3 years ago

You are buying carpet to cover a room that measures 21 feet by 30 feet. The carpet

Mathematics

1 answer:

Elina [12.6K]3 years ago

4 0

Answer:

20.97

Step-by-step explanation:

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3 years ago

Order these numbers from least to greatest.

Lorico [155]

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Step-by-step explanation:

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hannah's school hosted a book donation. there are 150 students at her school, and they donated b books! hannah donated 3 times a

MArishka [77]

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3 years ago

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2x≥12 <br>I can't figure this out

Serhud [2]

Answer:

$x \geq 6$

Step-by-step explanation:

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2 years ago

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A circle has centre (3,0) and radius 5. The line y = 2x + k intersects the circle in two points. Find the set

lara [203]

A circle with center $(3,0)$ and radius $5$ has equation

$(x-3)^2+y^2=25 \iff x^2 + y^2- 6 x = 16$

If we substitute $y=2x+k$ in this equation, we have

$x^2+(2x+k)^2-6x=16 \iff 5x^2+(4k-6)x+k^2-16=0$

This equation has two solutions (i.e. the line intersects the circle in two points) if and only if the determinant is greater than zero:

$\Delta=b^2-4ac=(4k-6)^2-4\cdot 5\cdot (k^2-16)>0$

The expression simplifies to

$-4 (k^2 + 12 k - 89)>0 \iff k^2 + 12 k - 89$

The solutions to the associated equation are

$k^2 + 12 k - 89=0 \iff k=-6\pm 5\sqrt{5}$

So, the parabola is negative between the two solutions:

$-6-5\sqrt{5}$

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3 years ago