The equation of the circle with center (0, 5) and a point on the circle (2, 4) is x² + (y - 5)² = 5
Define circleIn geometry, a circle is a closed two-dimensional shape that is formed by a set of points that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius.
The equation of a circle with center (h, k) and radius r is given by:
r²=(x - h)² + (y - k)²
In this case, the center of the circle is (0, 5) and a point on the circle is (2, 4). The radius of a circle, which is the separation between its centre and any point on the surface, may be calculated using the following formula:
r = √((2 - 0)² + (4 - 5)²) = √(5)
Now we can substitute the values of the center and the radius into the equation of the circle:
(x - 0)² + (y - 5)² = (√(5))²
Simplifying, we get:
x²+ (y - 5)² = 5
As a result, the circle's equation with its centre (0, 5) and a point on it (2, 4) is:
x² + (y - 5)² = 5
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please answer the question and add the label in your answer please I'm putting 30 points please
For the first graph the two lines are parallel, that is they do not intersect. Thus, the system has no solution. For the second graph the y-intercept is 3 units.
What is solution of system of equation?The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations. There is only ever one solution to a linear equation with one variable. The one and only position at which LHS and RHS are equivalent upon substitution is the unique solution of a linear equation. When there are two simultaneous linear equations, the answer must be an ordered pair (x, y). The ordered pair will in this instance satisfy the set of equations.
For the first graph the two lines are parallel, that is they do not intersect. Thus, the system has no solution.
For the second graph the y-intercept is 3 units.
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08.01 MC) Help ASAP!
The function h(x) is a continuous quadratic function with a domain of all real numbers. The table lists some of the points on the function.
x h(x)
−6 12
−5 7
−4 4
−3 3
−2 4
−1 7
What are the vertex and range of h(x)?
Vertex (−4, 4); Range ∞ ≤ y ≤ 4
Vertex (−4, 4); Range 4 ≤ y ≤ ∞
Vertex (−3, 3); Range 3 ≤ y ≤ ∞
Vertex (−3, 3); Range ∞ ≤ y ≤ 3
The vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).
What is the quadratic functiοn?A quadratic functiοn is a functiοn οf the fοrm where a, b, and c are cοnstants, and a is nοt equal tο 0. It is a type οf pοlynοmial functiοn that can be graphed as a parabοla, which is a symmetric curve that οpens either upwards οr dοwnwards.
Given the table οf pοints fοr the cοntinuοus quadratic functiοn h(x), we can find the vertex and range οf the functiοn. Since the functiοn is quadratic and cοntinuοus, it can be represented in the standard fοrm [tex]$f(x)=a(x-h)^{2}+k,$[/tex], where (h, k) is the vertex οf the parabοla.
Tο find the vertex, we can use the fact that the x-cοοrdinate οf the vertex is given by -b/2a, where a and b are the cοefficients οf the quadratic term and the linear term, respectively. In this case, a = 1 (since the functiοn is cοntinuοus and quadratic), and b can be fοund using any twο pοints οn the parabοla:
[tex]\rm b=(h(x_2)-h(x_1))/(x_2-x1)=(4-7)/(-2+1)=3$[/tex]
Therefοre, the x-cοοrdinate οf the vertex is x = -b/2a = -3/2. Tο find the y-cοοrdinate οf the vertex, we can evaluate the functiοn at this value οf x:
[tex]$\rm h(-3/2)=(1)(-3/2-h)^{2}+k$[/tex]
Tο sοlve fοr k, we can use οne οf the pοints οn the parabοla, say (-6, 12):
[tex]$12=(1)(-6-h)^{2}+k\,$[/tex]
Expanding and simplifying, we get:
[tex]$12=(h-6)^{2}+k$[/tex]
Substituting -3/2 fοr h, we get:
[tex]$\begin{array}{l}{{12=(-(3/2)-6)^{2}+k}}\\\\ {{12=81/4+k}}\\\\ {{k=-21/4}}\end{array}$[/tex]
Therefοre, the vertex οf the parabοla is at the pοint (-3/2, -21/4).
Tο find the range οf the functiοn, we can lοοk at the shape οf the parabοla. Since the cοefficient οf the quadratic term is pοsitive, the parabοla οpens upwards, and the vertex is the lοwest pοint οn the graph. Therefοre, the range οf the functiοn is all real numbers greater than οr equal tο the y-cοοrdinate οf the vertex, which is -21/4. In interval nοtatiοn, we can write the range as (-21/4, infinity).
Hence, the vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).
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A 14- ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?
The company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.
What is inequalities
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
To find the point at which the company starts to turn a profit, we need to find the value of x for which the revenue is greater than the cost of production.
The revenue function is R(x) = 7x, and the cost of production is C(x) = 13x + 132.
So, we need to solve the inequality:
R(x) > C(x)
7x > 13x + 132
Subtracting 13x from both sides, we get:
-6x > 132
Dividing both sides by -6 (and flipping the inequality because we're dividing by a negative number), we get:
x < -22
Therefore, the company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.
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Fill in the blanks using the available answer choices. The vertices of a quadrilateral are A(–3, 1) , B(4, 2) , C(9, –3) and D(2, –4) . Complete the statement to best classify what type of quadrilateral ABCD is. In quadrilateral ABCD , have equal length and there are right angles, so ABCD is best classified as a .
Answer:
Step-by-step explanation:
Fill in the blanks using the available answer choices. The vertices of a quadrilateral are A(–3, 1) , B(4, 2) , C(9, –3) and D(2, –4) . Complete the statement to best classify what type of quadrilateral ABCD is. In quadrilateral ABCD , have equal length and there are right angles, so ABCD is best classified as a .
If the variance of the data values in a population is 441, what is the standard deviation of the data values?
O A. 17
• B. 21
O C. 23
O D. 19
In the given situation if the variance of the data values in a population is 441, the standard deviation of the data values is (B) 21.
What is the standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
The variance's square root is the standard deviation of the data values:
S = √V = √441 = 21
Therefore, in the given situation if the variance of the data values in a population is 441, the standard deviation of the data values is (B) 21.
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Airplanes are sometimes used to fight fires. A certain airplane can deliver ×4104 liters of water in one trip. How much water can this airplane deliver in 38 trips?
Write your answer in scientific notation.
A club had 600 members. 60% of them were males. When 200 new members joined the club, the percentage of male members was reduced to 50%. How many of the new members were males?
Answer: 40
Step-by-step explanation: out of 600 members, 360 (600*0.6) of them were males. When 200 new members joined the club, the total number of members would be 800. If 50% of 800 members were males, then 400 are males. 40 new male members joined.
Solution check for this math problem
1. The solutions of the equation 6/(x+1)= x/(x-1) are x = 2 and x = 3.
2. The solutions of the equation x+ 4/x= -5 are x = -1 and x = -4.
What are the solutions ?
1. 6/(x+1) = x/(x-1)
To solve this equation, we first need to get rid of the fractions by multiplying both sides of the equation by the least common multiple of the denominators, which is (x+1)(x-1):
6(x-1) = x(x+1)
Expanding the left side, we get:
6x - 6 = x² + x
Moving all the terms to one side, we get:
x² - 5x + 6 = 0
This is a quadratic equation that can be factored as:
(x - 2)(x - 3) = 0
So, the solutions are x = 2 and x = 3. However, we need to check if these solutions are valid, because we cannot divide by zero.
Checking x = 2:
6/(2+1) = 2/(2-1)
2 = 2, which is true
Checking x = 3:
6/(3+1) = 3/(3-1)
3/2 = 3/2, which is true
Therefore, the solutions are x = 2 and x = 3.
2. x + 4/x = -5
To solve this equation, we first need to get rid of the fraction by multiplying both sides of the equation by x:
x² + 4 = -5x
Moving all the terms to one side, we get:
x² + 5x + 4 = 0
This is a quadratic equation that can be factored as:
(x + 1)(x + 4) = 0
So, the solutions are x = -1 and x = -4. However, we need to check if these solutions are valid, because we cannot divide by zero.
Checking x = -1:
-1 + 4/(-1) = -5
-1 - 4 = -5, which is true
Checking x = -4:
-4 + 4/(-4) = -5
-4 - 1 = -5, which is true
Therefore, the solutions are x = -1 and x = -4.
What is common multiple?
A common multiple is a number that is a multiple of two or more given numbers. For example, the common multiples of 2 and 3 are 6, 12, 18, 24, etc. These are all numbers that can be divided by both 2 and 3 without a remainder. A common multiple is "common" to the given numbers because it is a multiple of all of them.
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Complete question is:
1. The solutions of the equation 6/(x+1)= x/(x-1) are x = 2 and x = 3.
2. The solutions of the equation x+ 4/x= -5 are x = -1 and x = -4.
I need this in standard form and it’s not showing up??
An expression that equals 24 + 3B in standard form is: 36 + 9m
What is standard form ?
To find an expression that equals 24 + 3B in standard form, we first need to find the value of B and then substitute it into the expression.
Given that B = 3m + 4, we can substitute it into 24 + 3B to get:
24 + 3B = 24 + 3(3m + 4)
Simplifying the expression inside the parentheses, we get:
24 + 9m + 12
Combining like terms, we get:
36 + 9m
Therefore, an expression that equals 24 + 3B in standard form is:
36 + 9m
What is an expression?
In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, etc.) that represents a value or a relationship between values. Expressions can be simple, such as a single number or variable, or complex, such as a combination of several terms with different operators.
For example, 2x + 3y - 5 is an expression that consists of three terms (2x, 3y, and -5) with two operators (+ and -). This expression can be evaluated for different values of x and y to obtain different numerical results.
Expressions can be used to represent mathematical formulas, describe geometric shapes and patterns, and solve real-world problems in a wide range of fields, including science, engineering, finance, and statistics.
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Complete question is: An expression that equals 24 + 3B in standard form is: 36 + 9m,
whats is 100x+10=11 if x isn't a fraction???
I need help because i have work due tomorrow,
i would appreciate if you could help me, please and thank you.
3(2 +6j what’s the answer
Answer: 6 + 18j
Step-by-step explanation: you distribute the 3
Look at ZVSW and ZTSW in the image below.
W
Which of the following is the best description for this pair of angles?
O acute
O complementary
Osupplementary
O straight
VSW and TSW are supplementary angles.
What is supplementary angle?
Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, and you add them together, the result will be a straight line.
What is complementary angle?
Complementary angles are two angles whose sum is equal to 90 degrees (a right angle). In other words, when two angles are complementary, they "complete" a right angle when added together.
According to given information:In geometry, an angle is formed when two lines or rays intersect. Angles are measured in degrees and are classified based on their measures.
The pair of angles VSW and TSW in the image can be classified as supplementary angles.
Two angles are supplementary if their measures add up to 180 degrees.
In this case, angle VSW and angle TSW are adjacent angles that together form a straight angle, which measures 180 degrees. Therefore, VSW and TSW are supplementary angles.
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A painter uses 12 quarts of paint to paint a room and 6 gallons of paint to paint a fence. How many total gallons of paint does the painter use?
Responses
Answer:
9 gallons
Step-by-step explanation:
4 quarts = 1 gallon
12/4=3
3 + 6= 9
9 gallons
Sheila is climbing on a ladder that is attached against the side of a jungle gym wall. She is 7 feet off the ground and is 3 feet from the base of the ladder, which is 18 feet from the wall. How high up the wall is the top of the ladder?
The top of the ladder is about 24.81 feet up the wall.
EquationsWe can use the Pythagorean theorem to solve the problem and assume the height up the wall that the top of the ladder reaches "x". Then, we have a right triangle with legs of 3 feet and x feet and a hypotenuse of 18 + 7 = 25 feet (the length of the ladder). So, we can write:
[tex]3^{2}[/tex] + [tex]x^{2}[/tex] = [tex]25^{2}[/tex]
9 + [tex]x^{2}[/tex] = 625
[tex]x^{2}[/tex] = 616
x = [tex]\sqrt{616}[/tex]
x ≈ 24.81 feet
What are the components of Pythagoras Theorem?According to Pythagoras's Theorem, the square of the length of a right-angled triangle's hypotenuse (the side that faces the right angle) is equal to the sum of the squares of the lengths of the other two sides (the adjacent and opposite sides) and this can be expressed mathematically as follows [tex]c^{2}[/tex]= [tex]a^{2}[/tex] + [tex]b^{2}[/tex] where c is the hypotenuse's length and a and b are the lengths of the other two sides.
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Mona had 32 math problems for homework. She completed 3/4 of them before dinner and the remaining 1/4 after dinner. How many problems did she complete before dinner?
Answer: 24 problems done before dinner
Step-by-step explanation:
Take the 32 total math problems and divide it by 3/4 (the amount of problems done before dinner) getting you 24 problems done before dinner
HELP ASAP 20 POINTS
Answer: $ 16,740
Here's a trick:
Mark down, you subtract
Mark up, you add
**Please mark brainliest**Step-by-step explanation:
Hi, so I see you've been asking for help on these questions.
The concept is quite simple so I am going to walk you through it.
First, your going to multiply 55,800 x .7
Once you've done that you will receive 39,060 you will then subtract 39,060 from 55,800
55,800
-
39,060
= 16,740 is your answer
Find the y-intercept for the equation:
y=2x+6
Y=2x+6
x=2y+6
2y=6-x/÷2
y=[tex]\frac{6-x}{2}[/tex]
Millard Corporation is a wholesale distributor of office products. It purchases office products from manufacturers and distributes them in the West, Central, and East regions. Each of these regions is about the same size and each has its own manager and sales staff.
The company has been experiencing losses for many months. In an effort to improve performance, management has requested that the monthly income statement be segmented by sales region. The company's first effort at preparing a segmented income statement for May is given below.
By analyzing the segmented income statement, Millard Corporation can identify which sales regions are contributing to the overall losses and focus on improving their performance.
We analyze the segmented income statement for Millard Corporation.
Based on the given information, the company distributes office products to three sales regions:
West, Central, and East. Each region has its own manager and sales staff.
To prepare a segmented income statement for May, the company should follow these steps:
Identify the revenue generated by each sales region.
This can be found by tracking the sales from each region and recording them separately.
Allocate direct costs to each sales region.
Direct costs are those that can be directly traced to each region, such as the salaries of the regional manager and sales staff.
Allocate indirect costs to each sales region.
Calculate the contribution margin for each sales region by subtracting the direct costs from the revenue.
This will show the profitability of each region before accounting for the indirect costs.
Subtract the allocated indirect costs from the contribution margin to determine the operating income (or loss) for each sales region.
This information will also help management make informed decisions on resource allocation, budgeting, and strategic planning for the future.
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In Aspen Grove Park, 32 trees are over 15 feet tall. That is 40% of the trees in the park.
Shade the grid to show the percent of trees that are over 15 feet tall.
How many total trees are in the park? You can use your model to help.
trees
Submit HELP ME PLEASE THIS HW IS DUE IN TWO HRS
The trees in Aspen Grove Park are under 15 feet tall are 60%
the total number of trees in Aspen Grove Park, but we can find out that number by using the given percentage of trees that are over 15 feet tall.
To do this, we can use a proportion:
[tex]40/100 = 32/x [/tex]
Simplifying this, we can cross-multiply:
[tex]40x = 32 * 100 [/tex]
[tex]40x = 3200 [/tex]
[tex]x = 80[/tex]
So, there are a total of 80 trees in Aspen Grove Park.
Now, we can calculate the percentage of trees that are not over 15 feet tall by subtracting the percentage of trees that are over 15 feet tall from 100%:
[tex]100% - 40% = 60% [/tex]
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A survey of 240 families showed that
91 had a dog;
70 had a cat;
31 had a dog and a cat;
91 had neither a cat nor a dog, and in addition did not have a parakeet;
7 had a cat, a dog, and a parakeet.
How many had a parakeet only?
Ok
so the math that we need to do for this problem will be:
Total number of families = 240
minus the ones that don't have any pets = 91
minus the families that do have dogs = 91
minus the families that do have cats = 70
add back the overlap of dogs and cats = 31
add back the overlap of dogs cats parakeets = 7
240 - 91 - 91 - 70 + 31 + 7
^ this math will give us the families that ONLY have parakeets
so I stand by what I said before that this is the math you would to do get the answer to your problem
therefore its 26 buddy
Step-by-step explanation:
[tex]n(p) only= \: n(p) - n(c n d np) \\ = 91 - 7 \\ = 84[/tex]
Pete surveyed his friends as to the amount of their weekly allowance. the responses were $5, $0, $8, $10, $8, $10, $0, $0, and $1. Pete analyzed the results and stated that more than half of his friends earned $8 or more per week. Find his mistake and correct it. Statical queston
Answer:
Step-by-step explanation:
Bold = $8 or more per week, Underlined = less than 8 per week
$5 = 1 person
$0 = 3 people
$10 = 2 people
$1 = 1 person
$8 = 2 people
The total amount of people = 1+3+2+1+2 = 9
The total amount of people who earn less than $8/week = 1+3+1 = 5 people
The total amount of people who earn $8 or more/week = 2+2 = 4 people
Conclusion, 5/9 total people earned less than $8/week
4/9 people earn $8 or more/week
Mistake there were less than half people who earned $8 or more per week unlike Pete stated
Correction; more than half of Pete's friends earn less than 8 dollars per week
At a basketball game, a vender sold a combined total of 102 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
please help me to get this right i really need help
Answer:
The top on the left.
Step-by-step explanation:
The function is a square root function. The negative is a reflection across the x axis. The 2 is a vertical stretch by 2. The subtraction of 1 from the x is a horizontal shift right 1 and the addition of 5 to the function is a vertical shift upwards 5. If you would like more detail let met know.
12. Pure fruit concentrate must be diluted with water in the ratio 1:7.
How many millilitre of concentrate are needed to make 5litres cool drink?
After answering the presented question, we can conclude that As a equation result, 625 millilitres of pure fruit concentrate are required to generate 5 litres of cold drink.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
If we need to dilute the pure fruit concentrate with water in a 1:7 ratio, this means that we need 7 parts water for every 1 part concentrate.
As a result, in order to prepare 5 litres of cool drink, we will need:
0.625 litres of pure concentration = 1/8 x 5 litres
We multiply litres by 1000 to get millilitres:
625 millilitres of pure concentrate (0.625 x 1000).
As a result, 625 millilitres of pure fruit concentrate are required to generate 5 litres of cold drink.
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how to find area and perimeter of Rhombus
Answer:
To find the area and perimeter of a rhombus, you can follow these steps:
1. Find the length of one side of the rhombus.
2. Use the length of one side to find the length of the diagonals. The diagonals of a rhombus are perpendicular bisectors of each other, which means that they intersect at a 90-degree angle, and each diagonal cuts the rhombus into two congruent right triangles. The length of each diagonal can be found using the Pythagorean theorem: diagonal^2 = (side/2)^2 + (side/2)^2.
3. Once you have found the length of the diagonals, you can use them to calculate the area of the rhombus. The area of a rhombus is equal to half the product of the length of the diagonals: area = (diagonal1 x diagonal2) / 2.
4. To find the perimeter of the rhombus, you simply add up the lengths of all four sides: perimeter = 4 x side.
In summary, the steps to find the area and perimeter of a rhombus are:
1. Find the length of one side of the rhombus.
2. Use the length of one side to find the length of the diagonals.
3. Use the diagonals to calculate the area of the rhombus: area = (diagonal1 x diagonal2) / 2.
4. Add up the lengths of all four sides to find the perimeter: perimeter = 4 x side.
To find the area and perimeter of a rhombus, you can use the following formulas:
Area = (diagonal 1 × diagonal 2) / 2
Perimeter = 4 × side length
What is a rhombus?A rhombus is a quadrilateral that has four equal sides.
Some of the properties we need to know are:
- The opposite sides are parallel to each other.
- The opposite angles are equal.
- The adjacent angles add upto 180 degrees.
We have,
To find the area and perimeter of a rhombus, you can use the following formulas:
Area of a Rhombus:
The area of a rhombus can be found by multiplying the length of the two diagonals and dividing by 2. That is,
Area = (diagonal 1 × diagonal 2) / 2
The perimeter of a Rhombus:
The perimeter of a rhombus can be found by multiplying the length of one side by 4. That is,
Perimeter = 4 × side length
Thus,
To find the area and perimeter of a rhombus, you can use the following formulas:
Area = (diagonal 1 × diagonal 2) / 2
Perimeter = 4 × side length
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The quantity of a drug Q mg, present in the body is given by
Q = f(t) = 140te−0.5t
(a) Find f
′
(1), f′
(4)
Step-by-step explanation:
The quantity of a drug, Q mg, present in the body t hours after an injection of the drug is given is Q =f 140te 0.6t Find f (1) , f' (1) , f (6) ,and f' (6) .
Two students, Sean and Felisha, are doing a science project to create protective barrier for an egg. At the conclusion of the project they must drop an egg from a window that is off the ground and NOT break the egg. The trick is to create a barrier that can also slow down the velocity of the falling egg. The equation describes the drop that Sean's egg took The equation describes the drop that Felisha's egg took By how many did Felisha's egg land first? (round answer to decimal places)
The equations for Sean's and Felisha's eggs when dropped from a height of 120 feet are given. By solving for t in each equation, it is found that Felisha's egg landed first by approximately 0.53 seconds.
To find the time it takes for each egg to hit the ground, we need to solve for t in each equation:
For Sean's egg:
f(t) = -16t² + 75t + 120
We want to find t when f(t) = 0 (i.e., when the egg hits the ground)
-16t² + 75t + 120 = 0
Divide both sides by -1 to simplify the equation:
16t² - 75t - 120 = 0
Using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = 16, b = -75, and c = -120.
t = (-(-75) ± √((-75)² - 4(16)(-120))) / 2(16)
t = (75 ± √(75² + 4(16)(120))) / 32
t = (75 ± √(7955)) / 32
We know that the egg cannot hit the ground in negative time, so we can discard the negative solution:
t = (75 + √(7955)) / 32
t ≈ 3.742 seconds
For Felisha's egg:
f(t) = -16t² + 55t + 120
We want to find t when f(t) = 0 (i.e., when the egg hits the ground)
-16t² + 55t + 120 = 0
Divide both sides by -1 to simplify the equation:
16t² - 55t - 120 = 0
Using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = 16, b = -55, and c = -120.
t = (-(-55) ± √((-55)² - 4(16)(-120))) / 2(16)
t = (55 ± √(55² + 4(16)(120))) / 32
t = (55 ± √(7649)) / 32
We know that the egg cannot hit the ground in negative time, so we can discard the negative solution:
t = (55 + √(7649)) / 32
t ≈ 3.212 seconds
Therefore, Felisha's egg landed first by:
3.742 - 3.212 ≈ 0.53 seconds (rounded to 3 decimal places).
Answer: Felisha's egg landed first by approximately 0.53 seconds.
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Complete question is in the image attached below
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression. tan x(cot x - cos x)
Answer: Starting with the expression:
tan(x)(cot(x) - cos(x))
Recall that cot(x) is the reciprocal of tan(x), so we can substitute cot(x) = 1/tan(x):
tan(x)(1/tan(x) - cos(x))
Simplifying:
1 - cos(x)tan(x)
Next, we can use the identity cos(x) = 1/sec(x) to eliminate the cotangent term:
1 - (1/sec(x))tan(x)
Now, we can use the identity tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x) to express the expression in terms of sine and cosine:
1 - (1/cos(x))(sin(x)/cos(x))
Simplifying:
cos(x)/cos(x) - sin(x)/cos(x)
= (cos(x) - sin(x))/cos(x)
Therefore, the simplified expression in terms of sine and cosine is:
(cos(x) - sin(x))/cos(x)
Step-by-step explanation:
The function f is defined by f(x) = −x³ + 3x²
6x and the point (1,-4) is on
the graph of f. If f-¹ is the inverse function of f, what is the value of (ƒ-¹)' (-4)?
-
The inverse function of f, what is the value of (ƒ-¹)' (-4) -1/16 ∓ i/(8√3)
We know that the point (1,-4) is on the graph of f, so we can use this information to find the value of x for which f(x) = -4:
-4 = -x³ + 3x² + (6x)
-x³ + 3x² + 6x + 4 = 0
We can solve this equation using various methods, such as graphing, factoring, or using the cubic formula. One possible method is to use synthetic division to test factors of the constant term (4) and find one that gives a remainder of zero. By testing -1 as a factor, we get:
-1 | 1 -3 6 4
-1 4 -10
1 -4 10 -6
Therefore, the equation can be factored as:
-(x + 1)(x² - 4x + 6) = 0
Using the quadratic formula or completing the square, we can find the roots of the quadratic factor:
x = 2 ± √2i
Since the function f is not one-to-one, we must restrict its domain to make it invertible. One possible domain is x ≤ 2, so the inverse function f⁻¹(x) is:
f⁻¹(x) = 1 ± √(1 - 2x)/x
Note that there are two possible values for f⁻¹(-4), one for each branch of the inverse function. To find the value of (f⁻¹)'(-4), we need to take the derivative of the inverse function at x = -4:
(f⁻¹)'(x) = -1/x² ∓ √(1 - 2x)/2x³
(f⁻¹)'(-4) = -1/16 ∓ i/(8√3)
Therefore, the value of (f⁻¹)'(-4) is either -1/16 - i/(8√3) or -1/16 + i/(8√3), depending on which branch of the inverse function we choose.
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Chuck's Chops, an up-scale steak house, received an invoice for 800 pounds of baking potatoes with a cost of $.85 per pound. The terms were, n/30. Chuck was unable to pay the bill in full within the discount period but was able to remit a partial payment of $425.00 within the discount period. How much credit did Chuck receive for his payment?
Chuck received a credit of $369.15 for his partial payment.
What is simple interest?
The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.
The total cost of the baking potatoes is calculated by multiplying the weight of potatoes by the cost per pound:
800 pounds x $0.85/pound = $680
Since the terms are n/30, Chuck has 30 days to pay the invoice in full to receive the discount. He made a partial payment of $425 within the discount period, which means he has a remaining balance of:
$680 - $425 = $255
To determine how much credit Chuck received for his partial payment, we need to calculate the discount he would have received if he had paid the full amount within the discount period. The discount is calculated by multiplying the total cost by the discount rate, which is calculated by dividing the discount period by the number of days in the year:
Discount rate = discount period / number of days in the year
Discount rate = 30 / 365
Discount rate = 0.0822
Discount = total cost x discount rate
Discount = $680 x 0.0822
Discount = $55.85
Since Chuck only paid $425 within the discount period, he is entitled to a credit for the remaining discount amount:
Credit = Discount - Partial payment
Credit = $55.85 - $425
Credit = -$369.15
Therefore, Chuck received a credit of $369.15 for his partial payment.
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