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ss7ja [257]
3 years ago
5

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total numb

er of people that can be seated in the restaurant is 120.
a. Find some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers.
Mathematics
1 answer:
gayaneshka [121]3 years ago
4 0

Answer:

5 points for what

Step-by-step explanation:

HeY

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2logx=3-2log(x+3) solve for x​
AVprozaik [17]

Answer:

\large\boxed{x=\dfrac{-3+\sqrt{40+10\sqrt{10}}}{2}}

Step-by-step explanation:

2\log x=3-2\log(x+3)\\\\Domain:\ x>0\ \wedge\ x+3>0\to x>-3\\\\D:x>0\\============================\\2\log x=3-2\log(x+3)\qquad\text{add}\ 2\log(x+3)\ \text{to both sides}\\\\2\log x+2\log(x+3)=3\qquad\text{divide both sides by 2}\\\\\log x+\log(x+3)=\dfrac{3}{2}\qquad\text{use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log\bigg(x(x+3)\bigg)=\dfrac{3}{2}\qquad\text{use the de}\text{finition of a logarithm}\\\\x(x+3)=10^\frac{3}{2}\qquad\text{use the distributive property}

x^2+3x=10^{1\frac{1}{2}}\\\\x^2+3x=10^{1+\frac{1}{2}}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\x^2+3x=10\cdot10^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\x^2+3x=10\sqrt{10}\qquad\text{subtract}\ 10\sqrt{10}\ \text{from both sides}\\\\x^2+3x-10\sqrt{10}=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=3,\ c=-10\sqrt{10}\\\\b^2-4ac=3^2-4(1)(-10\sqrt{10})=9+40\sqrt{10}\\\\x=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2(1)}=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2}\\\\x=\dfrac{-3-\sqrt{10+10\sqrt{10}}}{2}\notin D

6 0
3 years ago
3.3.1. An urn contains five balls numbered 1 to 5. Two balls are drawn simultaneously. (a) Let X be the larger of the two number
hodyreva [135]

Answer:

Step-by-step explanation:

Given that an urn contains five balls numbered 1 to 5

Two balls are drawn simultaneously.

a) X = the larger of two numbers drawn

Assuming balls are drawn without replacement, (since simultaneously drawn)

the sample space would be (1,2) (1,3)(1,4)(1,5) (2,3)(2,4)(2,5) (3,4) (3,5) (4,5)

n(S) = 10

n(x=2) = 1,

n(x=3) =2

n(x=4) = 3

n(x=5) = 4

Larger value  X can take values only as 2,3,4 or 5

X          2              3            4               5

p          0.1           0.2       0.3             0.4

-------------------------------------------

b) V = sum of numbers drawn

V can take values as 3, 4, 5, 6, 7, 8 or 9

V                  3        4             5          6           7             8          9

p                  0.1     0.1         0.2      0.2         0.2        0.1        0.1

6 0
3 years ago
What could you use to show that opposite sides are congruent? Which quadrilaterals does it work for?
slega [8]
Square
as the sides are all equal
4 0
3 years ago
The differential cost was:
Alja [10]
What Exactly is the question?
3 0
4 years ago
Need help with this!!!!!!!!
zzz [600]
The linear combination method is the same as the elimination method.  Let's multiply the second equation by -2 so the x terms cancel each other out. When we do that we get a system of 2x-3y=13 and -2x-4y=8.  The x-terms cancel each other out giving us -7y=21 and y = -3.  Now sub -3 into one of the equations to solve for x.  x+2(-3)=-4, and x - 6 = -4.  x = 2.  So the solution for our system is (2, -3)
4 0
4 years ago
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