Rewrite the expression x^2-12x as a(x-h)^2+k

Answer:

16 50 min

Step-by-step explanation:

The domain of y = sec(x) is all real numbers except for values where the cosine function is zero.

The domain of y = sec(x) is all real numbers except for values where the cosine function is equal to zero. Since the secant function is the reciprocal of cosine, it is undefined when cosine is zero.

So, the domain of y = sec(x) is all real numbers except for values of x where cos(x) = 0.

For example, if we consider the unit circle, the cosine function is equal to zero at π/2 and 3π/2. Therefore, the domain of y = sec(x) would exclude these values.

The domain of [tex]\( y = \sec(x) \)[/tex] is all real numbers except [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex], [tex]\( n \)[/tex] integer.

Let's find the domain of [tex]\( y = \sec(x) \)[/tex].

The secant function, [tex]\( \sec(x) \)[/tex], is defined as the reciprocal of the cosine function, [tex]\( \cos(x) \)[/tex]. So, [tex]\( \sec(x) = \frac{1}{\cos(x)} \).[/tex]

The cosine function is defined for all real numbers, except where the denominator becomes zero, because division by zero is undefined.

So, to find the domain of [tex]\( \sec(x) \)[/tex], we need to find where [tex]\( \cos(x) \)[/tex] is not zero.

The cosine function has a range between -1 and 1. It equals zero at [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x = -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.

So, the domain of [tex]\( \sec(x) \)[/tex] is all real numbers except where [tex]\( \cos(x) = 0 \)[/tex]. Therefore, the domain of [tex]\( \sec(x) \)[/tex] is [tex]\( x \neq \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x \neq -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.

In interval notation, the domain of [tex]\( \sec(x) \)[/tex] is:

[tex]\[ (-\infty, -\frac{\pi}{2}) \cup (-\frac{\pi}{2}, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \infty) \][/tex]

Final answer:

In this question, the arrangements of characters sitting together and the options for hamburger toppings are explored using permutations and combinations in Mathematics for High School.

Explanation:

(1) When the elf and the dwarf insist on sitting next to each other, treat them as one entity. Then, there are 4 entities: {elf & dwarf}, hobbit, wizard, man. This gives 4! ways to arrange them, and the elf and dwarf can be arranged within their entity in 2! ways.

So, the total ways are 4! x 2! = 48 ways.

(2) For the hamburger order, since you can choose to include/exclude each topping independently, there are 2 options for each topping (with or without).

Hence, the total ways to order the hamburger are 2⁵ = 32 ways.

Answer:

Step-by-step explanation:

Givens

Now, remember that all coordinates with the form (a,0), represents points on the x-axis, because the y-coordinate is zero.

In this case, we have negative horizontal coordinates and a null vertical coordinate, like (-a,0).

This points is on the x-axis, because y-value is null. Actually, it's on the negative part of x-axis, because its horizontal coordinate is negative.

Therefore, the right answer is x-axis.

perimeter = 20 +20 +24 = 64 feet

 area = 12^2 + x^2 = 20^2

144 + x^2 = 400

x^2 = 256

x = sqrt(256) = 16 feet

area = 1/2 x 16 x 24 = 192 square feet

 cost = 192 x $2 = $384

The value of d, when the function is at its minimum is -4.

A function is a law that relates two variables namely, a dependent and an independent variable.

A function always has a defined range and domain, domain is all the value a function can have as an input and range is all the value that a function can have.

The function is of various types, logarithmic, exponential, quadratic, radical etc.

The function is y = cos [tex]\rm \theta[/tex] + d

The minimum value of the function, y = cos [tex]\rm \theta[/tex] + d is -5.

The minimum value is the lowest value of the function.

The minimum value of cos [tex]\rm \theta[/tex] is at 180 degree equals to  -1

Substituting the value in the equation.

-5 = - 1 + d

d = -5 +1

d = -4

To know more about Function

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Answer:

the answer is A

Step-by-step explanation:

ttm

Final answer:

The equation relating the total amount of money S in Carlos's savings to the number of weeks W he adds money is S = 750 + 40W. By substituting W with 11, we find that after 11 weeks, Carlos will have $1,190 in his savings account.

Explanation:

The question involves creating a linear equation to represent the relationship between the total amount of money S in Carlos's savings account and the number of weeks W he has been adding money. The equation can be written as S = 750 + 40W, where 750 represents the initial amount and 40 is the amount added each week. To find the total amount of money after 11 weeks, substitute W with 11:

S = 750 + 40(11) = 750 + 440 = 1190

Therefore, after 11 weeks, the total amount of money in the savings account would be $1,190.

The conjugate of the given complex number is:

                        [tex]2+8i[/tex]

We know that any complex number is written in the form of:

            [tex]z=a+ib[/tex]

where a and b are real numbers.

The conjugate of the complex number is given by:

              [tex]\bar z=\bar {a+ib}\\\\i.e.\\\\\bar z=a-ib[/tex]

Here we are given that:

We have a complex number such that the  real part of a complex number is 2 and it's imaginary part is -8.

i.e.

a=2 and b= -8

i.e. the complex number is:

[tex]z=2+(-8)i[/tex]

Hence, the conjugate of this number is:

[tex]\bar z=2-(-8)i\\\\i.e.\\\\\bar z=2+8i[/tex]

the answer is A

700 x 5 = 3500

30 x 5 = 150

7 x 5 = 35

3500 + 150 +35 = 3685

700 x 200 = 140,000

30 x 200 = 6000

7 x 200 = 1400

140000 + 6000 + 1400 = 147400

for the length of the side that is not given:

look at it as part of a triangle with the legs being 4m tall by 6 m wide

 so 4^2 + 6^2 = X62

16+36 = 52^2

square root(52) = 7.211 m

 does it as to round of to nearest whole number? nearest tenth?

round off answer as needed

Answer:

Step-by-step explanation:

The given function is

[tex]f(x)=x^{4}-32x^{2} -144[/tex]

The given zero to this function is

[tex]x=-2i[/tex]

Remember that a function has so many roots as its grade dictates. So, in this case, the function grade is four, which means it has four solutions.

Now, the given function is an imaginary number, which happens in pairs, that means the second root must be [tex]x=2i[/tex], because a function can have complex roots as pairs, 2, 4, 6,... many solutions.

The other two solutions are 6 and -6, because if we replace them into the function, it will give zero.

[tex]f(6)=6^{4}-32(6)^{2} -144=0\\f(-6)=(-6)^{4}-32(-6)^{2} -144=0[/tex]

Therefore, the other three solutions missing are: c) 2, 6, -6.

(The image attached shows the real solutions).