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3 years ago

Dan drove 845 miles in 13 hours. At the same rate, how many miles would he drive in 11 hours

Mathematics

1 answer:

denis23 [38]3 years ago

6 0

845 miles / 13 hours = 65 miles per hour

65 miles per hour x 11 hours = 715 miles

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The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

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3 years ago

How many liters is 350 milliliters?

Igoryamba

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Step-by-step explanation:

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What is the answer to this problem?

valkas [14]

Answer:

Step-by-step explanation:

DEF=180

DE=120

180-120=60

i hope this helps

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3 years ago

What expression has the estimated product of 60

balu736 [363]

Answer:

30x2

Step-by-step explanation:

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Explain how you would solve 5x - 3 = 9. (there should be a minimum of 2<br> complete sentences). *

SpyIntel [72]

Haha, you first start off with adding 3 to both sides, cancelling the -3, and adding it to 9. you end up with 5x=12, in which you divide both sides by 5. you get 2 and 2/5 or 12/5! hope that helps :)

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