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Svet_ta [14]
2 years ago
11

Find the equation of a line given 2 coordinates (5, 5) and (-2, -2)

Mathematics
2 answers:
suter [353]2 years ago
5 0

Answer:

y=x

Step-by-step explanation:

using slope intercept form and slope formula so y=x

Tcecarenko [31]2 years ago
3 0

Answer:

y=mx+c

x co-ordinates is 5 & -2

y co-ordinates is 5 & -2

m is the gradient so you have to do change in y over change in x (basically the difference in the y axis )

so change in y : (-2)-5 = -7

change in x: (-2)-5= -7

so divide this and you get 1 which is m

Now the equation is y= 1x+C but x=1 theoretically

therefore all you do now is substitute the values onto the equation to find C. ALWAYS USE THE SAME SET OF COORDINATES.

5=1(5)+ C

5=5+C

C= 0

equation is y=x

Step-by-step explanation:

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Miguel wants to build a container out of sheet metal that has a volume of about 320 cubic inches . He
ZanzabumX [31]

Answer:

  cylinder, has the least surface area

Step-by-step explanation:

We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.

__

We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.

<h3>Rectangular Prism</h3>

The relevant formulas are ...

  V = LWH

  A = 2(LW +H(L +W))

for length L, width W, and height H.

<u>a)</u><u> prism 1</u>

The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...

  V = (8 in)(8 in)(5 in) = 320 in³

  A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²

<u>b)</u><u> prism 2</u>

The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...

  V = (10 in)(8 in)(4 in) = 320 in³

  A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²

__

<h3>Cylinder</h3>

The relevant formulas are ...

  V = πr²h

  A = 2πr(r +h)

for radius r and height h.

c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...

  V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³

  A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²

__

<h3>Square Pyramid</h3>

The relevant formulas are ...

  V = 1/3s²h

  A = s(s +2H)

for base side dimension s, vertical height h, and slant height H.

d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...

  V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³

  A = (10 in)(10 in + 2×14 in) = 380 in²

__

<h3>Summary</h3>

The proposed figures have volume and area (rounded to the nearest unit) as follows:

  \begin{tabular}{|c|c|c|c|}\cline{1-4}&shape&V (in^3)&A (in^2)\\\cline{1-4}a&rect prism&320&288\\b&rect prism&320&304\\c&cylinder&314&\bf283\\d&pyramid&333&380\\\cline{1-4}\end{tabular}

The proposed <em>cylinder</em> requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.

_____

<em>Additional comment</em>

For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.

3 0
1 year ago
Subtract five from three times a number and the result is equal to the number plus five. find the number.
allsm [11]
3(x)-5=x+5
3x=-5+5+x
3x=x
0=x
because 3x=x is basically would make each part into 0 which would end up the same. 
6 0
3 years ago
The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of serv
Fudgin [204]
If we let x as the number of years of service in the company and f(x) as the increase in the wage, the step wise function that describes the scenario is
f(x) = { 0.5,   x < 3
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         { 1.5,   6 ≤ x < 9
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The point (2, 12) represents the wage increase of x < 12
5 0
3 years ago
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The radius of a circle is 7.2 cm. Find the circumference to the nearest tenth.
Lynna [10]

Answer: 45.24

Step-by-step explanation:

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3 years ago
Factorise fully the following:<br> a) 3x + 18<br> b) 2x - 14<br> c) 6x + 4<br> d) 9x - 15
JulsSmile [24]

Answer:

I have attached the work to your problem.

Please see the attachment below.

I hope this helps.

4 0
3 years ago
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