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kiruha [24]
3 years ago
7

Which algebraic expression represents “the difference of 54 and a number”? HELP I AM TIMED ASAP

Mathematics
1 answer:
DedPeter [7]3 years ago
7 0

Answer:

The first one

Step-by-step explanation:

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the weight M of an object on Mars varies directly as it’s weight E on Earth. A person who weighs 95 lb on Earth weighs 38 lb on
lorasvet [3.4K]

Answer:

A 100 lb person will weight 40 lb on Mars

Step-by-step explanation:

Given:

Weight on Mars directly varies as its weight on earth.

Let weight on Mars be = M

Let weight on Earth be = E

Its known that:

M ∝ E

Thus

M=kE

where k is constant of proportionality.

when  E=95\ lb, then M=38\ lb

thus, we have

38=k(95)

dividing both sides by 95.

\frac{38}{95}=\frac{k(95)}{95}

∴ k=\frac{38}{95}

Thus when E= 100, M would be calculated as

M=\frac{38}{95}\times 100

M=\frac{3800}{95}

∴ M=40\ lb  (Answer)

∴ A 100 lb person will weight 40 lb on Mars.

8 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
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Yuki888 [10]
R'S' is equal in length to RS.

length doesnt change, it was just rotated.
6 0
3 years ago
Read 2 more answers
Which number has a 6 that is 1/10 of the value of the 6 in 7,639
Shalnov [3]

Answer:

60

Step-by-step explanation:

the 6 in 7639 has a value of 600

600/10 = 60

5 0
2 years ago
Round 14.57 to nearest whole number
Galina-37 [17]
14.57 rounded to the nearest whole number is..... 15
8 0
3 years ago
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