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s2008m [1.1K]
3 years ago
5

The height of a trapezoid is 16in. The bases are 32in and 24in. What is the area of the trapezoid.

Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
4 0

Answer:

448in^2

Step-by-step explanation:

The area of a trapezoid is the bases added divided by two times the height.

(32+24)/2*16=28*16=448 in^2

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Solve the system of equations using substitution -3x + 2y = 12 x = 2y - 8
SCORPION-xisa [38]

Answer:

(-2, 3)

Step-by-step explanation:

Given the system of equations:

-3x + 2y = 12

x = 2y - 8

You can 'substitute' the expression '2y - 8' for the value of 'x' in the first equation and solve for 'y':

-3(2y - 8) + 2y = 12

Distribute: -6y + 24 + 2y = 12

Combine like terms: -4y + 24 = 12

Subtract 24 from both sides: -4y + 24 - 24 = 12 - 24 or -4y = -12

Divide both sides by -4: -4y/-4 = -12/-4  or y = 3

Use y = 3 to solve for 'x':

x = 2(3) - 8 or 6 - 8

x = -2

(-2, 3)

5 0
3 years ago
Bus A and Bus B leave the bus depot at 8 am.
LenaWriter [7]

Answer: 10:55

Step-by-step explanation:

Taking statement at face value and the simplest scenario that commencing from 08:00am the buses take a route from depot that returns bus A to depot at 25min intervals while Bus B returns at 35min intervals.

The time the buses will be back at the depot simultaneously will be when:

N(a) * 25mins = N(b) * 35mins

Therefore, when N(b) * 35 is divisible by 25 where N(a) and N(b) are integers.

Multiples of 25 (Bus A) = 25, 50, 75, 100, 125, 150, 175, 200 etc

Multiples of 35 (Bus B) = 35, 70, 105, 140, 175, 210, 245 etc

This shows that after 7 circuits by BUS A and 5 circuits by Bus B, there will be an equal number which is 175 minutes.

So both buses are next at Depot together after 175minutes (2hr 55min) on the clock that is

at 08:00 + 2:55 = 10:55

6 0
3 years ago
A typical marathon is 26.2 miles. Allan averages 12 kilometers per hour when running in marathons. Determine how long it would t
Natali [406]

Answer:

The time taken by Allan to complete the marathon 3.5 hours

Step-by-step explanation:

Given as :

The distance cover in marathon = d = 26.2 miles

∵ 1 mile = 1.609 km

So, d = 26.2 × 1.609 km

i.e d = 42.155 kilo meter

The average speed of Allan = s = 12 km per hour

Let the time taken by Allan to complete the marathon = t hours

Now, ∵ Time = \dfrac{\textrm Distance}{\textrm Speed}

Or, t =  \dfrac{\textrm d}{\textrm s}

Or, t =  \dfrac{\textrm 42.155 km}{\textrm 12 kmph}

or, t = 3.512 hours

So , The time taken by Allan to complete the marathon = t = 3.5 hours

Hence, The time taken by Allan to complete the marathon 3.5 hours Answer

4 0
3 years ago
Use the laplace transform to solve the given initial-value problem. y' + y = (t − 1), y(0) = 3
GaryK [48]

In mathematics, the Laplace transform, named after its discoverer Pierre Simon Laplace, transforms a function of real variables (usually in the time domain) into a function of complex variables (in the time domain). is the integral transform that Complex frequency domain, also called S-area or S-plane).

Learn more about Laplace transform here brainly.com/question/17062586

#SPJ4

5 0
2 years ago
3 L of water of density 1 gram per centimetre cubed is added to 12litres of alcohol of density of 0.8 gram per centimetre cubed,
Natasha2012 [34]

Answer:

84%

Step-by-step explanation:

each liter is 1000 cubic centimetre, so you have a total density of 3000, but instead think of 3 liters being 100% density and think of alcohol as 80% density, there are 4 times at much 80% than 100% liquid.

with 3 liters of alcohol, 3 liters of water is now 90% density or 0.9 gram per centimetre. add another 3 liters and it is 2/3, so the grams per centimetre would be 8.66667 or 8 2/3's

if you add another 3 liters, THEN it is 85%

add 12 liters in total and the final answer 84%

4 0
2 years ago
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