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Vsevolod [243]
3 years ago
11

30 POINTS AVAILABLE

Mathematics
1 answer:
kherson [118]3 years ago
3 0

Answer:

\large\boxed{(x-2)^2+(y-1)^2=34}

Step-by-step explanation:

The equation of a circle in standard form:

(x-h)^2+(y-k)^2=r^2

(h, k) - center

r - radius

We have the endpoints of the diameter: (-1, 6) and (5, -4).

Midpoint of diameter is a center of a circle.

The formula of a midpoint:

\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)

Substitute:

h=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\\k=\dfrac{6+(-4)}{2}=\dfrac{2}{2}=1

The center is in (2, 1).

The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.

The formula of a distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Substitute the coordinates of the points (2, 1) and (5, -4):

r=\sqrt{(5-2)^2+(-4-1)^2}=\sqrt{3^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}

Finally we have:

(x-2)^2+(y-1)^2=(\sqrt{34})^2

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Find the sum
lakkis [162]

Answer:

Numerator = 2(b^2+a^2)    or equivalently 2b^2+2a^2

Denominator = (b+a)^2*(b-a), or equivalently b^3+ab^2-a^2b0-a^3

Step-by-step explanation:

Let

S = 2b/(b+a)^2 + 2a/(b^2-a^2)   factor denominator

= 2b/(b+a)^2 + 2a/((b+a)(b-a))     factor denominators

= 1/(b+a) ( 2b/(b+a) + 2a/(b-a))    find common denominator

= 1/(b+a) ((2b*(b-a) + 2a*(b+a))/((b+a)(b-a))   expand

= 1/(b+a)(2b^2-2ab+2ab+2a^2)/((b+a)(b-a))  simplify & factor

= 2/(b+a)(b^2+a^2)/((b+a)(b-a))  simplify & rearrange

= 2(b^2+a^2)/((b+a)^2(b-a))

Numerator = 2(b^2+a^2)    or equivalently 2b^2+2a^2

Denominator = (b+a)^2*(b-a), or equivalently b^3+ab^2-a^2b0-a^3

4 0
2 years ago
10. DESIGN Mr. Hagarty is choosing tiles to design a kitche backsplash for a rectangular area 65 inches wide and 9 in tall . Des
DENIUS [597]

Answer:

I honeslty dont know I just need points to answer a question

Step-by-step explanation:

hope you find the answer youre looking for!

4 0
3 years ago
Help me help me help me help me ​
Nitella [24]

Answer:

1. 4/12, 3/9, 2/6, 5/15

2. 4/8, 8/16, 6/12

3. 2/8, 4/16, 3/12

4. 6/8, 9/12, 4/16

Step-by-step explanation:

I'm assuming your question is about all 4 problems shown so I'll explain how to solve all of them.

1. The question is asking you to find an equivalent fraction to 1/3. The easiest way to do this is to reduce all of the options given.

To reduce fractions, first determine if the numerator and denominator share any factors. If they do, divide both terms by the shared factors until you no longer get whole numbers.

Step 1: reduce answer choices

6/16 = 3/8 (done by dividing both terms by 2)

4/10 = 2/5 (divide both by 2)

3/8 = 3/8 (fully reduced)

2/5 = 2/5 (fully reduced)

4/12 = 1/3 (divide both by 4)

5/10 = 1/2 (divide both by 5)

1/2 = 1/2 (fully reduced)

3/9 = 1/3 (divide both by 3)

2/6 = 1/3 (divide both by 2)

5/15 = 1/3 (divide both by 5)

3/8 = 3/8 (fully reduced)

3/4 = 3/4 (fully reduced)

2. This question is solved the same way as question 1.

Step 1: reduce answer choices

2/5 = 2/5

6/9 = 2/3

4/8 = 1/2

3/9 = 1/3

8/16 = 1/2

8/10 = 4/5

7/12 = 7/12

6/12 = 1/2

3. This question is solved the same way as questions 1 and 2.

Step 1: reduce answer choices

3/8 = 3/8

2/8 = 1/4

4/9 = 4/9

2/7 = 2/7

4/16 = 1/4

10/14 = 5/7

6/9 = 2/3

3/12 = 1/4

4. This question is solved the same way as questions 1, 2, and 3.

Step 1: reduce answer choices

6/8 = 3/4

4/9 = 4/9

4/6 = 2/3

9/12 = 3/4

10/12 = 5/6

6/9 = 2/3

12/16 = 3/4

7/9 =7/9

7 0
2 years ago
Can someone help me with this question
Alex_Xolod [135]

Answer:

Yes.

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
In an ore, 9.8% of its total weight is metal. How many pounds of metal are in 1,950 lb of ore?
Fudgin [204]

Answer

Find out the  how many pounds of metal are in 1,950 lb of ore .

To proof

let us assume that the pounds of metal are in 1,950 lb of ore be x .

As given

In an ore, 9.8% of its total weight is metal.

ore weight = 1,950 lb

9.8% is written in the decimal form

= \frac{9.8}{100}

= 0.098

Than the equation becomes

x = 0.098 × 1950

x = 191.1 pounds

Therefore the 191.1 pounds of metal are in 1,950 lb of ore .

Hence proved



5 0
3 years ago
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