Select which angle is supplementary to angle 1

Step-by-step explanation:

x > 4

you see the line covers everything to the right (larger than) of +4.

the large empty circle at 4 means this value is not included.

that is the reason why we cannot use x >= 4.

to include the value the market has to be sold (not empty).

Answer: The first 3 options

Step-by-step explanation:

You have to make sure that the given variable would be able to equal -5. The  \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.

Answer:

g > -7, f ≤ -5 and g ≥ -5

Step-by-step explanation:

the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).

The answer to the problem is that the least number of gold coins the band of 17 pirates could have stolen is 122.

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It is a fundamental concept in algebra and is widely used in various areas of mathematics, science, and engineering.

To solve this problem, let's work through the information provided step by step.

When the pirates divided the coins into equal piles, 3 coins were left over. This means that the total number of coins must be a multiple of the number of pirates (17) plus 3. We can represent this as an equation: X = 17n + 3, where X is the total number of coins and n is an integer.

When one pirate was slain and the remaining pirates divided the coins into equal piles, 10 coins were left over. Since one pirate was killed, there are now 16 pirates left. Using the same equation, we can represent this situation as: X = 16m + 10, where X is the total number of coins and m is an integer.

Finally, when the pirates divided the coins into equal piles again, no coins were left over. This means that the total number of coins must be a multiple of the number of pirates (16) without any remainder. We can represent this as: X = 16p, where X is the total number of coins and p is an integer.

Now we have three equations:

X = 17n + 3

X = 16m + 10

X = 16p

To find the least number of gold coins that satisfy these conditions, we need to find the smallest value of X that satisfies all three equations.

To simplify the problem, we can start by finding a common solution for equations 1 and 2:

17n + 3 = 16m + 10

Subtracting 3 from both sides gives:

17n = 16m + 7

To find the smallest integer solutions for n and m, we can start by finding a particular solution. By trial and error, we find that n = 7 and m = 7 is one possible solution.

Substituting these values back into the equations:

X = 17 * 7 + 3 = 118

X = 16 * 7 + 10 = 122

We see that the only number that satisfies both equations 1 and 2 is X = 122. Now we can substitute this value into equation 3 to check if it satisfies all three equations:

122 = 16p

By trial and error, we find that p = 7 is the smallest integer solution.

Therefore, the answer to the problem is that the least number of gold coins the band of 17 pirates could have stolen is 122.

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Answer:

x=8

Step-by-step explanation:

4+4=x

4+4=8

x=8

Answer:

x(x-2)

Step-by-step explanation:

The area of the union, denoted as U, formed by all the disks in the plane that touch the line segment AB, where AB has a length of 1, is equal to π/4.

To find the area of the union of all disks in the plane that touch AB, we can consider the extreme cases where the disks are tangent to AB.

Let's assume a disk is centered at a point C on AB. The radius of this disk will be denoted by r.

Case 1: The disk touches AB externally

In this case, the distance from the center of the disk to AB is r. Therefore, the diameter of the disk (2r) is equal to the length of AB, which is 1. Hence, r = 1/2.

Case 2: The disk touches AB internally

In this case, the distance from the center of the disk to AB is 0. The radius (r) of the disk will be equal to the distance between the center of the disk and one of the endpoints of AB (A or B). Therefore, r = 0.

Now, let's consider all possible positions for the centers of these disks.

If the center of the disk is located outside the line segment AB, it will fall into Case 1. If the center is located on AB itself, it will fall into Case 2.

The set U, which represents the union of all such disks, will consist of two disks:

1. The disk with radius 1/2 and centered at the midpoint of AB.

2. The disk with radius 0 and centered at any point on AB.

The area of the disk with radius 1/2 is given by π(1/2)^2 = π/4.

The area of the disk with radius 0 is 0, as it degenerates into a single point. Therefore, the total area of U is π/4.

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The complete question is:

A plane contains points A and B with AB=1. Let U be the union of all disks of radius in the plane that touch AB. What is the area of U?

E, O, and U have symmetry with respect to a point. Q and Y do not have symmetry with respect to a point.

When we talk about symmetry with respect to a point, we mean that if we draw a line through that point, the shape on one side of the line will be an exact reflection of the shape on the other side. In other words, if we fold the shape along the line, the two halves will match perfectly.

Let's analyze the given letters one by one:

- E: This letter has a vertical line of symmetry. If we draw a line vertically through the middle of the letter E, the left and right halves of the letter will be mirror images of each other.

- O: The letter O has infinite lines of symmetry because it is a perfect circle. This means that no matter where we draw a line through the center of the O, the two halves will be identical.

- U: The letter U also has a vertical line of symmetry. If we draw a line vertically through the middle of the letter U, the left and right halves will be mirror images of each other.

So, the letters E, O, and U have symmetry with respect to a point. The letter Q and Y do not have symmetry with respect to a point.

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The total amount of pie Kevin and Su Yung ate together is 7/10 of the pie

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount of pie Kevin and Su Yung ate be = A

Now , the equation will be

The amount of pie Kevin ate = 2/5 of the total pie

And ,

The amount of pie Su Yung ate = 3/10 of the total pie

So , the equation is

Total amount of pie Kevin and Su Yung ate = amount of pie Kevin ate + amount of pie Su Yung ate

Substituting the values in the equation , we get

Total amount of pie Kevin and Su Yung ate A = 2/5 + 3/10

Total amount of pie Kevin and Su Yung ate A = ( 4 + 3 ) / 10

Total amount of pie Kevin and Su Yung ate A = 7 / 10 of the total pie

Therefore , the value of A is 7/10

Hence ,

The total amount of pie Kevin and Su Yung ate together is 7/10 of the pie

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The interval of convergence is (-18/5, 18/5).

To express f(x) as a power series, we first need to decompose it into partial fractions:

f(x) = 11/(x^2 - 7x - 18) = 11/[(x - 9)(x + 2)]

Using partial fractions, we can write:

11/[(x - 9)(x + 2)] = A/(x - 9) + B/(x + 2)

Multiplying both sides by the denominator (x - 9)(x + 2), we get:

11 = A(x + 2) + B(x - 9)

Setting x = 9, we get:

11 = A(9 + 2)

A = 1

Setting x = -2, we get:

11 = B(-2 - 9)

B = -1

Therefore, we have:

f(x) = 1/(x - 9) - 1/(x + 2)

Now, we can write the power series of each term using the formula for a geometric series:

1/(x - 9) = -1/18 (1 - x/9)^(-1) = -1/18 * sigma^n=0 to infinity (x/9)^n

1/(x + 2) = 1/11 (1 - x/(-2))^(-1) = 1/11 * sigma^n=0 to infinity (-x/2)^n

So, putting everything together, we get:

f(x) = 1/(x - 9) - 1/(x + 2) = -1/18 * sigma^n=0 to infinity (x/9)^n + 1/11 * sigma^n=0 to infinity (-x/2)^n

The interval of convergence can be found using the ratio test:

|a_n+1 / a_n| = |(-x/9)^(n+1) / (-x/9)^n| + |(-x/2)^(n+1) / (-x/2)^n|

= |x/9| + |x/2|

= (|x|/9) + (|x|/2)

For the series to converge, we need |a_n+1 / a_n| < 1. This happens when:

(|x|/9) + (|x|/2) < 1

Solving for |x|, we get:

|x| < 18/5

Therefore, the interval of convergence is (-18/5, 18/5).

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The cylindrical coordinates for point :

(a) (5, −5, 1) is  (√50, 3π/4, 1)

(b) (−4, −4sqrt(3), 1) is (8, 4π/3, 1)

To change from rectangular to cylindrical coordinates (with r ≥ 0 and 0 ≤ θ ≤ 2π), we'll convert the given points (a) and (b) using the following equations:

r = √(x² + y²)
θ = arctan(y/x) (adjusting for the correct quadrant)
z = z

(a) (5, -5, 1)
Step 1: Calculate r
r = √(5² + (-5)²) = √(25 + 25) = √50

Step 2: Calculate θ
θ = arctan((-5)/5) = arctan(-1)
Since we're in the third quadrant, θ = π + arctan(-1) = π + (-π/4) = 3π/4

Step 3: z remains the same
z = 1

So, the cylindrical coordinates for point (a) are (r, θ, z) = (√50, 3π/4, 1).

(b) (-4, -4√3, 1)
Step 1: Calculate r
r = √((-4)² + (-4√3)²) = √(16 + 48) = √64 = 8

Step 2: Calculate θ
θ = arctan((-4√3)/(-4)) = arctan(√3)
Since we're in the third quadrant, θ = π + arctan(√3) = π + (π/3) = 4π/3

Step 3: z remains the same
z = 1

So, the cylindrical coordinates for point (b) are (r, θ, z) = (8, 4π/3, 1).

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The first rest area from the starting point of the trail is 4.367 miles and the distance Anne walked is 10 miles.

Given that, a hiking trail is 24 miles from start to finish. There are two rest areas located along the trail.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other.

Given that the ratio of the distance from the start of the trail to the rest area and the distance from the rest area to the end of the trail is 2:9.

Now, 2/11 ×24=4.3636

The nearest hundredth of a mile is 4.367 miles.

Given that Anne claims that the distance she has walked and the distance she has left to walk has a ratio of 5:7.

Now, 5/12 ×24=10 miles

Anne walked 10 miles.

Therefore, the first rest area from the starting point of the trail is 4.367 miles and the distance Anne walked is 10 miles.

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Answer:

Step-by-step explanation:HI

You got answer already?

Just , look down as in rectangle A" (-6,1)

B"(-1,-3)

C"(-4, 4)

And you have wrong coordinates for C (-4,-4)

Answer:

D) 21,237.2

Step-by-step explanation:

V= πr^2h

D= 26

r= 13

V= π13^2(40)

V = 169(40)π

V = 6760π

V = 21226.4

Answer:

The interest rate is 5.278%

Step-by-step explanation:

4298.55=1987.22(1+r/100)^15

r=5.278%

To complete the tables, we multiply the given numbers:

First table:

Second table:

Now, to determine which option is less expensive we compute the total annual expenses for each case:

1.-Rental:

2.- Homeowner:

From the above calculations, we can conclude that the cheaper option based on the given annual expenses is to rent.

Renting is less expensive.

Step-by-step explanation:

1)  Total rectangle area =  W x H = 12 x 8 = 96 cm^2

 area of triangle (shaded portion) = 1/2 base * height = 1/2 * 7 x 8 = 28 cm^2

              Nonshaded portion = 96 - 28 cm^2 = 68 cm^2

          ratio shaded:nonshaded is then   28 : 68 = 7:17

2)   Look at the two middle triangles :  Height of each = 8 cm

       then reading across the diagram  height + base + height = 21 cm

            so base = 5 cm

   area of ONE triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 cm^2

        total area for FOUR of them  = 80 cm^2

Answer:

your answer would be y=-3x-15

Step-by-step explanation:

The to find the volume of the parallelepiped is V = |A · B × C| where A, B, and C are vectors representing three adjacent sides of the parallelepiped and | | denotes the magnitude of the cross product of two vectors.

The cross product of two vectors is a vector that is perpendicular to both the vectors, and its magnitude is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between the two vectors he three adjacent sides of the parallelepiped can be represented by the vectors v1, v2, and v3, and these vectors can be found by subtracting the coordinates of the vertices

:v1 = (-2, 5, -8) - (-2, -2, -5)

= (0, 7, -3)v2 = (-2, -8, -7) - (-2, -2, -5)

= (0, -6, -2)v3 = (-7, -9, -1) - (-2, -2, -5)

= (-5, -7, 4)

Using the formula V = |A · B × C|, we can find the volume of the parallelepiped as follows:

V = |v1 · (v2 × v3)|

where v2 × v3 is the cross product of vectors v2 and v3, and v1 · (v2 × v3) is the dot product of vector v1 and the cross product v2 × v3.Using the determinant formula for the cross-product, we can find that:

v2 × v3

= (-6)(4)i + (-2)(5)j + (-6)(-7)k

= -48i - 10j + 42k

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Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

To determine the optimal production quantity of tables and the maximum profit, we can set up a linear programming problem based on the given information.

Let's define the decision variables:

Let C represent the number of chairs produced.

Let T represent the number of tables produced.

Objective function:

The objective is to maximize profit. The profit for each chair is $150, and the profit for each table is $750. Therefore, the objective function can be expressed as:

Profit = 150C + 750T

Constraints:

Labor constraint: The total labor hours available is 240, and each chair requires 5 hours, while each table requires 3 hours. So the labor constraint can be represented as:

5C + 3T ≤ 240

Material constraint: The warehouse has 700 linear feet of rich mahogany available, and each chair requires 4 linear feet, while each table requires 20 linear feet. Therefore, the material constraint can be expressed as:

4C + 20T ≤ 700

Non-negativity constraint: Since we cannot produce a negative quantity of chairs or tables, both C and T should be greater than or equal to zero:

C ≥ 0

T ≥ 0

Now, we can solve the linear programming problem to find the optimal solution:

Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

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Answer:

1/10,1.5, 1/4, 1, 0.89, 0.26, 0.9,0.7

Step-by-step explanation:

Answer:

fist one is 36 and the second one is 238

Step-by-step explanation:

to find volume multiple length times width times height though in this case you only need to multiple two numbers to get the answer

Answer:

the 10 pound bag by $0.10 per pound

Answer: y = \(\frac{1}{2} x\) - 3

Step-by-step explanation:

You have the expression 3⁰

Take into account that any number powered to 0 is equal to 1.

Then, you have:

3⁰ = 1

Answer:

false

Step-by-step explanation:

The solutions are:  (A U B)' = {1, 7, 8, 9} and (A ∩ B) x A = {(3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4)}.

a. (A U B)' represents the complement of the union of sets A and B. To find (A U B)', we need to list all the elements in the universal set U that are not in the union of sets A and B. The union of sets A and B, A U B, includes all the elements that are in either set A or set B (or both). So, A U B = {2, 3, 4, 5, 6}. The complement of A U B, (A U B)', will contain all the elements in the universal set U that are not in the set A U B. Therefore, (A U B)' = {1, 7, 8, 9}.

b. (A ∩ B) x A represents the Cartesian product of the intersection of sets A and B with set A. To find (A ∩ B) x A, we need to list all possible ordered pairs that can be formed by selecting one element from the intersection of sets A and B and pairing it with an element from set A. The intersection of sets A and B, A ∩ B, contains the elements that are common to both sets A and B. In this case, A ∩ B = {3, 4}.

Now, we take each element from A ∩ B and pair it with each element from set A. So, (A ∩ B) x A = {(3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4)}. Therefore, (A U B)' = {1, 7, 8, 9} and (A ∩ B) x A = {(3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4)}.

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a. The length of the adjacent side to the given angle is 13.40.

b. The length of the hypotenuse is 51.78.

c. The other acute angle is 15°.

Given that,

In the picture we can see the triangle which is right angle triangle with one side as 50 cm and one acute angle as 75°.

a. We have to find the length of the adjacent side to the given angle.

By using trigonometric ratio,

tan75° = \(\frac{opp}{adj}\)

tan75° = \(\frac{50}{adj}\)

3.7321 = \(\frac{50}{adj}\)

Adjacent side = 13.40

Therefore, The length of the adjacent side to the given angle is 13.40.

b. We have to find the length of the hypothenuse.

sin75° = \(\frac{50}{h}\)

0.9659 = \(\frac{50}{h}\)

h = \(\frac{50}{0.9659}\)

h = 51.78

Therefore, the length of the hypotenuse is 51.78.

c. We have to find the measure of the other acute angle

By adding of the angles in the triangle is 180°

The measure of the other acute angle = 180° - (90+75) °

= 180°- 165°

= 15°

Therefore, The other acute angle is 15°.

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The complete question is :

The triangle which is right angle triangle with one side as 50 cm and one acute angle as 75°.

a. Find the length of the adjacent side.

b. Find the hypothenuse.

c. Find the other acute angle

There are a total of 10 slips.

8 slip with 3 on it

2 slips with 9  on it

value = Probability of 3 x 3 + Probability of 9 x 9.

=  (8 / 11)  x 3 + (2/ 11)  x 9

24 / 11 + 24 / 11 = 4.36

probability

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

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