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rewona [7]
4 years ago
15

Which set of ordered pairs gives the polygon shown?

Mathematics
1 answer:
makvit [3.9K]4 years ago
7 0
The correct answer is B.

Explanation
Since each interval mark is 1/4 of a unit, we will write this as 0.25.  For the first point, 4 interval marks to the left of the y-axis makes it a negative number; 4(0.25) = 1; this makes the x-coordinate of this point -1.  2 interval marks above the x-axis makes it positive; 2(0.25) = 0.5; this makes the y-coordinate 0.5.  This makes the first ordered pair (-1, 0.5).

The second point is on the y-axis.  This makes the x-coordinate 0.  It is 5 intervals above the x-axis; this makes it positive.  5(0.25) = 1.25 will be the y-coordinate, making the point (0, 1.25).

The third point is 3 intervals to the right of the y-axis; this makes it positive, and 3(0.25)=0.75 for the x-coordinate.  It is 3 intervals below the x-axis; this makes it negative, and 3(0.25) = 0.75, making the y-coordinate -0.75.  This puts the third point at (0.75, -0.75).
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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
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Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = xyz

with subject to x+2y+3z=9

So, let z=\dfrac{9-x-2y}{3}

So, Volume becomes,

V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}

Partially derivative wrt x and y we get that

9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9

By solving these two equations, we get that

x=3,y=\dfrac{3}{2}

So, z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1

So, Volume of largest rectangular box would be

xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5

Hence, the volume of largest rectangular box is 4.5 units.

4 0
3 years ago
What is the common difference of the sequence below?
vagabundo [1.1K]

Answer:

Step-by-step explanation:

In finding the COMMON DIFFERENCE, subtract the 2nd term and the first term.

a1 = -4

a2 = -2

Let "d" representing the COMMON DIFFERENCE.

d = -2 -(-4)

d = -2 + 4

d = 2

ANSWER:

THE COMMON DIFFERENCE OF THIS SEQUENCE IS 2

3 0
3 years ago
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Being fun again who whants points here is a question you'll get 50 points
stich3 [128]

Answer:

0.46

Step-by-step explanation:bark brainliest plz

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An empty tank is filled with water at a constant rate. The table shows w, the number of gallons of water in the tank after m min
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A manufacturer cuts squares from the corners of a rectangular plece of sheet metal that measures 2 inches by 7 inches (see Figur
Vladimir79 [104]

Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the open-topped box is equal to

V=LWH

where

L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in

substitute

V=(7-2x)(2-2x)x

Convert to expanded form

V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x

using a graphing tool

Graph the cubic equation

Remember that

The domain for x is the interval -----> (0,1)

Because

If x>1

then

the width is negative (W=2-2x)

so

The maximum is the point (0.46,3.02)

see the attached figure

therefore

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

8 0
3 years ago
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