Answers
The function is decreasing in the interval (3, ∞).
Explain about the decreasing function?You must first compute the derivative, then make it equal to 0, and then determine whether zero values your function is negative between in order to determine whether a function is decreasing. In order to determine once the function is negative and, consequently, decreasing, test values from all sides of these.f(x) = -x² + 6x - 4
Differentiate the equation with respect to 'x'.
f'(x) = -2x + 6
Put f'(x) = 0
-2x + 6 = 0
x = 6/2
x = 3 (critical point)
Now, write the function as:
f(x) = -x² + 6x - 4
-(x² - 6x + 4) (negative form)
Thus, the function is decreasing in the interval (3, ∞)
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Related Questions
Math 1050 Written Homework - Section 5.3
1. Find an equation fro the parabola with vertex (3,5) and focus
(7,5).
Answers
The equation of the parabola is (y-5)^2=16(x-3)
To find the equation for the parabola with vertex (3,5) and focus (7,5), we can use the formula for a parabola with a horizontal axis of symmetry:
(y-k)^2=4p(x-h)
Where (h,k) is the vertex and p is the distance from the vertex to the focus.
In this case, the vertex is (3,5) and the focus is (7,5), so we have:
(y-5)^2=4p(x-3)
The distance from the vertex to the focus is 4, so p=4. Plugging this value into the equation gives us:
(y-5)^2=16(x-3)
This is the equation for the parabola with vertex (3,5) and focus (7,5).
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plsplsplsss im struggling so bad- does anybody know how to do the attached question?
Answers
By angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.
Explain about the similarity of triangles?Triangles with exactly similar corresponding angle configurations are said to be similar triangles. This implies that equiangular triangles are comparable. All equilateral triangles are thus interpretations of similar triangles.
Two triangles are comparable if the determinations of their corresponding sides are proportionate. The same is true if the lengths of two sides for one triangle are proportional to the lengths of the corresponding sides inside a triangle and the included angles are congruent.In the given statements, thus the similar triangle are:
ΔWYZ ≈ Δ WZX ≈ ΔZYX
A,
∠Y is common
∠x = ∠z = 90°
Therefore, by angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.
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DEFG is definitely a parallelogram.
O A. True
O B. False
Answers
Answer: false
Step-by-step explanation:
since you do not know if EF and DG are the same it is not possible to know if it is true yet
ulas and Applications of A=P(1+(r)/(n))^(nt) Find A when P=2000,r=3%,n=12, and t=9.
Answers
The amount of money in the account after 9 years is $2549.68.
The formula A=P(1+(r)/(n))^(nt) is used to calculate the amount of money in an account after a certain amount of time, given the principal amount (P), the interest rate (r), the number of times interest is compounded per year (n), and the number of years (t).
To find A when P=2000, r=3%, n=12, and t=9, we can plug these values into the formula and simplify:
A = 2000(1+(0.03)/(12))^(12*9)
A = 2000(1+0.0025)^(108)
A = 2000(1.0025)^(108)
A = 2000(1.2748)
A = 2549.68
Therefore, $2549.68 is the amount of money in the account after 9 years.
"
Correct question
Ulas and Applications:
If A=P(1+(r)/(n))^(nt)
Find A when P=2000,r=3%,n=12, and t=9.
"
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Is the volume of the resulting sugar mixture equal, more than or less than the sum (20 mL sugar +50mL water ) of the volumes of the unmixed sugar and water?
Answers
The volume of the resulting sugar mixture is less than the sum (20 mL sugar + 50 mL water) of the volumes of the unmixed sugar and water.
About water moleculesWhen sugar is dissolved in water, the sugar molecules fit into the spaces between the water molecules, resulting in a decrease in volume. To explain this further, let's use the following steps:
1. Start with 20 mL of sugar and 50 mL of water in separate containers. 2. Pour the sugar into the water.
3. Stir the mixture until the sugar is completely dissolved.
4. Measure the volume of the resulting sugar mixture. You will notice that the volume of the sugar mixture is less than the sum of the volumes of the unmixed sugar and water (70 mL).
This is because the sugar molecules are now occupying the spaces between the water molecules, resulting in a decrease in volume.
In conclusion, the volume of the resulting sugar mixture is less than the sum (20 mL sugar + 50 mL water) of the volumes of the unmixed sugar and water.
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ght triangle and two of its side lengths are shown in the diagram.
12 cm
is the measurement of x?
39 cm
x cm
Answers
Determine the amount needed such that when it comes time for retirement, an individual can make semiannual withdrawals in the amount of $15,265 for 35 years from an account paying 4.5% compounded semiannually. Round your answer to the nearest cent.
Answers
The individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.
What is the Present Value of an Annuity?
With a specific rate of return, or discount rate, the present value of an annuity is the current value of the future payments from an annuity. The present value of the annuity decreases as the discount rate increases.
To determine the amount needed for retirement, we can use the formula for the present value of an annuity:
[tex]PV= PMT* \frac{1-\frac{1}{(1+r)^{n} } }{r}[/tex]
where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.
In this case, PMT = $15,265, r = 4.5%/2 = 0.0225 (since the interest is compounded semi-annually), and n = 35 x 2 = 70 (since there are 70 semiannual periods in 35 years).
Plugging in these values, we get:
[tex]PV = (15,265\times(1 - (1 + 0.0225)^{(-70))) / 0.0225[/tex]
PV = $405,840.13
Therefore, the individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.
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31. if ( f(x) = {x^{26}+x^{24}+2 x^{22}}{x-1} ), find f(i) where ( i ) is the imaginary unit. (a) ( -1-i ) (b) ( -1+i ) (c) \( 1-i ) (d) ( 1+i ) (e) none of these
Answers
To find f(i), we will substitute i for x in the given function and simplify:
f(i) = (i^{26} + i^{24} + 2i^{22})/(i-1)
= ((i^{22})(i^4 + i^2 + 2))/(i-1)
= ((i^{22})(1 + (-1) + 2))/(i-1)
= ((i^{22})(2))/(i-1)
= (2i^{22})/(i-1)
= (2i^{22})/((-1)(1-i))
= (2i^{22})/((-1)(1-i)) * ((1+i)/(1+i))
= (2i^{22})(1+i)/((-1)(1-i)(1+i))
= (2i^{22})(1+i)/((-1)(1^2 - i^2))
= (2i^{22})(1+i)/((-1)(1 - (-1)))
= (2i^{22})(1+i)/(2)
= i^{22} + i^{23}
= i^{22}(1 + i)
= (i^{22})(1 + i)
= (1)(1 + i)
= 1 + i
Therefore, the answer is (d) (1+i).
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Cos= 1/4, csc —>0 Find sin —/2
Please please help this is due by 11:59 and I’m struggling
Answers
The value of sin(θ/2) is √6/4.
What is the value of sin (θ/2)?
We can start by using the identity:
sin(θ/2) = ±√[(1 - cosθ)/2]
However, before we apply this identity, we need to determine the quadrant in which θ lies, so that we can determine the sign of sin(θ/2).
From the given information, we know that cos θ = 1/4. Using the unit circle or a trigonometric table, we find that θ is a first quadrant angle whose reference angle is arc cos(1/4) ≈ 75.52°.
Since csc > 0, we know that sinθ > 0, which means that θ is either in the first or second quadrant.
However, since cosθ is positive (i.e., in the first or fourth quadrant), we know that θ must be in the first quadrant, and so sinθ > 0.
Now we can use the half-angle identity:
sin(θ/2) = ±√[(1 - cosθ)/2]
Plugging in cosθ = 1/4, we get:
sin(θ/2) = ±√[(1 - 1/4)/2] = ±√(3/8) = ±(√3/2)(√2/2) = ±(√3/2)(1/√2)
Since θ is in the first quadrant, we know that sin(θ/2) > 0, so we take the positive root:
sin(θ/2) = (√3/2)(1/√2) = √3/2√2 = √6/4
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Write an equation of the line passing through the point $\left(1,\ 9\right)$ that is parallel to the line $y=3x-2$ .
Answers
Equation of straight line parallel to y = 3x - 2 and passing through (1, 9) is
y = 3x + 6
What is straight line?A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity. A straight line is a figure formed when two points A (x1, y1) and B (x2, y2) are connected with the shortest distance between them, and the line ends are extended to infinity.
Given,
Line y = 3x - 2
Comparing with y = mx + c
slope = 3
Line parallel to y = 3x - 2 and passing through (1, 9)
Slope of the parallel line = slope of line y = 3x - 2
slope m = 3
Equation of the line,
y - y' = m(x - x')
y - 9 = 3(x - 1)
y - 9 = 3x - 3
y = 3x + 6
Hence y = 3x + 6 is equation of line parallel to y = 3x - 2 and passing through (1, 9)
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If you sell 3 lobster ravialis and 5 steak salad about how much will you earn in commission (round to the nearest hundreath
Answers
Answer:
Step-by-step explanation:
based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number
The temperature in Austria one morning was -5°C at 08:00 and increased by 2°C every hour until 12:00. What temperature will the temperature be at 11:30?
Answers
From 8:00 to 12:00, the temperature increased by 2°C per hour for a total of 4 hours. Therefore, the temperature has increased by 2°C/hour x 4 hours = 8°C.
Starting from the initial temperature of -5°C at 8:00, the temperature would be:
-5°C + 8°C = 3°C at 12:00
To find the temperature at 11:30, we need to find the temperature halfway between 8:00 and 12:00, which is 10:00. At 10:00, the temperature would have increased by 2°C/hour x 2 hours = 4°C, so the temperature at 10:00 would be:
-5°C + 4°C = -1°C
From 10:00 to 11:30, which is 1.5 hours, the temperature would increase by 2°C/hour x 1.5 hours = 3°C. Therefore, the temperature at 11:30 would be:
-1°C + 3°C = 2°C
Therefore, the temperature in Austria at 11:30 would be 2°C.
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Which fraction makes the sentence true?
bjb
Answers
In the figure below, quadrilateral UVWX is a parallelogram.
Part a) What are the values of p, UV, and VW?
Part b) What property of a parallelogram did you use to solve?
Answers
a. The values of p = 8, UV = 70 and VW = 34
b. The property that we can use is "Opposite sides of the parallelogram are equal"
Parallelogram:A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other, and the opposite angles are also equal.
Here we have
Quadrilateral UVWX is a parallelogram
Here UV = 8p + 6, VW = 5p - 6, and XW = 9p - 2
Here the property that we can use is
The opposite sides of the parallelogram are equal
=> 8p+ 6 = 9p - 2
=> 9p - 8p = 6 + 2
=> p = 8
Hence, the lengths of UV and VW are calculated as
UV = 8p + 6 = 8(8) + 6 = 64 + 6 = 70
VW = 5p - 6 = 5(8) - 6 = 40 - 6 = 34
Therefore,
a. The values of p = 8, UV = 70 and VW = 34
b. The property that we can use is "Opposite sides of the parallelogram are equal"
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[tex]5^{-2} x 125 x p^{15} / 10^{3} x p^{-6}[/tex]
Answers
The expression when evaluated is p^21/200
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
[tex]5^{-2} x 125 x p^{15} / 10^{3} x p^{-6}[/tex]
Express properly
So, we have the following representation
(5^-2 * 125 * p^15)/(10^3 * p^-6)
Evaluate the products of common factors
This gives
(5 * p^15)/(10^3 * p^-6)
Apply the law of indices
(5 * p^21)/10^3
So, we have
5p^21/1000
Divide 5 and 1000 by 5
p^21/200
Hence, the expression is p^21/200
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Complete Question
Evaluate the expression:
[tex]5^{-2} x 125 x p^{15} / 10^{3} x p^{-6}[/tex]
A
Alisha works at an electronics store and each week is paid $350 plus a 15% commission on her sales.
Find her total earnings for the week if she sells $2000 worth of electronics.
Answers
Alisha's total earnings for the week would be $650.
Why it is and what is selling?
Alisha's total earnings for the week can be calculated as follows:
Commission earned on sales = 15% of $2000 = 0.15 x $2000 = $300
Total earnings for the week = Base salary + Commission earned
= $350 + $300
= $650
Therefore, Alisha's total earnings for the week would be $650.
Selling refers to the exchange of goods or services for money or other valuable consideration. It is the process of convincing or persuading potential customers to purchase a product or service. Selling involves various activities, including advertising, marketing, negotiating, and closing a sale.
The goal of selling is to create a relationship with the customer that leads to repeat business and referrals. It is an essential aspect of commerce and business, as it generates revenue and helps companies grow and expand.
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Evaluate the expression 8 - 4x * y ^ 2 for x = 3 and y = - 2
Answers
Answer:
16
Step-by-step explanation:
8-4x times y^2, x=3 and y=-2
First, plug in both variables. Since x=3, you would substitute 4x in the equation to 4(3). You would do the same to y, but instead it would be in replace of y^2. So it would be -2^2. You now have a new equation:
8-4(3) times -2^2
Next, you start solving the equation. You should follow PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction). This method is sometimes controversial, but it still works for this problem.
Start by multiplying 4 times 3 which equals 12. Then I solve the exponent. The exponent -2^2 is the same as -2 times -2. The -2 is the number that gets multiplied, and the exponent is how many times -2 gets multiplied times itself. -2 times -2 is 4. You can plug your new numbers back in the equation now.
8-12 times 4
The equation is much easier to solve now. 8-12 is -4. -4 times 4 is 16.
The answer is 16.
What is the equation of the line that passes through the point (4, 1) and has a slope
of ½?
Answers
Answer:
y = 1/2x -1
Step-by-step explanation:
A rectangle is
a trapezoid.
Answers
Answer: True
Step-by-step explanation:
Answer: No
Step-by-step explanation:
Definitely not.
read the ss
PLS HELP
Answers
Q.3 - (5,0)
Are these two matrices equal? Justify your answer. [[3,-1,7],[2,6,-9],[-5,4,-2]]*[[-2,-9,7],[4,6,-1],[-5,2,3]]
Answers
No, these two matrices are not equal.
The first matrix is a 3x3 matrix with the elements [[3,-1,7],[2,6,-9],[-5,4,-2]] and the second matrix is also a 3x3 matrix with the elements [[-2,-9,7],[4,6,-1],[-5,2,3]]. In order for two matrices to be equal, they must have the same dimensions and the corresponding elements must be equal. In this case, the dimensions are the same, but the corresponding elements are not equal. For example, the first element in the first matrix is 3, but the first element in the second matrix is -2. Therefore, these two matrices are not equal.
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Rewrite the equation by completing the square X^2 = -8 - 7
Answers
Answer: x= [tex]\sqrt{x=15i} or \sqrt{x=-5[/tex]
HELP PLEASE QUICK ITS DUE IN A BIT
Answers
The measures of the angles in the figure are DBE = 64 degrees, CBE = 26 degrees. Others are shown below
Calculating the measures of the angles
Figure 7
The angle DBC is right angled
So, we have
17x + 13 + 32 - 2x = 90
This gives
15x + 45 = 90
So, we have
x = 3
Solving for the other angles, we have
DBE = 17 * 3 + 13 = 64
CBE = 32 - 2 * 3 = 26
Figure 8
Here, we have
5x + 29 = 9x - 15 -- alternate angles
So, we have
4x = 44
Divide
x = 11
Solving for the other angles, we have
WVZ = 9 * 4 - 15 = 21
CBE = 90 - 21 = 69
Figure 9
Here, we have
8x - 17 = 5x + 13 -- alternate angles
So, we have
3x = 30
Divide
x = 10
Solving for the other angles, we have
RTS = 5 * 10 + 13 = 63
PTQ = 90 - 63 = 27
Figure 10
Here, we have
6x + 25 + 2x + 23 = 180 -- angles on a straight line
So, we have
8x = 132
Divide
x = 16.5
Solving for the other angles, we have
EFG = 6 * 16.5 + 25 = 124
IFH = 180 - 124 = 56
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Help I don't understand
Answers
Answer:
Step-by-step explanation:
The Domain is (x) values that a certain line covers on a graph.
This line is a segment, so it has a very specific domain.
The domain is written in the form of => [tex]a\leq x\leq b[/tex]
- In which (a) and (b) are the smallest and largest numbers on the domain, respectively.
Here, the line starts at (-11,6) and goes all the way to (2,1)
From here - we take out the y-values to get that the x-values go from (-11) to (2)
That means that the domain. of this here line, is:
[tex]Domain = -11\leq x\leq 2[/tex]
The variableais jointly proportional toband the cube ofc. Ifa=127whenb=6andc=8, what is the value ofawhenb=8andc=5?Rdecimal places if necessary.
Answers
The value of a when b = 8 and c = 5 is 41.351.
What is jointly proportional ?Jointly proportional refers to a relationship between two or more variables in which all of the variables increase or decrease together in the same ratio. For example, if one variable doubles, the other variables double as well.
The variable a is jointly proportional to b and the cube of c. This means that a = k*b*c^3, where k is a constant. We can use the given values to find k:
127 = k*6*8^3
127 = k*3072
k = 127/3072
k = 0.041351
Now we can use this value of k to find the value of a when b = 8 and c = 5:
a = 0.041351*8*5^3
a = 0.041351*8*125
a = 41.351
So the value of a when b = 8 and c = 5 is 41.351.
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Help pls!
Simplify arctan 5 + arctan 6
(round to the nearest degree).
a. 21°
b. 159°
c. 201°
Answers
The simplified expression is -22 degrees (rounded to the nearest degree).
What is Trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the functions that describe those relationships. It has applications in fields such as engineering, physics, astronomy, and navigation.
We can use the following trigonometric identity to simplify the expression:
arctan(x) + arctan(y) = arctan[(x+y) / (1-xy)]
In this case, we can substitute x = 5 and y = 6 to get:
arctan 5 + arctan 6 = arctan[(5+6) / (1 - 5*6)]
Simplifying the denominator, we get:
arctan 5 + arctan 6 = arctan(11/-29)
To find the degree measure of this angle, we can use a calculator to evaluate the inverse tangent of -11/29 and convert the result to degrees.
The result is approximately -22 degrees (rounded to the nearest degree).
Therefore, the simplified expression is:
arctan 5 + arctan 6 = -22 degrees (rounded to the nearest degree).
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Three vases have different sizes. the capacity of the big vase is half times bigger than the capacity of the middle sized vase. the capacity of the middle sized vase is four times bigger than the capacity of the small vase
mark the capacity of the middle vase as x
1. what is the capacity of the big vase (in x?)
2.what is the capacity of the small vase (in x?)
3.all of the 3 vases together have a capacity of 5,5 liters. What is the capacity of the middle vase in liters
middle = x
big = 1/2x + x
small = x/4 I need some help T^T
Answers
Answer:
The capacity of the big vase is half times bigger than the capacity of the middle sized vase, which means it is 1 + 1/2 times the capacity of the middle vase.
So, the capacity of the big vase in terms of x is:
1/2x + x = 3/2x
Therefore, the capacity of the big vase in x is 3/2x.
The capacity of the middle sized vase is four times bigger than the capacity of the small vase, which means it is 4 times the capacity of the small vase.
So, the capacity of the small vase in terms of x is:
x/4
Therefore, the capacity of the small vase in x is x/4.
The total capacity of the three vases is 5.5 liters. We can set up an equation based on this information:
x + 3/2x + x/4 = 5.5
Multiplying both sides by 4 to eliminate the fraction:
4x + 6x + x = 22
11x = 22
x = 2
Therefore, the capacity of the middle sized vase is 2 in terms of x. To find the capacity in liters, we can substitute x = 2 into any of the expressions we found earlier:
Capacity of the big vase: 3/2x = 3/2 * 2 = 3 liters
Capacity of the small vase: x/4 = 2/4 = 0.5 liters
So, the capacities of the three vases are 3 liters, 2 liters, and 0.5 liters, and their total capacity is 5.5 liters.
Solve the compound inequality and give your answer in interval notation. 8x-6>-30 OR -2x+4>=12
Answers
The solution to the compound inequality is x > -3 and x <= -4, or (-4, -3] in interval notation.
A compound inequality contains at least two inequalities that are separated by either "and" or "or. The graph of a compound inequality with an "and" represents the intersection of the graph of the inequalities.
The compound inequality 8x - 6 > -30 OR -2x + 4 >= 12 can be solved by solving each inequality separately and then combining the results.
Solve 8x - 6 > -30:
8x - 6 > -30
8x > -24
x > -3
Solve -2x + 4 >= 12:
-2x + 4 >= 12
-2x >= 8
x <= -4
The solution to the compound inequality is x > -3 and x <= -4, or (-4, -3] in interval notation.
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Answer:-4.5
Step-by-step explanation:
-6+-30=-36
-36 divided by 8= -4.5
Find an equation of the line passing through the given points. Express your answer in slope-intercept form. (3,9) and (3, -8) The equation of the line is (Type an expression using x as the variable.)
Answers
The equation of the line is x = 3.
To find the equation of a line passing through two points, we need to use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1)
Plugging in the given points, we get:
m = (-8 - 9) / (3 - 3) = -17 / 0
Since the denominator is zero, this means that the slope of the line is undefined. This means that the line is vertical and has an equation of the form x = c, where c is a constant.
Since both of the given points have an x-coordinate of 3, the equation of the line is:
x = 3
So, the equation of the line passing through the given points is x = 3. This is the final answer in slope-intercept form.
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FIRST TO ANSWER AND SHOW WORK GETS BRAINLIEST! PLEASE PLEASE PLEASE HURRY!!!!!!!!!!
Twelve cards are numbered from 1 to 12 and placed in a box. One card is selected at random and not replaced. Another card is randomly selected. What is the probability of selecting two even numbers?
PLEASE SHOW WORK!
Answers
Answer:
1/6
Step-by-step explanation:
Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.