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3 years ago

The shape of the solution region for the system (picture) can be described as which of the following? Select all that apply.

Mathematics

1 answer:

grandymaker [24]3 years ago

5 0

We have
x>=-2
x<=6
y>=-1
y<=4

using a graph tool
see the attached figure

the solution is the figure of a rectangle limited by points
(-2,-1) (6,-1) (-2,4) (6,4)

the answer is
a rectangle
a parallelogram (rectangles are subsets belonging to the set of parallelograms)

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Answer:

The Trout will have to jump 49 cm in order to catch the insect

Step-by-step explanation:

Here, we want to calculate the distance the Trout has to jump in order to catch the Insect

To calculate this, we need to know the difference in the distances

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The difference in height which will represent the distance that the Trout has to jump to catch the insect will be ;

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Answer:

<h3>Question 7</h3>

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Total Surface Area

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Total surface area:

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Volume

$\sf \implies Vol.=area\:of\:base \times height=\left(\dfrac{3\sqrt{391}}{4}\right) \times 6=88.98\:\:m^3\:(2\:d.p.)$

<h3>Question 8</h3>

Lateral Surface Area

The bases of a hexagonal prism are the pentagons.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the pentagons (bases).

$\implies \sf L.A.=5(5 \times 6)=150\:\:cm^2$

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Therefore:

$\implies \sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}\cdot 5^2=43.01\:\:cm^2\:(2\:d.p.)$

Total surface area:

$\sf \implies T.A.=2\:bases+L.A.=2(43.01)+150=236.02\:\:cm^2\:(2\:d.p.)$

Volume

$\sf \implies Vol.=area\:of\:base \times height=43.011193... \times 6=258.07\:\:cm^3\:(2\:d.p.)$

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