Right Angle Trigonometry

Answer:

y = (1/25)x^2 - 1

Step-by-step explanation:

To begin, we can use the fact that the x-intercepts of the parabola are at (5, 0) and (-6, 0) to determine the x-intercepts form of the equation. The x-intercepts form of a parabola is given by:

(x - r)(x - s) = 0,

where r and s are the x-coordinates of the x-intercepts.

Using this form, we can write:

(x - 5)(x + 6) = 0

Expanding this equation gives:

x^2 + x - 30 = 0

Next, we use the fact that the vertex of the parabola is at (0, -1) to determine the y-intercept form of the equation. The y-intercept form of a parabola is given by:

y = a(x - h)^2 + k,

where (h, k) is the vertex.

Substituting (0, -1) into this equation gives:

y = a(x - 0)^2 - 1

Simplifying gives:

y = ax^2 - 1

Now we can use the fact that the parabola passes through the point (5, 30) to determine the value of a. Substituting x = 5 and y = 0 into the equation above gives:

0 = a(5)^2 - 1

Solving for a gives:

a = 1/25

Substituting this value of a into the equation above gives the final equation of the parabola:

y = (1/25)x^2 - 1

5/0-6/0-41=

hope that helps okay :) if not really really sorry

Therefore , the solution of the given problem of equation comes out to be the system of equations has an answer of x = -10.51 and  y = 6.26.

In intricate algorithms, variable words are typically employed to demonstrate consistency between two opposing arguments. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider the specifics of the above x + 7 suggestions. improving in this case provides b + 7 while constructing y + 7 before integrating.

Here,

Let's apply these steps to the provided equation system:

=> -8y = 5x + 17 ...(1)

=> -7y = -2x - 17 ...(2)

Solve equation (1) for x in terms of y in step 1:

=> -8y = 5x + 17

=> 5x = -8y - 17

=> x = (-8y - 17)/5

Step 2: Replace the value of x in equation (2) with the expression from step 1:

=> -7y = -2((-8y - 17)/5) - 17

Step 3: Address the equation that results for y.

=> -7y = (-16y - 34)/5 - 17

=> -35y = -16y - 34 - 85

=> -35y + 16y = -119

=> -19y = -119

=> y = (-119)/(-19)

=> y = 6.26

Step 4: Replace the formula for x from step 1 with the value of y obtained in step 3:

=> x = (-8(6.26) - 17)/5

=> x = -10.51

Consequently, the system of equations has an answer of x = -10.51 and  y = 6.26.

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Answer:

69/5 or 13.8

Step-by-step explanation:

..…........

a. The difference between the high and the low prices on October 20 was $3.33.

b. The actual volume of Discovery Group shares posted on October 27 was 23,600.

c. The closing price for Discovery Group on October 19 was $38.50

The percentage decrease is calculated below as follows:

closing price on October 19 = $38.50

the opening price on October 20 = $37.22

the percentage decrease in prices = (37.22 - 38.50) / 38.50

the percentage decrease in prices = -3.33% to the nearest hundredth

e. The net change =  $32.00 - $38.50

The net change = -$6.50.

The percentage change = (-6.50 / 38.50) * 100

The percentage change  = -16.9% to the nearest tenth percent

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Answer:

P = 11 + (1/2)π(11) = 11 + 5.5π = 28.279 cm

Letting π = 3.142:

P = 11 + (1/2)(3.142)(11) = 28.281 cm

The equation will be w = 40b

To find the total weight (w) of the soil in pounds when Yuki stacks b bags, you can use a simple linear equation. Each bag weighs 40 pounds, so the equation will be: w = 40b

This equation shows that the total weight (w) of the soil in pounds is equal to the number of bags (b) multiplied by the weight of each bag (40 pounds).

The above answer is based on the information below as seen in the picture;

Yuki works at a garden store. She is stacking 40 pounds bags of soil.

write an equation that gives the total weight, w, of the soil in pounds when Yuki stacks b bags.

+ - . =         b, w, 40

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Answer: Ok so first you would take the 86 and multiply it by .2 or 20% and that would get you 17.2 for blank 2

then you would take 86 and subtract 17.2 to get 68.8 for blank 3

sooo... he would pay 68 dollars and 80 cents with the coupon

Step-by-step explanation:

im really smart and good at math : )

They form a parallelogram because opposite sides of the given points have an equal slope.

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To prove that the four points (2,1), (-1,-5), (1,5), and (-2,-1) are the vertices of a parallelogram, we need to show that opposite sides are parallel.

First, we can find the slope of the line connecting (2,1) and (-1,-5):

m1 = (1 - (-5)) / (2 - (-1)) = 6/3 = 2

Next, we can find the slope of the line connecting (1,5) and (-2,-1):

m2 = (5 - (-1)) / (1 - (-2)) = 6/3 = 2

Since the slopes are the same, the line segments connecting these points are parallel.

Now, we can find the slope of the line connecting (2,1) and (1,5):

m3 = (5 - 1) / (1 - 2) = -4

Next, we can find the slope of the line connecting (-1,-5) and (-2,-1):

m4 = (-1 - (-5)) / (-2 - (-1)) = 4/3

Since the slopes are different, the line segments connecting these points are not parallel.

However, we can also see that the line connecting (1,5) and (-1,-5) has the same slope as the line connecting (-2,-1) and (2,1), which is:

m5 = (5 - (-5)) / (1 - (-1)) = 10/2 = 5

Therefore, the line segments connecting (1,5) and (-1,-5), and (-2,-1) and (2,1) are parallel.

Since opposite sides are parallel, the four points (2,1), (-1,-5), (1,5), and (-2,-1) form a parallelogram.

Therefore, they form a parallelogram because opposite sides of the given points have an equal slope.

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Cash received for interest during  2014 was $3,500 .The following equation can be used to determine the amount of money received as interest in 2014:

Amount received as interest equals Interest Income for 2014 plus the decline in Interest Receivable

The difference between the balance of interest receivable at December 31, 2013, and at December 31, 2014, can be used to calculate the decline in interest receivable:

Reduced interest due = Interest due at December 31, 2013, minus Interest due at December 31, 2014, which equals $1,100 minus $1,400, or -$300.

The fact that the balance of interest receivable increased from 2013 to 2014 indicates that the company produced more interest money during the year than it received. In light of this, the money earned on interest in 2014 is:

Interest income from 2014 plus a decrease in interest receivable equals $3,200 minus (-$300) to $3,500 in interest payments received.

Hence, $3,500 is the correct response (C).

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Yes, the transformation is a rigid motion because the angle measures and the distances between the vertices of the image are the same as the corresponding angle measures and distances in the preimage.

Since the shape and size are the same in both the preimage and the image, and only the position has changed, this transformation is considered a rigid motion. Rigid motions, such as translations, rotations, and reflections, preserve the shape and size of the original figure.

Assuming the shape has been bent, it means that the angle measures and distances between the vertices have been altered. But this is not the case.

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the condition for a function's graph to pass through the origin in polar coordinates is that the function's value at θ=0 is equal to zero, while the condition for a function's graph to pass through the origin in rectangular coordinates is that the function's value at (0,0) is equal to zero.

How to solve the question?

In polar coordinates, a graph of a function passes through the origin if and only if the function's value at θ=0 is equal to zero. This is because the origin in polar coordinates represents the point (r=0, θ), where r is the distance from the origin and θ is the angle of the point with respect to the positive x-axis. When a function's value at θ=0 is equal to zero, it means that the point on the graph at θ=0 lies on the positive x-axis and has a distance of r=0 from the origin, which is the origin itself.

In contrast, a graph of a function in rectangular coordinates passes through the origin if and only if the function's value at (0,0) is equal to zero. This is because the origin in rectangular coordinates represents the point where the x and y axes intersect, and a point on the graph with coordinates (x,y) passes through the origin if and only if x=0 and y=0, which means the function's value at (0,0) is equal to zero.

In summary, the condition for a function's graph to pass through the origin in polar coordinates is that the function's value at θ=0 is equal to zero, while the condition for a function's graph to pass through the origin in rectangular coordinates is that the function's value at (0,0) is equal to zero.

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An equation that expresses the relationship between the lengths of the three sides is a^2 + b^2 = c^2.

In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.

The relationship between the lengths of the three sides in a right triangle is described by the Pythagorean Theorem, which states that the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

Mathematically, this can be represented as:

a^2 + b^2 = c^2

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

For the given right triangle with lengths 5, 2.2360679775, and 5.47722557505, we can plug in the values of a, b, and c to get:

5^2 + 2.2360679775^2 = 5.47722557505^2

which simplifies to:

25 + 5 = 30

This equation is true, indicating that the given lengths do indeed form a right triangle according to the Pythagorean Theorem.

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The missing measure of the square pyramid and the net would be 11.18 units.

The amount of wood that Dee needs to make the doghouse is 98 square feet of wood.

The missing measure is the side of the pyramid and this can be found using the Pythagorean Theorem with 11 ft being the height of the triangle and 4/ 2 = 2 being one of the sides and the missing measure being the hypotenuse.

The side length is:

= √ (2 ² + 11²)

= √ ( 4 + 121)

= 11.18 units

To determine the amount of wood needed for Dee's doghouse, we need to calculate the surface area of the square pyramid using its net.

Calculate the area of all four triangular faces:

Total area of triangular faces = 4 x area of one triangular face = 4 x 20.5 = 82 square feet

Calculate the total surface area of the pyramid (net):

Total surface area = area of base + total area of triangular faces = 16 + 82 = 98 square feet

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The graph of a quadratic function in the form of y = ax² + bx + c, where "a" is not equal to zero, has a minimum value when "a" is positive.

what is quadratic function ?

A quadratic function is a second-degree polynomial function of the form f(x) = ax² + bx + c, where "a", "b", and "c" are constants, and "a" is not equal to zero. The graph of a quadratic function is a U-shaped curve called a parabola.

In the given question,

The graph of a quadratic function in the form of y = ax² + bx + c, where "a" is not equal to zero, has a minimum value when "a" is positive. This is because the parabola opens upward, and the vertex of the parabola, which represents the minimum point of the function, is located at the point (-b/2a, c - b²/4a).

On the other hand, if "a" is negative, the graph of the quadratic function will have a maximum value. This is because the parabola opens downward, and the vertex of the parabola represents the maximum point of the function.

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Therefore, can b and c are the same better deal since they have the same price per cubic inch using the volume of a cylinder.

To compare which can of beans is a better deal, we need to calculate the volume of each can and divide it by the price. The can with the highest volume per dollar is the better deal.

a) The volume of the can is V=πr²h=(3.14)(3²)(9)=254.34 cubic inches. The price per cubic inch is $39.95/254.34 = $0.157, rounded to three decimal places.

b) The volume of the can is V=πr²h=(3.14)(2²)(3)=37.68 cubic inches. The price per cubic inch is $5.96/37.68 = $0.158, rounded to three decimal places.

c) The volume of the can is V=πr²h=(3.14)(3²)(3)=84.78 cubic inches. The price per cubic inch is $13.41/84.78 = $0.158, rounded to three decimal places.

Therefore, can b and c are the same better deal since they have the same price per cubic inch.

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The length of the diagonal from the given shape above would be = 12

To calculate the length of the diagonal from P to Q, the Pythagorean theorem should be used such as;

C² = a² + b²

The Pythagorean theorem states that the the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

Therefore;

C = ?

a = 8

b = 9

C² = 8²+9²

C² = 64+81

C² = 145

C = √145

= 12.

Therefore, the length of the diagonal P to Q of the given shape above is 12.

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Answer:

what are the options?

Step-by-step explanation:

Answer: the answer is d) 0.3466.

Step-by-step explanation:

Starting with the equation:

6e^(4x) - 3 = 21

Add 3 to both sides:

6e^(4x) = 24

Divide both sides by 6:

e^(4x) = 4

Take the natural logarithm of both sides:

ln(e^(4x)) = ln(4)

Use the property of logarithms that ln(e^y) = y:

4x ln(e) = ln(4)

Simplify:

4x = ln(4)

Solve for x by dividing both sides by 4:

x = (1/4) ln(4)

Using a calculator, we get:

x ≈ 0.3466

Therefore, the answer is d) 0.3466.

The table for the function f(x) = 2ˣ should be completed as follows;

x         -4      -3     -2    -1    0

f(x)      1/16   1/8    1/4   1/2  1

As x approaches negative infinity, f(x) decreases.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the negative power rule to the function based on each of the x-values, we have the following:

f(x) = 2⁰ = 1

f(x) = 2⁻¹ = 1/2

f(x) = 2⁻² = 1/2² = 1/4

f(x) = 2⁻³ = 1/2³ = 1/8

f(x) = 2⁻⁴ = 1/2⁴ = 1/16

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Answer:

425.2

Step-by-step explanation:

v = 1/3[tex]\pi r^{2} h[/tex]  If the diameter is 12,  then the radius is 6

v = [tex]\frac{3.14(6^{2})12 }{3}[/tex]

v = [tex]\frac{3.14(36)(12)}{3}[/tex]

v = 452.16

Helping in the name of Jesus.

After comparing the data, a measure of variability for both sets of data to  be utilised to find the place with the most stable temperature: C. Range, because Sunny Town is skewed.

Skewness is a measure of the asymmetry of a box plot (box-and-whisker plot) or histogram in mathematics, and as such, a box plot (box-and-whisker plot) or histogram has a normal distribution when it is symmetrical.

We may rationally establish that Sunny Town's box plot (box-and-whisker plot) is distorted by closely inspecting it.

Conversely, the Desert Landing box plot (box-and-whisker plot) is symmetrical (vertical line dividing the box into two equal halves), which simply means that both whiskers on either side of the box plot (box-and-whisker plot) are roughly equal and symmetric.

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Answer: To find the average change in temperature per hour, we need to divide the total change in temperature by the number of hours.

The temperature dropped 25 degrees over 8 hours, so the average change per hour is:

25 degrees / 8 hours = 3.125 degrees per hour

Therefore, the temperature on top of Mt. Katahdin dropped by an average of 3.125 degrees per hour.

Step-by-step explanation: The temperature on top of Mt. Katahdin dropped by an average of 3.125 degrees per hour.

The cost of the envelope and stamp may vary depending on the location and the method of delivery. In this example, we assumed that the cost of the envelope is $0.15 and the cost of the stamp is $0.39, but these values may change based on the specific circumstances.

What is cost?

Cost" is the amount of money or resources that are required to produce, acquire, or obtain something. In other words, cost refers to the expenses that are incurred in the process of acquiring or producing a good or service.

For example, the cost of producing a product may include the cost of raw materials, labor, overhead expenses, and other related costs. Similarly, the cost of acquiring a product may include the purchase price, taxes, shipping costs, and any other fees or expenses associated with the purchase. Overall, cost is a crucial factor in business and economics, as it determines the profitability of a venture and helps to make informed decisions regarding investments and pricing strategies

To find the cost of the laptop after the mail-in rebate and the cost of the envelope and stamp, we can follow these steps:

Subtract the mail-in rebate from the original price of the laptop:

$2,149.99 - $200 = $1,949.99

Add the cost of the envelope and stamp to the cost of the laptop after the mail-in rebate:

$1,949.99 + $0.15 + $0.39 = $2,090.53

Therefore, the cost of the laptop after the mail-in rebate and the cost of the envelope and stamp is $2,090.53.

To explain this calculation, we first subtract the mail-in rebate of $200 from the original price of the laptop, which gives us the price of the laptop after the rebate. Then, we add the cost of the envelope and the stamp to this price to get the total cost of the laptop after the rebate and the cost of the envelope and stamp.

Therefore, The cost of the envelope and stamp may vary depending on the location and the method of delivery. In this example, we assumed that the cost of the envelope is $0.15 and the cost of the stamp is $0.39, but these values may change based on the specific circumstances.

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By using slope intercept , These were the two points on the line: (0,-2) and (7,2).

A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.

We may use the slope-intercept form of a line, which is y=mx+b where m is the slope and b is the y-intercept, to graph the line y=4/7x-2. Therefore, m=4/7 and b=-2.

These variables allow us to plot two spots along the line. Since the line crosses the y-axis at (0,-2) (the y-intercept), that location will be one of the points.

We can utilize the slope of 4/7 to locate a different point along the line. This indicates that we advance up 4 units in the y direction for every 7 units we move to the right (in the x direction). We can therefore move 7 units to the right and then 4 units up, starting at (0,-2), to reach (7,2).

So now we have two points on the line: (0,-2) and (7,2). These points can be plotted on a coordinate plane, and then a straight line can be drawn through them to create the graph.

Graph given below:

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Answer: 3.610^5+4.810^4 in scientific notation is 4.08*10^5.

Step-by-step explanation: The initial step to convert 3.610^5+4.810^4 into scientific notation is to combine the two values.

The sum of 3610 multiplied by 10 to the power of 5 and 4810 multiplied by 10 to the power of 4 is equal to adding 3610 multiplied by 10 to the power of 4 and 4810 multiplied by 10 to the power of 4, resulting in 40.8 multiplied by 10 to the power of 4.

We can convert 40.8*10^4 to scientific notation by shifting the decimal point to the left until there is only one non-zero digit to the left of the decimal, and denoting the number of decimal places moved with a 10 exponent.

Rewording: When you raise 40.810 to the power of 4, the result is 4.0810 to the power of 5 when you add 1 to the exponent. This is equivalent to multiplying 4.08 by 10 and raising it to the power of 5.

The measure of angle ∠B in triangle ABC will be 35.89°.

Given that:

Sides, AC = 23 miles and AB = 22 miles

Angle, ∠A = 110°

The sine law in the triangle ΔABC is given as,

AB / sin C = BC / sin A = AC / sin B

23 / sin C = BC / sin 110° = 23 / sin B

The value of BC is calculated as,

BC² = AB² + AC² - 2 AB·AC cos A

BC² = 22² + 23² - 2 x 22 x 23 x cos 110°

BC² = 1359.124

BC = 36.87 miles

The value of angle B is calculated as,

36.87 / sin 110° = 23 / sin B

sin B = 0.586

∠B = 35.89°

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There are 46 students don't drink soda.

Let's use a Venn diagram to represent the information given in the problem:

                         Athletes

                          /        \

                         /          \

          Soda     /            \    No Soda

                       /              \

                      /                \

                     /                  \

       ----------------------------------------------

      |                                              |

      |                                              |

      |                                              |

Drink                                      No Drink

      |                                              |

      |                                              |

      |                                              |

       ----------------------------------------------

      |                                              |

      |                                              |

      |                                              |

     19                                            24

      |                                              |

      |                                              |

      |                                              

    ----------------------------------------------

      |                                              |

      |                                              |

      |                                              |

     33                                             10

      |                                              |

      |                                              |

      |                                              |

    ----------------------------------------------

      |                                              |

      |                                              |

      |                                              |

     24                                             22

      |                                              |

      |                                              |

      |                                              |

       ----------------------------------------------

The diagram, we can see that there are 24 students who drink soda and are athletes, 19 who drink soda but are not athletes, 33 who are not athletes but drink soda, and 22 who are neither athletes nor soda drinkers.

The number of students do not drink soda, we need to add the number of students who are athletes but do not drink soda to the number of students who are neither athletes nor soda drinkers:

Number of students who don't drink soda

= Number of athletes who don't drink soda + Number of students who are neither athletes nor soda drinkers

Number of athletes who don't drink soda = Total number of athletes - Number of athletes who drink soda = 43 - 19 = 24

Number of students who are neither athletes nor soda drinkers = 22

The number of students who don't drink soda is:

Number of students who don't drink soda = 24 + 22 = 46.

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The amount of the sales tax is 0.26

Now, The sales tax is 4%.

The cost of lunch is 6. 50.

=> 4% of 6.50

4/ 100 × 6.50

0.04 × 6.50

=> 0.26

Hence, The amount of the sales tax is 0.26

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Answer:

10 cm

Step-by-step explanation:

V =1/3 x π x r² x h

94.25 =1/3 x π x 3² x h

94.25 ÷ 3π =h

so, h= 10 cm