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alexandr402 [8]
3 years ago
10

All books in a store are being discounted by 40%. let x represent the regular price of any book in the store which expression de

scribes the sale price of a book ?
Mathematics
1 answer:
antoniya [11.8K]3 years ago
6 0
To find the sale price<span> we can set up a proportion. 25/100 = </span>x<span>/48. We keep the 100 and 48 both on the bottom of the fraction since they </span>represent<span> the "whole". </span>x represents<span> the </span>discount<span> off the </span>full price<span> of the dress. To solve this proportion, we cross multiply, yielding 48 * 25 = 100x. Alternatively, </span>if<span> you notice that 25/100 ...</span>
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Travka [436]
2 over 45 just so that you know
6 0
3 years ago
Two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 + 2t, 1 + 6t, 1 + 14t . Find the points at which their p
GuDViN [60]

Answer:

A) points at which paths intersect : (1,1,1) ; (2,4,8)

B) DNE

Step-by-step explanation:

A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:

t_1=1+2t_2\\\\t_1^2=1+6t_2\\\\t_1^3=1+14t_2

you replace t1 from the first equation in the second equation:

(1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}

Then, for t2 = 0 and t2=1/2 you obtain for t1:

t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2

Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.

The points at which the paths  intersect are:

r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)

B) You have the following two trajectories of two independent particles:

r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)

To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:

t=1+2t\\\\t^2=1+6t\\\\t^3=1+14t

From the first equation you have:

t=1+2t\\\\t=-1

This values does not have a physical meaning, then, the particle do not collide

answer: DNE

5 0
3 years ago
Find an equation for the line that passes through the point (-3, 6), parallel to the line through the points (0,-7) and (4,-15).
Vitek1552 [10]
Broken down into steps:

1.  Find the slope of the line segment that connecs the points (0,-7) and (4,-15).

2.  Start with the point-slope formula for the equation of a straight line:

y-b = m(x-a), where the given point is (a,b).  Borrow the value of m that you calculated in (1), above, and insert it into this point-slope formula.
Finish up by subst. the x- and y-values in (-3,6) into this formula.

Done!

You could, of course, solve this result for y if you wished.
8 0
3 years ago
a rectangular prism with a volume of 10 cubic units is filled with cubes with side lenghts of 1/2 unit how many 1/2 unit cubes d
Pachacha [2.7K]

Answer:

Step-by-step explanation:

The volume of a cube is

V=s^3, we are told the volume is 10u^3 and that it will be filled with cubes having a side of 1/2 so

n(1/2)^3=10, where n will be the number of these small cubes

n(1/8)=10 upon multiplying each side by 8

n=80

So it will take 80 cubes of side length 1/2 to have a volume equal to 10u^3

6 0
3 years ago
2 x -1^2 + 1<br><br> please show me how to get to the answer of 1
OLga [1]

Answer:

-1

Step-by-step explanation:

2 × (-1²) + 1 = 2 × (-1) + 1 = -2 + 1 = -1

7 0
2 years ago
Read 2 more answers
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