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3 years ago

Given the function f(x)=4|x-5|+3 for what values of x is f(x)=15

Mathematics

1 answer:

Andreyy893 years ago

3 0

Answer:

{2, 8}

Step-by-step explanation:

We want to find x for ...

15 = 4|x -5| +3

12 = 4|x -5| . . . . subtract 3

3 = |x -5| . . . . . . divide by 4

±3 = x -5 . . . . . . show the meaning of absolute value

5 ±3 = x = {2, 8} . . . . . add 5

The values of x for which f(x) = 15 are 2 and 8.

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Solve for a. 1/5(25−5a)=4−a

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A rectangular prism with a volume of four cubic units is filled with cubes and side links of 1/3 unit. How many 1/3 unit cubes d

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Answer:

Number of box that fills the prism=36.36 cubes

Step-by-step explanation:

Number of cubes that can fill the rectangular prism= Volume of the rectangular prism / Volume of the cube

Volume of the rectangular prism= $4 units ^3$

Side length of the cube= $1/3 unit$

Volume of the cube :

$Side*side*side\\\\=1/3*1/3*1/3\\\\=1/9$

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3 years ago

What is the length of the hypotenuse?<br> 12<br> 5<br> X=<br> Help

Temka [501]

Answer:

x = 13

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = x^2

25+144 = x^2

169 = x^2

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sqrt(169) = sqrt(x^2)

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2 years ago

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A recipe requires 1/3 cup of sugar for every 3/4 cup of flour. How many cups of sugar are required for every cup of flour?

Roman55 [17]

Answer:

2/3 CUPS OF SUGAR

Step-by-step explanation:

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3 years ago

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A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500

Vedmedyk [2.9K]

Answer:

The rate at which both of them are moving apart is 4.9761 ft/sec.

Step-by-step explanation:

Given:

Rate at which the woman is walking, $\frac{d(w)}{dt}$ = 3 ft/sec

Rate at which the man is walking, $\frac{d(m)}{dt}$ = 2 ft/sec

Collective rate of both, $\frac{d(m+w)}{dt}$ = 5 ft/sec

Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min

Now,

Distance traveled by man and woman are $m$ and $w$ ft respectively.

⇒ $m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft$

⇒ $w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft$

As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate $\frac{dh}{dt}$ .

Lets calculate h.

Applying Pythagoras formula.

⇒ $h^2=(m+w)^2+500^2$

⇒ $h=\sqrt{(2400+2700)^2+500^2} = 5124.45$

Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.

Differentiating with respect to time.

⇒ $h^2=(m+w)^2+500^2$

⇒ $2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt} + \frac{d(500)}{dt}$

⇒ $\frac{d(h)}{dt} =\frac{2(m+w)\frac{d(m+w)}{dt} }{2h}$ ...as $\frac{d(500)}{dt}= 0$

⇒ Plugging the values.

⇒ $\frac{d(h)}{dt} =\frac{2(2400+2700)(5)}{2\times 5124.45}$ ...as $\frac{d(m+w)}{dt} = 5$ ft/sec

⇒ $\frac{d(h)}{dt} =4.9761$ ft/sec

So the rate from which man and woman moving apart is 4.9761 ft/sec.

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3 years ago