To find h'(x), differentiate the function h(x) = (cos x)/f(x) using the product rule.
Explanation:To find h'(x), we need to differentiate the function h(x) = (cos x)/f(x).
First, let's find the derivative of cos x, which is -sin x.
Next, we need to find the derivative of f(x). Since f(π/3) = 3 and f '(π/3) = −7, we know the slope of the tangent line at x = π/3 is -7.
Using the product rule, we can now differentiate h(x) = (cos x)/f(x) as follows:
h'(x) = [f(x)(-sin x) - cos x(f '(x))]/[f(x)]^2
The solution x=1/5 is a solution to which of the following equations?
A. 5 x= 1
B. 4 = 15x
C. -4x = -20
D. 60 = 10x
5/16 = x/160 solve the proportion
Captain John Smith earns $3,300 a month in the Air Force. If the Air Force puts 6% into his pension, how much goes into his pension monthly?
$19,800
$1,980
$198
$19.80
????
The answer would be 198.
what does x equal in 28 = -2-5x
What is the answer of 11-(-2) 14?
Timed! Plz help
Heather is solving an equation by graphing the expressions on both sides. If her graph intersects at an infinite number of points, which statement could describe the equation Heather is attempting to solve?
One side of the equation is a constant, and the other side of the equation is a linear expression.
One side of the equation is a linear expression, and the other side of the equation is a quadratic expression.
One side of the equation is a constant, and the other side of the equation is a quadratic expression.
One side of the equation is a quadratic expression, and the other side of the equation is a quadratic expression.
Statement D may apply to the problem Heather is seeking to answer if her graph connects at an unlimited number of locations.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
One side of the equation is a quadratic expression, and the other side of the equation is a quadratic expression.
Since constants cannot intersect lines or parabolas in infinitely many points, and lines cannot intersect parabolas in more than two points,
Heather is solving an equation by graphing the expressions on both sides. If her graph intersects at an infinite number of points, Statement D could describe the equation Heather is attempting to solve.
By graphing the expressions on the two sides, Heather is resolving an equation. Statement D may apply to the problem Heather is seeking to answer if her graph connects at an unlimited number of locations.
Hence statement D is corect.
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-3.2 improper fraction
Andrea's family stopped at the gas station to get gas. At gas stations, the price of gas per gallon is given to the nearest thousandth. In order to determine how much money he would need to pay for the gas, Andrea's dad asked her to round the price of gas per gallon to the nearest hundredth. The gas price per gallon rounded to the nearest hundredth was $2.50. Which of the following prices could have been the original gas price?
Divide 4/5 by 2/3.
a. 8/15b. 5/6c. 1 1/5d. 1 7/8
Which expression uses the greatest common factor and distributive property to find 16+40?
2(8)+2(20)
4(4)+4(10)
8(2)+8(5)
16(1)+40(1)
Once a week you babysit your neighbor’s toddler after school, usually going to a local playground. You notice that each swing on the swing set takes about the same amount of time, about 2.2 seconds. Use the pendulum formula below to find out how long the swing is. Round your answer to the tenths place. (equation and answers attached)
a) 10 ft
b) 25 ft
c) 6 ft
d) 3.9 ft
Answer:
3.9
Step-by-step explanation:
APEX
A car sales person sell a car for $21,000 to receive a 5.25 percent commission on the sale of the car how much did she earn on the sale round your answer to the nearest cent
In the early months of some year, one site added 0.2 million new accounts every day. at this rate, how many days would be needed to add 10million new accounts?
Answer:
50 days
Step-by-step explanation:
It's simple, we just have to express this as an equation.
x we will take it as the number of days we do not know.
so..
(0.2 M * x) = 10 M
we divide on both sides by 0.2 M.
x * 0.2 M / 0.2M = 10 M / 0.2 M
we simplify
x = 10M / 0.2 M
finally we only solve and the result of x will be the days it took.
x = 50
50 days
If 8 pens cost 64p how much did 1 pen cost
The figure shows two triangles on a coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A’B’C’?
A 180-degree counterclockwise rotation about the origin followed by a translation 5 units down
A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin
A 270-degree counterclockwise rotation about the origin followed by a translation 5 units to the right
A translation 5 units to the right followed by a 270-degree counterclockwise rotation about the origin
Answer: A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin .
Step-by-step explanation:
From the given figure, the coordinates of ΔABC are A(-3,4), B(-3,1), C(-2,1) and the coordinates of ΔA'B'C' are A'(3,1), B'(3,4), C'(2,4).
When, a translation of 5 units down is applied to ΔABC, the coordinates of the image will be
[tex](x,y)\rightarrow(x,y-5)\\A(-3,4)\rightarrow(-3,-1)\\ B(-3,1)\rightarrow(-3,-4)\\ C(-2,1)\rightarrow(-2,-4)[/tex]
Then applying 180° counterclockwise rotation about the origin, the coordinates of the image will be :-
[tex](x,y)\rightarrow(-x,-y)\\(-3,-1)\rightarrow(3,1)\\(-3,-4)\rightarrow(3,4)\\(-2,-4)\rightarrow(2,4)[/tex] which are the coordinates of ΔA'B'C'.
Hence, the set of transformations is performed on triangle ABC to form triangle A’B’C’ is " A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin ".
The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side. Find the lengths of the medians of the triangle with vertices at A=(0,0), B=(6,0), C=(4,4) ...?
Answer:
[tex]\sqrt{29} , \sqrt{20} , \sqrt{17}[/tex]
Step-by-step explanation:
Consider ΔABC with vertices [tex]A\left ( 0,0 \right )\,,\,B\left ( 6,0 \right )\,,\,C\left ( 4,4 \right )[/tex] such that P , Q , R are midpoints of sides BC , AC and AB .
We know that midpoint of line segment joining points [tex]\left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )[/tex] is equal to [tex]\left ( \frac{x_1+x_2}{2}\,,\,\frac{y_1+y_2}{2} \right )[/tex]
Midpoints P , Q , R :
[tex]P\left ( \frac{6+4}{2}\,,\,\frac{0+4}{2} \right )=P\left ( 5\,,\,2 \right )\\Q\left ( \frac{0+4}{2}\,,\,\frac{0+4}{2} \right )=Q\left ( 2\,,\,2 \right )\\R\left ( \frac{6+0}{2}\,,\,\frac{0+0}{2} \right )=R\left ( 3\,,\,0 \right )[/tex]
We know that distance between points [tex]\left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )[/tex] is given by [tex]\sqrt{\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2}[/tex]
Length of AP :
AP = [tex]\sqrt{\left ( 5-0 \right )^2+\left ( 2-0\right )^2}=\sqrt{25+4}=\sqrt{29}[/tex]
Length of BQ :
BQ = [tex]\sqrt{\left (2-6 \right )^2+\left ( 2-0 \right )^2}=\sqrt{16+4}=\sqrt{20}[/tex]
Length of CR :
[tex]\sqrt{\left (3-4\right )^2+\left ( 0-4 \right )^2}=\sqrt{1+16}=\sqrt{17}[/tex]
Cars enter a car wash at a mean rate of 2 cars per half an hour. What is the probability that, in any hour, exactly 2 cars will enter the car wash? Round your answer to four decimal places. Poisson Distribution
The problem is a typical example of Poisson Distribution. The rate of cars entering the car wash is given as 2 per half an hour which is 4 per hour. Using the formula for Poisson Distribution, it can be calculated that the likelihood of exactly 2 cars entering the car wash in any given hour is 16 multiplied by exponential of -4.
Explanation:The given problem is a classical example of a Poisson Distribution in probability theory. In the given problem, cars enter a car wash at a mean rate of 2 cars per half an hour which is equivalent to 4 cars per hour.
So, assuming that the number of cars that enter the car wash independently in any given hour follows a Poisson distribution, we define λ (lambda) as the expected number of cars in an hour, which is 4.
To find the likelihood that exactly 2 cars enter the car wash in any given hour, we then use the formula for the Poisson distribution:
P(X = k) = λ^k * e ^−λ / k!
In this case, λ = 4 and k = 2. When we input λ and k into the formula, we get:
P(X = 2) = 4^2 * e ^-4/ 2! = 32 * e ^-4 / 2 = 16 * e ^-4.
It is important to note that e^-λ is the exponential distribution, a key part of understanding the poisson distribution.
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What does the upside-down "U" mean?
secx-cosx/tanx=___? Explain pls ...?
evaluate and use order of operation 9-2x3+5
Simplify the complex fraction .
[(2)/(5t) - (3)/3t)]/[(1)/(2t) + (1)/(2t)]
Answer:
The simplified form of the given expression [tex]\dfrac{\frac{2}{5t}-\frac{3}{3t} }{\frac{1}{2t}+\frac{1}{2t}}=-\frac{3}{5}[/tex]
Step-by-step explanation:
Given expression [tex]\dfrac{\frac{2}{5t}-\frac{3}{3t} }{\frac{1}{2t}+\frac{1}{2t} }[/tex]
We have to simplify the given expression [tex]\dfrac{\frac{2}{5t}-\frac{3}{3t} }{\frac{1}{2t}+\frac{1}{2t} }[/tex]
Consider the given expression [tex]\dfrac{\frac{2}{5t}-\frac{3}{3t} }{\frac{1}{2t}+\frac{1}{2t} }[/tex]
Consider denominator [tex]\frac{1}{2t}+\frac{1}{2t}[/tex]
Apply rule, [tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{1+1}{2t}=\frac{1}{t}[/tex]
Now, apply fraction rule, [tex]\frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}[/tex]
We get,
[tex]=\frac{\left(\frac{2}{5t}-\frac{3}{3t}\right)t}{1}[/tex]
Simplify, we get,
[tex]\frac{t\left(\frac{2}{5t}-\frac{1}{t}\right)}{1}[/tex]
Simplify, we get,
[tex]\frac{t\left(\frac{2}{5t}-\frac{1}{t}\right)}{1}[/tex]
Further simplify by [tex]\frac{-a}{b}=-\frac{a}{b} \ and\ a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
We get, [tex]=-\frac{3t}{5t}[/tex]
Thus, [tex]-\frac{3}{5}[/tex]
Evaluate |x-13| when x=5.
A.8
B.-8
C.21
D.-21
Which ordered pairs are solutions to the inequality 2y−x≤−6 ?
Select each correct answer.
(−3,0)
(0,−3)
(2,−2)
(1,−4)
(6,1)
Answer:
The answers to this question is:
(2,-2), (0,-3), and (1,-4). I just took the test.
The ordered pairs (0,-3), (2,-2), and (1,-4) are solutions to the inequality 2y-x≤-6, while the pairs (-3,0) and (6,1) are not.
Explanation:To determine which ordered pairs are solutions to the inequality 2y−x≤−6, we can substitute the x and y values from each pair into the inequality and check if it holds true.
Therefore, the ordered pairs that are solutions to the inequality 2y−x≤−6 are (0,−3), (2,−2), and (1,−4).
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how many four-digit numbers are possible in which the leftmost digit is odd, the rightmost digit is even, and all four digits are different
Answer:
1400
Step-by-step explanation:
Count from left to right: There are 5 choices for the first digit, 5 choices for the second, 8 remaining choices for the third, and 7 remaining for the fourth, so there are $5*5*8*7= 1400
:I
How do i graph:
x – 3y = –12
2x – y = 1
...?
To graph the given linear equations, convert them to slope-intercept form and plot their y-intercepts and slopes on a graph to draw the lines representing each equation.
Explanation:To graph the equations:
x − 3y = − 12
2x − y = 1
You can use the following steps:
Rearrange each equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.For the first equation, solve for y: y = (1/3)x + 4. For the second equation, y = 2x − 1.Plot the y-intercept of each line on the graph. For the first equation, the y-intercept is 4. For the second equation, the y-intercept is -1.Use the slope to determine another point on each line. For the first equation, from the y-intercept (0,4), go up 1 unit and right 3 units to plot another point. For the second equation, from the y-intercept (0,-1), go up 2 units and right 1 unit to plot another point.Draw a straight line through the points for each equation. These lines represent the equations on the graph.By following these steps, you will produce a graph with two lines, which could intersect at a point that represents the solution to the system of equations.
To graph the system of equations x - 3y = -12 and 2x - y = 1, convert each to slope-intercept form, plot the y-intercepts, use the slopes to determine another point for each line, and draw the lines through these points.
Explanation:To graph the system of equations given by x – 3y = –12 and 2x – y = 1, you need to follow these steps:
First, rearrange each equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.For the first equation x – 3y = –12, solving for y gives us y = \frac{x}{3} + 4.For the second equation 2x – y = 1, solving for y gives us y = 2x – 1.Once the equations are in slope-intercept form, you can plot the y-intercept of each line on the y-axis, which are (0, 4) for the first equation and (0, –1) for the second equation.Then, use the slope to determine another point for each line. For the first line with a slope of \frac{1}{3}, you can move right 3 units and up 1 unit from the y-intercept. For the second line with a slope of 2, move right 1 unit and up 2 units.Draw lines through the points you have plotted for each equation. The point where the lines cross is the solution to the system of equations.With consistent practice, graphing systems of equations can become a more straightforward process.
Admira is painting a rectangular banner 2 1/4 yards wide on a wall in the cafeteria. The Banner will have a blue background. Admira has enough blue paint to cover 1 1/2 square yards of wall. Find the height of the banner if Admira uses all of the blue paint.
Solve for x.
3(3x - 1) + 2(3 - x) = 0
A rope is 250 centimeters long. You need the rope to be 1 1/2 meters long. How many centimeters should you cut off?
Answer:
100 cm is the answer
Step-by-step explanation:
Which graph shows a triangle and its reflection image across the x-axis?
D is the correct answer
In january, wally's widget world had sales of $12,500 and expenses of $10,200. the profit for january was _____. 2,300 7,900 10,200 22,700
Answer:
Option A is correct.
the profit for January was $2,300
Step-by-step explanation:
As per the statement:
In January, wally's widget world had sales of $12,500 and expenses of $10,200
⇒wally's widget world had sales(S.P) = $12,00 and expenses = $10,200.
By using formula:
[tex]\text{Profit} = \text{Sales} - \text{Expenses}[/tex]
Substitute the given value we have;
[tex]\text{Profit} = 12500-10200 =\$ 2300[/tex]
Therefore, the profit for January was $2,300