if f(x) = -3 -5 and g(x) =4x - 2, find (f+g)(x)

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

x=26.44

rounded to the nearest hundredth.

Step-by-step explanation:

Soh Cah Toa

We need opposite for x and adjacent for 44

Length × Tan (Angle)

44 × Tan (31)=26.43786724

Answer:

1960 π

Step-by-step explanation:

If R is the outer radius and r the inner radius of a hollow cylinder of height h, then volume of cylinder = π (R² - r²)h

Here R = 18/2 = 9

and r= 10/2 =5

Volume = π (9² - 5²) . 35 =  π x 56 x 35 = 1960 π

Step-by-step explanation:

3 weeks=3x7 days

=21 days

3 weeks to 10 days

21/10

mark as brainliest

Answer:

C

Step-by-step explanation:

looked up on Quizlet so yeah

Step-by-step explanation:

in equation 1

y=4x+12

so now

eqs 2

2y=4+3x

then

-y=x+8

y= -x-8

so

-x-8=4x+12

-20=5x

-4=x

so

y= 4-8

y=-4

Answer:

a) -4(3x + 4)

Step-by-step explanation:

Factor -12w - 16.

-4(3x + 4)

Therefore, the value of x in the right triangle is 24 cm.

A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is formed by connecting three non-collinear points. The sum of the interior angles of a triangle is always 180 degrees, and the measure of each angle depends on the lengths of the sides and the type of triangle. There are different types of triangles based on their side and angle measures, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have various properties and formulas that are used in geometry and other fields.

Here,

In a right triangle, the side opposite to the right angle is the longest side and is called the hypotenuse. Therefore, in this case, 25 cm is the hypotenuse of the triangle.

Using the Pythagorean Theorem, we can find the missing length x:

a² + b² = c²

where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

In this case, a = 7 cm, b = x, and c = 25 cm.

Substituting these values into the Pythagorean Theorem, we get:

7² + x² = 25²

49 + x² = 625

x² = 625 - 49

x² = 576

x = √576

x = 24

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Answer:

A.=False

B.=True

C.=False

D.=True

Step-by-step explanation:

The original ration is 2 gallons of water for 4 players.

Each player requires 1/2 gallon of water.

To get the amount of water needed multiply 1/2 by the amount of players.

1*(1/2) does not equal 1

2*(1/2) equals 1

10*(1/2) does not equal 4

30*(1/2) equals 15

Answer:  540 ft

Step-by-step explanation:

When given the equation in standard form y = ax² + bx + c,

the Axis of Symmetry can be found using the formula x = -b/(2a).

Plug that x-value into the given equation to find the y-value which represents the max (if "a" is negative) or the min (if "a" is positive)

y = -10x² + 160x - 100

      ↓          ↓        ↓

   a= -10   b=160  c= -100

\(\text{AOS:}\quad x=\dfrac{-b}{2a}\quad =\dfrac{-(160)}{2(-10)}\quad =\dfrac{-160}{-20}\quad =8\)

Max: y = -10(8)² + 160(8) - 100

          = -10(64) + 1280 - 100

          = -640 + 1180

         =  540

Answer:

7 weeks.

Step-by-step explanation:

Divide 105 by 15, after working with all the numbers you should get 7. Your answer is 7 weeks! Hope it helped!

OwO

Answer:

SO EVERYONE WOULD SHOUT LOOK AT THE S CAR GO

Step-by-step explanation:

Answer:

= 15.285714285714

Step-by-step explanation:

A statistical test always produces evidence, but never complete evidence.

A statistical test is a way to determine if a claim (like a hypothesis) about a quantitative attribute of a population is true or not. As a result, it serves as a tool for making quantitative assessments of a process or processes.

The objective is to determine whether there is enough evidence to "reject" a process theory or hypothesis. In other words, a statistical test will always yield evidence, but this evidence is never a full indicator; it is either sufficient or it is not.

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Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

f(m) = 3 * 1.09 * m = 3.27 * m

A:

solve f(m) = 5.98 to find how long it takes for fish to reach that length

5.98 = 3.27 * m

m = 5.98/3.27 = 1.83 months

A reasonable domain would technically depend on other factors like standard deviation, however, a domain of [0,3] could be reasonable without further information.

B:

The y intercept (0 because f(0)=0 ) represents the length of fish at the beginning of the marine biologists study, or when the number of months is zero

C:

Rate of change equals the change in y over the change in x.

\(\frac{f(8)-f(2)}{8-2}=\frac{26.16-6.54}{6}=\frac{19.62}{6}=3.27\frac{cm}{month}\\\)

This represents the average number of cm the length of the fish change per month in the interval [2, 8]

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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Answer:

$1,007.81

Step-by-step explanation:

Mrs. Grubbs would get more cookie to eat by choosing the 4 smaller cookies with diameter 5 cm each rather than the single cookie with diameter 14 cm.

To compare the amount of cookie Mrs. Grubbs would get by eating a single cookie with diameter 14 cm and 4 smaller cookies with diameter 5 cm each, we need to consider the total area of the cookies.

The area of a cookie with diameter 14 cm can be calculated as follows:

A = πr^2 = π(7 cm)^2 = 49π cm^2

where r is the radius of the cookie.

On the other hand, the area of a single small cookie can be calculated as follows:

A1 = \(πr^2\) = \(π(2.5 cm)^2\)= \(6.25π cm^2\)

where r is the radius of the small cookie.

Therefore, the total area of 4 small cookies is:

A2 = 4A1 = \(4(6.25π cm^2)\) = \(25π cm^2\)

Comparing the two options, we see that the total area of the 4 small cookies is greater than the area of the single large cookie:

A2 > A

\(25π cm^2 > 49π cm^2\)

It's worth noting that this comparison assumes that the thickness or volume of the cookies is the same for both options. If the cookies have different thicknesses, then the comparison would need to take into account the volume of the cookies instead of just the area.

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Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

\( - 16 = a - 19\)

\(a = - 16 + 19\)

\(a = 3\)

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Answer: $ 73.20

Step-by-step explanation:

60+(60*0.07)+(60*0.15)=73.2

The restriction of the domain of the function will be y = (x - 2)², x ≥ 2. Then the correct option is B.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

Then the parabolic function is given below.

y = (x - 2)²

The restriction of the domain will result in the inverse being a function given as,

x - 2 ≥ 0

x ≥ 2

The restriction of the domain of the function will be y = (x - 2)², x ≥ 2. Then the correct option is B.

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\(\frac{2(3b+2)}{3a}\).

\(\frac{2}{3a} *(3b+2)\)

Take a look at the attached image.

\((\frac{2}{3a} *3b)+(\frac{2}{3a} *2)\\ \\\frac{2*3b}{3a} +\frac{2*2}{3a}\\ \\\frac{6b}{3a} +\frac{4}{3a}\)

\(\frac{6b+4}{3a}\)

\(\frac{2(3b+2)}{3a}\).

Answer:

\(\displaystyle F(v) = \frac{9}{5}(v-273)+32\)

Step-by-step explanation:

The temperature T(d) in degrees Fahrenheit in terms of Celsius d is given by:

\(\displaystyle T(d)=\frac{9}{5}d+32\)

And the temperature C(v) in degrees Celsius in terms of Kelvin v is given by:

\(C(v)=v-273\)

We want the formula for the temperature F(v) in degrees Fahrenheit in terms of the Kelvin temperature.

So, we can use a composition of functions. Since T(d) outputs the temperature in Fahrenheit and C(v) inputs the temperature in Kelvin, T(C(v)) will be the temperature in Fahrenheit given the temperature in Kelvin. So:

\(\displaystyle T(C(v))=\frac{9}{5}(C(v)))+32\)

Substitute:

\(\displaystyle T(C(v)) = F(v) = \frac{9}{5}(v-273)+32\)

Therefore:

\(\displaystyle F(v) = \frac{9}{5}(v-273)+32\)

Answer:

4y - 5x + 7 = 0

Step-by-step explanation:

To get to the equation of its perpendicular, firstly we'll need the slope of this line.

\( \boxed{ \mathfrak{slope = \red{ \mathsf{ \frac{y_{2} - y _{1}}{x_{2} - x _{1}} }}}}\)

(x1, y1) and (x2, y2) are any two points kn the given line.

I caught two points that lie on this graph, and they are :

\( \mathsf{ \implies \: slope = \frac{y_{2} - y _{1}}{x_{2} - x _{1}} }\)

\(\mathsf{ \implies \: slope = \frac{ - 6- 2}{8 - ( - 2)} }\)

\(\mathsf{ \implies \: slope = \frac{ -8}{8 + 2} }\)

(two minus make a plus)

\(\mathsf{ \implies \: slope = \frac{ -8}{10} }\)

\(\mathsf{ \implies \: slope = \frac{ \cancel{-8} {}^{ \: \: - 4} }{ \cancel{10} \: \: {}^{5} } }\)

slope = -4 /5

That's the slope of the given line.

Now, the slope of the line perpendicular to this one will be equal to its negative reciprocal.

slope (perpendicular) = 5/ 4

and they've given a point that lies in the perpendicular, it is = (3, 2)

For equation of a line thru a point, we have:

\( \boxed{ \mathsf{ \red {y} - {y}^{1} = slope \times (\red{x} - {x}^{1} }) }\)

the letters in red are the variables that won't be changed thruout.

and (x¹, y¹) are the points on the line.

\( \implies \mathsf{y - 2 = \frac{5}{4} \times (x - 3) }\)

\( \implies \mathsf{(y - 2)4 = 5x - 15}\)

\( \implies \mathsf{4y - 8 = 5x - 15}\)

\( \implies \mathsf{(4y - 5x) - 8 + 15 = 0}\)

\( \implies \mathsf{4y - 5x + 7 = 0}\)

and thats the required equation of the perpendicular.

It takes time of near about 35 year.

Given that,

Storage capability of computers has been doubling every 5 years

The date of 1st computer made = 1980

computer could store 5 megabytes,

Now,

We can use the following calculation to determine how long it took computers to store 100 megabytes:

Therefore,

Log₂ (final amount / beginning amount)

=  Log₂ (100 / 0.5)

= log₂ (200)

= 7.64 is the number of doublings.

If each doubling takes five years, then it would take computers just over seven doublings or almost 35 years to store 100 megabytes.

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