find the domain of f(x) = 1/√((3+X)(7+X))

1 + 2i in polar form is 5√2∠63.4°.

What is a polar form ?

In mathematics, the polar form is a way of representing complex numbers using their magnitude and angle. A complex number can be represented in the form r(cos θ + i sin θ), where r is the magnitude (or modulus) of the complex number, and θ is its argument (or phase angle). Alternatively, the polar form can be represented in terms of magnitude and angle as r ∠θ, where r is the magnitude and θ is the angle in radians. This form is also known as the exponential form of a complex number. The polar form is useful in calculations involving complex numbers, especially in multiplication and division, where it is often easier to work with the polar form rather than the rectangular form (a + bi).

D. 5√2∠63.4°

To convert a complex number from rectangular form to polar form, we use the following formulas:

r = √(a^2 + b^2)

θ = tan^-1 (b/a)

Where a and b are the real and imaginary parts of the complex number, respectively.

In this case, a = 1 and b = 2, so:

r = √(1^2 + 2^2) = √5

θ = tan^-1 (2/1) = 63.4°

Therefore, 1 + 2i in polar form is 5√2∠63.4°.

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Answer:

(x - 5)^2 = 15 and (x + 13)^2 = 3

Step-by-step explanation:

Sure, I can help you with that.

Let's start with the first equation:

0 = x^2 - 10x + 10

To rewrite this equation in the form (x - p)^2 = q, we need to complete the square.

First, let's factor out the coefficient of x^2:

0 = 1(x^2 - 10x + 10)

Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (10/2)^2 = 25:

0 = 1(x^2 - 10x + 25 - 25 + 10)

Now we can rearrange the terms inside the parentheses and simplify:

0 = 1((x - 5)^2 - 15)

Finally, we can rewrite the equation in the desired form by adding 15 to both sides:

15 = (x - 5)^2

So the first equation in the form (x - p)^2 = q is:

(x - 5)^2 = 15

Now let's move on to the second equation:

x^2 + 26x + 167.5 = 0

Again, we need to complete the square to rewrite this equation in the form (x - p)^2 = q.

First, let's factor out the coefficient of x^2:

x^2 + 26x + 167.5 = 1(x^2 + 26x + 167.5)

Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (26/2)^2 = 169:

x^2 + 26x + 167.5 = 1(x^2 + 26x + 169 - 169 + 167.5)

Now we can rearrange the terms inside the parentheses and simplify:

x^2 + 26x + 167.5 = 1((x + 13)^2 - 1.5)

Finally, we can rewrite the equation in the desired form by adding 1.5 to both sides:

1.5 = (x + 13)^2 - 1.5

So the second equation in the form (x - p)^2 = q is:

(x + 13)^2 = 3

Answer:

15 miles

Step-by-step explanation:

7 miles from game store to school plus another 8 miles from school to skate park equal 15.

Answer:

1. is 10

2. is 4

3. is 2

?= is 2

Consequently, the circle's diameter is 28π√3.

The radius of a circular or other curved geometry form refers to its length. It is the border across any two-dimensional circle surface measured linearly in one dimension.

Since the circle is divided into six equal pieces, the shaded region represents one-sixth of the total area of the circle. Therefore, the total area of the circle can be found by multiplying the shaded area by 6:

Total area of circle = 6 × 98π = 588π

The formula for the area of a circle is A = πr², where r is the radius of the circle. Solving for r, we get:

r² = A / π = 588π / π = 588

r = √588 = 2√147 = 2√3 × √49 = 14√3

C = 2r is the method for calculating a circle's diameter. Plugging in the value of r, we get:

C = 2π(14√3) = 28π√3

Therefore, the circumference of the circle is 28π√3.

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The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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Based on the given conditions, the lock solution is 205.

To solve the lock, to calculate the total score based on the given conditions:

Crocus: + 20

Daffodil: + 25

Snowflake: - 50

Tulip: + 30

Bird-Red: + 25, else + 10

Calculating the scores for each input:

TULIP: +30

CROCUS: +20

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

CROCUS: +20

Total score = 30 + 20 + 25 + 30 + 25 + 30 + 25 + 20 = 205

Therefore, the solution for the lock is 205.

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Image transcribed:

SPRING NOW LOADING.

<IF CROCUS, THEN +20>

<IF DAFFODIL, THEN +25>

<IF SNOWFLAKE, THEN -50>

<IF TULIP, THEN +30>

<IF BIRD-RED, THEN +25, ELSE + 10>

TULIP

CROCUS

DAFFODIL

TULIP

DAFFODIL

TULIP

DAFFODIL

CROCUS

Solve Lock

Answer: 14x(x−3)

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

translation :

140% of x = $63

x = $63 ÷ 1.4

x = $45

FUN FACTS :

interesting: 100% means double that number or times 2

if a price is $20 & it increases 100% in price that means its $20 times 2 or $40

percent means per 100

cent means 100 in latin

that's why the decimal moves 2 spaces

for the 2 zeros in 100

chatgpt

The number of bags that had exactly 27 orange candies is given as follows:

Zero.

A stem and leaf plot is a type of data visualization that displays numerical data in a way that shows the distribution of the data while also preserving the individual data points. It is particularly useful for small to medium-sized data sets.

In a stem and leaf plot, the digits in each data point are split into two parts: the stem and the leaf. The stem is usually the leftmost digits of the number, while the leaf is the rightmost digit. The stems are listed in a column from top to bottom, and each leaf is listed next to its corresponding stem. The resulting plot looks like a table with two columns, where the first column shows the stems and the second column shows the leaves.

From the plot given at the end of the answer, the measures are given as follows:

20, 22, 22, 22, 32, 33, 37, 37, 39, ..., 59.

As the number 27 does not show up in the data-set, there were zero bags with exactly 27 candies.

The plot is given by the image presented at the end of the answer.

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144q-15 can be expressed as a product of two factors: 3 and (48q-5). The greatest common factor between 144q and 15 is 3:144q = 3 x 48q15 = 3 x 5, so we can factor out the common factor.

The number or algebraic expression that divides another number or expression completely or with no remainder is factor of that expression ,1 is a factor of every number. It is also the smallest factor of a number. or we can say a factor of a number is defined as an exact divisor of the given number. example, the factors of 20 are 1, 2, 4, 5, 10, and 20.

Given that an equation 144q-15

express 144q-15 as a product of two factors,

we can use factorization by grouping:

144q-15 = 12*12q - 3*5 = 3(412q - 5)

Therefore, 144q-15 can be expressed as the product of two factors:

3(48q-5)

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Answer:

variable measurement

Step-by-step explanation:

The type of measurement you are referring to is called "variable measurement". In variable measurement, the quantity being measured can vary from one observation to another. This means that the measurement is not consistent or fixed, and can change each time it is taken. An example of variable measurement is measuring the weight of a person over time, as their weight can change from one day to another. Another example is measuring the temperature in a room throughout the day, as the temperature can fluctuate based on factors such as sunlight, air conditioning, and human activity.

Answer:

Step-by-step explanation:

To find the total distance traveled in the first second, we need to find the distance traveled during the first half-second and then double it.

The particle starts 2 cm to the right of 0, so its position function is given by:

s(t) = t - t^2 + 2

The distance traveled by the particle during the first half-second (from t = 0 to t = 0.5) is given by:

distance = |s(0.5) - s(0)|

We have:

s(0.5) = 0.5 - (0.5)^2 + 2 = 2.25 cm

s(0) = 0 - 0^2 + 2 = 2 cm

So, the distance traveled during the first half-second is:

|2.25 - 2| = 0.25 cm

To find the total distance traveled in the first second, we double this distance:

total distance = 2 * 0.25 = 0.5 cm

Therefore, the total distance traveled in the first second is 0.5 cm.

Answer:

7.2

Step-by-step explanation:

The 1 looks at the number to the right of it. If the number to the right is 5 or more, the 1 moves up to a 2. Hope this  helps!

All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]

We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.

Let's start with the original quadrilateral ABCD. The length of AB is:

[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]

Similarly, the lengths of BC, CD, and DA are:

[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]

[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]

[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]

Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:

[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]

Similarly, the lengths of B'C', C'D', and D'A' are:

[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]

[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]

[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]

Now we can find the ratio of corresponding side lengths:

[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]

[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]

Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.

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The total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

The interest you receive is referred to as compound interest. Using simple math, you can see how this works: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.

A = P*(1 + r/n)[tex]^(^n^*^t^)[/tex]

A is the total amount

P is the principal (initial amount borrowed), which is $1,000 in this case

r is the annual interest rate expressed as a decimal, which is 0.08 (8%)

n is the number of times the interest is compounded per year, which is usually 12 (monthly compounding) or 1 (annual compounding)

t is the time in years, which is 4 in this case

Assuming that the interest is compounded annually (n=1), we can plug in the values and simplify:

A = 1000*(1 + 0.08/1)¹⁴

= 1000(1.08)⁴

= 1000*1.3605

= $1,360.50

the total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

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Answer:

The area of a sector can be calculated using the formula:

A = (θ/360)πr^2

where θ is the central angle measure in degrees, r is the radius, and π is the mathematical constant pi.

Substituting the given values, we get:

A = (15/360)π(11)^2

≈ 16.2 ft^2

Rounding this to the nearest tenth gives:

A ≈ 15.8 ft^2

Therefore, the area of the sector rounded to the nearest tenth is 15.8 ft^2.

Step-by-step explanation:

hope its help <:

The probability that Angela gets to go to the meeting is 2/5 or 0.4.

What is probability?

There are a total of 5 people in the club, and they need to pick 2 people to go to the meeting. The number of ways to pick 2 people out of 5 is given by the binomial coefficient:

C(5,2) = 5! / (2! (5-2)!) = 10

This means there are 10 equally likely outcomes, which can be represented by the following probability model:

Outcome            Angela goes to meeting?                 Probability

A,B                                    Yes                                              1/10

A,C                                    Yes                                              1/10

A,D                                    Yes                                              1/10

A,E                                     Yes                                              1/10

B,C                                      No                                              1/10

B,D                                      No                                              1/10

B,E                                       No                                              1/10

C,D                                      No                                               1/10

C,E                                       No                                               1/10

D,E                                       No                                               1/10

The probability that Angela gets to go to the meeting is the sum of the probabilities of the outcomes where Angela goes to the meeting:

P(Angela goes to meeting) = P(A,B) + P(A,C) + P(A,D) + P(A,E)

= 1/10 + 1/10 + 1/10 + 1/10

= 4/10

= 2/5

Therefore, the probability that Angela gets to go to the meeting is 2/5 or 0.4.

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Ava walks 2.5 feet in one second.

Ava walks 5 feet in 2 seconds, which means that the ratio of feet to seconds is 5 to 2.

We will use proportionality  concept , to find out how many feet Ava walks in one second,

Let x be the number of feet Ava walks in one second. Then we can set up the proportion:

5 feet / 2 seconds = x feet / 1 second

solving for x, we can cross-multiply:

5 feet * 1 second = 2 seconds * x feet

Simplifying, we get:

5 feet = 2x feet

Dividing both sides by 2, we get:

x  =   2.5 feet

In conclusion, Ava walks 2.5 feet in one second.

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Complete question:

. Ava is walking at a constant speed where for every 5 feet it takes 2 seconds. So, the ratio of feet to seconds is 5 to 2.

(c) How many feet does Ava walk in one second?

Step-by-step explanation:

For x;

[tex]{ \tt{ \tan( \theta) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan( 60 \degree) = \frac{x}{5} }} \\ \\ { \tt{x = 5 \tan(60 \degree) }} \\ \\ { \tt{x = 5 \sqrt{3} }}[/tex]

For y;

[tex] { \tt{\cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{cos(60 \degree) = \frac{5}{y} }} \\ \\ { \tt{y = 5 \cos(60 \degree) }} \\ \\ { \tt{y = 2.5}}[/tex]

Step-by-step explanation:

FV = PV ( 1 + i)^n     FV = future value ....what you are looking for

                                  PV = present value = $ 6000

                                    i = decimal periodic interest = .07/12

                                        n = periods = 5 yr * 12 monts/yr = 60 periods

FV = $ 6000 ( 1 + .07/12)^60 = $  8505.75

Therefore  the probability of drawing a ball with a number less than 20 is 0.38 or 38%.

Probability is a measure of an event's likelihood or chance of occurring. It is usually expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is unavoidable.

The probability of drawing a ball with a number less than 20 is calculated by dividing the total number of balls by the number of balls less than 20.

There are 19 balls numbered 1 through 19. As a result, the likelihood of drawing a ball with a number less than 20 is:

P(less than 20) = total number of balls / total number of balls = 19 / 50 = 0.38

So the chance of drawing a ball with a value less than 20 is 0.38, or 38%.

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Answer:

trust yourself cuh

Step-by-step explanation:

Answer:

512 ft and 1,232 ft

Step-by-step explanation:

area is length x width

the pool's area can be calculated doing 32ft x 16ft

the area of the pool is 512 ft

the deck's area can be calculated doing 28ft x 44ft

the area of the deck is 1,232 ft

you're welcome<3

Answer:

50% chance

ur welcome-ssq

The image of the original figure after the translation and reflection is congruent to the original figure.

A particular type of transformation on the coordinate plane called translation keeps the size of the point or geometrical shape constant while only changing the position. Along the x-axis and y-axis in the coordinate system, the point or the figure can be moved in any direction, including up, down, right, left, and multiple directions.

1. By taking away 4 from the x-coordinate and adding 8 to the y-coordinate, we can translate a point 4 units left and 8 units up.

2. Point A after translation is situated at (-2, 9).

3. We negate the x-coordinate and leave the y-coordinate unaltered to indicate a point over the y-axis.

4. Point B is obtained by reflecting point A over the y-axis (2, 9).

5. Indeed, the resulting representation is consistent with the original figure since the rigid transformations of translation and reflection maintain angles and distances. As a result, the original figure's picture after translation and reflection corresponds to the original figure.

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