Step-by-step explanation:
(a) [1/2 x 1/4] + [1/2 x 6]
First, we can simplify each term separately:
1/2 x 1/4 = 1/8
1/2 x 6 = 3
Now, we can add these two simplified terms:
1/8 + 3 = 3 1/8
Therefore, [1/2 x 1/4] + [1/2 x 6] simplifies to 3 1/8.
(b) [1/5 x 2/15] - [1/5 x 2/15]
Both terms are the same, so when we subtract them, the result will be zero:
[1/5 x 2/15] - [1/5 x 2/15] = 0
Therefore, [1/5 x 2/15] - [1/5 x 2/15] simplifies to 0.
Select all ordered pairs that satisfy the function y=-4x+20
6,4
0,20
-4,20
10,-20
The ordered pairs that satisfy the function is B)(0,20) and D)(10,-20).
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here the given function is y=-4x+20.
Now put x=6 and y=4 then,
=> 4=-4(6)+20
=> 4 = -24+20
=> 4 ≠ -4.
Then the coordinate (6,4) dost not satisfy the function.
Put x=0 and y=20 then,
=> 20 = -4(0)+20
=> 20= 0+20
=> 20=20
Hence the coordinate (0,20) satisfy the function.
Now put x=-4 and y=20 then,
=> 20 = -4(-4)+20
=> 20 = 16+20
=> 20 ≠ 36
Hence the coordinate (-4,20) does not satisfy the function.
Now put x=10 and y=-20 then,
=> -20 = -4(10)+20
=> -20 = -40+20
=> -20=-20
Then the coordinate (10,-20) satisfy the function.
Hence the ordered pairs that satisfy the function is B)(0,20) and D)(10,-20).
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we introduced wind chill as a way of calculating the apparent temperature a person would feel as a function of the real air temperature, I, and V in
mph. Then the wind chill (i.e., the apparent temperature) is:
W(T, V) = (35.74 + 0.6215T - 35.75V^0.16) / 0.4275TV^0.16
(a) By calculating the appropriate partial derivative, show that
increasing T always increases W. (
b) Under what conditions does increasing V decrease W? Your
answer will take the form of an inequality involving T.
(c) Assuming that W should always decrease when V is in- creased, use your answer from (b) to determine the largest domain in which this formula for W can be used.
a) The partial derivative of W with respect to T is always positive, which means that increasing T always increases W.
b) Increasing V decreases W if V is greater than
[tex]((0.8T - 0.6215) / 5.71)^{(1/0.16)} .[/tex]
c) The largest domain in which the inequality derived in (b) holds true is:
T > 0.7769. This means that the wind chill formula can be used only for
air temperatures above 0.7769 degrees Fahrenheit.
(a) To show that increasing T always increases W, we need to calculate the partial derivative of W with respect to T and show that it is always positive.
∂W/∂T = [tex]0.6215/0.4275V^{0.16} - (35.75V^{0.16})/0.4275TV^{0.16}^{2}[/tex]
Simplifying this expression, we get:
∂W/∂T = [tex]1.44(0.6215 - 0.0275V^{0.16T}) / V^{0.16}T^{2}[/tex]
Since 1.44 and[tex]V^{0}.16T^{2}[/tex] are always positive, the sign of the partial derivative depends on the sign of[tex](0.6215 - 0.0275V^{0.16T} ).[/tex]
Since 0.0275 is always positive and [tex]V^{0.16T}[/tex] is also always positive, we see that [tex](0.6215 - 0.0275V^{0.16T} )[/tex] is always positive.
(b) To find the conditions under which increasing V decreases W, we need to calculate the partial derivative of W with respect to V and show that it is always negative.
∂W/∂V = [tex](-35.750.16V^{(-0.84)} (35.74+0.6215T-35.75V^{0.16} )-0.6215V^{(-0.16} ))/0.4275TV^{(0.16)}[/tex]
Simplifying this expression, we get:
∂W/∂V = [tex]-0.16(0.6215+5.71V^{0.16-0.8T} ) / TV^{0.84}[/tex]
The sign of the partial derivative depends on the sign of [tex](0.6215+5.71V^{0.16-0.8T} ).[/tex]
If [tex]0.6215+5.71V^{0.16-0.8T} < 0[/tex], then the partial derivative is negative and increasing V decreases W.
Solving this inequality for V, we get:
[tex]V > ((0.8T - 0.6215) / 5.71)^{(1/0.16)}[/tex]
(c) Assuming that W should always decrease when V is increased, we need to find the largest domain in which the inequality derived in (b) holds true.
Since the expression inside the parentheses must be positive for a real solution, we have:
0.8T - 0.6215 > 0
T > 0.7769
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bruce's weigh 11 each if bruce has 14 how many pounds do they weigh all together
All the Bruces together weigh a total of 154 pounds.
If each Bruce weighs 11 pounds and there are 14 Bruces, we can calculate the total weight by multiplying the weight of each Bruce by the number of Bruces.
Weight of each Bruce: 11 pounds
Number of Bruces: 14
To find the total weight, we multiply 11 pounds by 14 Bruces:
Total weight = 11 pounds/Bruce * 14 Bruces
= 154 pounds
Therefore, all the Bruces together weigh a total of 154 pounds.
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Calculate the derivative of the following function, 4 y=sin(cos (8x)) ) Find the critical points of the following function f(x) = xVx+6"
The critical points of f(x) are x = -3 and x = 4.
Derivative of 4y = sin(cos(8x)):
We can find the derivative of the given function using the chain rule of differentiation. Let u = cos(8x), then we have:
y = sin(u)
dy/du = cos(u) (derivative of sin(u))
du/dx = -8sin(8x) (derivative of cos(8x) using chain rule)
dy/dx = dy/du * du/dx = cos(cos(8x)) * (-8sin(8x))
Therefore, the derivative of 4y = sin(cos(8x)) is:
dy/dx = -32sin(8x)cos(cos(8x))
Critical points of f(x) = x√(x+6):
To find the critical points of f(x), we need to find where the derivative of the function is equal to zero or undefined.
f(x) = x√(x+6)
f'(x) = (√(x+6) + x/2√(x+6))
To find the critical points, we need to set f'(x) equal to zero and solve for x:
(√(x+6) + x/2√(x+6)) = 0
Multiplying both sides by 2√(x+6), we get:
2x + 6 = -x√(x+6)
Squaring both sides, we get:
4[tex]x^2[/tex] + 24x + 36 = [tex]x^3[/tex] + 6[tex]x^2[/tex]
Rearranging, we get:
[tex]x^3[/tex] + [tex]2x^2[/tex] - 24x - 36 = 0
We can solve this cubic equation using numerical methods or by factoring.
By testing values, we can see that x = -3 is a root of the equation. Dividing the equation by (x+3), we get:
[tex]x^2[/tex]- x - 12 = 0
This quadratic equation can be factored as (x-4)(x+3) = 0.
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Which equation represents the graph?
A: y = −2x + 1/2
B: y = −1/2x + 1/2
C: y = −2x − 2
D: y= -1/2 x -2
Answer: C
Step-by-step explanation:
since slope is rise/run its 2 and since the line is a negative slope the slope of the line is -2. and the y-intercept of the line is -2.
y = mx+b
m = -2
b= -2
Answer: C. y= -2x -2
Answer Immeditely Please
Answer:
it's ither 1 2 or 4 I'm still thinking but I'm pretty sure it's one of those answers
a teacher has an annual salary of 98,500. how much does that teacher make biweekly?
If a teacher has an annual salary of 98,500, the teacher makes $947.12 per biweekly period.
To calculate the teacher's biweekly salary, we need to divide their annual salary by the number of weeks in a year, and then divide that result by 2 (since there are 2 weeks in a biweekly period).
There are a few different ways to approach this calculation, but one common method is to use the following formula:
Biweekly Salary = (Annual Salary / Number of Weeks in a Year) / 2
Using this formula, we can calculate the teacher's biweekly salary as follows:
Biweekly Salary = (98,500 / 52) / 2
Biweekly Salary = (1,894.23) / 2
Biweekly Salary = 947.12
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Noel borrows $800
and is charged compound interest at 60%
per year. How much will he have to pay back in total after 8
years?
Answer:
Step-by-step explanation:
Find the absolute maximum and minimum values of f(x,y) = x^2 + 2y^2 on the square [0,1] x [0,1]
Answer:
The maximum is when both X and y = 1.The maximum value of the function is 3.When both X and YY are equal to 0, the minimum value is 0
The absolute maximum value is 3 and the absolute minimum value is 0.
To find the absolute maximum and minimum values of f(x,y) = x^2 + 2y^2 on the square [0,1] x [0,1], we need to consider both the interior and the boundary of the square.
First, check for critical points in the interior by finding the partial derivatives and setting them equal to zero:
fx = 2x and fy = 4y
Setting them equal to zero, we have:
2x = 0 => x = 0
4y = 0 => y = 0
The only critical point in the interior is (0,0).
Next, evaluate f(x,y) on the boundary of the square [0,1] x [0,1]. The boundary consists of four segments: x=0, x=1, y=0, and y=1.
1. x=0: f(0,y) = 2y^2 (for y in [0,1])
2. x=1: f(1,y) = 1 + 2y^2 (for y in [0,1])
3. y=0: f(x,0) = x^2 (for x in [0,1])
4. y=1: f(x,1) = x^2 + 2 (for x in [0,1])
Now, compare the values of f at the critical point and boundary points to find the absolute maximum and minimum:
Absolute minimum: f(0,0) = 0
Absolute maximum: f(1,1) = 3
So the absolute maximum value is 3 and the absolute minimum value is 0.
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1+x Evaluate the repeated integral: 6S6.5. 3 z dz dy dx a) 801 2 729 b) O 8 801 4 d) 729 2 2 729 4 f) None of these.
Without this information, I cannot evaluate the repeated integral or determine the correct answer choice. Please provide additional information so I can assist you better.
To evaluate the repeated integral, we must first understand the given question. It appears that some information is missing, making it difficult to provide a complete answer.
Please provide the complete problem statement, including the limits of integration for each variable (x, y, and z). This will allow me to accurately evaluate the repeated integral and provide you with the correct answer.
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Mr linden drives from his home to his office every day. if he drives at an average speed of 70 km/h for 45 min, what is the distance of the journey from his home to his office?
If he drives at an average speed of 70 km/h for 45 min, the distance of the journey from Mr. Linden's home to his office is 52.5 km.
To find the distance of Mr. Linden's journey from his home to his office, we can use the formula:
Distance = Speed x Time
Since Mr. Linden drives at an average speed of 70 km/h for 45 minutes, we first need to convert the time to hours:
45 minutes = 0.75 hours
Now, we can plug in the values we have into the formula:
Distance = 70 km/h x 0.75 hours
Distance = 52.5 km
Therefore, the distance of the journey from Mr. Linden's home to his office is 52.5 km.
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Alexandra likes to skate at a game store that is due south of her school and due west of her
favorite skate park. If the game store is 7.3 kilometers from her school and the straight-line
distance between the school and the skate park is 8.7 kilometers, how far is the game store
from the skate park? If necessary, round to the nearest tenth.
We can use the Pythagorean theorem to find the distance between the game store and the skate park.
Let's call the distance between the game store and the skate park "d". Then we have:
d^2 = (distance between school and game store)^2 + (distance between school and skate park)^2
d^2 = 7.3^2 + 8.7^2
d^2 = 106.18
d ≈ 10.3
Therefore, the game store is approximately 10.3 kilometers from the skate park.
A wildlife refuge in South America has howler monkeys and spider monkeys. A biologist working there randomly selected eight adults of each type of monkey, weighed them, and recorded their weights in pounds. Show your work.
howler monkey: {16, 17, 18, 18, 18, 20, 22, 23}
spider monkey: {8, 10, 10, 11, 11, 12, 14, 14}
Calculate the meaning and MAD for each type of monkey.
Calculate the means-to-MAD ratio for the two types of monkeys.
What inference can be made about the weight of both types of monkeys? Explain.
Howler monkeys are heavier on average than spider monkeys (17.75 lbs vs. 11.25 lbs).
How to solveCalculate the mean:
Some of the weights divided by the number of monkeys
Calculate the MAD:
Find the absolute deviation (difference) of each weight from the mean
Calculate the average of these deviations
Mean Howler Monkey = (16+17+18+18+18+20+22+23)/8 = 142/8 = 17.75 lbs
Mean Spider Monkey = (8+10+10+11+11+12+14+14)/8 = 90/8 = 11.25 lbs
Now, we calculate the MAD for each type of monkey:
MAD Howler Monkey= 1.875 lbs
MAD Spider Monkey= 1.5625 lbs
we calculate the means-to-MAD ratio for both types of monkeys:
Howler Monkey: Mean/MAD = 17.75/1.875 = 9.466
Spider Monkey: Mean/MAD = 11.25/1.5625 = 7.2
Inference:
Howler monkeys are heavier on average than spider monkeys (17.75 lbs vs. 11.25 lbs).
The means-to-MAD ratio shows that howler monkeys have more consistent weights (9.466) compared to spider monkeys (7.2), as a higher ratio indicates less variability in weights.
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Write a quadratic function in standard form that passes through (5,0) (9,0) (7,-20)
The quadratic function in standard form that passes through the given points would be f (x ) = 5x ² - 70x + 225
How to find the quadratic function ?A quadratic function in standard form is given by the equation:
f ( x ) = ax ² + bx + c
The system of equations would be:
25 a + 5b + c = 0
81 a + 9b + c = 0
49 a + 7b + c = -20
With a series of calculations, we can find the value of b and c :
b = - 14 a = - 14 ( 5 ) = -70
25 ( 5 ) - 70 (5) + c = 0
125 - 350 + c = 0
c = 225
This gives us the quadratic function of :
f ( x ) = 5x ² - 70x + 225
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(1 point) Use the method of undetermined coefficients to find a solution of a y" – 8y' + 297 = 48e4t cos(3t) + 80e4t sin(3t) + 3 - Use a and b for the constants of integration associated with the homogeneous solution. Use a as the constant in front of the cosine term. y = yh + yp = - = (1 point) Find y as a function of x if ' y" – 6y" + 8y' = 3e", - - = y(0) = 14, y'(0) = 29, y"(0) = 25. 33 4x y(x) = 37 91 e2x - tet 8 e 8 4
By using the method of undetermined coefficients, The general solution is y = ae^(4x)cos(3x) + be^(4x)sin(3x) + (7/2cos(3t) + 5/2sin(3t))e^(4t). The solution to the initial value problem is y = 3e^(2x) + 14e^(4x) - 3e^(3x).
By using the method of undetermined coefficients, the associated homogeneous equation is y''-8y'+297=0, which has the characteristic equation r^2-8r+297=0. The roots of this equation are r=4+3i and r=4-3i, so the homogeneous solution is yh=a*e^(4x)cos(3x)+be^(4x)*sin(3x).
To find the particular solution, we make the ansatz yp = (Acos(3t) + Bsin(3t))e^(4t), where A and B are constants to be determined. Substituting this into the differential equation, we get
y" - 8y' + 297 = (16A - 18B)e^(4t)cos(3t) + (16B + 18A)e^(4t)sin(3t)
On the right-hand side, we have 48e^4tcos(3t) + 80e^4tsin(3t), which suggests setting
16A - 18B = 48, and
16B + 18A = 80
Solving these equations simultaneously, we get A = 7/2 and B = 5/2. Therefore, the particular solution is
yp = (7/2cos(3t) + 5/2sin(3t))e^(4t)
And the general solution is
y = yh + yp = ae^(4x)cos(3x) + be^(4x)sin(3x) + (7/2cos(3t) + 5/2sin(3t))e^(4t)
For the second problem, the associated homogeneous equation is y''-6y'+8y=0, which has the characteristic equation r^2-6r+8=0. The roots of this equation are r=2 and r=4, so the homogeneous solution is yh=ae^(2x)+be^(4x).
To find the particular solution, we make the ansatz yp = Ce^3x, where C is a constant to be determined. Substituting this into the differential equation, we get
y" - 6y' + 8y = 9Ce^3x - 18Ce^3x + 8Ce^3x = (8C - 9C)e^3x = -C*e^3x
On the right-hand side, we have 3e^x, which suggests setting -C = 3. Therefore, the particular solution is
yp = -3e^(3x)
And the general solution is
y = yh + yp = ae^(2x) + be^(4x) - 3e^(3x)
To find the values of a and b, we use the initial conditions
y(0) = a + b - 3 = 14
y'(0) = 2a + 4b - 9 = 29
y''(0) = 2a + 8b = 25
Solving these equations simultaneously, we get a = 3 and b = 14. Therefore, the solution to the initial value problem is
y = 3e^(2x) + 14e^(4x) - 3e^(3x)
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--The given question is incomplete, the complete question is given
" (1 point) Use the method of undetermined coefficients to find a solution of a y" – 8y' + 297 = 48e4t cos(3t) + 80e4t sin(3t) + 3 - Use a and b for the constants of integration associated with the homogeneous solution. Use a as the constant in front of the cosine term. y = yh + yp = - = (1 point) Find y as a function of x if ' y" – 6y" + 8y' = 3e", - - = y(0) = 14, y'(0) = 29, y"(0) = 25."--
A home repair crew charges $75 dollars per day plus a $250 service fee. the total amount the home repair crew charges this client is $925.how many days did the crew work?
The home repair crew worked for 9 days.
What is the duration of the home repair crew's work to charge $925?To determine the number of days the home repair crew worked for, we can use algebra. Let's assume that the number of days they worked for is represented by "d". We know that they charge $75 per day plus a $250 service fee, so we can set up the following equation:
75d + 250 = 925
Simplifying the equation, we get:
75d = 675
Dividing both sides by 75, we get:
d = 9
However, we need to keep in mind that the $250 service fee is a one-time charge, not a daily charge. So we need to subtract that from the total amount to get the actual amount charged for the days worked:
925 - 250 = 675
Dividing 675 by the daily rate of $75, we get:
675 / 75 = 9
Therefore, the home repair crew worked for 9 days.
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in a recent poll, 410 people were asked if they liked dogs, and 12% said they did. find the margin of error for this poll, at the 95% confidence level. give your answer to four decimal places if possible.
The margin error for the given poll having 95% confidence level with sample size of 410 is equal to 3.15%.
Sample size n = 410
Confidence level = 95%
Margin of error for this poll, use the formula,
ME = Z× (√(p₁(1-p₁) / n))
where Z is the z-score corresponding to the desired level of confidence.
p₁ is the sample proportion = 0.12
Using attached z-score table,
For a 95% confidence level, the corresponding z-score is 1.96.
Substituting the given values, we get,
ME = 1.96 × (√(0.12× (1-0.12) / 410))
Simplifying the expression inside the parentheses, we get,
⇒ME = 1.96 × 0.0160
⇒ME = 0.0315
Margin of error for this poll at the 95% confidence level is approximately 0.0315.
Therefore, 95% confidence level represents that the true proportion of people who like dogs is within 3.15% of the observed proportion of 12%.
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the picture below is being enlarged by a scale factor of 2.5. how many inches of farming will the picture require? base 5 in high4 in
A. 12.5 in
B. 20 in
C. 45 in
D. 65 in
The inches of farming the picture require is 45 inches
How many inches of farming will the picture require?From the question, we have the following parameters that can be used in our computation:
Base = 5 in
High = 4 in
Scale factor = 2.5
The inches of farming the picture require is calculated as
Perimeter = 2 * (Base + High) * Scale factor
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (5 + 4) * 2.5
Evaluate
Perimeter = 45
Hence, the inches of farming the picture require 45 inches
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Circle A is located at (6, 5) and has a radius of 4 units. What is the equation of a line that is tangent to circle A from point C (2, 8)? x = 2 y = −0. 75x + 9. 5 y = 1. 33x + 1. 66 x = 8
We can use the point-slope form of the equation of a line to find the equation of the tangent line.
How to find the equation of the line that is tangent to circle A from point C (2, 8)?To find the equation of the line that is tangent to circle A from point C (2, 8), we need to first find the point of tangency, which is the point where the line intersects the circle.
Point C (2, 8) is outside the circle, so the tangent line will be perpendicular to the line connecting the center of the circle to point C and will pass through point C.
Step 1: Find the center of the circle
The center of the circle A is at (6, 5).
Step 2: Find the slope of the line connecting the center of the circle to point C
The slope of the line connecting the center of the circle (6, 5) and point C (2, 8) is:
m = (8 - 5) / (2 - 6) = -3/4
Step 3: Find the equation of the line perpendicular to the line from Step 2 passing through point C
The slope of the line perpendicular to the line from step 2 is the negative reciprocal of the slope:
m_perp = -1 / (-3/4) = 4/3
Now we can use the point-slope form of the equation of a line to find the equation of the tangent line:
y - 8 = (4/3)(x - 2)
Simplifying, we get:
y = (4/3)x + 4.67
So the equation of the line that is tangent to circle A from point C (2, 8) is y = (4/3)x + 4.67.
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PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!!
Answer:
75°
Step-by-step explanation:
Arc length LM is 108°, meaning that angle <K is half of the arc length, 54°.
*REMEMBER* all 3 angles inside a triangle must add up to 180° to make it a triangle.
We have angle <L, <K, and we are looking for angle <M.
51+54+?=180
105+?=180
?=75
Angle <M is 75°
Hope this helps :)
Doug is filing singly. his net taxable income is $80,575. every week, $304 is withheld from his earnings for income tax. based on the table below, what can doug expect when his taxes are due? between 80,550 and 80,600 dollars, for filing single, the amount of taxes is 16,539 dollars. a. doug will receive a refund of $123. b. doug will receive a refund of $2,977. c. doug will owe an additional $1,125. d. doug will owe an additional $731.
Doug is filing singly, and his net taxable income is $80,575. The tax amount for this income range is $16,539. Every week, $304 is withheld from his earnings for income tax. Doug can expect he will owe an additional $731. So option d is the correct answer.
Calculate the total amount withheld for the year.Since the result is a positive number, Doug will owe an additional $731 when his taxes are due. Therefore, the correct answer is d. Doug will owe an additional $731.
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For 50 points can you help me with this I really need help.
The coordinates of the points in the table indicates that the coordinates of the image following the reflections, can be presented on the coordinate plane as shown in the attached graph created with MS Excel.
What is a reflection transformation?A reflection transformation is one in which the mirror image of the preimage is created across a line of reflection.
The coordinate points of the image after the specified reflections can be presented as follows;
Original [tex]{}[/tex]Reflection across the x-axis Reflection across the y-axis y = -x
(0, 15) [tex]{}[/tex] (0, -15) (0, 15) (-15, 0)
(1, 15) [tex]{}[/tex] (1, -15) (-1, 15) (-15, -1)
(1, 13) [tex]{}[/tex] (1, -13) (-1, 13) (-13, -1)
(3, 15) [tex]{}[/tex] (3, -15) (-3, 15) (-15, -3)
(3, 12) [tex]{}[/tex] (3, -12) (-3, 12) (-12, -3)
(1, 10) [tex]{}[/tex] (1, -10) (-1, 10) (-10, -1)
(1, 8) [tex]{}[/tex] (1, -8) (-1, 8) (-8, -1)
(3, 10) [tex]{}[/tex](3, -10) (-3, 10) (-10, -3)
(3, 7) [tex]{}[/tex] (3, -7) (-3, 7) (-7, -3)
(1, 5) [tex]{}[/tex] (1, -5) (-1, 5) (-5, -1)
(1, 2) [tex]{}[/tex] (1, -2) (-1, 2) (-2, -1)
(4, 4) [tex]{}[/tex] (4, -4) (-4, 4) (-4, -4)
(5, 7) [tex]{}[/tex] (-5, 7) (5, -7) (-7, -5)
(7, 8) [tex]{}[/tex] (7, -8) (-7, 8) (-8, -7)
(6, 5) [tex]{}[/tex] (6, -5) (-6, 5) (-5, -6)
(8, 6) [tex]{}[/tex] (8, -6) (-8, 6) (-6, -8)
(9, 9) [tex]{}[/tex] (9, -9) (-9, 9) (-9, -9)
(11, 10) [tex]{}[/tex] (11, -10) (-11, 10) (-10, -11)
(10, 7) [tex]{}[/tex] (10, -7) (-10, 7) (-7, -10)
(12, 8) [tex]{}[/tex] (12, -8) (-12, 8) (-8, -12)
(13, 6) [tex]{}[/tex] (13, -6) (-13, 6) (-6, -13)
(11, 5) [tex]{}[/tex] (11, -5) (-11, 5) (-5, -11)
(14, 4) [tex]{}[/tex] (14, -4) [tex]{}[/tex] (-14, 4) (-4, -14)
(12, 3) [tex]{}[/tex] (12, -3) (-12, 3) (-3, -12)
(9, 4) [tex]{}[/tex] (9, -4) (-9, 4) (-4, -9)
(7, 3) [tex]{}[/tex] (7, -3) (-7, 3) (-3, -7)
(10, 2) [tex]{}[/tex] (10, -2) (-10, 2) (-2, -10)
(8, 1) [tex]{}[/tex] (8, -1) (-8, 1) (-1, -8)
(5, 2) [tex]{}[/tex] (5, -2) (-5, 2) (-2, -5)
(2, 0) [tex]{}[/tex] (2, 0) (-2, 0) (0, -2)
The above coordinate points can be used to plot the graphs showing the image of the points following the specified reflections across the x-, y-, and y = -x, axis.
Please find attached the required graph of the coordinate points following the reflection transformations, created with MS Excel.
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Write exponential functions given the following scenarios:
1. a business had a profit of $35,000 in 1998 that increased by 18% per year. write the equation to model the
situation. find the profit of the company after 8 years.
2. you buy a used truck for $4,000. the value of the truck depreciates at a yearly rate of 12%. write the equation to model the situation. find the value of the truck after 6 months.
3. between 1970 and 2000, the population of a town increased by approximately 2.5% each year. in 1970 there were 600 people. write the equation to model the situation. find the population of the city in 1999.
The profit of the company after 8 years is approximately $105,085.11.
The value of the truck after 6 months is approximately $3,677.49.
The population of the city in 1999 is approximately 1,457.66 people.
How we write the exponential functions?Let P(t) be the profit in year t, where t is the number of years after 1998. The initial profit in 1998 is $35,000.
The profit increases by 18% per year, which means the profit at time t is 1.18 times the profit at time t-1. Therefore, the equation to model the situation is: [tex]P(t) = 35000 * 1.18^t[/tex]
To find the profit of the company after 8 years:
[tex]P(8) = 35000 * 1.18^8[/tex] = $105,085.11
Let V(t) be the value of the truck in year t, where t is the number of years after the purchase. The initial value of the truck is $4,000.
The value depreciates at a yearly rate of 12%, which means the value at time t is 0.88 times the value at time t-1. Therefore, the equation to model the situation is: [tex]V(t) = 4000 * 0.88^t[/tex]
To find the value of the truck after 6 months (0.5 years):
[tex]V(0.5) = 4000 * 0.88^0^.^5[/tex] = $3,677.49
Let P(t) be the population of the town in year t, where t is the number of years after 1970. The initial population in 1970 is 600.
The population increases by 2.5% per year, which means the population at time t is 1.025 times the population at time t-1. Therefore, the equation to model the situation is: [tex]P(t) = 600 * 1.025^t[/tex]
To find the population of the city in 1999 (29 years after 1970):
[tex]P(29) = 600 * 1.025^2^9 = 1,457.66[/tex]
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Which is the simplest formula for working out probability
The simplest formula for working out probability is the following:
Probability (P) = Number of favorable outcomes (F) / Total number of possible outcomes (T)
In this formula, the probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is a measure of the likelihood or chance of an event occurring. It is represented as a value between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
To calculate the probability, you need to determine the number of favorable outcomes, which are the desired outcomes or the outcomes you are interested in. Then, you divide that by the total number of possible outcomes, which is the number of equally likely outcomes in the given situation.
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The polynomial
y
=
−
0.74
x
4
+
2.8
x
3
+
26.4
describes the billions of flu virus particles in a person’s body
x
days after being infected. find the number of virus particles, in billions, after 1 day.
The number of flu virus particles in a person's body after 1 day is 28.46 billion, based on the given polynomial function.
The polynomial given to us is, y = −0.74x⁴ + 2.8x³ + 26.4 which describes the billions of flu virus particles in a person’s body. To find the number of virus particles in a person's body after 1 day, we need to substitute x = 1 into the given polynomial and evaluate it.
So, we have,
y = -0.74(1)⁴ + 2.8(1)³ + 26.4
= -0.74 + 2.8 + 26.4
= 28.46
Therefore, the number of virus particles in a person's body after 1 day is 28.46 billion.
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Complete question - The polynomial y=−0.74x⁴ + 2.8x³ + 26.4 describes the billions of flu virus particles in a person’s body x days after being infected. find the number of virus particles, in billions, after 1 day.
Map of the city zoo a triangle with points zebras, monkeys, and lions. the distance from zebras to monkeys is 52 feet and from monkeys to lions is x feet. a triangle with points lions, tigers, elephants. the distance from lions to tigers is 96 feet and from tigers to elephants is 78 feet. the path from the zebras to the monkeys is parallel to the path from the tigers to the elephants. what is the distance between the lions and monkeys? 1. proportion: 52 78 = x 96 2. cross-multiply: 4992 = 78x 3. solve: the distance between the lions and the monkeys is feet.
The distance between the lions and the monkeys is 64 feet.
We can set up a proportion to find the distance between the lions and monkeys. Here's the step-by-step explanation:
1. Proportion: Since the path from zebras to monkeys is parallel to the path from tigers to elephants, we can set up a proportion using the given distances: 52/78 = x/96.
2. Cross-multiply: To solve for x, we can cross-multiply: 52 * 96 = 78 * x, which simplifies to 4992 = 78x.
3. Solve: Now we just need to solve for x. Divide both sides of the equation by 78: x = 4992 / 78. This gives x ≈ 64.
So, the distance between the lions and the monkeys is approximately 64 feet.
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I need this answer asap!!! Willa can cover 13. 5m squared with 3L of paint and complete the table using equivalent ratios.
13. 5sqaured to 3
? to1
? to 10
The completed table of equivalent ratios would be:
13.5 square meters : 3 liters of paint
4.5 square meters : 1 liter of paint
45 square meters : 10 liters of paint.
To find the missing ratios, we need to set up proportions using the given information.
13.5 square meters is covered by 3 liters of paint, so we can write:
13.5/3 = ?/1
To solve for the missing ratio, we can cross-multiply:
13.5 x 1 = 3 x ?
? = (13.5 x 1) / 3
? = 4.5
So, 4.5 square meters can be covered by 1 liter of paint.
To find the last missing ratio, we can use the same method:
13.5/3 = ?/10
10 x 13.5 = 3 x ?
? = (10 x 13.5) / 3
? = 45
So, 45 square meters can be covered by 10 liters of paint.
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Mathematical
PRACTICE
Use Algebra For Exercises 11-13,
2 x P
40
refer to the equation 5 x 9
100
2
11. What must be true about p and q if the equation show
equivalent fractions?
p and q both are equal and p=q=20.
Given are an equation show equivalent fractions 2p/5q = 40/100
We need to find the p and q,
So
2p/5q = 40/100
2p/5q = 2×20/2×20
p/q = 20/20
p/q = 1
p = q
Therefore p and q both are equal and p=q=20.
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Need help asap.
(Angles Formed by Chords, Tangents, Secants)
The value of angle LQ in the intersected arc is 34 degrees.
How to find arc angle when secant intersect?If two secants intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.
Therefore, let's find the arc angle LQ as follows:
let
x = arc angle LQ
m∠U = 1 / 2 (108 - x)
37 = 54 - 0.5x
subtract 54 from both sides of the equation
37 = 54 - 0.5x
37 - 54 = 54 - 54 - 0.5x
-17 = -0.5x
divide both sides by -0.5
x = -17 / -0.5
x = 34 degrees
Therefore,
arc angle LQ = 34 degrees
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please help.
1. Complete the Pythagorean triple. (24,143, ___)
2. Given the Pythagorean triple (5,12,13) find x and y
3. Given x=10 and y=6 find associated Pythagorean triple
4. Is the following a possible Pythagorean triple? (17,23,35)
The value that will complete Pythagorean triple would be = 24,143, 145 )
How to calculate the missing value of a triangle using the Pythagorean formula?To calculate the missing value of a triangle that completes a Pythagorean triple that formula that should be used is given as follows.
That is;
C ² = a² + b²
C = Missing value of the Pythagorean triple
a = 24
b.= 143
C² = 24²+143²
= 576+20,449
C =√21,025
= 125
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