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NeX [460]
3 years ago
11

Each lap around Spring Reservoir is 2 3/8 miles long. Terrence walked 2 1/2 laps around the Reservoir. How many miles did Terren

ce walk?
Mathematics
1 answer:
Arturiano [62]3 years ago
6 0
Namely, how much is 2 and 1/2 of 2 and 3/8 then, well is just their product, let's first convert them both from mixed to "improper" and proceed.

\bf \stackrel{mixed}{2\frac{3}{8}}\implies \cfrac{2\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{19}{8}}
\\\\\\
\stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}}\\\\
-------------------------------\\\\
\stackrel{laps~done}{\cfrac{5}{2}}\cdot \stackrel{\textit{miles in a lap}}{\cfrac{19}{8}}\implies \cfrac{95}{16}\implies \stackrel{miles}{5\frac{15}{16}}
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What is the length of x in the diagram below?
luda_lava [24]

Answer:

That is a 45-45-90 triangle next to a 30-60-90 triangle.  

So, the height of the left triangle equals 5.

That makes the short side of the 30-60-90 triangle also equal to 5.

In a 30-60-90 triangle, the hypotenuse (or "x") is exactly twice the length of the shortest side.

Therefore, the hypotenuse (or "x") equals 10.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Will mark brainliest
castortr0y [4]
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8 0
3 years ago
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Simora [160]
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8 0
3 years ago
Simplify the following expression below:
IrinaK [193]
So, 4/3 - 2i

4/3 - 2i = 12/13 + i8/13

multiply by the conjugate: 
3 + 2i/3 + 2i
= 4(3 + 2i)/(3 - 2i) (3 + 2i)
(3 - 2i) (3 + 2i) = 13

(3 - 2i) (3 + 2i)

apply complex arithmetic rule: (a + bi) (a - bi) = a^2 + b^2
a = 3, b =  - 2
= 3^2 + (- 2)^2

refine: = 13
= 4(3 + 2i)/13

distribute parentheses:
a(b + c) = ab + ac
a = 4, b = 3, c = 2i
= 4(3) + 4(2i)

Simplify:
4(3) + 4(2i)
12    +    8i


4(3) + 4(2i)
Multiply the numbers: 4(3) = 12
= 12 + 2(4i)

Multiply the numbers: 4(2) = 8
= 12 + 8i


   12 + 8i
= 12 + 8i/13

Group the real par, and the imaginary part of the complex numbers:


Your answer is: 12/13 + 8i/13





Hope that helps!!!
7 0
3 years ago
Given a 5 liter jar and a 3 liter jar and a unlimited supply of water, how do you measure out 4 liter exactly
andre [41]

Answer:

Given:

5 liter Jar

3 liter jar

Unlimited supply of water.

To measure out 4 liters exactly.

Steps to be carries out to measure out 4 liters of water exactly.

Water content: 3 liter jar = Empty , 5 liter jar = Empty

1) Fill the 3 liter jar completely with water.

3 liter jar = 3 liter , 5 liter jar = Empty

2) Empty the filled 3 liter jar of water by pouring it out into 5 liter jar.

Water content: 3 liter jar = Empty , 5 liter jar = 3 liter

3) Again fill the empty 3 liter jar completely.

Water content: 3 liter jar = 3 liter , 5 liter jar = 3 liter

4) Pour water from 3 liter jar into 5 liter jar until it is completely filled.

Water content: 3 liter jar = 1 liter , 5 liter jar = 5 liter

5)  Empty the 5 liter jar completely.

Water content: 3 liter jar = 1 liter , 5 liter jar = Empty

6) Empty the 3 liter jar by pouring the water into 5 liter jar.

Water content: 3 liter jar = Empty , 5 liter jar = 1 liter

7) Fill the 3 liter jar completely with water.

Water content: 3 liter jar = 3 liter , 5 liter jar = 1 liter

8) Empty the 3 liter jar by pouring it into 5 liter jar.

Water content: 3 liter jar = Empty , 5 liter jar = 4 liter

Now, we have exactly 4 liters of water in the 5 liter jar.

7 0
3 years ago
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