Combine the sum of the exterior angles and the sum of the interior angles of a triangle. Find the sum.

For the given triangle, the value of 'a' would be 41.41 degrees.

What is cosine angle?

In mathematics, the cosine of an angle is a trigonometric function that relates the ratio of the adjacent side of a right triangle to the hypotenuse.

More formally, the cosine of an angle is defined as the ratio of the length of the adjacent side of a right triangle to the length of the hypotenuse. It is denoted by the symbol cos and is calculated using the following formula:

cos(theta) = adjacent side / hypotenuse

where theta is the measure of the angle in radians or degrees.

By using the cosine definition,

cosθ = adjacent side/Hypotenuse

cos(a) = 45/50

[tex]a = cos^{-1}(\frac{45}{60})[/tex]

a = 41.41°

Hence, for the given triangle, the value of 'a' would be 41.41 degrees.

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The exact coordinates of points where the horizontal tangent exists are:

(0,2)

([tex]\pi[/tex],6)

([tex]-\pi[/tex],6)

What is meant by tangent?

A plane or straight line that meets a curve or curved surface at a particular place but does not cross it when extended.

Given function is f(x)=4-2secx

We can write it as

y=4-2secx

The slope of the tangent to this curve is:

[tex]\frac{dy}{dx} =-2secx*tanx[/tex]

Given that the tangent is horizontal, which means that the slope is zero.

-2secx*tanx =0 when x is multiples of [tex]\pi[/tex].

So we can take x=0, [tex]\pi[/tex], -[tex]\pi[/tex].

When x=0 ⇒ y=4-2sec0

⇒y=2

When x=π ⇒ y=4-2secπ

y=6

When x=-π⇒ y=4-2sec(-π)

y=6

Therefore the exact coordinates of points where the horizontal tangent exists are:

(0,2)

([tex]\pi[/tex],6)

([tex]-\pi[/tex],6)

The graph is attached below.

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Answer:

i think the answer is A and C, B and E

Answer:

D and F

A and C

B and E

Step-by-step explanation:

75

Step-by-step explanation:

I think this is the answer I'm not sure I hope this helps

Answer:

Step-by-step explanation: The expression for f(x) is not a valid mathematical equation. It should specify the relationship between x and the output value of f(x). If the correct equation for f(x) is given, we can then find the expression for (f + g)(x) and g(x).

Assuming that the equation for f(x) is as follows:

f(x) = 12 + x

Then, the expression for (f + g)(x) can be found by adding f(x) and g(x):

(f + g)(x) = f(x) + g(x) = 12 + x + (5 - x) = 17

So, (f + g)(x) is a constant function with a value of 17 for all values of x.

And the expression for g(x) was already given:

g(x) = 5 - x

The statements are (a) False, (b) True and (c) False

Right angles are angles whose measure is 90 degrees.

In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.

(a) ∠AHB and ∠AHG are vertical angles.

Vertical angles are angles which are formed on the opposite sides of two intersecting lines.

∠AHB and ∠AHG are not formed on the opposite sides, but are adjacent to each other.

So the statement is false.

(b) ∠EHF and ∠DHE are adjacent angles.

∠EHF and ∠DHE are two angles which are adjacent to each other. So they are adjacent angles.

So the statement is true.

(c) The measure of ∠FHG is equal to the measure ∠DHF.

We know that DG is a straight line.

∠FHG and ∠DHF are linear pair of angles.

So, ∠FHG + ∠DHF = 180°

Given that ∠FHG is right angle.

90° + ∠DHF = 180°

∠DHF = 180° - 90°

∠DHF = 90°

So the statement is true.

Hence the statements (a), (b) and (c) are false, true and true respectively.

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Your question is incomplete. The complete question with the figure is given below.

Answer:

the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.

Step-by-step explanation:

Step 1: Define the variables

Let's call the speed of the plane in still air "V". Let's call the speed of the wind "W".

Step 2: Write an equation for the distance traveled with the wind

The distance traveled by the plane with the wind in 6.5 hours can be represented by the equation:

D1 = (V + W) * t

where D1 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.

Substitute the known values into the equation:

3900 = (V + W) * 6.5

Step 3: Write an equation for the distance traveled against the wind

The distance traveled by the plane against the wind in 6.5 hours can be represented by the equation:

D2 = (V - W) * t

where D2 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.

Substitute the known values into the equation:

3120 = (V - W) * 6.5

Step 4: Solve for the speed of the wind

We can now use the two equations from Steps 2 and 3 to solve for the speed of the wind.

First, let's rearrange the equation from Step 2 to isolate "W":

W = (3900 / 6.5) - V

Next, substitute this expression for "W" into the equation from Step 3:

3120 = (V - ((3900 / 6.5) - V)) * 6.5

Expand the right side of the equation:

3120 = (V - 3900 / 6.5 + V) * 6.5

Simplify the equation:

3120 = 2V * 6.5 - 3900

Divide both sides of the equation by 2:

1560 = V * 6.5 - 1950

Multiply both sides of the equation by 2:

3120 = V * 13 - 3900

Add 3900 to both sides of the equation:

7020 = V * 13

Divide both sides of the equation by 13:

V = 540

Step 5: Solve for the speed of the wind

Now that we know the speed of the plane in still air, we can use the equation from Step 2 to find the speed of the wind:

W = (3900 / 6.5) - V

Substitute the value of "V" that we found in Step 4 into the equation:

W = (3900 / 6.5) - 540

Simplify the equation:

W = 280

Step 6: Conclusion

Therefore, the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.

Answer:The range rule of thumb states that the standard deviation (s) is approximately equal to the range (R) divided by 4, where the range is the difference between the maximum and minimum values of a data set.

Using this formula, we can estimate the standard deviation of the heights as:

s = R / 4 = (192.5 - 152.0) / 4 = 20.625 / 4 = 5.156 cm

Comparing this estimate to the actual standard deviation of 12.22 cm, we see that the estimate is off by a factor of approximately 2.37.

Since the estimate is not within 1.7 cm of the actual standard deviation, it suggests that the range rule of thumb is not a very accurate way to estimate the standard deviation of this data set. The standard deviation calculated using the full set of data is much larger than the estimate, which means that the spread of the data is greater than what would be expected based on the range rule of thumb.

Answer:

Step-by-step explanation:

Cardinality of a set refers to the number of elements in the set. There are two types of cardinality: finite and infinite. A set is considered to have finite cardinality if it has a finite number of elements, meaning that the elements can be counted. A set is considered to have infinite cardinality if it has an infinite number of elements and cannot be counted.

In the case of the set B = {x | x ∈ N and x > 5}, the set is comprised of all natural numbers greater than 5. The set of natural numbers is infinite, meaning that there are an infinite number of elements in the set B. As a result, the cardinality of the set B is also considered to be infinite.

The symbol "ℵ0" is used to represent the cardinality of the set of natural numbers, and it is often used to indicate the cardinality of infinite sets with the same size as the set of natural numbers. In this case, we can say that the cardinality of the set B is ℵ0, meaning that the set B has the same size as the set of natural numbers and therefore has infinite cardinality.

Answer:

Graph D is Greg's graph

From the resting point it goes up and then it straightens out and then increases again

The required, area of the triangle to the nearest 10th of a square inch is 34.1 square inches.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°

Here,
Calculating unknown angle v,
Since the sum of the angles in the triangle is equal to 180,
u + w+ v = 180
5 + 19 + v = 180
v = 180 - 24
v = 156°

Now,
Calculating the unknown side w,
U/sinu = W/sinw
6.7/sin5° = W/sin19°

W =25.0277

Now,
Area of the triangle is given as
= 1/2 UW sinv

= 1/2× (25.027)×(6.7)×(sin156°)

= 34.1 square inch

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The requried teacher needs $59.5 more to buy cups and napkins, as of the given condition.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
To find out how much more money the teachers will need to buy cups and napkins, we can first calculate the cost of each item and then add those costs together.

Each package of cups costs $3.50

The teachers need to buy 12 cups

So the total cost of cups is = 12 cups × ($3.50 per package) = $42

Now let's do the same thing for the napkins:

Each package of napkins costs $4.25

The teachers need to buy 10 napkins

So the total cost of napkins is = 10 napkins × ($4.25 per package) = $42.50

To find out how much more money the teachers will need to buy cups and napkins,

= $42 + $42.50 - $25
= $59.50 - $25 = $59.5

Therefore, the teachers will need $59.5 more to buy cups and napkins.

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Hi there, here's your answer:

The question asked here is, "Which of the following is a line segment in the  drawing?"

Let's review all the options first.

a) HD

H and D being two points of a line AK form a line segment.

b) HA

H being a point on the line AK and A being an end point of a line make HA a ray.

c) GH

Again, H being a point on line GJ and G being an end point of a line make GH a ray.

d) DI

DI are two distinct points and do not join, thus they don't form a line segment.

Therefore, the correct option is (a) HD

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The amount of force between two objects 10 mm away from each other is G[tex]m_1m_2[/tex] / 100.

All physical things with mass are drawn to the gravitational force, which can be thought of as an attracting force. It is the known natural force that is by far the weakest.

Given:

Distance = 10 mm

As, the Gravitation force between two objects

F = G[tex]m_1m_2[/tex] / r²

or, F = G[tex]m_1m_2[/tex] / 10²

F = G[tex]m_1m_2[/tex] / 100

Also, the force between two objects decreases as the far they are apart from each other.

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The Question attached is Incomplete/ inappropriate, the Complete Question is

What would be the amount of force between two objects 10 mm away from each other having the [tex]m_1[/tex] and [tex]m_2[/tex]?

The value of the angle is 120°.

The corresponding angle of a given angle refers to the angle in a congruent position in another figure. For example, if two lines intersect, the angle formed at one vertex of the intersection is called a vertex angle. The corresponding angle in the other figure is the angle in a congruent position, meaning that it has the same measure.

We are given two lines to be parallel

Hence the angle adjacent to x is 40°

Now Sum of All three angle is 180° (Angles in linear pair)

Hence we have

40 + x + 20 = 180°

x = 120°

Hence the measure of angle x is 120°

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The two integers are 1 and 2.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.

A number is positive if it is greater than zero, so they are positive integer.

A number is negative if it is less than zero, so they are negative integer.

A number line is a visual representation of numbers on a straight line. This line is used for comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

Given:

x be a positive number

x + 1 = y

The sum of reciprocal of the smaller and twice the reciprocal of the larger number

Substitute

[tex]\frac{1}{x} + \frac{2}{y} = 2[/tex]

[tex]\frac{1}{x} + \frac{2}{x + 1} = 2[/tex]

[tex]\frac{x+ 1 + 2x}{x(x +1)} = 2[/tex]

[tex]x + 1 + 2x = 2x^2 + 2x[/tex]

Subtracting 2x on both sides, we get

x + 1 + 2x - 2x = 2x² + 2x - 2x

x + 1 = 2x²

2x² - x - 1 = 0

2x² - 2x + x - 1 = 0

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

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

x = -1/2 and x = 1

But x = -1/2 is not possible. Becuase x is a positive number.

So, x = 1

y = x + 1

y = 2

The two integers are 1 and 2.

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With percentage=76% of foreign coins of total 150 coins, Other coins collected were 36.

What is the percentage?

In mathematics, a percentage is a statistic or ratio that may be expressed as a fraction of 100. To find the percentage of a number, divide it by its total and multiply by 100. Hence, the percentage represents one part of a hundred. The phrase % stands for one hundred percent. It is represented by the symbol "%".

Here are some instances of percentages:

Now,

Given that total coins=150

Foreign coins=76% of total

then other coins are 24% of total

so other coins=150*24/100

=72/2

=36

Hence,

          Other coins collected were 36.

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The x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.

In physics and mathematics, a vector is a mathematical object that has both magnitude and direction. Vectors are often represented by arrows, with the length of the arrow indicating the magnitude of the vector, and the direction of the arrow indicating the direction of the vector.

For example, the velocity of a moving object is a vector quantity, because it has both a magnitude (the speed of the object) and a direction (the direction in which the object is moving).

To find the x-components and y-components of the vector [tex]\mathbf{\hat d }[/tex] = (5.0 km, 29° left of +y-axis), we can use trigonometry.

The magnitude (or length) of the vector is given by the first component, which is 5.0 km.

The angle between the vector and the positive y-axis is 29° left of +y-axis, which means it forms a 61∘ angle with the negative y-axis (since 29∘ + 61° = 90°).

The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:

x-component = magnitude x cos(angle) = 5.0 km x cos(61°) ≈ -2.25 km

The negative sign indicates that the x-component is in the opposite direction of the positive x-axis.

The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:

y-component = magnitude x sin(angle) = 5.0 km x sin(61°) ≈ 4.30 km

Therefore, the x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.

Expressed as an ordered pair, the components are (-2.25 km, 4.30 km).

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Step-by-step explanation:

Zeros is another term for X intercepts.

We'd right the simplest form as (x-/+a), a being the zero

Just remember when you do that, change the signs. It shows -2, +2, +3. That becomes +2, -2, -3

Following that simple form, we get

[tex](x + 2)(x - 2)(x - 3)[/tex]

Answer: 4745

Step-by-step explanation:

3250 = 100%

Percent Increase = +46%

46% of 3250 = 1495

3250 (100%) + 1495 (46%) = 4745

The average rate of change of the function between x = a and x = a + h is -6

The slope is -6

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

g(x) = -6x + 1

The interval is given as

x = a and x = a + h

So, we have

g(a) = -6a + 1

g(a + h) = -6(a + h) + 1

This gives

g(a) = -6a + 1

g(a + h) = -6a + -6h + 1

Subtract the functions

g(a) = -6a + 1

g(a + h) = -6a + -6h + 1

g(a) - g(a + h) = -6h

The average rate is then calcualated as

Average = [g(a) - g(a + h)]/(a - a - h)

This gives

Average = (-6h)/-h

Evaluate

Average = -6

This also represents the slope

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Tony can afford the car insurance, and he has enough money($426.33) left over each month to cover other expenses.

Automobile, truck, motorbike, and other types of road vehicles are covered by vehicle insurance. Its main purpose is to offer financial security against property loss or personal injury brought on by auto accidents, as well as against liability that can emerge from related events.

According to the information given,

Tony's yearly pay is $8,320

and his monthly pay is $693.

If we round his yearly pay to $8,000, his monthly car insurance will be 1/30 of that amount, or $266.67.

Since Tony's monthly pay is $693, and his monthly car insurance will cost $266.67, he can afford the insurance. He will have $426.33 remaining each month after paying for the insurance.

Therefore, Tony can afford the car insurance, and he has enough money left over each month to cover other expenses. However, this calculation assumes that Tony has no other major expenses or debts, and it is always a good idea to budget carefully and consider all potential costs before making a significant purchase.

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Answer:

Step-by-step explanation:

Two angles are said to be supplementary when their sum is equal to 180°.

Given angle 1 and 50° are supplementary.So, angle1+50°= 1880°

angle1 =180°-50°

angle 1=130°

Given 50° and angle 3 are supplementary

So,50°+ angle 3=18=0°

angle 3=130°

So angle 1 equals to angle

∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

The total number of lattice points on the graph of x²+y²+11x-13y+73=0 is 0.

A point in a regularly spaced array of points, known as a point lattice, that is at the intersection of two or more grid lines is referred to as a lattice point.

Since in a Cartesian coordinate system, a lattice point is a point whose x-coordinate and y-coordinates are both integers. Therefore, it a defined point on the plane with both the coordinates known.
Further, if the given set of equation or function is plotted on the graph, then the graph of the function does not exist in the xy-plane.

Hence, there will be no lattice points on the given graph.

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The given amounts of money will be written as £5.37, £2.04 and £15.70 respectively. The solution has been obtained by using denominations of money.

What is denomination?

The term "denomination" refers to the units of measure that are used to categorize various financial products such as coins and paper money. Every country has different denomination.

We are given three different amounts of money in words which are to be written in denominations.

So,

a. Five pounds and thirty seven pence = £5.37

b. Two pounds and four pence = £2.04

c. Fifteen pounds and seventy pence = £15.70

Hence, the amounts in their denominations have been obtained.

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Answer:

Step-by-step explanation:

its Reduced to 2 / 5, which is 40 percent. Maria has 40 percent of her work completed

Answer:

Step-by-step explanation:

To solve this problem, we must first use an equation that reflects the amount of acid in each solution and its relationship to the total volume of the resulting solution. We can use the following equation:

(C1 * V1) + (C2 * V2) = (C3 * V3)

Where:

C1 = concentration of the acid solution at 60% (in percent)

V1 = volume of the acid solution at 60% (in ml)

C2 = concentration of the acid solution at 30% (in percent)

V2 = volume of the 30% acid solution (in ml)

C3 = concentration of the resulting 50% acid solution (in percent)

V3 = volume of the resulting 50% acid solution (in ml)

In this case, we know the total volume of the resulting solution (V3 = 300 ml) and the desired concentration (C3 = 50%). We also know the concentration of one of the original solutions (C1 = 60%). So we can plug the known values ​​into the equation:

(60 * V1) + (30 * V2) = (50 * 300)

Clearing V1:

V1 = (300 * 50 - 30 * V2) / 60

Now that we have V1 as a function of V2, we can solve the problem to find the volume of the 60% acid solution to mix with the 30% solution. Substitute the known values ​​into the equation:

V1 = (300 * 50 - 30 * V2) / 60

V1 = (15000 - 30 * V2) / 60

V1 = 250 - (V2 / 2)

We can use this last equation to find the volume of the 30% solution that we must mix with the 60% solution:

V2 = 2 * (250 - V1)

Clearing V1:

V1 = 250 - (V2 / 2)

V1 = 250 - (2 * (250 - V1) / 2)

V1 = 250 - 250 + V1

V1 = 250

Therefore, we must mix 250 ml of 60% acid solution with 250 ml of 30% solution to produce 300 ml of 50% solution.