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Hitman42 [59]
3 years ago
10

What is the solution to the inequality x2 < 16 – 6x?

Mathematics
1 answer:
zaharov [31]3 years ago
4 0

Answer:

D

Step-by-step explanation:

2x < 16 - 6x

Bring the variables to one side

2x < 16 - 6x

+6x       +6x

8x < 16

Divide both sides by the coefficient

8x/8 < 16?8

x < 2

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It is recommended that an adult drink 64 fluid ounces of water every day .Josey has already consumed 700 millimeters of water.ho
Reptile [31]

We know, 1 ounce = 29.57 ml

so, 64 ounces = 1892.71 ml

so, remaining drink would be: 1892.71-700 = 1192.71 ml

5 0
3 years ago
an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a
viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  \mathbf{\dfrac{dh}{dt}  = \dfrac{-25}{100  \pi} \  \ ft/s}

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

\dfrac{h}{r}= \dfrac{20}{8}    ( similar triangle property)

\dfrac{h}{r}= \dfrac{5}{2}

\dfrac{h}{r}= 2.5

h = 2.5r

r = \dfrac{h}{2.5}

The volume of the water in the tank is represented by the equation:

V = \dfrac{1}{3} \pi r^2 h

V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h

V = \dfrac{1}{18.75} \pi \ h^3

The rate of change of the water depth  is :

\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\  \dfrac{dh}{dt}

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

\dfrac{dv}{dt}= - 4  \ ft^3/sec

Therefore,

-4 = \dfrac{\pi r^2}{6.25}\  \dfrac{dh}{dt}

the rate of change of the water at depth h = 10 ft is:

-4 = \dfrac{ 100 \ \pi }{6.25}\  \dfrac{dh}{dt}

100 \pi \dfrac{dh}{dt}  = -4 \times 6.25

100  \pi \dfrac{dh}{dt}  = -25

\dfrac{dh}{dt}  = \dfrac{-25}{100  \pi}

Thus, the rate of change of the water depth when the water depth is 10 ft is;  \mathtt{\dfrac{dh}{dt}  = \dfrac{-25}{100  \pi} \  \ ft/s}

4 0
3 years ago
What property is -3(m+8)=-3m-24
Damm [24]

Answer:

All real numbers are solutions.

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−3(m+8)=−3m−24

(−3)(m)+(−3)(8)=−3m+−24(Distribute)

−3m+−24=−3m+−24

−3m−24=−3m−24

Step 2: Add 3m to both sides.

−3m−24+3m=−3m−24+3m

−24=−24

Step 3: Add 24 to both sides.

−24+24=−24+24

0=0

Answer:

All real numbers are solutions.

8 0
2 years ago
john is looking at a map with a scale of 1/4 inch=20 miles. he measured the distance from his home to the bowling alley in town
Sergio039 [100]
1 inch=80mi

2.5*80mi=200 mi
5 0
2 years ago
Answer for <br> D=<br> E=<br> F=
Natali [406]
All three of those angels are 98 degrees. F is supplementary, as the given angle and it must add up to 180. D is parallel to F. E is the same as D.
7 0
1 year ago
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