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Evgen [1.6K]
3 years ago
6

Find three positive numbers a, b and c such that 2 times a plus 14 times b plus 16 times c equals 176, and such that the product

of a, b and c is a maximum.
Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
5 0
33333333333333333333333333
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HELP ASAP A right rectangular prism has a length of 8 ft, width of 814 ft, and height of 412 ft. What is the volume of the prism
Lorico [155]
V = l x w x h
V = 8 x 814 x 412
V = 2682944
6 0
3 years ago
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(50 Points & Brainliest)
RUDIKE [14]

Answer:

16x-8

Step-by-step explanation:

We need to calculate the total time. We are given two functions that when summed up will give you total time.

(f + g)(x) = 5x - 7 + 11x - 1 \\  = 16x - 8

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3 years ago
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Find the solutions to x⁴-5x²-36=0 and the x-intercepts of the graph of y=x⁴-5x²-36.
disa [49]

Answer:

The solutions x^4-5x^2-36=0 are x=3,\:x=-3,\:x=2i,\:x=-2i and the x-intercepts of y=x^4-5x^2-36 are x=3,\:x=-3

Step-by-step explanation:

Finding the solutions to x^4-5x^2-36 means finding the roots, a root is where the function is equal to zero.

The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero.

To find the roots you need to:

Rewrite the equation with u=x^2 and u^2=x^4

u^2-5u-36=0

Solve by factoring

\mathrm{Break\:the\:expression\:into\:groups}\\u^2-5u-36=\left(u^2+4u\right)+\left(-9u-36\right)

\mathrm{Factor\:out\:}u\mathrm{\:from\:}u^2+4u=u\left(u+4\right)

\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9u-36=-9\left(u+4\right)

u^2-5u-36=u\left(u+4\right)-9\left(u+4\right)

\mathrm{Factor\:out\:common\:term\:}u+4\\\left(u+4\right)\left(u-9\right)

u^2-5u-36=\left(u+4\right)\left(u-9\right)=0

Using the Zero factor Theorem: if ab = 0 then a = 0 or b = 0 (or both a = 0 and b = 0)

The solutions to the quadratic equation are:

\:u=-4,\:u=9

Substitute back u=x^2, solve for x

x^4-5x^2-36=(u-9)(u+4)=(x^2-9)(x^2+4)

Apply the difference of squares formula

x^4-5x^2-36=(x^2-9)(x^2+4)=(x-3)(x+3)(x^2+4)

(x-3)(x+3)(x^2+4)=0

Using the Zero factor Theorem: if ab = 0 then a = 0 or b = 0 (or both a = 0 and b = 0)

The solutions are:

\:x=3,\:x=-3,\:x=2i,\:x=-2i

Because two of the solutions are complex roots the only x-intercepts are x=3,\:x=-3

3 0
3 years ago
Jude types 1,170 characters in 6 minutes. What is her typing rate in characters per minute? A. 200 characters per minute B. 197
Kisachek [45]

Answer:

Option C) 195 characters per minute

Step-by-step explanation:

We are given the following in the question:

Jude types 1,170 characters in 6 minutes..

We have to find the typing rate in characters per minute.

Thus can be done in the following manner:

Typing rate =

=\dfrac{1170\text{ characters}}{6\text{ minutes}}\\\\=195\text{ characters per minute}

Thus, Jude speed in characters per minute is

Option C) 195 characters per minute

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3 years ago
If I have $100 dollars and spend $99.99 dollars, how much money do I have left?
Brrunno [24]

Answer:

You have $00.01

Step-by-step explanation:

100-99.99=0.01

5 0
3 years ago
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