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emmainna [20.7K]
3 years ago
8

One of the roots of the equation x2−5x+q=0 is 2. Find the other root and the value of the coefficient q.

Mathematics
2 answers:
pishuonlain [190]3 years ago
8 0

Answer:

q=6

Step-by-step explanation:

A root can be plugged in for X, so 2(2)-5(2)+q=0. This means -6+q=0. We can now even them out and know q=6

ELEN [110]3 years ago
7 0

Answer:

x=3, and q=6

Step-by-step explanation:

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A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the
Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0
2 years ago
Patrick paid $4.00 for 5 organic peaches. How much did he pay per peach
leonid [27]

Answer:

80 cents

Step-by-step explanation:

divide the price by 5

4/5=.8

6 0
3 years ago
Read 2 more answers
the width of a rectangle is 12 cm less than the length the perimeter is 156 cm. Find the with and length
mamaluj [8]

We know that the perimeter of a rectangle is twice the length, plus twice the width.  

P = 2L + 2W  

We also know that the perimeter is 156.  

P = 156  

Finally, we know that the width is 12 less than the length.  

W = L - 12.  

The next thing that we do is substitute the information that we have into the original equation:  

P = 2L + 2W  

156 = 2L + 2(L - 12)  

From this point we start to solve  

156 = 2L + 2L - 24 <---we multiplied the '2' through the parenthesis  

156 + 24 = 2L + 2L - 24 + 24  

180 = 2L + 2L <--- getting like terms on same sides  

180 = 4L <---combining like terms  

180/4 = 4L/4 <--- getting like terms on same sides  

45 = L <---now we have a value for L  

Now we take the known value for L and substitute it in to our equation for W  

W = L - 12  

W = 45 - 12  

W = 33  

So now we have Length = 45 and Width = 33.

6 0
2 years ago
Read 2 more answers
Fatima is shading this model to show 0.08x3 . shade the correct amount of boxes that will show the product
Karo-lina-s [1.5K]
Shade 0.08 3 times

In total that's 24 hundreths to shade


For more help, please upload a picture

Hope this helps!!
7 0
2 years ago
A food factory produces trail mix containing raisins and cashews at a cost of $9 per pound. Every 3 pound container of trail mix
Svetllana [295]

Answer:

4r+8c = 27

Step-by-step explanation:

consider that 3 lbs will cost $27 at $9/lb

so, adding up the value of the raisins and cashews in a 3lb bag.

7 0
3 years ago
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