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diamong [38]
3 years ago
10

Reduce the linear equation 5x + 3y = 2 so that it is in the standard form

Mathematics
1 answer:
lesya [120]3 years ago
8 0

Answer:

The standard form of a linear equation is Ax+By=CAx+By=C.

5x+3y=2

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Find the volume of the garden shed
Leno4ka [110]

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

<h3><u>Volume of a rectangular prism</u></h3>

\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}

<h3><u>Volume of a pyramid</u></h3>

<u />

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.  

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}

Therefore:

\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}

<h3><u>Volume of the garden shed</u></h3>

\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}

6 0
1 year ago
Read 2 more answers
What is the slope of this line? −13 23 13 −23 Number graph ranging from negative 10 to 10 on both the x and y axis. A line passe
olasank [31]

slope is

y2-y1/x2-x1

= 1 - -3 / 6-0 =

4/6 = 2/3

 slope = 2/3

3 0
3 years ago
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A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She current
WINSTONCH [101]

Answer:

a.) w = 103 * 1.08^t

b.) 3.5weeks

Step-by-step explanation:

If Her current weight is 103 pounds and she hopes to multiply her her weight each week by 1.08, then

her weight after 1 week = 103 * 1.08 = 103 * 1.08¹

Her weight after 2 weeks = [weight of week 1] * 1.08 = [103* 1.08] * 1.08 = 103 * 1.08²

Weight after 3 weeks= [weight of week 2] * 1.08 = [103 * 1.08 * 1.08] * 1.08 = 103 * 1.08³

Hence weight (W) after t weeks = 103 * 1.08^t

b.) If W = 135, Then

103 * 1.08^t = 135

1.08^t = 135/103

1.08^t = 1.31

Taking log of both sides,

log 1.08^t = log 1.31

t log 1.08 = log 1.32

t = log 1.32/log 1.08

t = 3.5 weeks.

Hence, it will take her 3½ weeks to get to 135pounds weight.

7 0
3 years ago
Having trouble with ratio and proportional
yan [13]
A ratio is a comparison of two numbers that can be written in multiple ways such as:

Word: There are ___x for every ___ y
Fraction: y/x
Ordered pair: (x,y)
Ratio:x:y

Proportional is a type of relationship where, oh a graph, a line goes through the 0,0 point and when you divide y/x at any point, you will get the same answer.


Hope this helped!
6 0
3 years ago
The map shows the territories in Australia.
frutty [35]

Answer: 2000KM

Step-by-step explanation: I just took the quiz

5 0
3 years ago
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