given the expression (7-4i)-(2+6i), perform the indicated operation and write the answer in the form a+bi

Answer:

58

Step-by-step explanation:

Rule: the exterior angle = the sum of the two angles that do not share a side with the exterior angle. Put in much simpler terms <DAB = <B + <C

Solution

<C + <B = <DAB

<C + 56 = 114                    Subtract 56 from both sides

<C +56-56 = 114-56          Combine

<C = 58

x = 58

Answer:

A) Apples: $30x

    Cherry: $40y

B) ($30x)+($40y)=600

Answer:

0.37

Step-by-step explanation:

we have given that emails arrives at the server at the rate of 10 per hour means [tex]\frac{10}{60}=0.166[/tex]  per minute

we have to find the probability that the time difference between the two email is more than 2 minute

so probability [tex]P\left ( X> 2 \right )=e^{-2\lambda }=e^{-2\times 0.166}=0.7166[/tex]

The probability that the time between two consecutive emails arriving at the server is more than two minutes is 0.72 (or 72%).

Given:

- Average rate of email arrivals [tex](\( \lambda \))[/tex] = 10 per hour

1. Understanding the Poisson Process:

  - In a Poisson process, the time between events (in this case, email arrivals) follows an exponential distribution.

  - If [tex]\( \lambda \)[/tex] is the average rate of events per unit time (here, per hour), the time between events (interarrival time) T follows an exponential distribution with parameter [tex]\( \lambda \)[/tex].

2. Parameter Conversion:

  - Since [tex]\( \lambda = 10 \)[/tex] emails per hour, we convert this to the rate per minute:

 [tex]\[ \lambda_{\text{minute}} = \frac{10}{60} = \frac{1}{6} \text{ emails per minute} \][/tex]

3. Probability Calculation:

  - We are interested in the probability that the time between two consecutive emails is more than two minutes.

  - Let X denote the time between two consecutive emails. X follows an exponential distribution with rate [tex]\( \lambda_{\text{minute}} = \frac{1}{6} \)[/tex].

[tex]\[ P(X > 2) = e^{-\lambda_{\text{minute}} \cdot 2} \][/tex]

  Substitute [tex]\( \lambda_{\text{minute}} = \frac{1}{6} \)[/tex]:

 [tex]\[ P(X > 2) = e^{-\frac{1}{6} \cdot 2} \] \[ P(X > 2) = e^{-\frac{1}{3}} \][/tex]

4. Calculating the Probability:

  - Use a calculator to find [tex]\( e^{-\frac{1}{3}} \)[/tex].

[tex]\[ e^{-\frac{1}{3}} \approx 0.7165 \][/tex]

  Therefore, the probability that the time between two consecutive emails is more than two minutes is approximately 0.72 (rounded to two decimal places).

This result aligns with the characteristics of a Poisson process with an average arrival rate of 10 emails per hour.

Answer:

y = 500(1.05)^x.

Step-by-step explanation:

551.25 = 500x^2    where x is the multiplier for each year.

x^2 = 551.25/500

x =  1.05

So the value after x years is 500(1.05)^x.

Answer: [tex]y=500(1.05)^x[/tex]

Step-by-step explanation:

The exponential growth equation is given by :-

[tex]y=A(1+r)^x[/tex]              (1)

, where A is the initial value of ,  r is the rate of growth ( in decimal) and t is the time period ( in years).

Given : The value of a collector’s item is expected to increase exponentially each year.

The item is purchased for $500. After 2 years, the item is worth $551.25.

Put A= 500 ;  t= 2 and y= 551.25 in (1), we get

[tex]551.25=500(1+r)^2\\\\\Rightarrow\ (1+r)^2=\dfrac{551.25}{500}\\\\\Rightarrow (1+r)^2=1.1025[/tex]    

Taking square root on both sides , we get

[tex]1+r=\sqrt{1.1025}=1.05\\\\\Rightarrow\ r=1.05-1=0.5[/tex]

Now, put A= 500 and r= 0.5 in (1), we get the equation represents y, the value of the item after x years as :

[tex]y=500(1+0.5)^x\\\\\Rightarrow\ y=500(1.05)^x[/tex]    

Answer: OPTION D.

Step-by-step explanation:

The vertex form of a quadratic function is:

[tex]y= a(x - h)^2 + k[/tex]

Where (h, k) is the vertex of the parabola and "a" is the coefficient of the squared in the parabola's equation.

We know that the vertex of this parabola is at (5,5) and we also know that when the x-value is 6, the y-value is -1.

Then  we can substitute values into  [tex]f (x) = a(x - h)^2 + k[/tex] and solve for "a". This is:

[tex]-1= a(6- 5)^2 + 5\\\\-1=a+5\\\\-1-5=a\\\\a=-6[/tex]

Answer:

D

Step-by-step explanation:

Answer:

Option 2: Yes, the distance from (-2,0) to (1,√7) is 4 units

Step-by-step explanation:

The point is:

(1,√7)

If the point lies on the circle, then the distance of point and the center of circle should be equal to the radius of the circle.

The radius can be viewed from the diagram that it is 4 units.

The center is: (-2,0)

Now, distance:

[tex]d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}}\\ d = \sqrt{(-2-1)^{2}+ (0-\sqrt{7} )^{2}}\\ d = \sqrt{(-3)^{2}+ (-\sqrt{7} )^{2}}\\=\sqrt{9+7}\\ =\sqrt{16}\\ =4[/tex]

Hence, option 2 is correct ..

For this case we must find the product of the following expression:

[tex]8y ^ 3 (-3y ^ 2) =[/tex]

We have to by law of signs of multiplication:

[tex]+ * - = -[/tex]

Also, by definition of multiplication of powers of the same base, we put the same base and add the exponents, then the expression is rewritten as:

[tex]-24y ^ {3 + 2} =\\-24y ^ 5[/tex]

Answer:

[tex]-24y ^ 5[/tex]

Answer:

The Answer is -24y^5

Step-by-step explanation:

We know this because multiplying 8 by -3 = -24

Then we have to combine the exponents and we get 5.  

Hope I helped.  I used a website called mathwa3 to help, the 3 stands for a y.

Have a great day!!!

Answer:

ΔKLJ ~ ΔRPQ by AA~

Step-by-step explanation:

Angle angle similarity needs two corresponding angles in two triangles to be same. The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~

It is a theorem in mathematics that sum of internal angles of a triangle equate to [tex]180^\circ[/tex]

Suppose that two angles are given as   [tex]a^\circ[/tex] and  [tex]b^\circ[/tex] and let there is one angle missing. Let its measure be [tex]x^\circ[/tex]

Then, by the aforesaid theorem, we get:

[tex]a^\circ + b^\circ + x^\circ = 180^\circ\\\\ \text{Subtracting a + b degrees from both sides} \\\\x^\circ = 180^\circ - (a^\circ + b^\circ)[/tex]

Two triangles are similar if two corresponding angles of them are of same measure. It is because when two pairs of angles are similar, then as the third angle is fixed if two angles are fixed, thus, third angle pair also gets proved to be of same measure. This makes all three angles same and thus, those two triangles are scaled copies of each other. Thus, they're called similar.

For given case, we've got

[tex]m\angle K = m\angle R\\m\angle J = m\angle Q\\[/tex]

Thus, for the rest of the angle pair, we have:

[tex]m\angle L = 180 - (m\angle J + m\angle K) = 180 - (m\angle Q + m\angle R) = m\angle P\\\\m\angle L = m\angle P[/tex]

Thus, given two triangles are similar by angle-angle similarity.

Thus,

The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~

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Answer:

  $26.40

Step-by-step explanation:

For a linear function, the mean of the function is the function of the mean:

  20 + 2.00·μX = 20 + 2.00·3.2 = 20 + 6.40 = 26.40 . . . . dollars

The mean total amount collected per car entering the Safari Adventure Theme Park is $26.40.

The mean of the total amount of money collected per car entering the park can be calculated by finding the expected value of the total amount, considering the price per car and per person. In this case, the mean total amount collected per car = price per car + (mean number of people per car) * price per person. Substituting the given values: 20 + 3.2 * 2 = $26.40.

Answer:

23 out of 91

around 1/3 of the class

Step-by-step explanation:

the total number of students so around the third part of the class

Answer: Adjacent Angles

A pair of angles which share a common side and vertex is called adjacent angles.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

A pair of angles which share a common side and vertex.

If two angles share a side and a vertex, they are said to be adjacent in geometry.

In other words, adjacent angles do not overlap and are placed precisely next to one another.

Therefore, the right definition is adjacent angles.

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Answer:

(a) The expression for the average cost per pair of shoes is [tex]A(x)=\frac{12000}{x}+19[/tex] and equation for the situation is [tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex].

(b) x=[tex]x\approx 4806[/tex]

(c) The average function is not defined for x=0, so the domain of the function is all real numbers except 0.

(d) The reasonable domain is all natural numbers.

Step-by-step explanation:

The cost in dollars to manufacture x pairs of shoes is given by

[tex]C(x)=12000+19x[/tex]

where, x is the pairs of shoes.

(a)

The expression for the average cost per pair of shoes.

[tex]A(x)=\frac{C(x)}{x}[/tex]

[tex]A(x)=\frac{12000+19x}{x}[/tex]

[tex]A(x)=\frac{12000}{x}+19[/tex]

This month, the manufacturer produced 1000 more pairs of shoes than last month. The average cost per pair dropped by $0.43.

[tex]A(x)-A(x+1000)=0.43[/tex]

[tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex]

Therefore the expression for the average cost per pair of shoes is [tex]A(x)=\frac{12000}{x}+19[/tex] and equation for the situation is [tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex].

(b)

On solving the above equation we get

[tex]\frac{12000}{x}-\frac{12000}{x+1000}=0.43[/tex]

[tex]\frac{12000000}{x^2 + 1000 x} = 0.43[/tex]

[tex]12000000=0.43(x^2 + 1000 x)[/tex]

[tex]12000000=0.43x^2 + 430x[/tex]

[tex]0=0.43x^2 + 430x-12000000[/tex]

Using graphing calculator we get

[tex]x\approx -5806.31,4806.31[/tex]

The pair of shoe can not be native and decimal value.

[tex]x\approx 4806[/tex]

Therefore the solution is [tex]x\approx 4806[/tex].

(c)

The average cost function is

[tex]A(x)=\frac{12000}{x}+19[/tex]

The function is not defined if the denominator is 0.

The above function is not defined for x=0, so the domain of the function is all real numbers except 0.

(d)

In the average function x represents the number of pair of shoe.

It means the value of x must be a positive integer.

Since the average function is not defined for x=0, So the reasonable domain of average function is

Domain={x : x∈Z⁺, x≠0}

Domain=N

Therefore the reasonable domain is all natural numbers.

Answer:

A

Step-by-step explanation:

Subtraction means "difference".  The only choice there that has the word "difference" in it is choice A.  

Answer:

The last choice is the one you want.

Step-by-step explanation:

Use the 5th row of Pascal's Triangle.  Since you have a 4th degree polynomial, there will be 5 terms in it.  The 5 coefficients, in order, are:

1, 4, 6, 4, 1

We will use these coefficients only up to and including the third one, since that is the one you want.  Binomial expansion using Pascal's Triangle looks like this:

[tex]1(3x)^4(y^3)^0+4(3x)^3(y^3)^1+6(3x)^2(y^3)^2+...[/tex]

That third term is the one we are interested in.  That simplification gives us:

[tex]6(9x^2)(y^6)[/tex]

Multiply 6 and 9 to get 54, and a final term of:

[tex]54x^2y^6[/tex]

The third term of the given binomial expansion is [tex]54(x^{2})(y^{5})\\[/tex]

The binomial expansion is based on a theorem that specifies the expansion of any power [tex](a+b)^{m}[/tex] of a binomial (a + b) as a certain sum of products [tex]a^{i} b^{i}[/tex], such as (a + b)² = a² + 2ab + b².

The given term is [tex](3x + y^{3}) ^{4}[/tex]

The third term in the expansion will be

[tex]4C_{2}(9x^{2})(y^{3})^{2}\\ = 54(x^{2})(y^{5})\\[/tex]

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Answer:

[tex](-\frac{3}{4})(\frac{7}{8})[/tex] ↔ [tex]-\frac{21}{32}[/tex]

[tex](\frac{2}{3})(-4)(9)[/tex] ↔ [tex]-24[/tex]

[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})[/tex] ↔ [tex]-2[/tex]

[tex](2\frac{3}{5})(\frac{7}{9})[/tex] ↔ [tex]\frac{91}{45}[/tex]

Step-by-step explanation:

The first expression is

[tex](-\frac{3}{4})(\frac{7}{8})[/tex]

On simplification we get

[tex]-\frac{3\times 7}{4\times 8}[/tex]

[tex]-\frac{21}{32}[/tex]

Therefore the product of [tex](-\frac{3}{4})(\frac{7}{8})[/tex] is [tex]-\frac{21}{32}[/tex].

The second expression is

[tex](\frac{2}{3})(-4)(9)[/tex]

On simplification we get

[tex](\frac{2}{3})(-36)[/tex]

[tex]-\frac{72}{3}[/tex]

[tex]-24[/tex]

Therefore, the product of [tex](\frac{2}{3})(-4)(9)[/tex] is [tex]-24[/tex].

Similarly,

[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})\Rightarrow (\frac{5}{16})(8)(-\frac{4}{5})=(\frac{5}{2})(-\frac{4}{5})=-2[/tex]

[tex](2\frac{3}{5})(\frac{7}{9})=(\frac{13}{5})(\frac{7}{9})=\frac{91}{45}[/tex]

The sets of numbers are:

(-7)(-1.2) <-> 8.4

(-2 1/2)(-2) <-> 5

(2.5)(-2)<->-5              

(7) (-1.2) <-> -8.4  

The given expressions involve multiplication and follow the product rule of signs. According to this rule, the product of two numbers with the same sign is positive, while the product of two numbers with different signs is negative.

(-7)(-1.2) = 8.4: Both numbers have the same sign (negative * negative), so the product is positive. The result is 8.4.

(-2 1/2)(-2) = (-5/2)(-2) = 5: Again, both numbers are negative, so the product is positive. The calculation involves multiplying mixed numbers, where -2 1/2 is equivalent to -5/2. The result is 5.

(2.5)(-2) = -5: The numbers have different signs (positive * negative), so the product is negative. The result is -5.

(7)(-1.2) = -8.4: Once more, the numbers have different signs (positive * negative), leading to a negative product. The result is -8.4.

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Answer:

2

Step-by-step explanation:

The degree of the vertex B is 2 because from vertex B there are 2 line segments coming out of it.

Another example, C has degree 4 because from it there are 4 line segments coming from it.

The intersection of plane GFL and a plane that contains points A and C can be any plane that passes through those two points.

In mathematics, an intersection of two planes is the set of points that are common to both planes.

In this case, we want to find the intersection of plane GFL and a plane that contains points A and C.

Since both points A and C lie on the same plane, any plane that contains both points A and C would intersect plane GFL at those points.

Therefore, any plane that passes through points A and C would be an intersection of plane GFL and a plane that contains points A and C.

Examples of planes that contain points A and C are:

A plane that contains the line segment AC

A plane that is perpendicular to line AC at point A

A plane that is perpendicular to line AC at point C

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Answer:

  Your work is correct as far as it goes. Now eliminate the terms that are zero.

Step-by-step explanation:

Multiplying anything by zero gives zero. Adding zero is like adding nothing. Zero is called the "additive identity element" because ...

  a + 0 = a

Adding zero doesn't change anything. You can (and should) drop the zero if your goal is to simplify the expression.

[tex]a. \quad x_{f}=v_{0}\\\\b. \quad x_{f}=v_{0}t\\\\c. \quad v_{f}^2=v_{0}^2[/tex]

Answer:

  216

Step-by-step explanation:

(g∘f)(x) = g(f(x))

f(2) = 2·2 +2 = 6

g(f(2)) = g(6) = 6³ = 216

Answer:

216

Step-by-step explanation:

Correct Plato

Answer:

5

Step-by-step explanation:

Plug in 24 for x in your g(x) equation.

[tex]g(24)=\sqrt{24-8} \\g(24)=\sqrt{16} \\g(24)=4[/tex]

Next, plug in your g(x) value, 4, to your f(x) equation for x.

[tex]f(4)=2(4)-3\\f(4)=8-3\\f(4)=5[/tex]

Answer:

  573.6 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship of right triangle sides and angles:

  Tan = Opposite/Adjacent

This tells us ...

  tan(61°) = (height)/(distance to first point)

or

  distance to first point = height/tan(61°)

Likewise, ...

  distance to second point = height/tan(32°)

Then the difference of the distances is ...

  distance to second point - distance to first point

     = height/tan(32°) -height/tan(61°)

  600 ft = height × (1/tan(32°) -1/tan(61°))

Dividing by the coefficient of height, we have ...

  height = (600 ft)/(1/tan(32°) -1/tan(61°)) ≈ (600 ft)/(1.04603) ≈ 573.6 ft

Answer:

574

Step-by-step explanation:

Answer:

  Yes

Step-by-step explanation:

The law of cosines relates the three sides of a triangle with the cosine of the angle opposite one of them. It is useful for finding an angle of the triangle when only the side lengths are given, as here.

Answer:

Step-by-step explanation:

The base of the exponential function is 1 + r.

The initial value is P.

The exponent is t.

The base of the exponential function is 1 + r

exponent is t, and

initial value is P

The mathematical expression for an exponential function is f (x) = a ˣ, where “x” denotes a variable and “a” denotes a constant. This constant is referred to as the base of the function and should be greater than zero. The most common use exponential function is with base e

Given A coin formula V(t) = P(1+r)^t

to find the initial value put t = 0

V(0) = P(1+r)⁰

V(0) = P

P is the initial value

and exponent is the term which is in the power of any exponential function

here t is exponent and (1+r) is base function

Hence according to coin formula The base of the exponential function is 1 + r; exponent is t;  and initial value is P.

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For this case, we have by definition that:

[tex]C = (F-32) * \frac {5} {9}[/tex]

If they tell us that the base temperature is 50 degrees Fahrenheit, then we substitute:

[tex]C = (50-32) * \frac {5} {9}\\C = 18 * \frac {5} {9}\\C = 2 * 5\\C = 10[/tex]

Finally, the temperature equals 10 degrees Celsius.

Answer:

10 degrees Celsius

The temperature in Celsius when it is 50 degrees Fahrenheit is 10 degrees Celsius, calculated using the conversion formula Celsius = (Fahrenheit - 32) × 5/9.

To convert a temperature from Fahrenheit to Celsius, we use the formula: Celsius = (Fahrenheit - 32) × 5/9. If the temperature is 50 degrees Fahrenheit, we subtract 32 from 50, giving us 18. Then we multiply 18 by 5/9, resulting in 10. Therefore, the temperature in Celsius is 10 degrees Celsius.

Thus, when the temperature is 50°F, it is equivalent to 10°C.

Answer:

  [tex]\cos{A}=\pm\sqrt{\dfrac{1+\cos{x}}{2}}[/tex]

Step-by-step explanation:

[tex]\cos{A}=\cos{\frac{x}{2}}=\pm\sqrt{\dfrac{1+\cos{x}}{2}}[/tex]

Apparently, you're supposed to recognize that the formula tells you the value of cos(x/2).

Answer:

[tex]\large\boxed{|5x-2|\leq8}[/tex]

Step-by-step explanation:

[tex]-1.2\leq x\leq2\qquad\text{multiply all sides by 5}\\\\-6\leq5x\leq10\qquad\text{subtract 2 from both sides}\\\\-8\leq5x-2\leq8\iff|5x-2|\leq8[/tex]

Answer:

1/3 = .33

THE UNIT RATE IS 1 TO 3

Answer:

infinite slope

Step-by-step explanation:

Note that x=3 is simply a vertical straight line that passes through the point (3,y) for all real values of y

Also recall that the slope of a vertical straight line is undefined  (or infinite slope)

hence the slope of x=3 is infinite.

Answer:

Step-by-step explanation:

when logs are added, they can be multiplied to produce a simplified log.

log_5(4*7) + log_5(2)

log_5(4*7*2)

log_5(56)

The simplified expression for [tex]\((5 \cdot x^3) / (x^2)\) is \(5 \cdot x\).[/tex]

When x = 2, the result is [tex]\(5 \times 2 = 10.[/tex]

The answer is 10.

To evaluate the expression[tex]\((5 \cdot x^3) / (x^2)\) for \(x = 2\),[/tex]  we first need to simplify the given expression.

Given:

[tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]

Simplifying, we divide the powers of x :

[tex]\[ x^3 / x^2 = x^{3-2} = x^1 = x. \][/tex]

So the expression simplifies to:

[tex]\[ 5 \cdot x. \][/tex]

Now substitute x = 2 :

[tex]\[ 5 \cdot 2 = 10[/tex]

Thus, the value of [tex]\((5 \cdot x^3) / (x^2)\) when \(x = 2\)[/tex] is: 10.

Question : Evaluate the expression [tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]for  x = 2.​ start fraction, 5, dot, x, cubed, divided by, x, squared, end fraction for x=2x=2x, equals, 2.