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Gwar [14]
3 years ago
7

What's the GCF of 20, 28, 24

Mathematics
2 answers:
zimovet [89]3 years ago
8 0
The answer would be 4
Pie3 years ago
7 0
The greatest common factor is 4

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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}

8 0
3 years ago
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mamaluj [8]
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6 0
4 years ago
The Rational Number<br>0​
mafiozo [28]

Answer:

yes the rational no.is 0

8 0
3 years ago
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Convert 112 degrees Fahrenheit to degrees Celsius
harkovskaia [24]

Equation

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Step-by-step explanation:

5x^2-6x-7=0

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4 0
3 years ago
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