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3 years ago

Select the number line that shows that two opposite numbers have a sum of 0.

Mathematics

2 answers:

dimulka [17.4K]3 years ago

5 0

Answer:

Step-by-step explanation:

When you have two opposite numbers on a numberline, that is, a digit that has a negative value and the same digit having a positive value, when you add them together, we would have 0.

i.e. -a + b = 0

In the above options given, the numberline that shows this particular case is the numberline in option D.

In option D numberline, the sum of -1 and +1 equals zero.

dimulka [17.4K]3 years ago

4 0

Answer:

It's B

Step-by-step explanation:

It goes up 7 and then goes down 7 making go back to zero

It is NOT D

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2 years ago

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Answers:

a) 1/6

b) 0

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3 years ago

4x^2+12x+9-2x^2-7x-15

Ilia_Sergeevich [38]

4x^2 + 12x + 9 - 2x^2 - 7x - 15

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3 years ago

The graph below shows the rate that water leaves a tank, in gallons per hour, where t is measured in hours. (Please give exact a

defon

Answer:

Part a) 10 gallons

Part b) 4.59 hours

Step-by-step explanation:

The picture of the question in the attached figure

Part a) How much water left the tank during the 6 hours shown?

To find out how much water left the tank during the 6 hours, determine the area of the graph in that interval

Calculate the area of the rectangle plus the area of the triangle

$(4)(2)+\frac{1}{2}(6-4)(2)$

$8+2=10\ gal$

Part b) How many hours did it take for 9 gallons to leave the tank?

we know that

In the interval [0,4]

8 gallons of water leaves the tank in 4 hours (remember that the area in that interval is equal to 8 gallons)

Find out in the interval (4,6] how many hours did it take for 1 gallon to leave the tank

First determine the equation of the line in the interval (4,6)

we have the points (4,2) and (6,0)

The slope is equal to

$m=(6-2)/(0-4)=-1$

The equation of the line is

$y=-(x-6)\\y=-x+6$

Determine the area of graph in the interval (4,x) (Is the area of trapezoid)

$A=\frac{1}{2}(2+(-x+6))((x-4)$

$A=\frac{1}{2}(8-x)((x-4)$

$A=\frac{1}{2}(-x^2+12x-32)\\\\A=-\frac{1}{2}x^{2}+6x-16$

For A=1 gal

$1=-\frac{1}{2}x^{2}+6x-16$

$-\frac{1}{2}x^{2}+6x-17=0$

solve the quadratic equation by graphing

The solution is x=4.59 hours

see the attached figure N 2

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3 years ago