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3 years ago

Find the following f(x)=x^2 - 4x - 12 A) f(a+2) B) f(a+h)

Mathematics

1 answer:

NikAS [45]3 years ago

6 0

(A) f(a + 2) = a² - 16

substitute x = a + 2 into f(x)

f(a + 2) = (a + 2)² - 4(a + 2) - 12

= a² + 4a + 4 - 4a - 8 - 12

= a² - 16

(B ) f(a + h) = a² + 2ah + h² - 4a - 4h - 12

substitute x = a + h into f(x)

f(a + h) = a² + 2ah + h² - 4a - 4h - 12

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Circle O, with center (x, y) passes through the points A(0, 0), B(-3, 0), and C(1, 2). Find the coordinates of the center of the

KonstantinChe [14]

Answer:

The center of the circle is

$(-\frac{3}{2},2)$

Step-by-step explanation:

Let the equation of the circle be

$x^2+y^2+2ax+2by+c=0$ , where (-a,-b) is the center of this circle.

The points lying the circle must satisfy the equation of this circle.

A(0,0)

We substitute this point to get;

$0^2+0^2+2a(0)+2b(0)+c=0$

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$(-3)^2+0^2+2a(-3)+2b(0)+c=0$

$\implies 9+0-6a+0+c=0$

$\implies -6a+c=-9$

But c=0

$\implies -6a=-9$

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C(1,2)

$1^2+2^2+2a(1)+2b(2)+c=0$

$1+4+2a+4b+c=0$

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Put the value of 'a' and 'c' to find 'b'

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3 years ago

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We are given an angle of 60° and a side of 15 cm.

We are given the opposite and is looking for the hypotenuse so we will use the sine ratio to find x.

sin = opp/hyp

hyp = 15 / sin 60

hyp = 17.32...

We can also use the tangent ratio to find the adjecent and then use pythagorean to find x.

tan = opp/adj

adj = 15 / tan 60

adj = 8.660.....

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since the square root of 300 is an irrational number, we have to turn it into a mixed radical.

The answer would be the top one.

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3 years ago

The two triangles are similar to each other. How long is the side labeled “?”

Mandarinka [93]

Answer:

Step-by-step explanation:

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3 years ago

4. The population of Bay Village is 35,000 today. Every year the

frosja888 [35]

Answer:

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Step-by-step explanation:

In principle Linear Models are employed when we want to define a relationship between an independent and a dependent variable. Linear Models are also known as Functions , where one variable is expressed as a function of at least one other variable. The most common example would be a dependent variable $y$ that is directly linked as a response to any changes of an independent variable $x$ . The most common expression of such relationship would be $y=ax$ where $a$ is the relationship factor between $y$ and $x$ and is also known as the slope of the function (representing a rate of change of that function).

In this question we are told that the population of Bay Village today is 35,000. So we know this is our constant variable, lets call it $b$ .

Next we know that every year the population is increased by 750 people. So we know that our variable and thus our independent variable is every year which we shall call $x$ and our fixed factor is the 750 increment which we will call $a$ .

From that we can conclude that:

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Year 3 Population: 35,750 + 750 = 36,500

And so on and so forth.

So we want to express the above as a Linear Model of the form:

$y = ax + b$ Eqn(1).