Find the value of x to
the nearest degree.

Answer:

〖(x+4)〗^2=33

Step-by-step explanation:

x^2+8x=17

∴Multiplying the coefficient of "x" with  "1" /"2"  and adding "square\""  of the answer of multiplication on both sides  

x^2+1/2 (8x)+(4)^2=17+(4)^2

〖(x+4)〗^2=17+16

〖(x+4)〗^2=33

The solution sets are  {√5, -√5}, {√61, -√61}, {5√2, -5√2}, {5√2, -5√2},  {3√3, -3√3}, {2√2, -2√2}, {7√3, -7√3}, {2√7, -2√7},  {√2, -√2}, {2√21, -2√21}

Let's solve each quadratic equation one by one:

1. 3x^2 + 4x^2 = 35

Combine like terms:

7x^2 = 35

Divide by 7:

x^2 = 5

Take the square root of both sides:

x = ±√5

Solution set: {√5, -√5}

2. 3x^2 – 28 = 2x^2 + 33

Combine like terms:

x^2 = 61

Take the square root of both sides:

x = ±√61

Solution set: {√61, -√61}

3. x^2 – 25 = 25

Move 25 to the other side:

x^2 = 50

Take the square root of both sides:

x = ±√50

Simplify the square root:

x = ±5√2

Solution set: {5√2, -5√2}

4. 2x^2 – 30 = 70

Move 30 to the other side:

2x^2 = 100

Divide by 2:

x^2 = 50

Take the square root of both sides:

x = ±√50

Simplify the square root:

x = ±5√2

Solution set: {5√2, -5√2}

5. 8x^2 – 6x^2 = 54

Combine like terms:

2x^2 = 54

Divide by 2:

x^2 = 27

Take the square root of both sides:

x = ±√27

Simplify the square root:

x = ±3√3

Solution set: {3√3, -3√3}

6. 3x^2 – 6 = 34 – 2x^2

Move all terms to one side:

5x^2 = 40

Divide by 5:

x^2 = 8

Take the square root of both sides:

x = ±√8

Simplify the square root:

x = ±2√2

Solution set: {2√2, -2√2}

7. x^2 + 49 = 196

Move 49 to the other side:

x^2 = 147

Take the square root of both sides:

x = ±√147

Simplify the square root:

x = ±7√3

Solution set: {7√3, -7√3}

8. 5x^2 – 40 = 100

Move 40 to the other side:

5x^2 = 140

Divide by 5:

x^2 = 28

Take the square root of both sides:

x = ±√28

Simplify the square root:

x = ±2√7

Solution set: {2√7, -2√7}

9. 9x^2 = 4x^2 + 10

Move 4x^2 to the other side:

5x^2 = 10

Divide by 5:

x^2 = 2

Take the square root of both sides:

x = ±√2

Solution set: {√2, -√2}

10. x^2 – 4 = 80

Move 4 to the other side:

x^2 = 84

Take the square root of both sides:

x = ±√84

Simplify the square root:

x = ±2√21

Solution set: {2√21, -2√21}

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Answer:

Answer below.

Step-by-step explanation:

Just take f(x) and subtract g(x) expression

So that equals....  4-x^2 -(2-x)

Always write exponents in descending order -x^2-(-x)+4-2

answer = -x^2+x+2

The value of the segment RS for the secant through R which intersect the circle at points S and T is equal to 46.4 to the nearest tenth.

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the tangent RS and the secant through R which intersect the circle at points S and T;

RQ² = RS × ST {secant tangent segments}

42² = x × 38

1764 = 38x

x = 1764/38

x = 46.4211

Therefore, the value of the segment RS for the secant through R which intersect the circle at points S and T is equal to 46.4 to the nearest tenth.

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The numerical value of x in the triangle is approximately 2.67.

The figure in the image are two similar triangles.

Side length A of the smaller triangle = 8

Side length B of the smaller triangle = 6

Side length A of the bigger triangle = ( 8 + x )

Side length B of the biger triangle = ( 6 + 2 )

To solve for the value of x, we use ratios and proportions, since the triangles are similar.

Hence:

Side length A of the smaller triangle : Side length B of the smaller triangle = Side length A of the bigger triangle : Side length B of the biger triangle

Plug in the values:

8 : 6 = ( 8 + x ) : ( 6 + 2 )

8/6 = ( 8 + x ) / ( 6 + 2 )

Cross multiply:

6( 8 + x ) = 8( 6 + 2 )

6( 8 + x ) = 8( 8 )

6( 8 + x ) = 8( 8 )

48 + 6x = 64

6x = 64 - 48

6x = 16

x = 16/6

x = 2.67

Therefore, the value of x is approximately 2.67.

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Answer:

Mean=22

Median=19.5

Mode=12

range=26

Step-by-step explanation:

mean - 12 +12+15+24+31+38 = 132 / 6 =22

median - 15+24 / 2 = 39/2=19.5

mode - 12

range - 38-12 = 26

The correct answer is (D) 6 x 6 x 6 x 6, which represents the number of possible outcomes when rolling the die 4 times.

The Fundamental Counting Principle states that if there are m ways to do one thing and n ways to do another thing, then there are m * n ways to do both things.

In this case, a die is rolled 4 times. Each time the die is rolled, there are 6 possible outcomes (numbers 1 to 6). Therefore, using the Fundamental Counting Principle, the number of possible outcomes for rolling the die 4 times can be calculated as:

6 * 6 * 6 * 6

Simplifying the expression, we get: 6^4

Note: Option (A) 4 x 3 x 2 x 1 represents the number of permutations of 4 distinct items, and option (B) 6 x 5 x 4 x 3 represents the number of permutations of choosing 4 items from 6 distinct items. Option (C) 6 x 4 does not account for rolling the die multiple times.

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Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

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Dividing by 3x is not a reliable way to solve the equation because it captures only one solution of the equation, instead of the two solutions.

The equation in the context of this problem is defined as follows:

3x² = 6x.

We must bunch together all the terms with the variable x, hence:

3x² - 6x = 0

3x(x - 2) = 0.

Hence, applying the factor theorem, the solutions are given as follows:

Dividing both sides, we have that:

3x = 6

x = 2.

Hence only one solution would be captured.

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Answer:

x=12

Step-by-step explanation:

Answer:

49°

Step-by-step explanation:

since line PT is a tangent to the circle

angle OPT is 90°

and PTO is 41°

sum of angles in a triangle is 180°

angle PTO + angle OPT+ angle TOP=180°

41°+90°+ TOP=180°

angle TOP=180°-41°-90°

angle TOP=49°

x = 180-73 = 107

6z-103 = x = 107

6x = 107+103 = 210

z = 35

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

We have,

In a parallelogram,

- Opposite sides are congruent:

The opposite sides of a parallelogram have equal lengths.

- Opposite angles are congruent:

The opposite angles of a parallelogram have equal

Now,

a)

Opposite angles are congruent:

So,

5x + 29 = 7x - 11

29 + 11 = 7x - 5x

40 = 2x

2x = 40

x = 40/2

x = 20

And,

3y + 15 = 5y - 9

15 + 9 = 5y - 3y

24 = 2y

y = 24/2

y = 12

b)

Opposite sides are congruent:

So,

-6x = -4x + 6

-6x + 4x = 6

-2x = 6

x = -3

And,

7y + 3 = 12y - 7

12y - 7y = 3 + 7

5y = 10

y = 2

Thus,

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

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Answer:

B.) 108

Step-by-step explanation:

V=1/2 bhl

Approximately 107 people prefer taking a cab based on the given ratios.

To determine the number of people who prefer taking a cab based on the given ratios, we need to find the common ratio between the number of people who prefer buses and cabs.

The ratio of Bus to Train is given as 3:2, which means out of every 5 people, 3 prefer the bus and 2 prefer the train.Similarly, the ratio of Bus to Cab is given as 9:5, which means out of every 14 people, 9 prefer the bus and 5 prefer the cab.

Since the ratios of Bus to Train and Bus to Cab need to be consistent, we can find the common ratio by determining the least common multiple of the denominators, which is 14.

So, for every 14 people, 9 prefer the bus and 5 prefer the cab.To find the number of people who prefer the cab, we need to calculate 5/14 of the total surveyed population:

(5/14) * 300 = 107.14 (approximately)

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The commonly used domains for the sine function are options A, B, and C, depending on the specific context and requirements of the problem.

Option A, B, C are correct.

The domain of the sine function depends on the unit used to measure angles. The sine function is defined for all real numbers, but its values repeat periodically.

In trigonometry, angles are commonly measured in radians. The sine function is periodic with a period of 2π radians. This means that the values of the sine function repeat every 2π radians. Therefore, the domain of the sine function in radians is all real numbers, or in other words, angle measures can be any real number.

However, if we consider specific ranges or intervals, we can determine the domain within those intervals where the sine function takes on unique values. For example:

Option A: Angle measures between 0 and π radians

This represents the interval from 0 to 180 degrees. In this range, the sine function takes on unique values and has a one-to-one correspondence with the input values. So, option A is a valid domain for the sine function.

Option B: Angle measures less than 90°

This represents the interval from 0 to 90 degrees. Similar to option A, the sine function takes on unique values within this interval. So, option B is also a valid domain for the sine function.

Option C: Angle measures between 0 and 2π radians

This represents the interval from 0 to 360 degrees. In this range, the sine function completes one full period and repeats its values. So, option C is a valid domain for the sine function as well.

Option D: All angle measures, including negative angles

This option suggests that the domain of the sine function includes all possible angle measures, both positive and negative. However, negative angles would lead to repeated values since the sine function is periodic. Therefore, option D is not the typical or commonly used domain for the sine function. Option A, B, C are correct.

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Answer:

  y = 0

Step-by-step explanation:

You want the horizontal asymptote of y=2x^2/3x^3.

Degree of numerator: 2

Degree of denominator: 3

When the degree of the denominator (3) is greater than the degree of the numerator (2), the horizontal asymptote is ...

  y = 0

__

Additional comment

This reduces to (2/3)(1/x). The value of 1/x approaches zero when the magnitude of x gets large.

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The circle centered at the point (3, 1) and has a radius of length 2 is,

⇒ (x - 3)² + (y - 1)² = 2²

Given that,

Center ⇒ (3, 1)

Radius ⇒ 2

We know that,

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center

And the standard equation of circle is,

(x - a)² + (y - b)² = r²

Where (a, b) is center of circle

R is radius of circle

So here,

(a, b) = (3, 1)

r = 2

Therefore the required equation of circle is,

⇒ (x - 3)² + (y - 1)² = 2²

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The rental cost for each movie (m) is approximately $3.25, and the rental Cost for each video game (v) is approximately $5.25.

The rental cost for each movie and each video game, let's assign variables to represent the rental cost per movie and per video game. Let's use "m" for the rental cost of a movie and "v" for the rental cost of a video game.

From the given information, we have two equations:

Equation 1: 2m + 6v = 38

Equation 2: 5m + 3v = 32

We now have a system of equations that we can solve to find the values of m and v.

We can start by multiplying Equation 1 by 5 and Equation 2 by 2 to eliminate the m variable:

10m + 30v = 190   ... Equation 3

10m + 6v = 64     ... Equation 4

Now, subtracting Equation 4 from Equation 3, we can eliminate the m variable:

(10m + 30v) - (10m + 6v) = 190 - 64

24v = 126

v = 126/24

v ≈ 5.25

Substituting the value of v into Equation 1, we can solve for m:

2m + 6(5.25) = 38

2m + 31.5 = 38

2m = 38 - 31.5

2m = 6.5

m = 6.5/2

m ≈ 3.25

Therefore, the rental cost for each movie (m) is approximately $3.25, and the rental cost for each video game (v) is approximately $5.25.

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To find the number of distinct proper subsets of a set, we need to consider that a proper subset is a subset that includes some, but not all, of the elements of the original set.

The set N = {2, 50, 62, 13, 40} contains 5 elements. For each element, we have two choices: include it in a subset or exclude it. This means that for each element, there are 2 possibilities: it can be in the subset or not in the subset.

Therefore, the total number of distinct subsets of a set with 5 elements is 2^5, which is equal to 32.

However, since we are looking for proper subsets, we need to exclude the empty set and N itself from the count. So, the total number of distinct proper subsets of the set N = {2, 50, 62, 13, 40} is 32 - 2 = 30.

The length of line a is equal to sqrt(x^2/3).

To solve this problem, we need to use some basic geometry concepts. First, we can label the sides of the larger square as x, and thus the area of the larger square is x^2. We can also label the sides of the smaller squares as y, and thus the area of each smaller square is y^2.

Since the three smaller squares do not overlap, we know that their combined area is equal to the area of the larger square. Thus, 3y^2 = x^2.

We also know that line a is equal to the side length of one of the smaller squares, which is y. Thus, we need to solve for y in the equation 3y^2 = x^2.

Taking the square root of both sides, we get y = sqrt(x^2/3).
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Jane because she has a higher credit score.

Given,

Jane and Stephanie both borrow $15,000 from the same bank to purchase the same make and model car. Jane's credit score is 732 and Stephanie's credit score is 588 .

Now,

For taking loan from the bank the most important thing is the credit score of the individual. If the individual has higher credit score than the person gets loan more easily and will pay less finance charges.

In our case,

Jane has a credit score of 732 which is higher than that of Stephanie .

So, jane will pay less finance cost as compared to Stephanie.

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Answer:

D. Circle

Step-by-step explanation:

The horizontal cross section of a cone is a circle. This is because the cone is a three-dimensional object that has a circular base.

Answer:

65,150

Step-by-step explanation:

Plugging in the given values, we get: P(2025) = 50,000 * (1 + 0.037)^7 P(2025) = 50,000 * 1.303 P(2025) = 65,150 Therefore, the estimated population of the town in 2025 is 65,150 (rounded to the nearest whole number)

Answer:Therefore, the estimated population of the town in 2025 is approximately 63,825.

Step-by-step explanation:  To estimate the population of the town in 2025, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (population in 2025)

P = Initial amount (population in 2018)

r = Annual growth rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

Given:

P = 50,000

r = 3.7% = 0.037 (converted to decimal)

n = 1 (compounded annually)

t = 2025 - 2018 = 7 years

Substituting the values into the formula, we have:

A = 50,000(1 + 0.037/1)^(1*7)

A = 50,000(1 + 0.037)^7

A = 50,000(1.037)^7

A ≈ 50,000(1.2765)

A ≈ 63,825

The correct option is,

D. Yes, because each x-value has exactly one corresponding y-value

We have to given that,

The graph of a quadratic equation is shown in image.

Since, We know that,

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable (the dependent variable).

Now, When we apply Vertical line test on the graph.

We get;

Each x-value has exactly one corresponding y-value.

Therefore, The graph of equation is function because each x-value has exactly one corresponding y-value.

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The formula for the given function y = 0.9cos(2π/4(x - 0.55)).

Amplitude: The given function oscillates between a maximum value of 0.9 and a minimum value of -0.9.

Period: From the graph, we can see that the function completes one full cycle between x = 0 and x = 4.

Phase Shift: The function is horizontally shifted to the right. We need to find the amount of this shift.

The distance between x = 0 and x = 2.2 is 2.2 units.

Since the period of the function is 4 units, the phase shift is 2.2/4 = 0.55 units.

Vertical Shift: The vertical shift of the function is also 0.

Frequency: From the period, the frequency of the function is 1/4.

So, the formula of function is y = 0.9cos(2π/4(x - 0.55)).

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The calculated measure of the angle ABC is 57.5 degrees

From the question, we have the following parameters that can be used in our computation:

Arc AC = 115 degrees

The angle ABC subtends the arc AC

using the above as a guide, we have the following:

Angle ABC = 1/2 * Arc AC

substitute the known values in the above equation, so, we have the following representation

Angle ABC = 1/2 * 115 degrees

Evaluate the equation

Angle ABC = 57.5 degrees

Hence, the measure of angle ABC is 57.5 degrees

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The negatively skewed distribution is option A.

We have,

A negatively skewed distribution means that the distribution is skewed to the left.

In this case, the mean will be less than the median, indicating that the tail of the distribution is elongated to the left side.

Now,

We see that,

Option B is a normal distribution.

Option C is also a normal distribution.

Option D is distributed on both sides.

But,

Option A is a negatively skewed distribution.

Since the distribution is skewed to the left.

Thus,

The negatively skewed distribution is option A.

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