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BabaBlast [244]
3 years ago
15

Complete the table so that the cost per banana remains the same.

Mathematics
1 answer:
Aneli [31]3 years ago
3 0

Step-by-step explanation:

No. of banana    Cost      Unit price

4                            2            0.50

6                            3             0.50

7                           3.5           0.50

20                         10            0.50

20                          10             0.50

33                          16.50        0.50

Cost = No of banana x unit price

Cost = 4 x 0.50 = 2

Cost = 6 x 0.50 = 3

Cost = 7 x 0.50 = 3.50

Cost = 20 x 0.50 = 10

No of banana = Cost / Unit price

No of banana = 10 / 0.50 = 20

No of banana = 16.50 / 0.50 = 33

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Select all that apply. Which of the following are proportions? 25/10=5/2,3/4=8/10,2/8=3/12,3/4=15/20
8_murik_8 [283]

Answer:

\frac{25}{10} = \frac{5}{2} is in proportion.

\frac{3}{4} = \frac{8}{10} is not in proportion.

\frac{2}{8} = \frac{3}{12} is in proportion.

\frac{3}{4} = \frac{15}{20} is in proportion.

Step-by-step explanation:

The first example is \frac{25}{10} = \frac{5}{2} and it is in proportion.

This is because, you will get the same simplest fraction (\frac{5}{2}) from the fraction \frac{25}{10} by dividing its numerator and denominator by 5.

The second example is \frac{3}{4} = \frac{8}{10} and it is not in proportion.

This is because, you can not  get the simplest fraction (\frac{3}{4}) from the fraction \frac{8}{10} after simplification.

The third example is \frac{2}{8} = \frac{3}{12} and it is in proportion.

This is because, you will get the same simplest fraction (\frac{1}{4}) from the fraction \frac{2}{8} by dividing its numerator and denominator by 2 and from the fraction \frac{3}{12} by dividing its numerator and denominator by 3.

The fourth example is \frac{3}{4} = \frac{15}{20} and it is in proportion.

This is because, you will get the same simplest fraction (\frac{3}{4}) from the fraction \frac{15}{20} by dividing its numerator and denominator by 5. (Answer)

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Draw the dilation image of the triangle with a center at the origin and a scale factor of two.
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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

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Step-by-step explanation:

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