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salantis [7]
3 years ago
10

At the beginning of a month your account balance was $53. During the month you deposited $562 and wrote a check for $486. What w

as your balance at the end of the month
Mathematics
1 answer:
alexdok [17]3 years ago
5 0

53+562-486= 129

Add then subtract

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the time it takes to fill a water tank varies inversely with the water rate of the hose. At 8 gallons per minute, a hose can fil
Readme [11.4K]
\bf \qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad  y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad  variation
\end{array}\\\\
-------------------------------\\\\
\textit{time it takes to fill a tank varies inversely with the water rate}\\\\
t=\cfrac{k}{w}\quad 
\begin{cases}
t=\textit{time to fill}\\
w=\textit{water rate}
\end{cases}

\bf \textit{we also know that }
\begin{cases}
w=\stackrel{g/min}{8}\\
t=\stackrel{min}{45}
\end{cases}\implies 45=\cfrac{k}{8}\implies 360=k
\\\\\\
therefore\qquad \boxed{t=\cfrac{360}{w}}
\\\\\\
\textit{now if w = 15, what is \underline{t}?}\qquad t=\cfrac{360}{15}
4 0
3 years ago
For ΔABC, ∠A = x + 30, ∠B = 2x - 4, and ∠C = 4x. If ΔABC undergoes a dilation by a scale factor of 1 2 to create ΔA'B'C' with ∠A
Marina86 [1]
ABC
Solve for x
x + 30 + 2x - 4 + 4x = 180 All triangles have 180°. collect like terms.
7x + 26 = 180 subtract 26 to both sides.
7x = 154 Divide by 7
x = 154/7
x = 22
A = x + 30 = 22 + 30 = 52
B = 2x - 4 = 2(22) + 30 = 44 - 4 = 40
C = 4x = 4*22 = 88

Check
<A + <B + <C = 180
<52 + <40 + <88 = 180°
180 = 180

It checks and we are done with this triangle.

A'B'C' 
2x + 8 + x + 18 + 5x - 22 = 180 Collect the like terms.
8x + 4 = 180 Subtract 4 from both sides.
8x = 180 - 4
8x = 176 Divide by 8
x = 176 / 8
x = 22
 
A' = 2x + 8
A' = 2(22) + 8 = 44 + 8 = 52
B' = x + 18 = 22 + 18 = 40
C' = 5x - 22 = 5*22 - 22 = 110 - 22 = 88

Conclusion
A = A'
B = B'
C = C'

All three angles of one triangle are equal to all three angles of the other. So by AA the two triangles are similar.

Comment
Note: the dilation of 12 has nothing to do with this answer. If you were asked about similarity of sides then the 12 would be something to do with the problem. 


3 0
3 years ago
Please help if anyone knows this!:)
tekilochka [14]

Answer:

d

Step-by-step explanation:

because the 15ft length is the same as x

4 0
3 years ago
in a survey of 3,100 people who owned a certain type of car, 2,015 said they would buy that type of car again. What percent of p
fomenos

The percent of people of the people surveyed were satisfied with the car is  the percent of people of the people would buy that type of car again, so we have:  2015 ÷ 3100 × 100% = 65%

ANSWER: 65%

Ok done. Thank to me :3

8 0
1 year ago
Read 2 more answers
Identify the property of equality illustrated by the statement: If 5m = 25, then m = 5.
Sergio [31]
Its Addition property of equality
3 0
3 years ago
Read 2 more answers
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