Evaluate the expression when x= -7 and y=2 .
X - 2y

The value of variables x and y are,

⇒ x = 80°

⇒ y = 130°

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Since, A parallelogram is forming here,

Then, Opposite angels are going to be equal.

Thus, We get;

⇒ y = (x + 50)°

Now, As you know that sum of all angles of a quadrilateral equals 360°

Hence, We get;

2 {(x + 50) + (x - 30)} = 360°

(x + 50) + (x - 30) = 180°

2x + 20 = 180

2x = 160

x = 80°

So, We get;

⇒ y = (x+50)

      = 80 +50

      = 130°

And,

⇒ x = 80°

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Answer:

AAS

Step-by-step explanation:

[tex]\overline{PR} \cong \overline{PR}[/tex] by the reflexive property.

Answer: D

Step-by-step explanation:

Answer:

0.32958 kilometers per minute

Step-by-step explanation:

Distance covered = 26.219 miles

Step 1: Convert this distance to kilometers using the conversion( 1mi = 1.609  km)

==> 26.219 miles = 26.219 miles x 1.609 km/mile = 42.186371 km

This distance was covered in 128 minutes

Step 2: To find the speed in km/min, divide 42.186371 by 128
= 42.186371/128

= 0.32958 kilometers per minute
------------------------------------------------------------------------------------
We could also solve this problem using the following alternative technique
Step 1 Determine speed in miles/minute = 26.219/128 = 0.2048 m per min

Step 2: Multiply by conversion factor 1.609:
0.2048 x 1.609 = 0.32958 kilometers per minute

The speed of the plane is 135 km/h and wind speed is 23 km/h. The solution has been obtained by forming linear equations.

What is a linear equation?

This is the linear equation with the largest degree of one. This demonstrates that there are no variables in linear equations with exponents greater than 1. A straight line appears on the graph as a result of such an equation.

Let the plane speed be 'P' and the wind speed be 'W'.

We are given that while flying to Kampala with a tailwind a plane averaged 158 km/h.

So, we get an equation as

P + W = 158       ...(1)

Also, on the return trip plane only averaged 112 km/h while flying back into the same wind.

So, we get another equation as

P - W = 112       ...(2)

Now, on adding the equations we get,

⇒P + W + P - W = 158 + 112

⇒2P = 270

⇒P = 135

Now substituting the value into either equation, we get

⇒P + W = 158

⇒135 + W = 158

⇒W = 23

Hence, the speed of the plane is 135 km/h and wind speed is 23 km/h.

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The minimum number of tables the store must sell is 5.

Two or more expressions with an Equal sign is called as Equation.

Using t and c as variables, we get

100c + 400t ≥ 3000

c+t≤16

The online furniture store must sell at least $3000 worth of chairs and tables each day, and can ship at most 16 pieces of furniture.

If the store sells 9 chairs for a total of $900, it needs to sell at least 5 tables to reach a total revenue of $3000.

Since the total number of pieces of furniture sold is 14 (9 chairs + 5 tables), which is less than the maximum of 16, the store meets the daily shipping requirement.

Therefore, the minimum number of tables the store must sell is 5.

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Answer: Correct answer is -1

Step-by-step explanation:

Based on the information provided, the number of guests was 8 guests and the equation to represent this situation is 3/8 x + 2 = 5.

The first step to get to know the number of guests is to write an equation, this will help us discover the number of x  or guests. To write the equation, let's include the variable and values given:

3/8 x + 2 = 5

Now, let's solve this equation:

0.375x + 2 = 5

x = 5 -2/ 0.375

x = 3 / 0.375

x = 8 guests

Based on the above, it can be concluded that the number of guests, in this case, was 8.

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Which quantity is unknown?

the number of guest

_____________________________________

Write an equation that represents the situation.

3/8g + 2 = 5

_____________________________________

How many guests does David have?

g = 8

Answer:

The ratio computed shows that the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.

How to illustrate the ratio?

From the information given, there are 36 marbles in the bag. The number of red marbles will be:

= 5/9 × 36

= 20 marbles

The number of blue marbles will be:

= 4/9 × 36

= 16 marbles

When a student removes 1 blue marble from the bag, the number of blue marbles will be:

= 16 - 1

= 15 marbles.

Therefore, the ratio of red to blue marbles will be:

= 20:15 = 4:3

Therefore, the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.

The polynomial expression cannot be divided

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

(x + 1) /x³ − 3x² + 6x +11.

The degree of the numerator is 1

While the degree of the denominator is 3

For a polynomial quotient to be evaluated, the degree of the numerator must be greater than the degree of the denominator

Because 1 is less than 3, then the polynomial expression cannot be divided

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If a plumber cut a pipe into 5 equal pieces and had 27 cm of the pipe left. the length of the first pipe originally is 702 cm.

Let's call the original length of the first pipe "L"

Let the length of each of the 5 equal pieces "x".

set up the equation:

5x + 27 = L

Each piece of the second pipe is "x" cm long. The second pipe is 15 m long, which is equivalent to 1500 cm. The plumber cut 11 pieces of the same length as each of the 5 equal pieces from the first pipe, so the total length of the 11 pieces is:

11x

The plumber had 15 cm of the second pipe left over after cutting 11 pieces, so we can set up another equation:

1500 - 11x = 15

Solving for "x" in the second equation:

11x = 1485

x = 135

So each piece of the second pipe is 135 cm long.

To find the original length of the first pipe, we can substitute x = 135 into the first equation and solve for L:

5x + 27 = L

5(135) + 27 = L

L = 702

Therefore, the original length of the first pipe was 702 cm.

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Answer: To convert a Senary (base 6) number to decimal, we can use the following formula:

Decimal = (5 * 6^4) + (4 * 6^3) + (7 * 6^2) + (2 * 6^1) + (5 * 6^0)

= (5 * 1296) + (4 * 216) + (7 * 36) + (2 * 6) + (5 * 1)

= 6480 + 864 + 252 + 12 + 5

= 7603

So the Senary (base 6) number 54724 is equivalent to the decimal number 7603.

Step-by-step explanation:

The height of the flagpole is 110 feet.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

tan 19 = f/x

tan 21 = f/(600 - x)

Now,

tan 16 x = tan 21 x (600 - x)

0.34x = 0.38 x 600 - 0.38x

0.34x = 230 - 0.38x

0.34x + 0.38x = 230

0.72x = 230

x = 319

Now,

tan 19 = f/319

0.34 x 319 = f

f = 109.8

f = 110 feet

Thus,

110 feet is the height of the flagpole.

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Answer:

(assuming the 2 was an exponent, if I am wrong don't use this answer) 6a^2 + 12b

Step-by-step explanation:

Add like terms

6a^2 + 12b

Answer:

-47

Step-by-step explanation:

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b^2−4 (ac)

Substitute in the values of a, b, and c.

1^2 − 4 (4 x 3)

Evaluate the result to find the discriminant.

Simplify each term.

One to any power is one.

1 − 4 (4 x 3)

Multiply

−4 (4 x 3)

Subtract 48 from 1.

-47

Answer:

6 is not the solution.  7 is the solution.

Step-by-step explanation:

5(x -3) = x + 13  Substitute 6 for x

5(6 -3) = 6 + 13

5(3) = 19

15 ≠ 19

6 is not a solution because it results in a false statement.  The two sides do not equal each other.

5(x - 3) = x + 13   Distribute the 5

5x -15 = x + 13  Subtract x from both sides

5x - x - 15 = x - x + 13

4x - 15 = 13  Add 15 to both sides

4x - 15 + 15 = 15 + 13

4x = 28  Divide both sides by 4

x = 7

7 is the solution to the equaion.

The size of the key space is 256^8, or 2^64. The average key search time would be 2^64/processing power of PC, which would be a very large number.

The question is asking about the size of the key space if 8 randomly chosen 8-bit ASCII characters are used, and how long it would take to find a key on a single PC.

The size of the key space if all 8 characters are randomly chosen 8-bit ASCII characters is 256^8 = 2^64 = 18,446,744,073,709,551,616.

The average key search time with a single PC would be 18,446,744,073,709,551,616 / 2,000,000,000,000 (2 trillion) operations per second = 9,223,372,036,854,775.8 seconds, which is approximately 292,030 years.

The size of the key space for an 8-bit ASCII character is 2^64 combinations. On average, it will take a single PC 2^64 / (processing speed of PC in Hz) seconds to search through the entire key space.

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The number of books to read per month is 3 or more.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

14x ≥ 42

Solve for x.

14x ≥ 42

Divide both sides by 14.

x ≥ 42/14

x ≥ 3

This means,

The number of books to read per month is 3 or more.

Thus,

The number of books to read per month is 3 or more.

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Answer:

m<20

Step-by-step explanation:

Answer: eat grass whor

Step-by-step explanation:

If we are only interested in the total number of games the Yankees win, the possible events for the two games are: 0 wins: LL , 1 win: LW, WL and 2 wins: WW

What is event in probability ?

In probability, an event is a subset of the sample space of a random experiment. In other words, an event is a collection of possible outcomes of the experiment.

For example, consider flipping a fair coin. The sample space of this experiment is {heads, tails}. An event could be defined as "getting heads", which is a subset of the sample space that includes only one outcome.

There are four possible outcomes for the double-header, which can be represented using W for a win and L for a loss:

WW (Yankees win both games)

WL (Yankees win the first game, but lose the second game)

LW (Yankees lose the first game, but win the second game)

LL (Yankees lose both games)

Therefore , If we are only interested in the total number of games the Yankees win, the possible events for the two games are: 0 wins: LL , 1 win: LW, WL and 2 wins: WW

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The hourly rate that the batches of cookies were made is given as follows:

4.85 batches per hour.

The hourly rate is obtained applying the proportions in the context of the problem.

A proportion is applied as the rate is obtained dividing the total production by the time in hours.

The parameters for this problem are given as follows:

Hence the rate is given as follows:

40/8.25 = 4.85 batches per hour.

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The boat will coast approximately 16752.9 feet (or about 3.17 miles) in the first 2 minutes after its motor quits.

From the problem statement, we know that the velocity of the boat, v, changes from 83 ft/s to 23 ft/s over a period of 1 second. Therefore, we can write:

[tex]dv/dt = -k v^2[/tex]

Separating variables and integrating from v = 83 at t = 0 to v = 23 at t = 1, we get:

[tex]∫83^23 dv / v^2 = ∫0^1 -k dt[/tex]

=> [1/83 - 1/23] = k

So the equation for the velocity of the boat as it coasts is:

[tex]dv/dt = -[(1/83 - 1/23)] v^2[/tex]

The differential equation is separable:

[tex]dv/v^2 = -[(1/83 - 1/23)] dt[/tex]

Integrating both sides, we get:

-1/v = [(1/83 - 1/23)] t + C

where C is an integration constant. Using the initial condition v(0) = 83, we get:

C = -1/83

Substituting this back, we have:

-1/v = [(1/83 - 1/23)] t - 1/83

Solving for v, we have:

v(t) = 83 / [1 + (83/23 - 1) t]

To find the distance traveled, we integrate v(t) from t = 0 to t = 120:

s =[tex]∫0^120 v(t) dt[/tex]

Substituting v(t) and simplifying, we have:

s = 23 ln(1 + 3.6087t) + 60.391t + C

where C is another integration constant. Using the initial condition s(0) = 0, we get:

C = 0

Therefore, the distance traveled by the boat in the first 2 minutes after its motor quits is:

s = 23 ln(1 + 3.6087t) + 60.391t

Evaluating this expression at t = 120 seconds, we get:

s = 23 ln(433.044) + 7246.92 ≈ 16752.9 ft

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We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix

Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.

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There are two solutions to the system of linear equations depicted in the graph: one at (0,4) and one at (-3,0). There is only one distinct solution to the system of equations where the two lines intersect at the points (-3,0) and (0,4).

If the slopes are the same but the y-intercepts vary, the system has no solution. If the slopes are different, the system only has one solution. The system has an endless number of solutions if the slopes and y-intercepts match.

There are therefore countless possible answers. A different kind of linear equation system is a system with two parallel lines represented by the equations is referred to be an inconsistent system. The lines have distinct y-intercepts but the same slope.

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Answer:

98 km

Step-by-step explanation:

To find the area of the figure;

Total Area = Area A + Area B + Area C

Area A = 14 * 2 = 28 km2

Area B = 11 * 2 = 22 km2

Area C = 12 * 4 = 48 km2

Total Area = 98 km2

The absolute value function on the graph is:

f(x) = |x + 2| + 3

We know that for an absolute value function with a vertex at (a, b), then the absolute value function is:

f(x) = |x - a| + b

Here we can see that the vertex is at the point (-2, 3)

Then:

a = 2

b = 3

The function will be:

f(x) = |x + 2| + 3

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Answer: s≥3

Step-by-step explanation: fist you need to get the variable by itself on one side. So subtract the 10 from each side and you have 3s≥9. Then you divide each side ny 3 to get s by itself, divide 9 by 3. Then your answer is s≥3

The total area of the quilt is: 166.5 square inches

The six-sided figure is given, and we can deduce the following parameters from the question:

The shape is made of a triangle and a rectangle

The side lengths derived from the question are:

The triangle on top:

base: 6 inches and height: 7.5 inches

The rectangle at the bottom:

Base: 16 inches with a height of 9 inches

So, we have the total area of the figure to be

Area of figure = (1/2 * 7.5 * 6) + (16 * 9)

Area of figure = 22.5 + 144

Area of figure = 166.5 in²

Based on the parameters, the total area is 166.5 square inches

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Sum of the given geometric sequence is -100.

A geometric sequence is the special type of sequence in which the ratio of every two successive terms is constant.

Sum of each infinite geometric sequence

-50, -25, -12.5, ...

The infinite sum of geometric sequence is given by,

[tex]s_{\infty} =\frac{a}{1-r}[/tex]

Where a is the first term in the sequence and r is the common ratio.

[tex]s_{\infty} =\frac{-50}{1-(-0.5)}[/tex]

      = -100.

Hence, sum of the given geometric sequence is -100.

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