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bearhunter [10]

3 years ago

12

Explain how you can write a quadratic function in a factored form that would have a vertex with an x-coordinate of 3 and two dis

tant roots

1 answer:

Elena-2011 [213]3 years ago

3 0

Answer:

Step-by-step explanation:

(x-3)²-4=0

(x-3)²=4=2²

x-3=±2

x=3±2

x=3-2,3+2

x=1,5

it has two distinct roots and a vertex at x=3

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Masha biked 20km 20 minutes faster than Dasha biked 20km. Find the speed of each cyclist if one biked 2km/h faster than the othe

motikmotik

Answer:

12 km/h and 10 km/h

Step-by-step explanation:

Let the speed of Masha = s, speed of Dasha = d

Distance = 20 km
Time difference = 20 min = 1/3 hr
Speed difference = 2 km/h

<u>As per above info we get following equations:</u>

s = d + 2
20/s + 1/3 = 20/d

<u>Substitute s and solve for d:</u>

20/(d + 2) + 1/3 = 20/d

<u>Get rid of fraction by multiplying all terms by 3d(d + 2):</u>

60d + d(d + 2) = 60(d + 2)
60d + d² + 2d = 60d + 120
d² + 2d = 120
d² + 2d + 1 = 121
(d + 1)² = 11²
d + 1 = 11
d = 10

<u>Find s:</u>

s = 10 + 2 = 12

<u>The answer is</u>

Masha's speed 12 km/h and Dasha's speed 10 km/h

3 0

3 years ago

Which of the following is in Integrity but not a whole number A -9.6 B -4

abruzzese [7]

Answer:

B. -4.

Step-by-step explanation:

3 0

3 years ago

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t

Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = $xyz$

with subject to $x+2y+3z=9$

So, let $z=\dfrac{9-x-2y}{3}$

So, Volume becomes,

$V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}$

Partially derivative wrt x and y we get that

$9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9$

By solving these two equations, we get that

$x=3,y=\dfrac{3}{2}$

So, $z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1$

So, Volume of largest rectangular box would be

$xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5$

Hence, the volume of largest rectangular box is 4.5 units.

4 0

3 years ago

If you know the answer for this please help me I would really appreciate it thank you!

STALIN [3.7K]

Answer:

line QR

Step-by-step explanation:

Plane QRB is the front face. Plane TSR is the top face. The planes intersect at the top front edge, line QR.

3 0

3 years ago

How do i divide and multiply rational expressions?

notka56 [123]

Answer:

To multiply rational expressions, first factor all numerators and denominators and cancel any factors you can. Then multiply what you have left.

Step-by-step explanation:

4 0

3 years ago