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3 years ago

Find the equation of the circle that passes through the origin and has its center at (-3,-4).

2 answers:

6 0

$equation\ of\ the\ circle:(x-a)^2+(y-b)^2=r^2\\\\(a;\ b)\ is\ a\ cener\ of\ the\ circle\\\\(a;\ b)=(-3;-4)\\\\r-radius\ of\ the\ circle\\\\r=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\Answer:(x+3)^2+(y+4)^2=5^2\to(x+3)^2+(y+4)^2=25$

Xelga [282]3 years ago

6 0

If the center is at (-3, -4) and the origin is on the circle, then the radius
of the circle is the distance between the origin and (-3, -4).

R² = (-3)² + (-4)²
R² = 9 + 16
R² = 25
R = 5

The equation of the circle is [ (x + 3)² + (y + 4)² = 25 ].

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Find two positive numbers so that twice their sum equals their product and one number is 10 times the other number. Enter the sm

Softa [21]

Answer:

Step-by-step explanation:

We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:

y = 10x

Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:

2(x + y) = xy and we know that y = 10x so

2(x + 10x) = x(10x) and

$2(11x)=10x^2$ and

$10x^2-22x=0$ and

x(10x - 22) = 0 so

x = 0 or 10x - 22 = 0 which makes

x equal to $\frac{22}{10}=2.2$

So x = 2.2 and y = 22.

7 0

3 years ago

Which expression is equivalent to ( 4mn / m^-2n^6)^-2a. n^6 / 16m^8b. n^10 / 16m^6c. n^10 / 8m^8d. 4m^3 / n^8?

Eva8 [605]

$\huge{(} \small{\frac{4mn}{ {m}^{ - 2} {n}^{6} }} \huge{) } \small{{}^{ {}^{ {}^{ {}^{ - 2} } } } }\\ \\ \\ \huge{(} \small{ \frac{4 \times m {}^{1} \times n {}^{1} }{ {m}^{ - 2} \times {n}^{6} }} \huge{)} \small{^{ {}^{ {}^{ {}^{ - 2} } } }} \\ \\ \\ \huge{(} \small{4 \times {m}^{1 - ( - 2)} \times {n}^{1 - 6}} \huge{)} \small{ {}^{ {}^{ {}^{ {}^{ - 2} } } } } \\ \\ \\ \huge{(} \small{ 4 \times {m}^{1 + 2} \times {n}^{ - 5} } \huge{)} \small{ { }^{ {}^{ {}^{ {}^{ - 2} } } } } \\ \\ \\ \small{ {(4)}^{ - 2} \times ({m}^{3} ) ^{ - 2} \times {(n{}^{ - 5} )}^{ - 2} } \\ \\ \\ \frac{1}{ {4}^{2} } \times {m}^{ - 6} \times {n}^{ 10} \\ \\ \\ \frac{1}{16} \times \frac{1}{ {m}^{6} } \times {n}^{10} \\ \\ \\ \frac{ {n}^{10} }{16{m}^{6} }$

$\text{ Hence, option B is correct }$

7 0

3 years ago

What are symbols of inclusion

Kipish [7]

Answer:

Symbols of inclusion are symbols used in mathematical expressions that group terms or factors together. They indicate that when we are simplifying expressions, we are to perform what's inside the symbols first. The three types of symbols of inclusion are parentheses, brackets, and braces.

5 0

3 years ago

How many odd numbers with 4 different digits, can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8? (No repetition is allowed)

olga55 [171]

Answer:

840 ( D )

Step-by-step explanation:

GIVEN DIGITS : 1,2,3,4,5,6,7,8

Number of odd numbers = 4

Number of even numbers = 4

therefore the number of odd numbers with 4 different digits can be formed by the same way the number of even numbers ( without repetition )

Hence the number of ways odd numbers with 4 different digits = Total number of ways of forming 4 digit numbers / 2

8*7*6*5 = 1680 / 2 = 840 ways

6 0

3 years ago

Please help! 50 pts for answer!! and a thank you

Dmitrij [34]

Answer:

It decreases.

Step-by-step explanation:

$4.28 will go up because it is greater.

3 0

3 years ago