help!
Can you please give me the area of this. I would really like it.

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Answer:

(-2,0)

Step-by-step explanation:

the x-intercept is when the y = 0 and you have to make one of them has to equal to 0 ;  (4,0) or (-2,0) and the only one is (-2,0).

Answer:

(-2, 0)

Step-by-step explanation:

As shown in this picture

The sum of all the positive numbers from 1 to 116, inclusive, is 6350.

The sum of the first n positive integers can be found using the formula n(n+1)/2. In this case, n=116, so the sum of all the positive numbers from 1 to 116, inclusive, is 116 * 117 / 2 = 6350. This formula can be useful in a variety of mathematical and real-world applications, such as finding the total number of objects in a sequence or the total distance traveled by an object moving at a constant speed.

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Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

April bought 16 kilograms of soil in total.

We need to add the amounts of soil she used for her violets and tulips. Since April used kilograms for violets and tulips, we need to convert the 3,000 grams to kilograms before we can add them up.

April bought:

9 kilograms of soil for violets

4 kilograms of soil for tulips

3 kilograms of soil for daisies (since 3,000 grams is 3 kilograms)

Therefore, April bought 16 kilograms of soil in total.

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Answer:

Surface area of triangular pyramid = 48 inch²

Step-by-step explanation:

Given:

Base length of triangle = 6 inches

Height of triangle = 4 inches

Find:

Surface area of triangular pyramid

Computation:

Surface area of triangular pyramid = 4 x [Surface area of triangle]

Surface area of triangular pyramid = 4 x [(1/2)(b)(h)

Surface area of triangular pyramid = 4 x [(1/2)(6)(4)

Surface area of triangular pyramid = 4 x [(1/2)(24)]

Surface area of triangular pyramid = 4 x 12

Surface area of triangular pyramid = 48 inch²

Answer:

??

Step-by-step explanation:

is there an image or something?

Answer:

80

Step-by-step explanation:

The answers are GBACGFI and when put in backward alphabetical order it becomes IGFDCBA.

The code is IGFDCBA.

The code is determined as follows:

1. 1/6 of students are trying out for a fall sport, then 5/6 are not.

The probability of selecting a student who is not trying out for a fall sport = 5/6.

Thus, the probability of students trying out for a spring sport = 5/6

To get 20 students who are trying out for a spring sport = 20 / (5/6)

To get 20 students who are trying out for a spring sport = 48 students.

Letter G

The smaller the mean absolute deviation the farther apart the data set is:  False; Letter B

Every part of the population has an equal chance of being selected when dealing with random sampling: True; Letter A

Rolling a number larger than one on a regular six-sided dice;

Likely; Letter C

The probability of pulling out a green marble and keeping it = 7/12.

The probability of pulling out another green marble = 6/11

Therefore, the probability of pulling out two consecutive green marbles = 7/12 * 6/11

The probability of pulling out two consecutive green marbles = 31.8%; Letter G

If an event is most likely to not happen then the probability gets close to 0; Letter F

B has a probability of 1/4 of being landed on

If you spin the spinner 500 times, you can land B 500 x 1/4 = 125 times.; Letter I

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The probability that the randomly chosen marble will be red is 1/6 or 0.1667.

The probability of an event is the possibility, chance, or likelihood for an event to take place or occur.

From the given information:
Let us find the probability that if marble is drawn at random from the jar, the given marble will be red:

The total number of marble = 10 + 2 = 12 marbles.

The probability that the randomly chosen marble will be red is:

P(red) = 2/12

P(red) = 1/6

P(red) = 0.1667

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Answer:

im not 100% sure...but i think its integer

Step-by-step explanation:

i read on google

Answer:

all fractions can be written as a rational number like 1/5 it would be 0.2 its a rational number

Answer:

14

Step-by-step explanation:

The two chords are both 5 units from the center, so they are congruent.  The two segments marked congruent must be of equal length (both 7 units long), making the whole chord 14 units long.

The chord marked x must also be 14 units long.

2916 ft³

Volume helps describe the amount of space that a shape takes up.

Volume of a Sphere

Volume describes the 3-dimensional size of a shape. Since volume is a 3-D measurement, the units should be cubed; this explains why the answer is given in feet cubed. In order to find the volume, we need to use the radius. The radius of a sphere is the distance from the center to the outside. In this case, we are told that the radius is 9 ft.

Volume Formula

Every regular shape has its own volume formula. For a sphere, the formula is:

So, to find the volume, all we need to do is plug in the radius. For this sphere, r = 9.

When using 3 for pi, the volume of the sphere is 2916 ft³.

Answer:

166.4

Step-by-step explanation:

Percentage of 12.8% of 1300 = ? 12.8% of 1300 is equivalent to multiplying them: 12.8% × 1300. 12.7% of 1300 = ? 12.9% of 1300 = ? 1% of 1300 = ? Detailed ...

Work Shown:

s = false

p = true

r = false

-p = false, which is the opposite of statement p

s or -p = false or false = false

The result of an 'or' operation is false only when both parts are false; otherwise, it is true

(s or -p) or r = false or false = false

(s or -p) or r = false

The system of inequalities that represent the graph is

y ≤ -x +4

y < 3x-1

The correct option is the third option

From the question, we are to determine the system of inequalities that represents the graph

The equation of the solid line is  y = -x +4

Since the lower part of the graph was shaded

Then,

The inequality that represents the solid line is

y ≤ -x +4

The equation of the dotted line is  y = 3x -1

Since the lower part of the graph was shaded,

Then,

The inequality that represents the solid line is

y < 3x-1

Hence, the system of inequalities that represent the graph is

y ≤ -x +4

y < 3x-1

The correct option is the third option

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Hey there! :)

Answer:

y = z/8x.

Step-by-step explanation:

Solve for y by isolating y on the left side of the equal sign. Therefore:

8xy = z

Divide both sides by 8x:

8xy/8x = z/8x

y = z/8x.

Answer:

36

Step-by-step explanation:

8x-20=5x+1

-5       -5

3x=-20+1

+20 +20

3x=21

3  3

x=7

8(7)-20

FED=36

Answer:

Abby's mother spent $9.75 for the classroom not including tax.

Step-by-step explanation:

Know:

5 bags for 1 dollar

10 candy bars for 50 cents

3 whistles for 75 cents

5×6=30

10×3=30

3×10=30

The total cost of rents is $180.

In the given table,

The cost of skis per day  = $48

The cost of pole per day = $12

Now since given that,

Alveres rents for 3 days

Therefore,

The cost of skis for 3 days  = $48 x 3

                                             =  $144

The cost of pole for 3 days = $12 x 3

                                             = $36

To find the total cost of rental,

Adding the cost of 3 days of skis and cost of 3 days of poles,

Hence,

Total cost of rents = $144 + $36

                               = $180

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Answer:

Step-by-step explanation:

7h - 5 = 4

    7h = 9

      h = 9/7

21(9/7) - 15 = 12

The average distance is 300 yards

The ratio is given as:

Driver : 2-iron = 5 : 4

When the iron driver is 240 yards, we have:

Driver : 240 = 5 : 4

Express as fraction

Driver/240 = 5/4

Multiply both sides by 240

Driver= 300

Hence, the average distance is 300 yards

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Answer:

c. both of the above statements are false

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Distribution skewed to the right

This means that the Empirical Rule is not applicable, and the two statements are false, and thus, the correct answer is given by option c.

The first would be false nonetheless, but the second would be true if the distribution was normal.

Answer:

0.45 ft/min

Step-by-step explanation:

Given:-

- The flow rate of the gravel, \(\frac{dV}{dt} = 35 \frac{ft^3}{min}\)

- The base diameter ( d ) of cone = x

- The height ( h ) of cone = x

Find:-

How fast is the height of the pile increasing when the pile is 10 ft high?

Solution:-

- The constant flow rate of gravel dumped onto the conveyor belt is given to be 35 ft^3 / min.

- The gravel pile up into a heap of a conical shape such that base diameter ( d ) and the height ( h ) always remain the same. That is these parameter increase at the same rate.

- We develop a function of volume ( V ) of the heap piled up on conveyor belt in a conical shape as follows:

                                \(V = \frac{\pi }{12}*d^2*h\\\\V = \frac{\pi }{12}*x^3\)

- Now we know that the volume ( V ) is a function of its base diameter and height ( x ). Where x is an implicit function of time ( t ). We will develop a rate of change expression of the volume of gravel piled as follows Use the chain rule of ordinary derivatives:

                               \(\frac{dV}{dt} = \frac{dV}{dx} * \frac{dx}{dt}\\\\\frac{dV}{dt} = \frac{\pi }{4} x^2 * \frac{dx}{dt}\\\\\frac{dx}{dt} = \frac{\frac{dV}{dt}}{\frac{\pi }{4} x^2}\)

- Determine the rate of change of height ( h ) using the relation developed above when height is 10 ft:

                              \(h = x\\\\\frac{dh}{dt} = \frac{dx}{dt} = \frac{35 \frac{ft^3}{min} }{\frac{\pi }{4}*10^2 ft^2 } \\\\\frac{dh}{dt} = \frac{dx}{dt} = 0.45 \frac{ft}{min}\)

Answer:

Option D

Explanation:

The real answer would be a bit higher if you use the formula:

Area=π×r^2

Answer:

4d - c + 3

4(6) - 3 + 3

24 - 3 + 3

24

Step-by-step explanation:

24

Hope this helps :T

Answer:

Multiplicative inverse property

Step-by-step explanation:

Multiplicative inverse property states that

For example

A number 4

Reciprocal=1/4

Product

Verified

Answer:

Inverse Property of Multiplication

Step-by-step explanation:

Inverse Property of Multiplication

The product of a number and its reciprocal is always 1.

The reciprocal of a number is 1 divided by the number.

Therefore, the reciprocal of a rational number is its inverse (swap the numerator and denominator).

For example:

\(\textsf{The reciprocal of 6 is}\:\:\sf \dfrac{1}{6}\)

\(\implies \sf 6 \times \dfrac{1}{6}=\dfrac{6 \times 1}{6}=\dfrac{\diagup\!\!\!\!6 \times 1}{\diagup\!\!\!\!6}=1\)

\(\sf \textsf{The reciprocal of }\:\dfrac{3}{4} \sf \:\:is\:\:\sf \dfrac{4}{3}\)

\(\sf \implies \dfrac{3}{4} \times \dfrac{4}{3}=\dfrac{3 \times 4}{4 \times 3}=\dfrac{12}{12}=1\)

Traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Earth to Mars is compared to traveling from Earth to the moon, we need to calculate the difference between the distances.

The distance from Earth to the moon is approximately 3.74 x 10^5 km.

The distance from Earth to Mars is approximately 9.25 x 10^7 km.

To find the difference, we subtract the distance to the moon from the distance to Mars:

9.25 x 10^7 km - 3.74 x 10^5 km

To subtract these numbers, we need to make sure the exponents are the same. We can rewrite the distance to the moon in scientific notation with the same exponent as the distance to Mars:

3.74 x 10^5 km = 0.374 x 10^6 km (since 0.374 = 3.74 x 10^5 / 10^6)

Now we can perform the subtraction:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 km - 0.374 x 10^6 km

To subtract, we subtract the coefficients and keep the same exponent:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 - 0.374 x 10^6 km

Simplifying the subtraction:

9.25 x 10^7 - 0.374 x 10^6 km = 9.249626 x 10^7 km

Therefore, traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Scientific notation is a convenient way to express very large or very small numbers. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10 (exponent). It allows us to write and manipulate such numbers in a compact and standardized form.

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Answer:

the distance between the 2 points is 6.4 units.

Step-by-step explanation:

point 1 has the coordinates (-4, -2).

point 2 has the coordinates (1, 2).

the distance between both points is the Hypotenuse of the right- angled triangle of the coordinate difference lines in parallel to x- and y-axis.

so, how long is the difference in x dimension ?

and his long is the difference in y dimension ?

these are the sides of the triangle.

the difference in x dimension :

1 - -4 = 1 + 4 = 5

the difference in y dimension :

2 - -2 = 2 + 2 = 4

P1P2² = 4² + 5² = 16 + 25 = 41

P1P2 = sqrt(41) = 6.4

Answer:

Step-by-step explanation:

3 * 4 = 12 - 6

12 = 6

This statement is false

Answer:

False.

Explanation:

3 * 4 = 12 -6

12 = 6

...............

False, the sides are not equal.