Graham wants to take snowboarding lessons at a nearby ski resort that charges $40 per week. The resort also charges a one-time equipment-rental fee of $99 for uninterrupted enrollment in classes. The resort requires that learners pay for three weeks of classes at a time​

Step-by-step explanation:

law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a,b,c being the sides of the triangle, A, B, C are the corresponding opposite angles in the triangle.

the angle of depression is the external angle of the triangle vertex at the balloon. that means the internal angle is 60°, as both together must be 90° (the angle between the height of the balloon and the horizontal line at the balloon).

the angles at the ground at the fire are mirrored : the internal angle there is 30°, the external angle is 60°.

and so,

height/sin(30) = 150/0.5 = distance/sin(60)

distance = sin(60)×150/0.5 = sin(60)×300 =

= 259.8076211... ft ≈ 260 ft

Answer:

Its d ik becuse im smart and i lernt this in like 2nd grade

Answer: 1/24

Step-by-step explanation:

Multiply the denominator with 6 to divide it into 6 equal parts

= 1/(4•6)

= 1/24

Answer:

y = -x

Step-by-step explanation:

We can use two points on the line to write the equation.

Using ( 0,0) and (2,-2), we can find the slope.

m = ( y2-y1)/(x2-x1)

    = ( -2-0)/(2-0)

    = -2/2

    = -1

The y intercept is 0.

y = mx+b where m is the slope and b is the y intercept.

y = -x+0

y = -x

Answer:

first option (30x4 − 20x3 + 15x2)

Answer:

2 cups of flour

Step-by-step explanation:

We want to find the total amount of flour, which means we need to add.

3/4 + 2/4 + 3/4 =

8/4

We can simplify this term.

8/4 =2

2 cups of flour

Answer:

2 cups of flour

Step-by-step explanation:

A bread recipe has,

3/4 cup of rye flour

2/4 cup of wheat flour

3/4 cup of white flour

So, to find the total amount of flour, add all the given fractions together.

[tex]\sf Total\: amount\: of\: flour = rye \:flour + wheat\: flour + white \:flour\\\\\sf Total\: amount\: of\: flour =\frac{3}{4} +\frac{2}{4} +\frac{3}{4} \\\\\sf Total\: amount\: of\: flour =\frac{3+2+3}{4} \\\\\sf Total\: amount\: of\: flour =\frac{8}{4} \\\\\sf Total\: amount\: of\: flour =2 \:cups[/tex]

f[g(-2)] = 2 as the function f(x) = x - 5 must then be used to evaluate the function f[g(-2)] .

A function is a mathematical construct that transforms a set of inputs (referred to as the domain) into a single output from another set (called the range). A function is, in other words, a rule that allots precisely one output to each input in the domain. The notation f(x) is frequently used to denote functions, where f stands for the function name and x for the input value. As an illustration, the function f(x) = 2x + 1 doubles any input x, adds 1, and returns the result.

given

To begin, we must calculate g(-2) using the formula g(x) = x2 + 3:

[tex]g(-2) = (-2)^2 + 3 = 4 + 3 = 7[/tex]

The function f(x) = x - 5 must then be used to evaluate the function f[g(-2)]:

f[g(-2)] = f(7) = 7 - 5 = 2

Hence, f[g(-2)] = 2.

f[g(-2)] = 2 as the function f(x) = x - 5 must then be used to evaluate the function f[g(-2)] .

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

Triangle JKL's area is 3 square units as a result.

The vertices' coordinates and the following formula must be used to determine the area of triangle JKL:

Area equals 1/2*base*height

We must first determine the triangle's height and base length. The distance between points J and K, which is the base, is:

base = √[(x2 - x1)² + (y2 - y1)²]

= √[(-4 - (-7))² + (-8 - (-9))²]

= √[3² + 1²]

= √10

The height is calculated as the distance between point L and the base-containment line. To calculate it, we can use the following formula for the separation between a point and a line:

height = |(y2 - y1)x0 - (x2 - x1)y0 + x2y1 - y2x1| / √[(y2 - y1)² + (x2 - x1)²]

= |(-9 - (-8))(-5) - (-7 - (-4))(-6) + (-4)(-9) - (-8)(-7)| / √[(1)² + (3)²]

= 6 / √10

Now, we can enter the height and base values into the triangle's area formula:

Area = 1/2 * √10 * 6 / √10

= 3

Triangle JKL's area is 3 square units as a result.

Learn more about Coordinate geometry here:

brainly.com/question/18269861

#SPJ1

The amount of coffee of type A that was used is given as follows:

27 lbs.

The amounts of each type of coffee used are obtained using a system of equations, for which the variables are given as follows:

The total cost was of 503.55, hence:

5.75x + 4.3y = 503.55.

The amount of coffee B used was the triple of the amount of coffee A used, hence:

y = 3x.

Replacing the second equation into the first, the amount of coffee A used is given as follows:

5.75x +  4.3(3x) = 503.55

x = 503.55/18.65

x = 27 lbs.

More can be learned about a system of equations at https://brainly.com/question/30374328

#SPJ1

A. The equation that relates these variables is:

d = s * t. B. The biker would travel 10 miles in 20 minutes. C. The biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.

a. Let's define the variables:

t = time in minutes

d = distance traveled by the biker in miles

s = speed of the biker in miles per minute

The equation that relates these variables is:

d = s * t

b. If the biker travels for 20 minutes, we can use the equation above to find the distance traveled:

d = s * t

d = s * 20 (since t = 20 minutes)

We need to know the speed of the biker to calculate the distance traveled. Let's assume that the biker's speed is 0.5 miles per minute (which is equivalent to 30 miles per hour):

d = 0.5 * 20

d = 10

Therefore, the biker would travel 10 miles in 20 minutes.

c. If the biker traveled 48 miles, we can rearrange the equation above to find the time:

d = s * t

t = d / s

We need to know the speed of the biker to calculate the time. Let's assume that the biker's speed is still 0.5 miles per minute:

t = 48 / 0.5

t = 96

Therefore, the biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.

learn more about distance: https://brainly.com/question/26046491

#SPJ1

After solving the given equation 3x+7y=11 we know that (A) (6, -1)  lies on the graph of the given equation.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2.

A noun that counts.

When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.

So, we are asked to identify the point on its graph.

(6, -1)

Adding "x=6" and "y=-1"

3x+7y=3×6+7×(-1)

= 18-7

= 11

Thus, on the graph of 3x+7y=11, (6, -1) is located.

(1,-2)

X = 1 and Y = -2

3x+7y=3×1+7×(-2)

= 3-14

= -11

As a result, the graph of 3x+7y=11 does not contain (1, -2)

(0,-4)

X = 0 and Y = -4

3x+7y=3×0+7×(-4)

= -28

Hence, the graph of 3x+7y=11 does not contain (0, -4)

(0,4)

By setting x=0 and y=4,

3x+7y=3×0+7×4

= 28

In light of this, the graph of 3x+7y=11 does not contain (0, 4)

Therefore, after solving the given equation 3x+7y=11 we know that (A) (6, -1)  lies on the graph of the given equation.

Know more about an equation here:

https://brainly.com/question/2972832

#SPJ1

Complete question:

Which ordered pair is on the graph of equation 3x+7y=11?

a. (6,-1)

b. (1,-2)

c. (0,-4)

d. (0,4)

Answer:

differentiate between tropical and subtropical climate zone on the basis of climate and economic activities in 4 points class 10

Answer:

960 pages

Step-by-step explanation:

Answer:g/2h

Step-by-step explanation:

Answer:

The area of the shaded region is 21.

Step-by-step explanation:

Since point E lies halfway between AB and BC, the area of the shaded region (As) consists of two identical triangles with base equal to AB and height equal to half the measure of BC:

[tex]A_s=2\times A_t[/tex]

Where At is the area of each triangle.

[tex]A_t=\dfrac{AB\times BC/2}{2}[/tex]

[tex]A_t=\dfrac{AB\times BC}{4}[/tex]

We know AB=7 and BC=6, thus:

[tex]A_t=\dfrac{7\times6}{4} =\dfrac{42}{4}[/tex]

Simplifying:

[tex]A_t=\dfrac{21}{2}[/tex]

Finally:

[tex]A_s=2\times\dfrac{21}{2}[/tex]

[tex]A_s=21[/tex]

The area of the shaded region is 21.

Note the area of the shaded region is half the area of the rectangle.

Answer:

x = -9

Step-by-step explanation:

To solve for x in this equation, we first need to simplify the right-hand side by distributing the 3:

189 = -6x + (-21x - 54)

Next, we can combine like terms on the right-hand side:

189 = -27x - 54

Adding 54 to both sides:

243 = -27x

Dividing both sides by -27:

x = -9

Therefore, the solution to the equation 189=-6x+3(-7x-18) is x = -9.

Answer:

To solve for x in the equation 189=-6x+3(-7x-18), we can use the following steps:

Distribute the 3 to the terms inside the parentheses:

189 = -6x + (-21x - 54)

Combine like terms on the right side of the equation:

189 = -27x - 54

Add 54 to both sides of the equation:

189 + 54 = -27x

Simplify the left side of the equation:

243 = -27x

Divide both sides by -27:

x = -9

Therefore, x is equal to -9.

Hope This Helps!

The lengths of the edges of the cubes are 45cm and 63cm respectively.

To determine the edge length of a cube with a volume of 91,125 cm³, we can use the formula:

Volume of a cube = edge length³

Plugging in the given value, we get:

91,125 = edge length³

Taking the cube root of both sides, we get edge length

edge length ≈ 45

Therefore, the edge length of the cube is approximately 45 cm.

To determine the side length of a square with an area of 3,969 cm², we can use the formula

Area of a square = side length²

Plugging in the given value, we get:

3,969 = side length²

side length = √3,969

Using a calculator, we can simplify this to

side length ≈ 63

To know more about surface area of cube, click here,

https://brainly.com/question/13789496

#SPJ1

Answer:

[tex]1 \frac{1}{81} \ [/tex]

Solution:

[tex] \frac{a - 1}{a} = \frac{2}{3} [/tex]

1) 2a = 3(a - 1)

2a = 3a - 3

2a - 3a = -3

-a = -3 / * (-1)

a = 3

2) Replace the a with 3 in this:

[tex] \frac{ {a}^{4} + 1}{ {a}^{4} } [/tex]

[tex] \frac{ {3}^{4} + 1}{ {3}^{4} } = \frac{81 + 1}{81} = \frac{82}{81} = 1 \frac{1}{81} [/tex]

I don't know if I got this right, but at least I tried

Answer:

I think its C. sorry if I'm wrong.

Answer: -7

Step-by-step explanation:

in the linear equation, y=mx+b, m represents the slope of the line, so when looking at an equation the best way to find the slope is to find where the m variable would be

The function oscillates between two horizontal asymptotes, y=3 and y=-3, as x approaches the vertical asymptotes.

How to study graph?

To graph the function y=3cot(x) between 0 and 2, we can start by identifying the key characteristics of the cotangent function. The cotangent function is defined as the ratio of the adjacent side to the opposite side of a right triangle, with respect to a given angle. As such, the cotangent function is periodic with a period of π and has vertical asymptotes at x=nπ, where n is an integer.

The coefficient of 3 in the given function y=3cot(x) vertically stretches the function by a factor of 3, and does not affect the period or the vertical asymptotes.

Between 0 and 2, there are two vertical asymptotes at x=0 and x=π. To graph the function, we can plot a few points along the curve, using the symmetry properties of the cotangent function. Specifically, the cotangent function is odd, meaning that cot(-x)=-cot(x), and thus the graph is symmetric about the origin.

At x=π/4, we have cot(π/4)=1, and thus y=3cot(π/4)=3. Similarly, at x=3π/4, we have cot(3π/4)=-1, and thus y=3cot(3π/4)=-3. Using the symmetry property, we can also plot points at x=-π/4 and x=-3π/4, with y=3cot(-π/4)=-3 and y=3cot(-3π/4)=3, respectively.

Connecting these points with smooth curves, we can see that the graph of y=3cot(x) oscillates between two horizontal asymptotes, y=3 and y=-3, as x approaches the vertical asymptotes at x=0 and x=π.

Overall, the graph of y=3cot(x) between 0 and 2 can be summarized as follows:

There are two vertical asymptotes at x=0 and x=π.

The function oscillates between two horizontal asymptotes, y=3 and y=-3, as x approaches the vertical asymptotes.

The graph is symmetric about the origin.

To know more about functions visit :-

https://brainly.com/question/11624077

#SPJ1

Answer:

d ≈ 546 m

Step-by-step explanation:

using the sine ratio in the right triangle

sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{313}{d}[/tex] ( multiply both sides by d )

d × sin35° = 313 ( divide both sides by sin35° )

d = [tex]\frac{313}{sin35}[/tex] ≈ 546 m ( to the nearest whole number )

The answer of the given question based on series to match the correct summation is the given series matches with option 2: 1 + 0.5 + 0.25 + 0.125 + ...

In mathematics, an infinite series is a sum of infinitely many terms. An infinite series can be thought of as the limit of the sequence of partial sums, which is obtained by adding only the first n terms of the series. If the limit of the sequence of partial sums exists and is finite, then the infinite series is said to be convergent; otherwise, it is said to be divergent.

Infinite series have many applications in mathematics, science, and engineering, and are used to approximate functions, solve differential equations, and model physical phenomena.

The given infinite series is: 3 - 9/4 + 27/16 - 81/64 + ...

This series is a geometric series with first term a = 3 and common ratio r = -3/4.

The formula for the sum of an infinite geometric series with first term a and common ratio r (|r| < 1) is given by:

S = a / (1 - r)

Plugging in the values of a and r, we get:

S = 3 / (1 - (-3/4)) = 3 / (7/4) = 12/7

Therefore, the given series matches with option 2: 1 + 0.5 + 0.25 + 0.125 + ...

To know more about Geometric series visit:

https://brainly.com/question/12383793

#SPJ1

Answer:

a hard one

Step-by-step explanation:

The answer of A is The point (-2,2) is included in the graph of g(x) regardless of the value of b and c.The answer of B the point (2,2) would be transformed to the point (2,1) on the graph of h(x).

What is graph?

A graph is a visual representation of data, functions, or relationships between variables. It is a way of displaying information in a way that is easy to interpret and understand. Graphs typically consist of two axes, the x-axis and y-axis, and points or lines plotted on the graph to represent the data or function being displayed.

There are many different types of graphs, including line graphs, bar graphs, pie charts, scatter plots, and more. Each type of graph is used for different purposes and can display different types of data.

Graphs are commonly used in many fields, including science, economics, finance, engineering, and more. They allow researchers and analysts to easily visualize data and identify trends or patterns, making it easier to draw conclusions and make informed decisions based on the data.

A. To include the point (-2,2), we need to shift the graph of f(x) two units to the right and two units upwards. So we have:

g(x) = a f(x - (-2)) + 2

g(x) = a f(x + 2) + 2

Now we need to find the value of "a". Since the point (3,4) on the graph of f(x) is mapped to the point (2,2) on the graph of g(x), we have:

g(3) = a f(3 + 2) + 2 = 2

4a + 2 = 2

4a = 0

a = 0

Therefore, the function g(x) is:

g(x) = 0 f(x + 2) + 2

g(x) = 2

So the point (-2,2) is included in the graph of g(x) regardless of the value of b and c.

B. The function h(x) is a linear function with slope 2 and y-intercept -1. To find where the point (2,2) would end up after the transformations, we plug in x=2 into h(x) and get:

h(2) = 2(2+1)-3 = 1

So the point (2,2) would be transformed to the point (2,1) on the graph of h(x).

The transformations made to f(x) to obtain h(x) are a horizontal shift to the left by one unit (x+1), a vertical stretch by a factor of 2 (2(x+1)), and a vertical shift downwards by three units (-3).

To know more about graph visit:-

https://brainly.com/question/19040584

#SPJ1

Therefore, the solutions to the quadratic equation x² + 7x - 8 = 0 are -8 and 1. The answers are D and E.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations. Equations can be solved by manipulating the expressions to find the value of the variables that satisfy the equation. Equations can be used to model real-world situations, and they are an important tool in many fields, including mathematics, physics, engineering, and economics.

Here,

To check which values are solutions to the quadratic equation, we can substitute each value into the equation and see if it equals zero.

Substituting -1 into the equation:

(-1)² + 7(-1) - 8 = 1 - 7 - 8 = -14, which is not equal to zero.

Substituting 2 into the equation:

2² + 7(2) - 8 = 4 + 14 - 8 = 10, which is not equal to zero.

Substituting -4 into the equation:

(-4)² + 7(-4) - 8 = 16 - 28 - 8 = -20, which is not equal to zero.

Substituting -8 into the equation:

(-8)² + 7(-8) - 8 = 64 - 56 - 8 = 0, which is equal to zero. Therefore, -8 is a solution to the equation.

Substituting 1 into the equation:

1² + 7(1) - 8 = 1 + 7 - 8 = 0, which is equal to zero. Therefore, 1 is a solution to the equation.

To know more about equation,

https://brainly.com/question/28243079

#SPJ1

Answer:

a. $682.09

Step-by-step explanation:

We can use the present value formula to find the value of the bond today:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

Substituting the given values, we get:

PV = 1000 / (1 + 0.045)^8 = $682.09

Therefore, the bond is worth $682.09 today, which is option (a).

Answer: 80 mph fet stream

Step-by-step explanation:

2576/4 + the jet stream=3216/4- jet stream

simplified, 80 mph