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balu736 [363]
3 years ago
7

Solve the equation 3(x+2) = 2(2 - x)

Mathematics
2 answers:
andrew-mc [135]3 years ago
7 0

Answer:

x=

−2

5


Step-by-step explanation:


RideAnS [48]3 years ago
6 0

Answer:

x=-2/5

Step-by-step explanation:


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HELP ME ON GEOMETRY!!​
Nikolay [14]

Answer:

12 units²

Step-by-step explanation:

The two are congruent, so C'D' is still 6units long. L*W = 6 * 2 = 12 units^2

6 0
3 years ago
Suppose that you roll a pair of honest dice. If you roll a total of​ 6, you win​ $18; if you roll a total of​ 11, you win​ $72;
ser-zykov [4K]

You can roll a total of 6 by rolling (1, 5), (2, 4), (3, 3), (4, 2), or (5, 1). There are 36 total possible rolls that can be obtained, so you roll a total of 6 with probability 5/36.

You can roll a total of 11 by rolling (5, 6) or (6, 5), hence with probability 2/36 = 1/18.

Any of the other remaining 29 outcomes occurs with probability 29/36.

The expected value of your winnings is

$18*5/36 + $72*1/18 - $9*29/36 = -$0.75

so the answer is E.

7 0
3 years ago
6. What is the Greatest Common Factor of 45<br> and 60?<br> 14560
bazaltina [42]

Answer:

15  15 goes into 45 5 times and 60 5 times. highest number that goes into both numbers evenly

5 0
3 years ago
Read 2 more answers
Use lagrange multipliers to find the shortest distance, d, from the point (4, 0, −5 to the plane x y z = 1
Varvara68 [4.7K]
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be x+y+z=1.

You're minimizing d(x,y,z)=\sqrt{(x-4)^2+y^2+(z+5)^2} subject to the constraint f(x,y,z)=x+y+z=1. Note that d(x,y,z) and d(x,y,z)^2 attain their extrema at the same values of x,y,z, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.

The Lagrangian is

L(x,y,z,\lambda)=(x-4)^2+y^2+(z+5)^2+\lambda(x+y+z-1)

Take your partial derivatives and set them equal to 0:

\begin{cases}\dfrac{\partial L}{\partial x}=2(x-4)+\lambda=0\\\\\dfrac{\partial L}{\partial y}=2y+\lambda=0\\\\\dfrac{\partial L}{\partial z}=2(z+5)+\lambda=0\\\\\dfrac{\partial L}{\partial\lambda}=x+y+z-1=0\end{cases}\implies\begin{cases}2x+\lambda=8\\2y+\lambda=0\\2z+\lambda=-10\\x+y+z=1\end{cases}

Adding the first three equations together yields

2x+2y+2z+3\lambda=2(x+y+z)+3\lambda=2+3\lambda=-2\implies \lambda=-\dfrac43

and plugging this into the first three equations, you find a critical point at (x,y,z)=\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right).

The squared distance is then d\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)^2=\dfrac43, which means the shortest distance must be \sqrt{\dfrac43}=\dfrac2{\sqrt3}.
7 0
3 years ago
Chipper ran 1 mile in 8 minutes. How long would it take him to run 5 miles?
balandron [24]

Answer:

40 minutes

Step-by-step explanation:

Given 1 mile = 8 minutes

5 miles = (5 × 8) minutes

5 miles = 40 minutes

It would take 40 minutes to run 5 miles

7 0
2 years ago
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