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sattari [20]
3 years ago
11

Use completing the square to rewrite the equation in the form (x-h)^2 +(y-k)^2 = r^2. State the center (h, k) and radius r of th

e circle
2x^2 + 2y^2 + 4x + 8y - 20 = 0
Mathematics
1 answer:
Lisa [10]3 years ago
3 0

Answer:

The equation is (x + 1)^2 + (y + 2)^2 = 15

Center is at  (-1, -2) and radius = √15

Step-by-step explanation:

2x^2 + 2y^2 + 4x + 8y - 20 = 0

Divide through by 2:-

x^2 + y^2 + 2x + 4y - 10 = 0

x^2 + 2x + y^2 + 4x = 10

Completing the square on the x and y terms:-

(x + 1)^2 - 1 + (y + 2)^2 - 4 = 10

(x + 1)^2 + (y + 2)^2 = 10 + 1 + 4

(x + 1)^2 + (y + 2)^2 = 15    

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In the number 15.2201 how does the value of 2 in the tenths place compare to the value of the 2 in the hundredths place
lakkis [162]

Answer:

The 2 in the hundreths is 10% of the 2 in the tenths

Step-by-step explanation:

We are given the number 15.2201

#The value of 2 in the tenths:

0.2

#The value of 2 in the hundredths:

0.02

The difference of the 2 in the tenths and in the hundredths is:

=2_t-2_h\\\\=0.2-0.02\\\\=0.18\\\\\#2_h \ as \ a \ \% \ of \ 2_t\\=\frac{2_h}{2_t}\times 100\%\\\\=\frac{0.02}{0.2}\times100\%\\\\2_h=10\% \ of\  2_t

Hence, the difference between the 2 in the tenths  minus 2 in the hundreths is 0.18, 2 in the hundreths is 10% the 2 in the tenths.

6 0
3 years ago
Jada and Noah wanted to find the total volume of a cube and a rectangular prism. They know the prism's volume is 20 cubic units,
jeyben [28]

Answer:

Volume of the cube = 10^3 = 1000 units.

Total volume of the cube + the prism = 1000 + 2

= 1020 cubic units.

Step-by-step explanation:

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5 0
3 years ago
Read 2 more answers
Determine whether the set of all linear combinations of the following set of vector in R^3 is a line or a plane or all of R^3.a.
Temka [501]

Answer:

a. Line

b. Plane

c. All of R^3

Step-by-step explanation:

In order to answer this question, we need to study the linear independence between the vectors :

1 - A set of three linearly independent vectors in R^3 generates R^3.

2 - A set of two linearly independent vectors in R^3 generates a plane.

3 - A set of one vector in R^3 generates a line.

The next step to answer this question is to analyze the independence between the vectors of each set. We can do this by putting the vectors into the row of a R^(3x3) matrix. Then, by working out with the matrix we will find how many linearly independent vectors the set has :

a. Let's put the vectors into the rows of a matrix :

\left[\begin{array}{ccc}-2&5&-3\\6&-15&9\\-10&25&-15\end{array}\right] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix  ⇒

\left[\begin{array}{ccc}-2&5&-3\\0&0&0\\0&0&0\end{array}\right]

We find that the second vector is a linear combination from the first and the third one (in fact, the second vector is the first vector multiply by -3).

We also find that the third vector is a linear combination from the first and the second one (in fact, the third vector is the first vector multiply by 5).

At the end, we only have one vector in R^3 ⇒ The set of all linear combinations of the set a. is a line in R^3.

b. Again, let's put the vectors into the rows of a matrix :

\left[\begin{array}{ccc}1&2&0\\1&1&1\\4&5&3\end{array}\right] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

\left[\begin{array}{ccc}1&1&1\\0&1&-1\\0&0&0\end{array}\right]

We find that there are only two linearly independent vectors in the set so the set of all linear combinations of the set b. is a plane (in fact, the third vector is equivalent to the first vector plus three times the second vector).

c. Finally :

\left[\begin{array}{ccc}0&0&3\\0&1&2\\1&1&0\end{array}\right] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

\left[\begin{array}{ccc}1&1&0\\0&1&2\\0&0&3\end{array}\right]

The set is linearly independent so the set of all linear combination of the set c. is all of R^3.

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2 years ago
One car traveled 220 miles and drove 10 mph hour slower than a second car which drove 260 miles. If the cars were traveling for
Colt1911 [192]
55 mph...if the 1st one drove 260 miles, that's 65mph for 4 hours...1st car has to be 55mph for 4 hours to get 220 miles.
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If it is a square is it a quadrilateral
Alina [70]
Yes  a square is a type of quadrilateral  ( quadrilateral means 'four sides').
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