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Scrat [10]
4 years ago
15

a straight highway is 100 mile long and each mile is marked by a milepost numbered from 0 to 100. a rest area is going to be bui

lt along the highway exactly 5 miles away from milepost 63. if m is the milepost number of the rest area which of the following equations represents the possible locations for the rest area? A |63-m|=5 B |m-5|=63 C |m+5|=63 D |63+m|=5
Mathematics
2 answers:
Gnom [1K]4 years ago
7 0
B) m-5=63 is the answer
Alinara [238K]4 years ago
7 0
The answer is A

m is 5 miles away from mile post 63,so it's either
m=63+5 or m=63-5
63-m+5=0 or 63-m-5=0
63-m=-5 or 63-m=5

|63-m|=5
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6. We want to build the smallest cube possible using bricks with dimensions 8 cm - 12 cm 20 cm. How many bricks do we need?​
Georgia [21]

Answer:

1200

Step-by-step explanation:

We’ll need a number that is evenly dividable by all three values: 8,12 & 15. We can develop the generic common multiple by multiplying all three numbers and get 1440. But is that the smallest common multiple? The quick and dirty way to factor the number is to divide it by it’s various elements and see what works. In this case 1440/12=120 which is the smallest common multiple of the three numbers. The smallest length is therefore 120.

In order to find how many bricks just divide (120x120x120)/(8x12x15)=1200 bricks

7 0
2 years ago
Graph the line that has a slope of 1/4.
andre [41]

Answer:

Just find the line with a rise of 1 and a run of 4.

Step-by-step explanation:

To find a line first find a actual point that connects and just go up 1 and go to the right of 4. It has to go right becuase since it’s a positive slope it’d have to go right for the run. FInd a point go up 1 and right 4 and if the results gets you landed on a another point, you have suceded to find the graph with A s lope of 1/4

3 0
3 years ago
Write an inequality for the graph below
Xelga [282]

Answer: what graph...?

8 0
3 years ago
A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th
Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let S(t) be the amount of sugar in the tank at time t. Then S(0)=25.

Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of

\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}

Separate variables, integrate, and solve for <em>S</em>.

\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt

\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt

-100\ln\left|P-\dfrac S{100}\right|=t+C

\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t

P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}

\dfrac S{100}=P-Ce^{-100t}

S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}

Use the initial value to solve for <em>C</em> :

S(0)=25\implies 25=100P-C\implies C=100P-25

\implies S(t)=100P-(100P-25)e^{-100t}

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick <em>P</em> such that

S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}

5 0
3 years ago
A train leaves boston at 2:00 pm. a second train leaves the same city in the same direction at 6:00 pm. the second train travels
AURORKA [14]
\boxed {\boxed { \text {Distance = Speed x Time}}}

<u>First Train:</u>
Time taken = 9 hours (2pm to 11pm)
Let the speed be x 
Distance = Time x Speed = 9x

<u>Second Train:</u>
Time taken = 5 hours (6pm to 11pm)
Speed = x + 48
Distance = Time x Speed = 5(x + 48)

Since both the distance they traveled are the same, we equate the distance to solve for x.

<u>Solve for x:</u>
9x = 5(x + 48)
9x = 5x + 240
4x = 240
x = 60

<u>Find the speed:</u>
x = 60 mph
x + 48= 108 mph

Answer: The spend of the two trains are 60 mph and 108 mph.
3 0
3 years ago
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