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ser-zykov [4K]
1 year ago
11

Read a system of equations to describe the situation below solve using illumination and fill in the blanks

Mathematics
1 answer:
Lana71 [14]1 year ago
4 0

System of Equations

Let:

x = number of people that can be seated at a table

y = number of people that can be seated at a booth

The first plan consists of 23 tables and 10 booths and then 228 people could be seated, thus:

23x + 10y = 228

The second plan consists of 12 tables and 12 booths and that way 180 people could be seated, thus:

12x + 12y = 180

The method of elimination requires equating the coefficients of one variable and eliminating it by adding the equations.

Multiply the first equation by 12:

276x + 120y = 2736

Multiply the second equation by -23:

-276x - 276y = -4140

Add the last two equations (the variable x cancels out):

120y - 276y = 2736 - 4140

Simplifying:

-156y = -1404

Dividing by -156:

y = -1404/(-156)

y = 9

Substitute this value in the first equation:

23x + 10(9) = 228

Operate:

23x + 90 = 228

Subtract 90:

23x = 138

Divide by 23:

x = 138/23

x = 6

Every table can seat 6 people, and every booth can seat 9 people

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Savatey [412]
Middle one is the answer

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Which equation is equivalent to I = prt?
horsena [70]

Answer: Choice D.  P = i/rt

This is the same as saying P = i/(rt). The parenthesis are preferred in my opinion to indicate we have rt in the denominator and not just r.

======================================

Explanation:

In the original equation, prt is the same as p*r*t. So we multiply p, r and t to get prt.

This can be thought of as p*(rt). To isolate p, we undo the multiplication done to the variable p. We will divide both sides by rt to get

i = prt

i = p*(rt)

i/(rt) = p*(rt)/(rt) ... dividing both sides by rt

i/(rt) = p

p = i/(rt)

5 0
3 years ago
(5^49/5^48)+4^0−(1)^79⋅(−3/−4^9)^0
MrMuchimi

Answer:

I believe it is 3.75

Step-by-step explanation:

(5^49/5^48)+4^0−(1)^79⋅(−3/−4^9)^0

5+1−(1)^79⋅(−3/−4^9)^0

5+1−(1)^79

5⋅(−3/−4^9)^0

-3 divided by -4 to the power of 9 to the power of 0=0.75

5 times 0.75=3.75

Hope this is correct! xx

3 0
2 years ago
What is the reason for each step in the solution of the inequality?<br><br> −2(x+3)−4&gt;4x+30
DochEvi [55]
You would have to first distribute the -2 to the x+3 which gives you -2x-6.  Then you would subtract the 4 which gives you -2x-10 on the left side.  Now you have the equation -2x-10>4x+30.  Move the 4x to the other side giving you         -6x-10>30.  Now add the 10 from the other side which leaves you with -6x>40.  Now remember when you divide by a negative in an inequality, you HAVE TO flip the sign giving you the answer of x<-20/3.

5 0
3 years ago
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Find the value of x in the following diagram,<br> 3x + 10<br> Here, B and D are points of tangency.
SVEN [57.7K]

<u>Given</u>:

The given circle with center at C. The lines AB and AD are tangents to the circle C.

The length of AB is (3x + 10)

The length of AD is (7x - 6)

We need to determine the value of x.

<u>Value of x:</u>

Since, we know the property of tangent that, "if two tangents from the same exterior point are tangent to a circle, then they are congruent".

We shall determine the value of x using the above property.

Thus, we have;

AB = AD

Substituting the values, we get;

3x+10=7x-6

Subtracting both sides of the equation by 7x, we get;

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Subtracting both sides of the equation by 10, we get;

-4x=-16

Dividing both sides of the equation by -4, we get;

x=4

Thus, the value of x is 4.

5 0
3 years ago
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