h()=2²+(k+4)+k where k is a real constant
a) Find the discriminant of h() in terms of k
b Hence or otherwise, prove that h() has two distinct real roots for all values of k.
Answer:
here is the answer I simply don't the answer to
Step-by-step explanation:
a) 2 square.
b)because there is two k's
- A segment has a midpoint at (2, -7) and an
endpoint at (8, -5). What are the coordinates
of the other endpoint?
The coordinates for the other endpoint of the line segment will be (-4,-9).
What are coordinates of a line segment?
The location of a line segment on the coordinate plane is defined by two endpoints whose coordinates are known. The line links the two endpoints but does not extend beyond them. It is a segment (piece) of a line.
This is the same as the definition of a line segment in ordinary plane geometry, the only difference being that we know the coordinates of the points involved.
Coordinates - Coordinates are the components of an ordered pair. In an ordered pair, the first number is called the x-coordinate and the second number is called the y-coordinate.
Now
Given,
One endpoint (x2,y2) having coordinates= (8,-5)
Let other endpoint be = (x1,y1)
Midpoint (x, y) = (2,-7)
Therefore,
x=(x1+x2)/2 and y=(y1+y2)/2
x1=2x-x2 y1=2y-y2
x1=4-8 y1=-14+5
x1=-4 y1=-9
Hence, other endpoint is (4,-9).
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The measure of 2A is 18° greater than the measure of 2B. The two angles are complementary. Find
the measure of each angle.
The MzA is
and mzB is
lo
Answer:
2A=54°
2B=36°
Step-by-step explanation:
2A=x+18
2B=x
x+x+18=90
2x=90=18
2x=72
x=36
2A=x+18=36+18=54
2B=x=36
what is ur favorite anime mine is attack on titan
hello there good people here is 50 points for free have a good day
Answer:
I can't decide
Step-by-step explanation:
Answer:
Mine is one piece and kumo desu nani ga i love it lol
Step-by-step explanation:
Which point is located at (-0.50 -1.25)?
Answer:
Your answer is going to be point W.
Your welcome
Answer: Your answer is Point W, my brainly friends
Step-by-step explanation:
Find intervals of concavity for f(x) = 3 cos x, with 0 < x < 21. Show your work for full credit.
The intervals of concavity for f(x) = 3 cos x, with 0 < x < 21, are (0, π/2) and (3π/2, 2π).
To find the intervals of concavity for f(x) = 3 cos x, we need to analyze the second derivative of the function.
First, let's find the second derivative of f(x):
f'(x) = -3 sin x (derivative of cos x)
f''(x) = -3 cos x (derivative of -3 sin x)
Now, we can analyze the concavity of f(x) by considering the sign of the second derivative:
When x ∈ (0, π/2): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.
When x ∈ (π/2, 3π/2): In this interval, cos x < 0, so f''(x) > 0. The second derivative is positive, indicating concavity upwards.
When x ∈ (3π/2, 2π): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.
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is n/3 =15 a one solution, infinite solution, or no solution?
Helen's Shop is 60 meters wide and 80 meters long. The parking lot in front of Helen's Shop is twice as long as it is wide and is 50 meters wide.
Answer:
The sum of the area is 9800 m^2
Step-by-step explanation:
( A= L x W )
Helens shop, A=(60m)x(80m)=4800 m^2
Parking lot, A=2W x W = 2(50m) x (50m)=5000 m²
The sum is 9800 m^2.
find x and y this is geometry
There are 85 girls and 70 boys in the sixth grade. Of these students, 14
girls and 8 boys take piano lessons. What percentage of the sixth
graders at this school take piano lessons?
Answer:
14.2%
Step-by-step explanation:
85+70= 155
155=100%
22=?
22×100%÷155
= 14.1935
hence answer is 14.2%
5. The football team lost 3
yards on the first play,
gained 8 on the next play,
and lost 2 on the last play.
What were the total yards
gained or lost?
Answer:
they have gained 3 yards
Step-by-step explanation:
they were at -3 then gained 8 which put them at 5 then lost 2 which put them at 3
Use the figure below to complete the following problem.Given:R, S, T are midpoints of AC, AB, and CB.RS =½CB½RT½AB
The answer is 1/2 CB , because CB is the segment parallel to RS. And since the midpoints are joined it must be half
A full grown German Shepherd weighs about 35 kg on Earth and only 13.3 kg on Mars. How much would a German Shepherd puppy weigh on Earth if it was 1.9 kg on Mars
Answer:
Step-by-step explanation:5 pounds
35/13.3=2.63. 1.9x2.63=5kg
Quadratic equations and variation
POSSIBLE POINTS
y is inversely proportional to x and y is equal to 10 when x is equal to 2. find the constant of proportionality and the value of x then y is equal to 8
K=
X=
The constant of proportionality is 20 and y is equal to 8, x is equal to 2.5.
Calculating the value of x and the constantIf y is inversely proportional to x, then we can write:
y = k/x
where k is the constant of proportionality.
To find the value of k, we can use the given information that y is equal to 10 when x is equal to 2.
Substituting these values, we get:
10 = k/2
Multiplying both sides by 2, we get:
k = 20
Therefore, the constant of proportionality is 20.
Now, we can use the equation y = k/x and the value of k to find the value of x when y is equal to 8.
Substituting y = 8 and k = 20, we get:
8 = 20/x
Multiplying both sides by x, we get:
8x = 20
Dividing both sides by 8, we get:
x = 2.5
Therefore, when y is equal to 8, x is equal to 2.5.
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calculate the expected value of the sample mean of mpg derived from a random sample of four passengers
The expected value of the sample mean of mpg derived from a random sample of four passengers is 30.5 mpg.
The expected value of the sample mean can be calculated using the formula
E(x) = μ
where x is the sample mean, and μ is the population mean.
In this case, the population mean is given as 30.5 mpg. The standard deviation of the population is also given as 4.1 mpg.
The standard deviation of the sample mean can be calculated using the formula
σx = σ/√n
where σ is the population standard deviation and n is the sample size.
Substituting the given values, we get:
σx = 4.1/√4 = 2.05
So the expected value of the sample mean is
E(x) = μ = 30.5 mpg.
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hey please help where it says the > thing it says fives, eights, threes
Answer:
\(8 \\ = 40 + 24 \\ = 64\)
I hope I helped you^_^
Answer:
\(8 \times 8 = 5eights + 3eight \\ 8 \times 8 = 40 + 24 \\ 8 \times 8 = 64 \\ thank \: you\)
Using the quadratic formula, solve 0 = 2x² 2x² - 10x + 7 Give each of your answers to 2 d.p.
Answer:
x1 ≈ 0,84; x2 ≈ 4,16
Step-by-step explanation:
Find the discriminant and then both values of x according to the formulas (I added a photo of my solution)
What is the sum of the infinite geometric series?
25 minus 10 plus 4 minus eight fifths plus continuing
The series diverges.
5/2
50/7
125/7
87/5
The sum of infinite geometric series is
\(25 - 10 + 4 - \frac{8}{5}\)
is \(\frac{125}{7}\)
What is geometric series?
The series where the ratio between the consecutive terms of the series are same is called geometric series.
The sum of infinite geometric series is
\(25 - 10 + 4 - \frac{8}{5}\)
Here
common ratio (r) = \(-\frac{10}{25} = -\frac{2}{5}\)
Here r lies between -1 and 1
So the given geometric series converges
First term is 25
Sum =
\(\frac{25}{1 -(-\frac{2}{5})}\\\\\frac{25}{\frac{5+2}{5}}\\\\\frac{25}{\frac{7}{5}}\\\\\frac{25 \times 5}{7}\\\\\frac{125}{7}\)
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You are given n = 8 measurements: 4, 4, 7, 6, 4, 6, 6, 8. (a) Calculate the range. 4 (b) Calculate the sample mean, x. x=5625 (c) Calculate the sample variance, s2, and standard deviation
(a)The range of the given set of measurements is 4.
(b)The sample mean of the given set of measurements is approximately 5.625.
(c)The sample variance of the given set of measurements is approximately 2.337768, and the sample standard deviation is approximately 1.529.
(a) The range is the difference between the largest and smallest values in the set of measurements. In this case, the largest value is 8 and the smallest value is 4, so the range is 8 - 4 = 4.
To calculate the range, we subtract the smallest value from the largest value. In this case, the largest value is 8 and the smallest value is 4.
Range = Largest value - Smallest value
Range = 8 - 4
Range = 4
The range provides a simple measure of the spread or dispersion of the data. In this case, the range tells us that the values range from the smallest value of 4 to the largest value of 8, with a difference of 4 between them.
(b) The sample mean, denoted as x, is the sum of all the measurements divided by the total number of measurements.
To calculate the sample mean, we add up all the measurements and then divide by the total number of measurements. In this case, we have 8 measurements.
Sum of measurements = 4 + 4 + 7 + 6 + 4 + 6 + 6 + 8 = 45
Sample mean = Sum of measurements / Total number of measurements
Sample mean = 45 / 8
Sample mean ≈ 5.625
The sample mean represents the average value of the measurements and provides a measure of central tendency.
(c) The sample variance, denoted as s^2, measures the variability or dispersion of the data points around the sample mean. It is calculated as the average of the squared differences between each measurement and the sample mean.
To calculate the sample variance, we first calculate the squared difference between each measurement and the sample mean. Then, we average those squared differences.
Squared difference for each measurement:
(4 - 5.625)^2 = 2.890625
(4 - 5.625)^2 = 2.890625
(7 - 5.625)^2 = 1.890625
(6 - 5.625)^2 = 0.140625
(4 - 5.625)^2 = 2.890625
(6 - 5.625)^2 = 0.140625
(6 - 5.625)^2 = 0.140625
(8 - 5.625)^2 = 5.390625
Sum of squared differences = 2.890625 + 2.890625 + 1.890625 + 0.140625 + 2.890625 + 0.140625 + 0.140625 + 5.390625 = 16.364375
Sample variance = Sum of squared differences / (Total number of measurements - 1)
Sample variance = 16.364375 / (8 - 1)
Sample variance ≈ 2.337768
The standard deviation, denoted as s, is the square root of the sample variance.
Sample standard deviation = √(Sample variance)
Sample standard deviation = √(2.337768)
Sample standard deviation ≈ 1.529
These measures provide information about the dispersion or spread of the data points around the sample mean. A higher variance or standard deviation indicates greater variability in the measurements.
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use the quadratic formula to solve x^2-10x+21=0
By using the quadratic formula, the roots of the quadratic equation are x = -7 and x = -3.
What is a quadratic equation?In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph with a maximum exponent of two (2).
In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Mathematically, the quadratic formula is represented by this mathematical equation:
\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\)
For the given quadratic equation x² + 10x + 21 = 0, we have:
\(x = \frac{-(10)\; \pm \;\sqrt{(10)^2 - 4(1)(21)}}{2(1)}\\\\x = \frac{-(10)\; \pm \;\sqrt{100 - 84}}{2}\\\\x = \frac{-(10)\; \pm \;\sqrt{(10)^2 - 4(1)(21)}}{2(1)}\\\\x = \frac{-(10)\; \pm \;\sqrt{16}}{2}\\\\x = \frac{-(10)\; \pm \;4}{2}\)
x = (-10 - 4)/2 = -14/2 = -7
x = (-10 + 4)/2 = -6/2 = -3
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Find the sum. (w+8) + 2(w +9)
Is augmented matri invertible if linear system has a unique solution
An augmented matrix is invertible if the linear system has a unique solution.
What is an augmented matrix?
The augmented matrix is known as a rectangular matrix.
The properties of an augmented matrix includes:
The number of columns is equal to the number of variables in the linear equations. The number of rows is the same as the number of linear equations.The rows of the augmented matrix can be also be interchanged.Note that the inverse of a matrix must be unique
And If A is invertible, then its inverse is unique.
If the linear system is unique, then the augmented matrix is invertible.
Thus, an augmented matrix is invertible if the linear system has a unique solution.
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For the December food drive the Sophomores collected 125 pounds of food. The Seniors collected two and a half times more food than the Sopohmores.How much food did the Seniors collect?
The first step is to find out how much more food the Seniors collected than the Sophomores. We know that they collected two and a half times more, which is the same as 2.5 times 125 = 312.5 pounds of food.
Therefore, the Seniors collected 312.5 pounds of food.
Which ordered pair is a solution of thisequation?8x + 7y = -50Click on the correct answer.(-6,-1)(0,-6)(-6,0)(-1,-6)
Given the equation:
8x + 7y = -50
We will check the options to find which order pair is the solution of the equation
Point (-6 , -1)
8 * -6 + 7 * -1 = -48 - 7 = -55 ≠ -50
Point ( 0 , -6)
8 * 0 + 7 * - 6 = -42 ≠ -50
Point (-6, 0 )
8 * - 6 + 7 * 0 = -48 ≠ -50
Point (-1 , -6)
8 * -1 + 7 * -6 = -8 - 42 = -50
so, the order pair which is a solution for the equation is (-1 , -6 )
At a sale, books are sold at $90.75 each, which is 75% of the original price.
(i) what is the original price of the book?
(II) Paul buys 10 books at the sale and pays VAT of 16% on the sale price. Calculate the TOTAL amount he paid for 10 books.
Answer:
Selling Price= $90.75
(i) Original Price= $90.75/0.75= $ 121.00
(ii) 1 Book= $90.75
10 Books= $90.75*10= $907.50
Total Amount Paid= $907.50*1.16 =$1052.70
Si a:b:c= 4:3:2 ayudaaaa
Answer:
a=6 b=4 3=2.55555555567
PLEASE HELP ME I REALLH NEED IT
if the third term is 20 and 7th is 1.25, find the 11th term
Answer:
the 11th term is 0.0000488 or 4.88*10^-5.
Step-by-step explanation:
a3 = 20, a7 = 1.25
a7 = a3r^7-3
1.25 = 20r^4
r^4 = 0.0625
r = 4th root of 0.0625
r = 0.5
a3 = a1r^3-1
20 = a1(20)^2
400a1 = 20
a1 = 0.05
a11 = 0.05(0.5)^11-1 = 0.0000488 or 4.88*10^-5
Arik invested $500 in a savings account that earns 6.25% interest compounded monthly. Assuming there are no other deposits or withdrawals, what is the total amount in his account after 4 years?
The total amount that would be found in the account after 4 years, would be $ 641. 69
How to find the total amount ?The total amount after 4 years in Arik's account can be found by the formula :
= A = Amount invested x ( 1 + r /n )ⁿ
The variables are:
Amount invested = $ 500
r = 6.25% = 0. 0625
n = 12
t = 4 years
The total amount is then :
A = 500 x ( 1 + 0. 0625 / 12 ) ^ ⁽¹² ˣ ⁴ ⁾
A = $ 641. 69
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a helium filled balloon has a volume of 50.0 l at 25 and 1.08 atm what volume will it have at .855 atm and 10.0 c
The volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L, calculated using the ideal gas law equation.
To compute this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the initial temperature of 25 °C to Kelvin:
T1 = 25 + 273.15 = 298.15 K
Next, we can rearrange the ideal gas law equation to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
We have:
P1 = 1.08 atm (initial pressure)
V1 = 50.0 L (initial volume)
P2 = 0.855 atm (final pressure)
T2 = 10.0 °C (final temperature)
Converting the final temperature to Kelvin:
T2 = 10 + 273.15 = 283.15 K
Substituting the values into the equation:
V2 = (1.08 * 50.0 * 283.15) / (0.855 * 298.15)
V2 ≈ 42.81 L
Therefore, the volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L.
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