2 years ago

Which equation matched the graph ?

Mathematics

1 answer:

Nady [450]2 years ago

8 0

D. y - 2 = -3(x - 2)

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Five less than three times a number

Radda [10]

That would turn into 3x-5

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2 years ago

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

Write 39,005 in expanded form

vlada-n [284]

(3 * 10,000) + ( 9* 1,000) + ( 5* 1)

8 0

2 years ago

Read 2 more answers

Answer yes or no to determine whether 268 is divisible by each number:

d1i1m1o1n [39]

2 yes 4 yes 6 no 9 no 10 no

Step-by-step explanation:

268÷2=134

268÷4= 67

4 0

2 years ago

Read 2 more answers

Some money is shared between erin, faye and sachin in the ratio 5:2:7. Faye gets £90 less than sachin. How much money did Erin g

VARVARA [1.3K]

Answer:

Erin gets £90

Step-by-step explanation:

Ratio = 5 : 2 : 7

Money with Erin = 5x

Money with Faye = 2x

Money with Sachin = 7x

Faye gets £90 less than Sachin

7x - 2x = 90

5x = 90

x = 90/5

x = 18

Money with Erin = 5*18 = 90

7 0

2 years ago