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3 years ago

Shen is on the swim team. Each week he swims a total of 5000 meters. How many kilometers does he swim each week?

Mathematics

1 answer:

Volgvan3 years ago

7 0

Answer:

5 km

Step-by-step explanation:

to convert m to km you have to divide by 1000.

5000/1000=5

hope this helps!

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Find the measure of angle ADE.

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The answer is 135 degrees as 45 add 135 equals 180 degrees as it's a straight line

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The measures of the angles of a convex polygon form an arithmetic sequence. The least measurement in the sequence is 128º. The g

Over [174]

$\bf \qquad \qquad \textit{sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n}{2}(a_1+a_n)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\ a_n=n^{th}~value\\
----------\\
\stackrel{least}{a_1}=128\\\\
\stackrel{greatest}{a_n}=172
\end{cases}$

$\bf S_n=\cfrac{n}{2}(128~+~172)\implies S_n=\cfrac{n}{2}(300)\implies S_n=150n
\\\\\\
\textit{but we also know that sum of all interior angles is }180(n-2)
\\\\\\
\stackrel{\textit{sum of the angles}}{S_n}=\stackrel{\textit{sum of the angles}}{180(n-2)}=150n
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180n-360=150n\implies 30n=360\implies n=\cfrac{360}{30}\implies n=12$

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3 years ago

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Error Analysis: George was trying to rearrange the formula below to slope-intercept form, y = mx + b. by

Nat2105 [25]

Answer:

George's mistake would be:

Instead of 2x + 40, she has made - x + 20.

Step-by-step explanation:

Slope - Intercept Form = y = mx + b

y + 20 = 2(x +20)

y + 20 = 2x + 40

- 20 - 20

----------------------

y = 2x + 20

(Should have been the answer)

BUT,

George's Solving:

y + 20 = 2(x + 20)

y + 20 = -x + 20

George's Mistake would be her miscalculation during her 2nd step. Where instead of distributing 2 to (x + 20), she has changed it to -x + 20, when in reality, it should have been 2x + 40.

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3 years ago

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denpristay [2]

Answer:

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Step-by-step explanation:

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3 years ago

The supplement of an angle is 50 less than 3 times its complement, find the measure of the angle

Lelechka [254]

Answer:

$20^{\circ}$ .

Step-by-step explanation:

Two angles are supplements of one another if their sum is $180^{\circ}$ .

Two angles are complements of one another if their sum is $90^{\circ}$ .

Let $x^{\circ}$ be the measure of the angle in question.

The supplement of this angle would be $(180 - x)^{\circ}$ .

The complement of this angle would be $(90 - x)^{\circ}$ .

According to the question:

$(180 - x) + 50 = 3\, (90 - x)$ .

Solve this equation for $x$ :

$x = 20$ .

Thus, this angle would measure should $20^{\circ}$ .

The supplement of this angle would measure $(180 - 20)^{\circ} = 160^{\circ}$ . The complement of this angle would measure $(90 - 20)^{\circ} = 70^{\circ}$ .

Three times the complement of this angle would be $3 \times 70^{\circ} = 210^{\circ}$ , which is indeed $50^{\circ}$ greater than the supplement of this angle.

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