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ZanzabumX [31]
3 years ago
10

Marvin has 4 books to read for homework this week. If he reads 2/3 of a book each night, how many nights will it take him t read

all four books?
Mathematics
1 answer:
Elenna [48]3 years ago
8 0
2/3
4/3-one books, 2 nights
6/3-2 books, 3 nights
8/3
10/3-3 books, 5 nights
12/3=4 books in 6 nighs
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Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)

We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>

The vector product pq x pr gives a vector perpendicular to both pq and pr.  This vector is the normal vector of a plane passing through all three points
pq x pr
=
  i   j   k
-4 -2 -4
-3  5  1
=<-2+20,12+4,-20-6>
=<18,16,-26>

Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>

The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).

The equation of the required plane is therefore
Π :  9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π  :  9x+8y-13z=24

Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.

3 0
3 years ago
The function y= -16t^2 +24t represents the height y (in feet) of a tennis ball bouncing straight up from the ground t seconds af
taurus [48]
We want to know the time, <em>t</em>, it takes the ball to reach a height (<em>y</em>) of 0.
0=-16t^2+24t
We can factor out the GCF first.  The largest number that will divide evenly into 16 and 24 is 8.  Also, both terms have a <em>t</em>, so we can factor that out as well:
0=8t(-2t+3) (-16/8 = -2 and 24/8 = 3)
Using the zero product property, we know that either 8t=0 or -2t+3=0.  Solving the first equation, we would divide both sides by 8:
8t/8=0/8
t=0
This is at 0 seconds, before the ball is in the air at all.
Solving the second equation, we start by subtracting 3 from both sides:
-2t+3-3=0-3
-2t=-3
Now we divide both sides by -2
-2t/-2=-3/-2
t=1.5
After 1.5 seconds, the ball will hit the ground again.
5 0
4 years ago
For his troops' popcorn fundraiser sale, Mike sold caramel corn for $10, buttered microwave popcorn for $8, and lightly buttered
Bad White [126]
\bf \begin{cases}&#10;c=\textit{caramel corn}\\&#10;b=\textit{buttered microwave popcorn}\\&#10;p=\textit{lightly buttered popcorn}&#10;\end{cases}

so... he sold 400 items, that means, whatever those quantities of c,b,p are, they add up to 400, thus

c+b+p = 400

now, the "c" sold for $10
the "b" sold for $8
and the "p" sold for $7

so, the amount of revenue on the "c" is 10 * c, or 10c
the revenue on "b" is 8*b or 8b
and the revenue on "p" is 7*p or 7p

whatever those amounts are, they ended up in $3,272
thus
10c + 8b + 7p = 3,272

now, he sold more lightly buttered, or "p", than just buttered corn or "b"
he actually sold twice as much, so whatever "b" is, "p" is twice that much
or 
p = 2b

thus      \bf \begin{cases}&#10;c+b+\boxed{p}=400\\\\&#10;\boxed{p}=2b\qquad thus\\\\&#10;c+b+\boxed{2b}=400\qquad or\\\\&#10;c+3b=400\implies c=\underline{400-3b}\\&#10;--------------\\&#10;10c+8b+7p=3272\qquad or\\\\&#10;10(\underline{400-3b})+8b+7(\boxed{2b})=3272&#10;\end{cases}

solve for "b", to see how many buttered microwave popcorn Mike sold

how many lightly buttered?  well, p = 2b
how many caramel ones?   well  c = 400 - 3b
5 0
4 years ago
What is10 + 9 <br><br> i really dont know <br><br> can someone help me
Tresset [83]

\huge \green{ \boxed{ANSWER}}

10  \:  +  \: 9 \:  =  {\boxed{19}}

USE CALCULATOR -_-

\mathfrak{JazmineChoi}

<em><u>STAN </u></em><em><u>TREASURE</u></em>

8 0
3 years ago
Read 2 more answers
What is 657 divided by 2 in long division? ​
Anvisha [2.4K]
The answer is going to 328.5 or 328.50 is the same thing
4 0
3 years ago
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