Your friend wants to mark her favorite campsite on the map. She knows that the campsite is 65 miles north of her town. what distance on the map (in inches) represents the actual distance of 65 miles? show your work and explain your reasoning.

Using the scale 1/2 in. : 10 mi.

Since AD is the angle bisector of <BAC, then BD is 1.9 inches.

An angle bisector is a line that divides a given angle into two equal measure after its construction.

Given that AD is the angle bisector of <BAC, then we have;

From triangle ADC, applying the Pythagorean theorem;

/Hyp/^2 = /Adj/^2 + /Opp/^2

4^2 = 3^2 + AD^2

16 = 9 + AD^2

AD^2 = 16 - 9

         = 7

AD = 7^1/2

     = 2.64

AD = 2.6

So that, from triangle ABD we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

3.2^2 = 2.6^2 + BD^2

10.24 = 6.76 + BD^2

BD^2 = 10.24 - 6.76

         = 3.48

BD = 3.48^1/2

     = 1.8655

BD = 1.9 inches

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The measure of the missing side lengths of the triangle is adjacent side = 5 and hypotenuse =  5√2.

What are trigonometric ratios?

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle.

To find the side of a right triangle:

A right-angle triangle has one of its angles as 90 degrees.

Therefore,

using trigonometric ratios,

tan 45 = opposite/adjacent

tan 45 = opposite / 5

opposite side = (tan 45)  * 5

opposite side = 1 * 5 = 5

Therefore,

adjacent side = 5

sin 45 = opposite / hypotenuse

1/√2  = 5 / hypotenuse

hypotenuse = 5√2 /1

hypotenuse =  5√2

Hence, the missing side lengths of the triangle are adjacent side = 5 and hypotenuse =  5√2.

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-16 5/7 is the additive inverse of 16 5/7.

An additive inverse of a number is the value, which on adding with the original number results in zero value.

given a number 16 5/7

The additive inverse of a number is the number that completes the number to '0' when added.

thus,

the additive inverse of  16 5/7 is -  16 5/7.

Therefore, the additive inverse of 16 5/7 is -16 5/7.

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Complete question:

What is the additive inverse of 16 5/7?

The three types of graphs are bar graphs, line graphs and pie chart

The three types of graphs can be noted as -

Bar graph - It is a form of a chart in which distinct values or data sets are represented by rectangular bars. The bars, which can be horizontal or vertical, can be used to compare various values or data sets. A bar graph might be used, for instance, to compare the population of several cities or the sales of various items.

Line graph - It changes or trends over time are represented by a series of points connected by lines. To track changes in data, such as stock prices, temperature, or population increase, line graphs are frequently utilised. The progression of the data through time can be demonstrated by the line.

Pie chart - This chart employs a circular shape divided into wedges to depict percentages or proportions of a whole. The size of wedges indicates the percentage or proportion of each wedge's respective category, with each wedge standing for a separate category. A pie chart could be used to display the allocation of revenue among various departments within a corporation or the breakdown of spending in a budget.

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The relation between logarithmic function and exponential function is they both are inverse of each other.

As given in the question,

Relation between logarithmic function and exponential function is given by:

Therefore, relation between the logarithmic function and the exponential function is  that both are inverse of each other.

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The number that represent the product of ac is 18 and the sum of b is -9 .

The factored form of the trinomials is (x-3)(x-6)

An algebraic statement with three on-zero terms separated by + or - is called a trinomial. A trinomial exists when three monomials are separated by addition or subtraction. The formula for a quadratic trinomial is ax² + bx + c, where a, b, and c are real, non-zero values.

An algebraic statement with variables and constants is a quadratic trinomial. It is written as ax² + bx + c, where a, b, and c are real non-zero values and x is the variable. Leading coefficient "a," linear coefficient "b," and additive constant "c" all refer to the same constant. A quadratic trinomial is also used to explain the discriminant D, which is expressed as D = b² - 4ac and determines the quantity of an expression. The discriminant aids in categorizing the many quadratic trinomial instances. A quadratic equation, such as ax² + bx + c = 0, is one in which the value of a quadratic trinomial with a single variable is zero.

The trinomial is x² - 9x + 18

In the expression ax² + bx + c

here a = 1,  b = -9 and c = 18

The term that represent the product of ac = 1* 18 = 18

The term represent the sum of b = -9

Factoring The trinomial we get,

x² -9x + 18

= x² - 3x - 6x + 18

= x(x-3) -6(x-3)

=(x-3)(x-6)

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Answer:

You should expect to draw a consonant about 560 times.

Step-by-step explanation:

The word FOOTBALL has 5 consonants - F, T, B, L and L. Therefore, you should expect to draw a consonant 5 times out of every 8 draws. 5/8 = 0.625, so for 840 draws you should expect to draw a consonant approximately 840 x 0.625 = 560 times.

The number of times you should expect to draw a consonant is 525.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

The letters from the word FOOTBALL are written on 8 cards with one letter on each card.

One card will be drawn randomly and then placed back into the stack.

Number of consonants in the word = 5 [F, T, B, L and L]

Total number of letters = 8

Probability of finding consonant each time = 5/8

If this experiment is repeated 840 times,

Number of times you should draw a consonant = 840 × (5/8) = 525

Hence the required number of times is 525.

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To find the acute angle of a right triangle with side lengths divide the length of side "a" by the length of the hypotenuse, side "c."

A right triangle is a kind of triangle with a right, or 90-degree, angle. Since the sum of the angles in a triangle must be 180 degrees, the remaining two angles are acute, which implies they are less than 90 degrees.

Orient the triangle in such a way one leg of the 90-degree angle will be vertical. Mark this leg as "a." The other leg of the 90-degree angle will be horizontal. Mark that leg "b." Mark the third side, the hypotenuse, "c."

Measure the length of the three sides. In some applications, you will only be able to calculate sides "a" and "b." In this case, use the Pythagorean Theorem to calculate side "c."

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Answer:

[tex]f(x)=-2(x+2)(x-4)[/tex]

Step-by-step explanation:

In factored form, [tex]f(x)=a(x+2)(x-4)[/tex].

To solve for [tex]a[/tex], use the point [tex](-1,10)[/tex].

[tex]10=a(-1+2)(-1-4) \implies a=-2 \\ \\ \therefore f(x)=-2(x+2)(x-4)[/tex]

The distance that is closes to the distance that Steven walked around the pool is B. 62. 83 ft

The perimeter of a circle refers to the distance around that circle and it is also called the circumference of the circle.

This circumference can be found by the formula:

= π x diameter

This means that the closest distance that Steven walked around the circular swimming pool is:

= π x 20

= 62. 86 ft

In conclusion, the distance that Steven was able to walk around the pool is closest to 62. 83 ft.

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The distance Joe climbed up the ladder is c.

3.22 + b2 = 2.42 is the correct equation.

What is the Pythagoras theorem?

The Pythagorean theorem is a fundamental concept in geometry and mathematics, named after the ancient Greek mathematician Pythagoras. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

3.22 + b2 = 2.42 is the correct equation that represents the situation of Joe's position on the ladder. It uses the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the lengths of the other two sides (the horizontal and vertical distances from the base of the ladder to Joe's feet). In this case, c is the distance that Joe climbed up the ladder, and b and a are the horizontal and vertical distances, respectively.

So, by solving the equation:

3.22 + b2 = 2.42

b = √ (2.42 - 3.22)

Then use the Pythagorean theorem again to find the length of the ladder (c)

c = √(3.22 + b^2)

Hence, the distance Joe climbed up the ladder is c.

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Answer:

To reflect a triangle across the y-axis, you need to negate the x-coordinate of each vertex.

The original triangle with vertices (1, 3), (2, 5), and (4, 3) will be reflected across the y-axis to become a new triangle with the following vertices: (-1, 3), (-2, 5), and (-4, 3).

Keep in mind that a reflection across the y-axis means that the object is flipped along the y-axis. Therefore, the x-coordinate of each vertex is multiplied by -1, which flips the object horizontally.

Answer:

Step-by-step explanation:

Here, 4 teams given. Each teams has played every other teams 4 times.

so here we will name each team

team a = bulls

team b = lakers

team c = knickers

team c = warriors

So to find total number of games, we know that Bulls played with the other 3 teams by 4 times that is (4×3) = 12, Lakers played with the other two teams by 4 times that is (4×2) = 8, Knicks played with Warriors 4 times.

Therefore, total number of games = .

Total points given, for Bulls = 22, for Lakers = 19, for Knickers = 14, for Warriors = 12.

So sum of total points =

For a win a team earned 3 points and for a tie two teams win 1 point.

That means for tie total point = 1+1 = 2.

Let's take total number of game which ended as win played be x and total number of game which ended as a tie be y.

We have got total number of games is 24.

So we can write the equations as,

.......Equation 1

And also we have got total number of points is 67. So the equation is,

.......Equation 2

From equation 1, if we move x to the right side we will get,

Now let's substitute this value in equation 2, to get the value of x. By substituting the value we will get,

We will expand 2 now.

We will move 48 to the other side by subtracting it from both sides. We will get,

So the number of games which ended as a win = 19

The number of games which ended as a tie = 24 -19 =5  

So we have got the required answers.

u can just check the answer and this answer is copy righted from its rightful owner

Thus the numbers are 1411 and 1079 respectively.

The mean of the data in the dot plot is equal to 1.6.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the dot plot, the number of jokers include the following:

Number of jokers                frequency            

0                                               1

1                                                1

2                                               2

3                                               1

Next, we would determine the total number of jokers as follows;

Total number of jokers = 0 + 1 + 2 + 2 + 3

Total number of jokers = 8

Now, we can calculate the mean of the data as follows;

Mean = F(x)/n

Mean = 8/5

Mean = 1.6.

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Therefore , the solution of the given problem of trigonometry comes out to be  - (√2-+√6 ) / 4.

The connection between trigonometric and square spline The field is believed to have been founded in the late 1700s, but it really began in the third-century BC when the mathematical and astronomy sciences were combined. Numerous geometric equations can be solved or the results of calculations using them can be computed using precise mathematical methods. Trigonometry is the study of the six basic trigonometric operations.

Here,

Given :

cos(x + y)

cos(x) cos(y) -  sin(x) sin(y)  by the cosine addition identity.

We receive:

If we look just at unit circle, we should notice that cos(x) = √2/2 instead than sin(x) = √2/2.

Additionally, we are told that cos(y)= -1/2,

but if we look at the unit circle, we should find that sin(y)=√3/2.

Use both of them to the following: cos(x + y).

cos(x) sin - cos(y) (x) sin(y) via the cosine addition identity.

=> √2/2 - 1/2 - √2/2*√3/2

=> -√2/4   - √6/4

=> -√2- √6 / 4

=> - (√2-+√6 ) / 4

Therefore , the solution of the given problem of trigonometry comes out to be  - (√2-+√6 ) / 4.

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Answer:

it is + 10 then + 4 and that is how you get your answer

Things that must you include in every confidence argument you write in order to receive full points and have a complete argument are:

Confidence argument is An explanation for why there should be confidence is emphasized in a confidence argument (a case mostly supported by evidence that a process is safe).

The system's overall assurance case must have certain elements in a confidence argument. This contains:

Your question is incomplete but most probably your full question attached below

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Answer: 1 5/8 is indeed greater than 1.6. 5/8 equals to decimal form 0.625 add the one and we get 1.625. Which is only a bit bigger than 1.6 hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 5/8 (1.625) is greater than 1.6 

1.625 > 1.6

The solution set for the system of inequalities is (-1, -2).

Option A is the correct answer.

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,

y ≤ 3x + 1 ____(1)

x - y > 1 _____(2)

From (1 ) and (2) we get,

y = 3x + 1

Substituting in x - y = 1

x = 1 + y

x = 1 + 3x + 1

x - 3x = 2

-2x = 2

x = -1

Substituting in x = 1 + y

-1 = 1 + y

y = -1 - 1

y = -2

This means,

The solution set is (-1, -2).

Thus,

The solution set is (-1, -2).

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Triangle ABC is first mirrored over the x-axis, then across the y-axis, to form triangle A'B'C.

The Complete Question.

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13 units is the distance from the given point (-12, 5) to the origin.

Both statistical and qualitative methods can be used to determine how far apart two things or points are.

The word "distance" in physics can refer to an actual length or, more frequently, to an estimate based on a range of other factors.

The length of the line segment that connects any two points on a plane provides the distance between those spots.

To calculate the distance between two points, one commonly uses the equation d=((((x2 - x1)2 + (y2 - y1)2).

So, the given point is:

(-12, 5)

Assume that O (0, 0) is the origin and that M (-12, 5) is the provided location.

The distance between M and O is:

= √(−12−0)2+(5−0)2

= √(−12)2+(5)2

= √144+25

= √169

= √13×13

= 13 units

Therefore, 13 units is the distance from the given point (-12, 5) to the origin.

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The composite number between 71, 81, 41 and 61 is 71.

A composite number is a positive integer that can be divided by at least one positive integer other than itself and one. It is the opposite of a prime number, which can only be divided by itself and one. Composite numbers are also referred to as composite integers, composite numbers, or simply composites. Examples of composite numbers include 4, 6, 8, 9, 10, 12, 14, 15, and 16.

A composite number is a positive integer that has more than two factors. 71 is a composite number because it has the factors 1, 71, and itself. It also has the factors 11, 7, and 7. Thus, 71 is the composite number between 71, 81, 41, and 61.

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Answer:

f(10) = 340

Step-by-step explanation:

to find f(10) substitute x = 10 into f(x) , that is

f(10)

= 4(10)² - 4(10) - 20

= 4(100) - 40 - 20

= 400 - 60

= 340

This exponential function can be used to model the value of a dirt bike valued at $9000 over time. The function expresses the amount of value the bike loses each year, which is 18%. This means that the value of the bike decreases by 18% each year.

f(x) = 9000(0.82)^x

After 4 years, the bike costs $6955.12.

f(x) = 9000(0.82)^x

After 100 years, the bike costs $8.87.

This exponential function can be used to model the value of a dirt bike valued at $9000 over time. The function expresses the amount of value the bike loses each year, which is 18%. This means that the value of the bike decreases by 18% each year. After 4 years, the bike would cost $6955.12. After 100 years, the bike would cost $8.87. This exponential function can be used to determine the value of the bike at any given time, depending on the number of years that have passed since the bike was purchased.

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For given linear equations the values for following are m= -9, x=2, b=10, w=-4.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As given linear equations are

4m-5=-41

m= -9

-11=1-6x

x=2

4/5*b+13

b=10

-1/2*w-8=-6

w= -4

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Considering the figure in the problem the longest side is

In a triangle, the longest side is located opposite from the largest angle, while the shortest side is located across from the smallest angle.

Triangle inequity: Any triangle in which the total of any two sides is greater than the length of the third side is a proper way a to form a triangle

According to the figure, the largest angle is 74 degrees.

The side opposite the largest angle is GH which is in the option A

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Answer:

are know :D Hello, what are you doing

Answer:

The average points received by those students who did not pass the test successfully would be 4 points.

Step-by-step explanation:

Step 1: We know that all students wrote the test and received an average of 6 points.

Step 2: We also know that 60% of those students passed the test successfully and received an average of 8 points.

Step 3: This means that the remaining 40% of students did not pass the test successfully.

Step 4: Since the average points for all students was 6 points and the average points for those who passed the test was 8 points, the average points for those who did not pass the test would be 4 points.

The speed of Mr. Black to his friend's house is 60 miles per hour.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Speed = Distance travelled / Time taken

Let x be the speed of Mr. Black to his friend's house.

Let d be the distance in miles that Mr. Black travelled to reach friend's house.

Time taken to reach friend's house = 2 hours

x = d / 2 ⇒ d = 2x

Speed of Mr. Black during return is 20 mph slower.

Speed during return = x - 20

The trip back took 1 hour longer.

Time = 2 + 1 = 3 hours

x - 20 = d / 3

Substituting d = 2x in the above equation,

x - 20 = 2x / 3

3 (x - 20) = 2x

3x - 60 = 2x

x = 60

Hence the speed is 60 mph to his friend's house.

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