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Andreas93 [3]
3 years ago
5

Which expression represents the algebraic phrase “the sum of negative three-eighths and four times x minus nine times z”?

Mathematics
1 answer:
sesenic [268]3 years ago
7 0

Answer:

(-3/8+4x)-9z            

C. Negative StartFraction 3 over 8 EndFraction + 4 x minus 9 z

Step-by-step explanation:

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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

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
In an isosceles trapezoid, each pair of base angles is
arsen [322]
Congruent is ur answer
6 0
3 years ago
You and two friends got jobs at stores in the mall. You earn $117.60$117.60 for 1414 hours of work. Ty earns $148.50$148.50 in 1
erica [24]
U : 117.6 / 14 = 8.40 per hr
Ty : 148.5 / 18 = 8.25 per hr
Kim : 137.6 / 16 = 8.60 per hr

highest pay rate is Kim
6 0
3 years ago
If letters of the word COMPUTER are randomly arranged in a row, what is the probability that the letters CO remain next to each
Mariana [72]

The probability that the letters CO remain next to each other (in order) as a unit is \frac{1}{8} .

<h3>What is probability?</h3>

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. It is more likely that an event will occur if its probability is higher.

When the letters are arranged randomly in a row, the total number of arrangements is 40,320 , and the number of arrangements with the letters CO next to each other (in order) as a unit is 5,040.

Therefore, possible outcomes = 5040 and

Total outcomes = 40320

Probability = \frac{Possible outcomes}{Total outcomes}

p = \frac{5040}{40320} = \frac{1}{8}

Therefore, the probability that the letters CO remain next to each other (in order) as a unit is \frac{1}{8} .

To learn more about probability with the given link

brainly.com/question/11234923

#SPJ4

4 0
2 years ago
Jimmy wants a burger. It is $30 but he has a coupon for 10% off. How much does he spend?
zalisa [80]
He spends $27.00 because you multiply the 10% by 30 and subtract the two
4 0
3 years ago
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