14).

Step-by-step explanation:

we are given the equation

y + 11 = -2(x + 1.5)

The y-intercept of the line is the point where x = 0,

Substituting x = 0 into the expression:

y + 11 = -2(0 + 1.5)

y + 11 = -0 – 3

y + 11 = -3

y = 11 – 11 = -3 – 11

y = -14

Thus, The y intercept of the line is (0, -14).

 

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3 years ago
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Veseljchak [2.6K]

Answer:

The area of the rectangle <em>TOUR</em> is 80.00 unit².

Step-by-step explanation:

The area of a rectangle is computed using the formula:

Area\ of\ a\ Rectangle=length\times width

Since the dimensions of the rectangle are not provided we can compute the dimensions using the distance formula for two points.

The distance formula using the two point is:

distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

Considering the rectangle <em>TOUR</em> the area formula will be:

Area of Rectangle <em>TOUR</em> = <em>TO × OU</em>

The co-ordinates of the four vertices of a triangle are:

T = (-8, 0), O = (4, 4), U = (6, -2) and R = (-6, -6)

Compute the distance between the vertices <em>T</em> and <em>O</em> as:

TO=\sqrt{(4-(-8))^{2}+(4-0)^{2}}\\=\sqrt{12^{2}+4^{2}} \\=\sqrt{160} \\=4\sqrt{10}

Compute the distance between the vertices <em>O </em>and <em>U</em> as:

OU=\sqrt{(6-4)^{2}+(-2-4)^{2}}\\=\sqrt{2^{2}+6^{2}} \\=\sqrt{40} \\=2\sqrt{10}

Compute the area of rectangle TOUR as follows:

Area\ of\ TOUR=TO\times OU\\=4\sqrt{10}\times 2\sqrt{10}\\=80\\\approx80.00 unit^{2}

Thus, the area of the rectangle <em>TOUR</em> is 80.00 unit².

6 0
3 years ago
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