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Gwar [14]
3 years ago
11

Mr. frankel bought 7 tickets to a puppet show and spent $24. he bought a combination of child tickets for $2 each and adult tick

ets for $4 each. which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought
Mathematics
1 answer:
nydimaria [60]3 years ago
6 0
Let x be the number of child tickets he bought
Let y be the number of adult tickers he bought

① x+y=7 (child tickets+adult ticket=7 tickets in total)
② 2x+4y=24 (price of child tickets+price of adult tickets=$24 in total)

We may simply the second equation since all of the coefficients are divisible by 2.

① x+y=7
② x+2y=12

We can now use elimination by multiplying the second equation by -1.

② -(x+2y=12)
② -x-2y=-12

① x+y=7
② -x-2y=-12

Now putting the equations together,
-y=-5
y=5
x=2

Therefore he bought 2 child tickets and 5 adult tickets
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PLEASE help!!!!!! You can get 50 points and a brainliest if you help me.
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7 0
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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning.
Alborosie
Assume that the rule connecting height of the candle to time is a linear one.  If you do, then we have to find the equation of this line, and then use this equation to predict the height of the candle after 11 hours.

Two points on this line are (6,17.4) and (23, 7.2).  The slope is thus
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m = ---------------  =  -----------  or   -3/5.
           23-6                 10

Find the equation of the line.  I'm going to use the slope-intercept formula:

y = mx + b  =>   7.2 = (-3/5)(23) + b.  Solving for b,   b = 21.

Now    we know that y = (-3/5)x + 21

Let x=11 to predict the height of the candle at that time.

y = (-3/5)(11) + 21 = 14.4 inches  (answer)
7 0
3 years ago
Write the standard form of the equation for the circle that passes through the points (2,31),(-15,14),(33,0)
stepladder [879]

Answer:

Step-by-step explanation:

Begin with the standard form of a circle as a conic:

Ax^2+Bxy+Cy^2+Dx+Ey+F=0

For a circle, A and C will be the exact same, and B will equal 0.  If B is non-zero, the equation represents a rotation of a conic, which is reserved for college-level courses.  Shortening this, then:

x^2+y^2+Dx+Ey+F=0 is good enough for us for this.  Start with the first point on the circle, (2, 31) and fill in the equation above with x and y:

2^2+31^2+2D+31E+F=0 which simplifies down to:

(1):2D+31E+F=-965

Do the same with the next point on the circle, (-15, 14):

-15^2+14^2-15D+14E+F=0 which simplifies down to:

(2):-15D+14E+F=0

Do the same with the last point, (33, 0):

33^2+0^2+33D+0E+F=0 which simplifies down to:

(3):33D+F=-1089

Now we will add (1) and (2) to get (4):

 2D + 31E + F = -965

-15D + 14E + F = -421

Multiply the top equatio by -1 to get rid of the F terms:

 -2D - 31E - F = 965

-15D + 14E + F = -421

which simplifies to

(4): -17D - 17E = 544

Now add (2) and (3) to get (5):

-15D + 14E + F = -421

33D           + F = -1089

Multiply the bottom equation by -1 to get rid of the F terms:

-15D + 14E + F = -421

-33D          - F = 1089

which simplifies to

(5): -48D + 14E = 668

Now add (4) and (5) together and eliminate the E terms:

-17D - 17E = 544

-48D + 14E = 668

In order to eliminate the E terms, multiply the top equation by 14 and the bottom equation by 17 to solve for D:

-238D - 238E = 7616

-816D + 238E = 11356

Which gives you that

D = -18

Now plug the value for D into (4) to find E:

-17(-18) - 17E = 544 and

306 - 17E = 544 and

-17E = 238 so

E = -14

Now plug the values for both D and E into (1) to find F:

2(-18) + 31(-14) + F = -965 and

-36 - 434 + F = -965 and

-470 + F = -965 so

F = -495

Now we can fill in the standard form of the conic:

x^2+y^2-18x-14y=495

but we're not done til we complete the square on both the x terms and the y terms (and I am assuming you know how to complete the square):

(x^2-18x+81)+(y^2-14y+49)=495+81+49 which simplifies to

(x-9)^2+(y-7)^2=625

The second choice down matches that equation, but the center they have there is not correct.  The center of that circle is (9, 7) and they have it as being (7, 10) with a radius of 5.  The radius is 25.  The center is wrong in the equation that represents the circle as is the radius.  Maybe let someone know that...

4 0
3 years ago
Read 2 more answers
Helpppppppppppppppppppp
Ivan
I believe the answer is B and E
7 0
3 years ago
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