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Nata [24]
3 years ago
5

Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books. One-third of Jason's collection

and Nathan's entire collection add up to 31 books. How many books do Jason’s and Nathan’s collections have?
Mathematics
1 answer:
siniylev [52]3 years ago
3 0
6j+\frac{1}{3}n=134

\frac{1}{3} j+n=31 you multiply this by 18

6j+18n=558
6j+1/3*n=134
___________(-)

53n/3=424 => 53n=1272 => n=24

You put n in the first equation:
6j+8=134
6j=126 => j=21

Final answer:  Nathan has 24 books and Jason 21.
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Elena-2011 [213]

Answer:

d. linear; $25/hour

Step-by-step explanation:

From looking at the graph, we have that renting for 2 hours costs $50, for 4 hours costs $100, for 6 hours costs $150, and for 8 hours costs $200. To find out whether the quantities described in the table are linear, we have to see if there is a constant rate of change of price.

For hour 2 to hour 4, we can see that the price increases by $50. This is the same for hour 4 to hour 6 and hour 6 to hour 8. For every 2 hour time interval, the price increases by $50. Therefore, there is a constant rate of change and the quantities described in the table are linear.

Now we have to find the constant rate of change per hour. We know that the price increases by $50 every 2 hours, so, by dividing both the hours and price increase by 2, the price increases by $25 per hour. So the constant rate of change is $25/hour.

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Answer choice d.

I hope you find my answer and explanation to be helpful. Happy studying.

6 0
3 years ago
find the component equation of the plane which is normal to the vector -2i+5j+k and which contains the point (-10;7;5).​
maksim [4K]

Given:

A plane is normal to the vector = -2i+5j+k

It contains the point (-10,7,5).​

To find:

The component equation of the plane.

Solution:

The equation of plane is

a(x-x_0)+b(y-y_0)+c(z-z_0)=0

Where, (x_0,y_0,z_0) is the point on the plane and \left< a,b,c\right> is normal vector.

Normal vector is -2i+5j+k and plane passes through (-10,7,5). So, the equation of the plane is

-2(x-(-10))+5(y-7)+1(z-5)=0

-2(x+10)+5y-35+z-5=0

-2x-20+5y-35+z-5=0

-2x+5y+z-60=0

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Therefore, the equation of the plane is -2x+5y+z=60.

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2 years ago
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Answer:

$105.25

Step-by-step explanation:

First we need to know to price of the blender after the sale, so we are going to pay the 88% of the blender's price so the final price without the sale tax is going to be

\$130\times .88=\$ 114.4      (1)

Knowing this price we need to calculate the 8% of the total price

\$ 114.4 \times .08=\$ 9.152    (2)

We substract the result (2) from (1)

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3 years ago
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Answer:

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Step-by-step explanation:

1. The definition of a circle is all the points in a plane that are at some radius r from a given point (the circle center). That is what you have, with a radius of 2 cm.

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2. Parallel lines are the same distance apart everywhere. Each line will have two parallel lines at some given distance from it, one on each side. Here, the separation distance from AB is 1 cm, so your locus of points is the two lines parallel AB that are 1 cm from it on either side.

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3 years ago
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