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3 years ago

14

Read the following statement. If a number is divisible by 2,then it is even what is the inverse of this statement?

1 answer:

Lapatulllka [165]3 years ago

7 0

Answer:

If it is an even number, then it is divisible by 2

Step-by-step explanation:

You flip the order of statements. One statement is "a number is divisible by 2", the other is "it is even" is the other.

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The set of ordered pairs (–1, 8), (0, 3), (1, –2), and (2, –7) represent a function. What is the range of the function? {x: x =

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The graph above is a transformation of the function x2 Write an equation for the function graphed above

lutik1710 [3]

Answer: y=0,5x²-x-1,5.

Step-by-step explanation:

$(-1;0)\ \ \ \ (3;0)\ \ \ \ (1;-2) \ \ \ \ y=ax^2+bx+c\ ?\\\left\{\begin{array}{ccc}a*(-1)^2+b*(-1)+c=0\\a*3^2+b*3+c=0\\a*1^2+b*1+c=-2\end{array}\right \ \ \ \ \ \left\{\begin{array}{ccc}a-b+c=0\ \ (1)\\9a+3b+c=0\ (2)\\a+b+c=-2\ (3)\end{array}\right \\$

We summarize (1) and (3):

$2a+2c=-2\ |:2\\a+c=-1\ \ \ \ \Rightarrow\\a+b+c=-2\\(a+s)+b=-2\\-1+b=-2\\b=-1.$

Substitute b=-1 into (2):

$9a+3*(-1)+c=0\\9a-3+c=0\\9a+c=3\ \ (5).\\$

From (5) subtract (4):

$8a=4\ |:8\\a=0,5.\ \ \ \ \Rightarrow\\$

Substitute a=0,5 into (4):

$0,5+c=-1\\c=-1,5.$

Hense:

y=0,5x²-x-1,5.

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2 years ago

In Sahara Desert one day it was 130°F. In the Gobi Desert a temperature of -40°F was recorded. What is the difference between th

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3 years ago

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A waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must ho

photoshop1234 [79]

Answer:

The dimensions that minimize the surface are:

Wide: 1.65 yd

Long: 3.30 yd

Height: 2.20 yd

Step-by-step explanation:

We have a rectangular base, that its twice as long as it is wide.

It must hold 12 yd^3 of debris.

We have to minimize the surface area, subjet to the restriction of volume (12 yd^3).

The surface is equal to:

$S=2(w*h+w*2w+2wh)=2(3wh+2w^2)$

The volume restriction is:

$V=w*2w*h=2w^2h=12\\\\h=\frac{6}{w^2}$

If we replace h in the surface equation, we have:

$S=2(3wh+2w^2)=6w(\frac{6}{w^2})+4w^2=36w^{-1}+4w^2$

To optimize, we derive and equal to zero:

$dS/dw=36(-1)w^{-2} + 8w=0\\\\36w^{-2}=8w\\\\w^3=36/8=4.5\\\\w=\sqrt[3]{4.5} =1.65$

Then, the height h is:

$h=6/w^2=6/(1.65^2)=6/2.7225=2.2$

The dimensions that minimize the surface are:

Wide: 1.65 yd

Long: 3.30 yd

Height: 2.20 yd

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3 years ago