A number written in the form a + bi is called a _____ number.

A. Discriminant

B. Quadratic

C. Complex

D. Linear

Answer:

[tex] \: [/tex]

Step-by-step explanation:

It is given that, the radius of a circle is 8 inches and we are to find the circumference of the circle.

[tex] \: [/tex]

To find the circumference of the circle we must know this formula first :

[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: Circumference_{(circle)}= 2 \pi r}}}}}} \: \: \bigstar \\ \\[/tex]

Where

Now substituting the values in the formula :

[tex]\\{ \longrightarrow \qquad{ {{\sf{{ \: Circumference_{(circle)}= 2 \times 3.14 \times 8}}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{\sf{{ \: Circumference_{(circle)}= 3.14 \times 16}}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ { \pmb{\frak{{ \: Circumference_{(circle)}= 50.24}}}}}} \: \: \\ \\[/tex]

Therefore,

Answer:

C = 50.24 in

Step-by-step explanation:

Given that,

→ Radius (r) = 8 in

Formula we use,

→ 2πr

The circumference of the circle will be,

→ 2πr

→ 2 × 3.14 × 8

→ 6.28 × 8

→ [ 50.24 in ]

Hence, the circumference is 50.24 in.

Answer:

4/50

Step-by-step explanation:

12,24,36,48 are multiples of 12

Answer:

Domain is all real #s

Range is (-∞, 4]  or y < 4

Step-by-step explanation:

The volume is 54,437.52.

Answer:

54,437.52 ( fifty four thousand four hundred thirty seven and fifty two thousanths.)

Step-by-step explanation:

The number of ways to arrange the 9 paintings is 362880, and there are 126 ways to display only 4 out of the 9 paintings

The number of paintings is given as:

n = 9

The number of arrangement is then calculated using:

n! = 9!

Evaluate the factorial

n! = 362880

To select 4 paintings from a total of 9, we make use of the following combination formula

Ways  = 9C4

Evaluate the above expression using a calculator

Ways  = 126

Hence, there are 126 ways to display only 4 out of the 9 paintings

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The total amounts of money which Mrs. Reynolds now has according to the descriptions in the task content is; $68.

It follows from the task content that;

On this note;

Hence, it follows that the amount of money, s she has now is;

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Answer:

¿Cuál es la probabilidad de aprobar un examen al azar?

Resultado de imagen para ¿Cuál es la probabilidad de adivinar correctamente al azar exactamente una respuesta correcta?

La probabilidad de acertar respondiendo al azar una pregunta es de una entre cuatro: 1/4 = 0.25. Normalmente decimos un 25% de probabilidad de acertar. La probabilidad de fallar sería tres entre cuatro: 3/4 = 0.75. O sea un 75%.

Step-by-step explanation:

this is the best ✔️ 5+(2-3)49_.56837659=0-9

Step-by-step explanation:

0 upto 9

Answer:

6

Step-by-step explanation:

Find the cube root of 216

Answer:

Step-by-step explanation:

The solution is given

[tex] |6x + 2| - 6 > 8[/tex]

[tex] |6x + 2| > 8 + 6[/tex]

[tex] |6x + 2| > 14[/tex]

Now wit will be swprated into two parts

First part

[tex]6x + 2 > 14 [/tex]

[tex]6x > 14 - 2[/tex]

[tex]x > 12 \div 6[/tex]

[tex]x > 8[/tex]

The second part is

[tex]6x + 2 > - 14[/tex]

[tex]6x > - 14 - 2[/tex]

[tex]x > - 16 \div 6[/tex]

This question has two answers

Answer:

The length of the hypotenuse ≈ 39.7 cm

Explanation:

Since the given triangle is a right-angled triangle, this means that we can apply the Pythagorean theorem.

The equation for Pythagorean calculation is:

(hypotenuse)² = (first leg)² + (second leg)²

In the given, we have:

first leg = 30 cm

second leg = 26 cm

Substitute with the givens in the above equation to get the hypotenuse as follows:

(hypotenuse)² = (30)² + (26)²

(hypotenuse)² = 1576

This means that:

either hypotenuse = √1576 = 39.69 ≈ 39.7 cm ..........> accepted

or hypotenuse = -√1576 = -39.69 ......> rejected as length can't be negative

Hope this helps :)

Answer:

C

Step-by-step explanation:

Answer:

75 ounces

Step-by-step explanation:

Divide 180 by 12 to see how much a single jar weighs

180/12 = 15

Multiply the weight of one jar by how many jars you need

15x5 = 75

Answer: 75 ounces

Step-by-step explanation:

The 12 jars combined weigh 180 ounces in total. We find the weight per jar by dividing 180 ounces by 12 which gives is 15 ounces per jar. We find the weight of 5 jars by multiplying 5 jars by 15 ounces. Here are the calculations as follows.

Answer:

The survey sample is residents of the neighboring city with a last name starting with ”S” and whose phone number is listed in the phone book.

Step-by-step explanation:

that one makes the most sense

Answer:

24sq.ft

Step-by-step explanation:

Here,

→Base = 6ft, Height = 4ft

→ 6*4ft

→24sq.ft

Please mark me as brainliest

Answer:

I) 23

K) 96

J) 77

Step-by-step explanation:

All angles of a triangle equal up to 180

6x+4x-3+x+7=180

11x+4=180

11x=176

x=16

Answer:

See below for answers and explanations (along with a graph for #3)

Step-by-step explanation:

Problem #1

Applying scalar multiplication, [tex]-4w=-4\langle-96,-180\rangle=\langle384,720\rangle[/tex].

Its magnitude would be [tex]||-4w||=\sqrt{384^2+720^2}=816[/tex].

Its direction would be [tex]\displaystyle\theta=tan^{-1}\biggr(\frac{720}{384}\biggr)\approx61.927^\circ\approx62^\circ[/tex].

Thus, B) 816; 62° is the correct answer

Problem #2

Find the time it takes for the ball to cover 13ft:

[tex]x=(24\cos48^\circ)t\\13=(24\cos48^\circ)t\\t\approx0.8095[/tex]

Find the height of the ball at the time it takes for the ball to cover 13ft:

[tex]y=6.1+(24\sin48^\circ)t-16t^2\\y=6.1+(24\sin48^\circ)(0.8095)-16(0.8095)^2\\y\approx10.053[/tex]

Thus, A) 10.053 is the correct answer

Problem #3

We have [tex]u=\langle0,-8\rangle[/tex] and [tex]v=\langle6,0\rangle[/tex] as our vectors. Thus, [tex]u+v=\langle0+6,-8+0\rangle=\langle6,-8\rangle[/tex]. Attached below is the correct graph. You can also solve the problem visually by using the parallelogram method where the resultant vector is the diagonal of the parallelogram.

Problem 4 (#7)

[tex]\displaystyle t \cdot v=(7)(-10)+(-3)(-8)=-70+24=-46[/tex]

Thus, C) -46 is the correct answer

Problem 5 (#8)

Find [tex]r[/tex] and [tex]\theta[/tex]:

[tex]r=\sqrt{x^2+y^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}\approx8.246[/tex]

[tex]\displaystyle\theta=tan^{-1}\biggr(\frac{y}{x}\biggr)=tan^{-1}\biggr(\frac{-8}{2}\biggr)\approx-75.964^\circ[/tex]

Find the true direction angle accounting for Quadrant IV:

[tex]\theta=360^\circ-75.964^\circ=284.036^\circ[/tex]

Write the complex number in polar/trigonometric form:

[tex]z=8.246(\cos284.036^\circ+i\sin284.036^\circ)[/tex]

Thus, C) 8.246(cos 284.036° + i sin 284.036°) is the correct answer

Problem 6 (#12)

Eliminate the parameter and find the rectangular equation:

[tex]x=3t\\\frac{x}{3}=t\\ \\y=t^2+5\\y=(\frac{x}{3})^2+5\\y=\frac{x^2}{9}+5\\9y=x^2+45\\0=x^2-9y+45\\x^2-9y+45=0[/tex]

Thus, D) x^2-9y+45=0 is the correct answer

Problem 7 (#13)

Find the magnitude of the vector:

[tex]||v||=\sqrt{(-77)^2+36^2}=85[/tex]

Find the true direction of the vector accounting for Quadrant II:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{36}{-77}\biggr)\approx-25^\circ=180^\circ-25^\circ=155^\circ[/tex]

Write the vector in trigonometric form:

[tex]w=85\cos155^\circ i+85\sin155^\circ j[/tex]

Thus, D) w=85cos155°i+85sin155°j is the corrwect answer

Problem 8 (#15)

[tex]\frac{z_1+z_2}{2}=\frac{(3-7i)+(-9-19i)}{2}=\frac{-6-26i}{2}=-3-13i=(-3,-13)[/tex]

Thus, C) (-3,-13) is the correct answer

Problem 9 (#16)

Treat the golf ball and wind as vectors:

[tex]u=\langle1.3\cos140^\circ,1.3\sin140^\circ\rangle[/tex] <-- Golf Ball

[tex]v=\langle1.2\cos50^\circ,1.2\sin50^\circ\rangle[/tex] <-- Wind

Add the vectors:

[tex]u+v=\langle1.3\cos140^\circ+1.2\cos50^\circ,1.3\sin140^\circ+1.2\sin50^\circ\rangle\approx\langle-0.225,1.755\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v||=\sqrt{(-0.225)^2+1.755^2}\approx1.769[/tex]

Find the true direction of the resultant vector accounting for Quadrant II:

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{1.755}{-0.225}\biggr)\approx-82.694^\circ\approx-83^\circ=180^\circ-83^\circ=97^\circ[/tex]

Thus, B) 1.769 m/s; 97° is the correct answer

Problem 10 (#17)

Identify the vectors and add them:

[tex]u+v+w=\langle50\cos20^\circ,50\sin20^\circ\rangle+\langle13\cos90^\circ,13\sin90^\circ\rangle+\langle35\cos280^\circ,35\sin280^\circ\rangle=\langle50\cos20^\circ+13\cos90^\circ+35\cos280^\circ,50\sin20^\circ+13\sin90^\circ+35\sin280^\circ\rangle=\langle53.062,-4.367\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v+w||=\sqrt{53.062^2+(-4.367)^2}\approx53.241[/tex]

Find the true direction of the resultant vector accounting for Quadrant IV:

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{-4.367}{53.062}\biggr)\approx-4.705^\circ\approx-5^\circ=360^\circ-5^\circ=355^\circ[/tex]

Thus, A) 53.241, 355° is the correct answer

Problem 11 (#18)

We observe that [tex]z_1=-8-6i[/tex] and [tex]z_2=4-4i[/tex], hence, [tex]z_1+z_2=(-8-6i)+(4-4i)=-4-10i[/tex]

Thus, Q is the correct answer

Problem 12 (#19)

Find the dot product of the vectors:

[tex]F_1\cdot F_2=(12000*14500)+(7000*-5000)=174000000+(-35000000)=139000000[/tex]

Find the magnitude of each vector:

[tex]||F_1||=\sqrt{12000^2+7000^2}=1000\sqrt{193}\\||F_2||=\sqrt{14500^2+(-5000)^2}=500\sqrt{941}[/tex]

Find the angle between the two vectors:

[tex]\displaystyle \theta=\cos^{-1}\biggr(\frac{F_1\cdot F_2}{||F_1||||F_2||}\biggr)\\ \theta=\cos^{-1}\biggr(\frac{139000000}{(1000\sqrt{193})(500\sqrt{941})}\biggr)\\\theta\approx49.282^\circ\approx49^\circ[/tex]

Thus, C) 49° is the correct answer

Problem 13 (#20)

Using scalar multiplication, [tex]7v-2w=7\langle8,-3\rangle-2\langle-12,4\rangle=\langle56,-21\rangle-\langle-24,8\rangle=\langle56-(-24),-21-8\rangle=\langle80,-29\rangle=80i-29j[/tex]

Thus, A) -80i - 29j is the correct answer

Answer:

The equation of the tangent line is given by the following equation:

[tex]\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)[/tex]

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

*Note:

Recall that the definition of the derivative is the slope of the tangent line.

Step 1: Define

Identify given.

[tex]\displaystylef(x) = e^{-x} \\x = -1[/tex]

Step 2: Differentiate

Step 3: Find Tangent Slope

∴ the slope of the tangent line is equal to  [tex]\displaystyle \frac{-1}{e}[/tex].

Step 4: Find Equation

∴ our point is equal to  [tex]\displaystyle \bigg( 1, \frac{1}{e} \bigg)[/tex].

Substituting in our variables we found into the point-slope form general equation, we get our final answer of:

[tex]\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }[/tex]

∴ we have our final answer.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

there are $624.00 $5 in the money drawer

The maximum amount, in dollars, the customer could have spent for the mounting kit after purchasing the television is $125.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the customer spend $x on television, and $y on mounting kit.

x + y = 500

x = 300 + 75 = 375

y = 500 - 375 = $125

Thus, the maximum amount, in dollars, the customer could have spent for the mounting kit after purchasing the television is $125.

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32 because you add all the number the divide by the total amount witch is 19

Answer:

bc it dose

Step-by-step explanation:

Answer:

Option B will be the correct option.

Step-by-step explanation:

The given expression is

We can rewrite the term as

[As we know ]

Now we will simplify the expression

=

=

Therefore, Option B will be the correct option.

Answer:

a. 6ab +( - 3x) + 2ab

=6ab - 3x +2ab

=6ab + 2ab - 3x

=8ab - 3x

Step-by-step explanation:

Eliminated the brackets first

Collected like terms

Then I solved

Answer:

b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

Given the  following data shows the age of thirteen different dogs at a dog park:

3, 3, 7, 2, 11, 4, 8, 14, 10, 8, 13, 5, 4

The frequency table is as shown below;

Age   |   number of dogs

0 - 2  |    1

3 - 5  |    5

6 - 8  |    3

9 - 11  |    2

12 - 14  |  2

Step-by-step explanation:

To create a histogram of the given data, you would have to plot the ages of the dogs against the number of dogs.

Given the set of data: 3, 3, 7, 2, 11, 4, 8, 14, 10, 8, 13, 5, 4

You would have to create a frequency table and this would contain the ages and number of the dogs as displayed below:

Age   |   number of dogs

0 - 2  |    1

3 - 5  |    5

6 - 8  |    3

9 - 11  |    2

12 - 14  |  2

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Answer:

97.2 ft

Step-by-step explanation:

4 1/2*3*7 1/5=13.5*7.2=

97.2