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NemiM [27]
3 years ago
7

I for really need help with this one and a couple of others HELPPPP

Mathematics
1 answer:
Keith_Richards [23]3 years ago
8 0

Check the picture below.

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Find the equation of the circle with center (4,5) which passes through the y-intercept of the line 5x-2y+6=0​
Elena-2011 [213]

Answer:

(x-4)^2 + (y-5)^2 = 20

Step-by-step explanation:

Rearrange the line equation of 5x - 2y + 6 = 0

So y = 5/2x +3

The y-intercept of the line equation is 3 as when x=0, y=3.

We know the Circle has the formula (x-4)^2 + (y-5)^2 = ?^2 from the question but with the intercept, we can find the entire equation as the y-intercept is (0,3) so we can substitute it into the equation to find the full equations so:

(0-4)^2 + (3-5)^2 = ?^2

This simplifies to:

(-4)^2 +(-2)^2 = ?^2

16 + 4 = 20 = ?^2

The answer is 20 so the equation of the circle is (x-4)^2 + (y-5)^2 = 20

3 0
2 years ago
From 1990 to 2000, the population of Florida increased by 2.13% per year. The population (in millions) in the year 1990 was 16 E
belka [17]

Answer:

19 million

Step-by-step explanation:

So generally whenever we express a exponential function, it's in the form: y=a(b)^x

where a=initial value aka when x=0

in this case, b can be expressed as: 1+r, where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213

This gives us the following equation: y=16(1.0213)^x

To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.

So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.

When x=1, we get: 1.0213(16), which can be expressed as a 2.13% increase from year 0

When x=2, we get: 1.0213(1.0213(16)), which can be expressed as a 2.13% increase from year 1

when x=3, we get: 1.0213(1.0213(1.0213(16))), which can be expressed as a 2.13% increase from year 2.

In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).

So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990

We get the following equation: y=16(1.0213)^7

Using a calculator this simplifies to approximately: 18.5436

Rounding this to the nearest integer would yield 19, and since the values are expressed in millions, the answer would be 19 million

4 0
1 year ago
Which relation is a function
faltersainse [42]

Answer:

The relation on the bottom left, where the mouse is, is the function. Hope this helps :)

4 0
3 years ago
Math worth 10 points thx
bija089 [108]

what thy answer child

6 0
3 years ago
Find the 8th term of the geometric sequence 5, -15, 45
FrozenT [24]

Answer:

a₈ = - 10935

Step-by-step explanation:

the nth term of a geometric sequence is

a_{n} = a₁ (r)^{n-1}

where a₁ is the first term and r the common ratio

here a₁ = 5 and r = \frac{a_{2} }{a_{1} } = \frac{-15}{5} = - 3 , then

a₈ = 5 × (-3)^{7} = 5 × - 2187 = - 10935

6 0
2 years ago
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