What information does the source supply?

The height of the mountain using the angle of elevation is 3858.85 units.

The three basic categories of trigonometric functions are sine, cosine, and tangent. And from the basic functions, one can deduce the three cotangent, secant, and cosecant functions. In contrast to the fundamental trigonometric functions, the other three functions are essentially employed more frequently.

Let the distance between the mountain and Matt = x.

Then the distance of Susie will be:

S = x - 1200

Matt measure the angle of elevation as 35 degrees.

Using the trigonometric function we have:

tan (35) = h / x

x = h/ 0.7.......(1)

For Susie:

tan(42) = h / x - 1200

0.9(x - 1200) = h

0.9x - 1080.48 = h .........(2)

Substitute the value of x in equation 2:

0.9 ( h/ 0.7) - 1080.48 = h

1.28h - 1080.48 = h

1.28h - h = 1080.48

0.28h = 1080.48

h = 3858.85

Hence, the height of the mountain using the angle of elevation is 3858.85 units.

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Answer:

-2x + 10

Step-by-step explanation:

When you add units you affect the y axis.

Knowing this you can translate it 14 units up by adding 14 + (-4).

By using Python to calculate the value of sin4 is a simple process that involves understanding the concept of radians and using the sine function available in Python's math module.

A radian is a unit of measurement for angles. It is defined as the angle formed when the arc length of a circle is equal to the radius of that circle. This means that an angle of 1 radian is equal to the angle formed by an arc length of 1 radius on a circle.

The sine function, denoted as sin(x), is a mathematical function that takes an angle x as input and returns the ratio of the opposite side to the hypotenuse in a right-angled triangle with an angle x.

Now, we can proceed to calculate the value of sin4 using Python. In Python, the sine function is available in the math module, so we will need to import this module at the beginning of our code. We will then use the sin() function to calculate the sine of 4 radians as follows:

import math

sin4 = math.sin(4)

Here, we are calling the sin() function and passing it the value of 4 as an argument. Since the sine function in Python accepts radians, we do not need to convert 4 to degrees.

Finally, we store the result of this calculation in a variable called sin4. This variable will now hold the value of the sine of 4 radians, which we can use in our program as needed.

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The probability using the fair spinner to get P less than 4 is 3/8.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The total sections = 8.

The probability of less than 4 is:

P(less than 4) = Number of outcomes less than 4/ Total sections

P(less than 4) = 3/8

Hence, the probability using the fair spinner to get P less than 4 is 3/8.

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Answer: ITS 0.25!

Step-by-step explanation: i took the test

All the values of y are calculated, the function table is complete. In this case, the final table looks like this

| x   | -2x | -2x-3 | y  |

| -2  | 4   | 1     | -3 |

| -1  | 2   | -1    | -5 |

| 0   | 0   | -3    | -3 |

| 1   | -2  | -5    | -7 |

| 2   | -4  | -7    | -9 |

The function y=-2x-3 is a linear equation. This means that the graph of the equation is a line with a constant slope. The slope of this line is -2 and the y-intercept is -3. The table above shows the output of the function for different values of x. To calculate the value of y for a given x, the first step is to calculate -2x. Then subtract 3 from the result to get the value of y. For example, for x=-2, -2*(-2)=-4 and -4-3=-3, so y=-3. For x=1, -2*(1)=-2 and -2-3=-5, so y=-5. In this way, the output of the function can be calculated for any given value of x.

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One term in the original equation that needs to be changed to create a new equation with infinitely many solutions is 20 to 21.

An equation is a mathematical or algebraic statement that shows that two or more mathematical expressions are equal or equivalent.

Equations are depicted using the equal symbol (=), unlike mathematical expressions, which consist of variables, constants, numbers, and values.

7(2W + 3) = 14W + 20 does not have a solution because the first expression is unequal to the second expression and cannot be said to be an equation.

7(2W + 3) = 14W + 21 have many solutions for W.

Thus, changing 20 to 21 gives the original equation an indefinite number of solutions for W.

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Peter the rabbit have  51 carrots are left.

one fourth means A quarter is represented in mathematics using fractions. Mathematically, a quarter fraction is a whole divided into four equal parts. where 1 indicates the part being referenced and 4 indicates the number of parts the whole is divided into. In numeric format, it is written as ¼.

so total carrot is 84

and he ate one fourth on that day

so remaining are

84*1/4= 21

21 he eat on that the then remaining =

84 - 21  = 63

63 carrots are remain for next day and

he eat 12 carrot on next day

so remaining = 63 - 12 = 51

so 51 carrot left .

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The sum of expression is 8a + 5b - 9.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

(8a + 2b -4) and (3b-5)

Now, adding the above expression we get

(8a + 2b -4) + (3b-5)

= 8a + 2b - 4 + 3b - 5

= 8a + 2b + 3b -4 - 5

= 8a + b(2+ 3) - 9

= 8a + b(5) -9

= 8a + 5b - 9

Hence, the simplified expression is 8a + 5b - 9.

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We have drawn the graph for the given inequality.

What is inequality?

Inequality is a mathematical statement that compares two values or expressions and shows their relative size. It is represented by the symbols >, <, ≥, or ≤, which respectively mean "greater than", "less than", "greater than or equal to", and "less than or equal to". Inequalities can also include variables and can be used to describe a range of possible values for that variables.

For the given inequality y > -x - 5

we can draw the graph as shown below:

Hence, we have drawn the graph for the given inequality.

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WE CAN USE THE GRAPH THAG CA HELP US IN THE PROBLEM

Answer: 2707

Step-by-step explanation: just  multipli

Answer:

186m^2

Step-by-step explanation:

This compound figure will be divided to three rectangular.

1) 18x9=162

2) (18-12)x2=12

3) 2x6=12

so, total is 161+12+12=186^2

The slope of this situation is equal to: C. 0.85.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = 10.20/12

Slope (m) = 0.85.

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a. yes because they = 0

b. no, negative + negative = negative

c. yeah cause 3 >

d. no, its 0

e. no

The 66 percent in the form of fraction representing the national average of the students graduating within six years from a private and non profit institution  is given by 33 / 50.

Percent of students graduating from private nonprofit institution within six years is equal to 66 percent

Value of one percent is equal to one part of  100

Percent in the form of fraction is given by :

⇒  1 percent = one part of hundred

⇒ 1 percent = ( 1 / 100 )

⇒ 66 percent  = ( 66 / 100 ) in fraction form

Simplify the fraction in more reduced form we get,

⇒ 66 percent  = ( 33 / 50 ) in fraction form

Therefore, the fraction form of the 66 percent students who have graduate within six years from private non-profit institution is equal to  ( 33 / 50 ).

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It will take 10 years for the account to reach $200, as determined by solving the equation A = [tex]325(1 + 0.047/12)^(12t)[/tex] for t.

[tex]A = 325(1+0.047/12)^(12t)[/tex]

[tex]200 = 325(1+0.047/12)^(12t)[/tex]

[tex]200/325 = (1+0.047/12)^(12t)[/tex]

[tex]log_((1+0.047/12))(200/325) = 12t[/tex]

[tex]t = log_((1+0.047/12))(200/325) / 12[/tex]

t = 8.75 years

It will take 9 years for the account to reach $200.

Hassan deposited $325 into an account that pays 4.7% annual interest compounded monthly. We can use a system of equations to determine how many years it will take for the account to reach $200. To do this, we first write an equation to represent Hassan's account balance A after t years. This equation is[tex]A = 325(1+0.047/12)^(12t)[/tex]. We then solve for t by taking the logarithm of both sides, which gives us means that it will take 8.75 years for the account to reach $200, which we round up to 9 years.

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Probability of a successful call 0.3157 = 31.57%  

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

A probability is the number of desired outcomes divided by the number of total outcomes.

The odds of making a sale on a single call are 6 to 13.

This means that in 6+13 = 19 calls, 6 are successful.

What is the probability of a successful call?

p = 6/19 =

0.3157 = 31.57% probability of a successful call.

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The solutions of the system of equations are (-1, 2) and (3, -5)

Here we have a graph of a system of equations. The solutions are all the points where the graphs of the two equations intersect.

Here we can see two intersection points, thus, we have two solutions. We can see that the first intersection is at (-1, 2) and the second intersection is at (3, -5)

So these two are the solutions of the system of equations.

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The given Expression simplifies to -8.1069556e+27

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. A mathematical expression's order of execution is explained using the BODMAS.

Given an equation to solve,

6234653928 + 294292342 - 424624642 x 16515615615165161 x 1156 + 6466456

Let us consider this Expression as A + B - C * D * E + F, with the corresponding terms being equal

By, the BODMAS rule,

First step: Multiply C, D, E. Let this be G

Now, the equation will look like this: A + B - G + F

Second step: We can add and subtract according to the signs now

On solving, the expression simplifies to -8.1069556e+27

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Answer:

Step-by-step explanation:

A square has 4 equal sides therefore to find the side of one we would divide the perimeter by 4. Doing that we get 7 inches.

Now seeing as it has four equal sides in order for us to find the area we would do:

Area = side x side = 7x7 = 49 squared inches

The lower quartile for the given data is -2, since it is the 25th percentile and is the value that lies at the 25th position when the data is sorted in ascending order.

1. Sort the data in ascending order: -4, -2, 1, 1, 6, 8, 12, 15

2. Calculate the 25th percentile: 25th percentile = (n + 1) * 0.25 = (8 + 1) * 0.25 = 2.25

3. The 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively.

4. The lower quartile is -2.

The lower quartile (also known as the 25th percentile) is the value that lies at the 25th position when the data is sorted in ascending order. To find the lower quartile of the given set of data (1, 8, 1, -4, 12, -2, 15, 6), the data needs to be sorted in ascending order. This gives us the following data: -4, -2, 1, 1, 6, 8, 12, 15. Now, to calculate the 25th percentile, we use the formula (n + 1) * 0.25, where n is the number of data points. In this case, n = 8, so the 25th percentile = (8 + 1) * 0.25 = 2.25. This means the 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively. Therefore, the lower quartile for the given data is -2.

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Answer:

Step-by-step explanation:

The formula to calculate the future value of an investment with compounded interest is:

Future value = Principal * (1 + rate/compoundings per year)^(number of years * compoundings per year)

In this case, the principal is $10,000, the interest rate is 2.5%, compounded annually, and the number of years is 20. So, the future value can be calculated as follows:

Future value = $10,000 * (1 + 2.5%/1)^(20 * 1)

Future value = $10,000 * (1.025)^20

Future value = $10,000 * 1.62897526

Future value = $16,289.75

Therefore, $10,000 deposited in an account earning 2.5% interest compounded annually would be worth $16,289.75 in 20 years.

The equivalent expressions are 7(2)^3x = 7(8)^x, 7(1/2)^x = 7(2)^-x, 7(4)^(3x + 1) = 7(2)^(6x + 2), 14(2)^x = 7(2)^(x + 1) and 14(2)^x = 14(4)^(x/2)

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

The expressions on the left and those on the right

To do this, we solve the expressions on the left and look for a match

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

(a) 7(2)^3x

Evaluate the exponent

7(2)^3x = 7(8)^x

(b) 7(1/2)^x

Apply the law of indices

7(1/2)^x = 7(2^-1)^x

So, we have

7(1/2)^x = 7(2)^-x

(c) 7(4)^(3x + 1)

Apply the law of indices

7(4)^(3x + 1) = 7(2^2)^(3x + 1)

So, we have

7(4)^(3x + 1) = 7(2)^(6x + 2)

(d) 14(2)^x and (e) 14(2)^x

Without solving them, we have

14(2)^x = 7(2)^(x + 1)

14(2)^x = 14(4)^(x/2)

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Answer:

3

Step-by-step explanation:

The measure of each angle is [tex]3(75)-100=125^{\circ}[/tex].

Answer:

To find a slope intercept in a table look what x is like this. ( 2,9) 2 is the x-intercept and 9 is the y-intercept. Furthermore, if you get a slope like 0,0 which is the origin put a dot on there.

Answer:

Step-by-step explanation:

use this equation

(y1-y2)/(x1-x2)

The distance Danny travelled in 4 trips is 12 kilometres.

Danny cycled a total of 9 kilometres by making 3 trips to work. After 4 trips to work, the number of kilometres Danny would have cycled in total can be calculated as follows:

Using the proportional relationship,

3 trips = 9 kilometres

4 trips = ?

cross multiply

Distance cycled by Danny = 4 × 9 / 3

Distance cycled by Danny = 36 / 3

Distance cycled by Danny = 12 kilometres

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Variable y in equilateral 60°, Thus correct option is C) 60°.

An equilateral triangle is one with equal-sized sides on all three sides and angles that can all reach a maximum of 60 degrees. An equilateral triangle is a triangle with three equal sides, also referred to as a "regular" triangle. Since all three sides of an isosceles triangle are equal, an equilateral triangle is a special case of an isosceles triangle. Three equal angles of 60 degrees also make up an equilateral triangle.

The sum of all the angles in a triangle is 180.

It is given that the triangle ABC is an equilateral triangle.

So ∠A+∠B+∠C =180°

∠A=B=∠C

3∠A=180°

∠A=60°

Therefore y in ΔABC is C) 60°

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Answer:

c

Step-by-step explanation:

Answer:

x=120

Step-by-step explanation:

sum of angles is 540

given two right angles which is 90

90+90=180

540-180=360

360/3=120

Lines a, b, c, and d are all straight lines in a two-dimensional coordinate system.

Line a has an equation of y=-x-2, which is the slope-intercept form of the equation of a line. This line has a slope of -1 and a y-intercept of -2. Line b is defined by two points (-6,1) and (3,-14), which can be used to find the equation of the line using the point-slope form of a line.

This line has a negative slope and passes through the points (-6,1) and (3,-14). Line c has two points (-1,8) and (4,11), which can also be used to find its equation using the point-slope form. This line has a positive slope and passes through the points (-1,8) and (4,11). Finally, line d has the equation -5x+3y=6, which is the standard form of the equation of a line. This line has a slope of -5/3 and a y-intercept of 2. These four lines are all different but all exist in the same two-dimensional coordinate system.

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