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3 years ago

Factor 4x squared-35x+4

1 answer:

8 0

$4x^2-35x+4\\\\a=4;\ b=-35;\ c=4\\\\\Delta=b^2-4ac\to\Delta=(-35)^2-4\cdot4\cdot4=1225-64=1161\\\\x=\frac{-b\pm\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{1161}=\sqrt{9\cdot129}=3\sqrt{129}\\\\x=\frac{-(-35)\pm3\sqrt{129}}{2\cdot4}=\frac{35\pm3\sqrt{129}}{8}\\\\4x^2-35x+4=4\left(x-\frac{35-3\sqrt{129}}{8}\right)\left(x-\frac{35+3\sqrt{129}}{8}\right)$

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Casey has 5/6 left of a section of sidewalk to clean. If he can clean 5/18 of a section in 1 minute, how long will it take him t

GaryK [48]

Answer:

Casey will take 3 minutes to clean $\frac{5}{6}$ part of the section.

Step-by-step explanation:

∵ Casey takes the time to cleans $\frac{5}{18}$ of a section = 1 minute

∴ He will take the time to clean complete section = $\frac{1}{\frac{5}{18} }$

= $1\times \frac{18}{5}$

= 3.6 minutes

Now time taken to clean $\frac{5}{6}$ part of the section = $\frac{5}{6}\times 3.6$

= 3 minutes

Therefore, left part of the section will be cleaned by Casey in 3 minutes.

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3 years ago

a pottery maker can make 24 vases in 8 days. if the pottery maker works 6 hours each day. how long does it take to make 1 vase

Eva8 [605]

It would take the pottery maker 2 hours to make a vase.

5 0

3 years ago

Read 2 more answers

2. Which of the following expressions is equivalent to 322?<br> 01<br> 08.1/1<br> 032.2<br> 08-2

Vanyuwa [196]

Answer:

C. (32/4)*2

Step-by-step explanation:

C is the correct answer because when we divide 4/2 it equals 2.

Hope this helps!

3 0

2 years ago

Read 2 more answers

Find the coordinates of the midpoint of the segment whose endpoints are H(5, 13) and K(7, 5).

guapka [62]

Coordinates of mid point=(x1+x2/2 , y1+y2/2)
=(5+7/2 , 13+5/2)
=(12/2 , 18/2)
=(6 , 9)
Use this formula to get coordinates of mid point
here the coordinates of mid point are (6,9)

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3 years ago

A 50 foot rope weighing a total of 32 lbs extended over a cliff that is 35 feet to the ground. A large 8 pound bucket with 19 ga

larisa86 [58]

Answer:

A function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is $W=16(50-x)+(19-\frac{x}{5})(8.3)x$ and the work to get the bucket to the top of the cliff is 3726 foot-lbs

Step-by-step explanation:

Work done to lift the rope by distance x feet:

$W_1=32(\frac{50-x}{2})$

Work done to lift the bucket by distance x feet:

$W_2=(19-\frac{x}{5})(8.3)x$

On reaching top 7 gallons of water spilled out so , on going up by x feet $\frac{7x}{35}=\frac{x}{5}$ gallons of water spilled out.

a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground:

$W=16(50-x)+(19-\frac{x}{5})(8.3)x$

Now the work to get the bucket to the top of the cliff i.e. x =35

$W=16(50-35)+(19-\frac{35}{5})(8.3)(35)$

W=3726

Hence, a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is $W=16(50-x)+(19-\frac{x}{5})(8.3)x$ and the work to get the bucket to the top of the cliff is 3726 foot-lbs

5 0

3 years ago