The value of [tex]k = 2P/x^2[/tex]
We are aware that an object's location might cause it to store energy. When a bow and arrow are used, the energy that is stored when the bow is pulled is what gives the arrow its kinetic energy when it is released.
when a spring is moved away from its equilibrium position, it gains some energy, which we can notice by the tension our hands experience as we stretch it. Potential energy is a type of energy that arises from a change in its position or condition, according to our definition
We know that P=1/2kx^2
Now solving for k
2P = kx^2
Therefore
k = 2P/x^2
Hence the value of k is 2P/kx^2
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52 = -5x - 3 i need help with a math test and this one question i do not understand
Answer:
x=-52/5-i3/5Step-by-step explanation:
[tex]52 = - 5x - 3i...given \: expression \\ - 5x - 3i = 52...switch \: sides \\ - 5x - 3i + 3i = 52 + 3i...add \: 3i \: to \: both \: sides \\ - 5x = 52 + 3i...simplify \\ \frac{ - 5x}{ - 5} = \frac{52}{ - 5} + \frac{3i}{ - 5} ...divide \: both \: sides \: by \: - 5 \\ x = \frac{ - 52}{5} - i \frac{3}{5} ...simplified[/tex]
A gym class has $12$ students, $6$ girls and $6$ boys. The teacher has $4$ jerseys in each of $3$ colors to mark $3$ teams for a soccer tournament. If the teacher wants at least one girl and at least one boy on each team, how many ways can he give out the jerseys
Answer:
2700
Step-by-step explanation:
*6*10*9/4!*4*4*6*5/4!
Several friends bought flowers to make table centerpieces. write the ratios of purple flowers to white flowers for each friend. bouquets of flowers purple flowers white flowers rowan 8 2 marcia 10 1 jillian 10 2 lulua 18 3 who has the smallest ratio of purple to white flowers? rowan marcia jillian lulua
The ratio for Rowan = 4:1.
The ratio for Marcia = 10:1.
The ratio for Jillian = 5:1.
The ratio for Lulua = 6:1.
The smallest ratio among these for purple to white flowers is for Rowan, that is, 4:1.
Ratios are fractions in the simplest form representing the relationship between two quantities.
The ratio of purple to white flowers for each friend can be shown as:-
Rowan:
The number of purple flowers = 8
The number of white flowers = 2
Thus, the fraction of purple to white flowers = 8/2 = 4/1.
Thus, the ratio for Rowan = 4:1.
Marcia:
The number of purple flowers = 10
The number of white flowers = 1
Thus, the fraction of purple to white flowers = 10/1.
Thus, the ratio for Marcia = 10:1.
Jillian:
The number of purple flowers = 10
The number of white flowers = 2
Thus, the fraction of purple to white flowers = 10/2 = 5/1.
Thus, the ratio for Jillian = 5:1.
Lulua:
The number of purple flowers = 18
The number of white flowers = 3
Thus, the fraction of purple to white flowers = 18/3 = 6/1.
Thus, the ratio for Lulua = 6:1.
The smallest ratio among these for purple to white flowers is for Rowan, that is, 4:1.
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Answer:Its rowan
Step-by-step explanation:Mark me brainliest need award
A rectangle is 8 feet longer than it is wide. find the dimensions of the rectangle if its area is 345 sq-feet.
The width of rectangle is 15 feet and the length of rectangle is 23 feet.
According to the statement
Width of rectangle = x
Length of rectangle = x+10
Area of rectangle = 345 sq-feet.
we know that the area of rectangle is
Area of rectangle = L*W
Substitute the values in it then
345 = (x) (x+8)
345= (x)^2 + 8x
(x)^2 + 8x - 345 = 0
By factorisation
(x-15) (x+23) = 0
So, width of rectangle is 15 feet and the length of rectangle is 23 feet.
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A square has a perimeter of 12x 52 units. which expression represents the side length of the square in units?
Answer:
X
Step-by-step explanation:
KHAN ACADEMY
Given a polynomial function f(x) = 2x2 – 3x 5 and an exponential function g(x) = 2x – 5, what key features do f(x) and g(x) have in common? both f(x) and g(x) have the same domain of ([infinity], -[infinity]). both f(x) and g(x) have the same range of [0, -[infinity]). both f(x) and g(x) have the same x-intercept of (2, 0). both f(x) and g(x) increase over the interval of [-4 , [infinity]).
Both f(x) and g(x) have the same domain of (9,-infinity).
What is a function?A function is an expression that shows the relationship between two or more numbers and variables.
Plotting the functions f(x) = 2x² – 3x + 5 and g(x) = 2ˣ - 5:
Both f(x) and g(x) have the same domain of (9,-infinity).
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Find the gradient and the intercept shown by the straight line 2x + 3y = 6
Answer:
The gradient is -[tex]\frac{2}{3}[/tex] and the intercept is 2.
Step-by-step explanation:
First, transform the given equation into the slope-intercept form, y = mx + b. The variable m represents slope (gradient) and the variable b represents the intercept.
2x + 3y = 6
3y = -2x + 6
y = -[tex]\frac{2}{3}[/tex]x + 2
The gradient is -[tex]\frac{2}{3}[/tex] and the intercept is 2.
Answer:
[tex]\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2[/tex]
Step-by-step explanation:
Equation of the line in slope intercept form:[tex]\sf \boxed{\bf y = mx +b}[/tex]
Here m is the slope or gradient and b is the y-intercept.
Write the given equation in slope-intercept form.
2x + 3y = 6
3y = -2x + 6
[tex]\sf y =\dfrac{-2}{3}x +\dfrac{6}{3}\\\\ y = \dfrac{-2}{3}x + 2[/tex]
[tex]\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2[/tex]
The length of a rectangle is 5 5/3 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68
(question and answers attached)
The perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The perimeter of any object is the total sum length of its boundary.
The perimeter of a rectangle with length l units and width w units is given as:
Perimeter = 2(l + w) units.
In the question, we are given that the length of a rectangle is 5 3/5 inches and its width is half of its length. We are asked to find the perimeter of the rectangle.
The length of the given rectangle (l) = 5 3/5 inches = 28/5 inches.
The width of the given rectangle (w) = Half of length = 1/2 * 28/5 inches = 14/5 inches.
Thus, the perimeter of the rectangle = 2(l + b) = 2(28/5 + 14/5) inches,
or, the perimeter = 2(42/5) inches,
or, the perimeter = 84/5 inches,
or, the perimeter = 16.8 inches.
Thus, the perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The given question is incorrect. The correct question is:
"The length of a rectangle is 5 3/5 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68"
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Triangle E D F is shown. Angle E D F is 43 degrees and angle D F E is 82 degrees. The length of D F is 15.
What is the measure of angle E?
m∠E =
°
What is the length of EF rounded to the nearest hundredth?
EF ≈
Part 1
Angles in a triangle add to 180 degrees, so
[tex]m\angle E=180^{\circ}-82^{\circ}-43^{\circ}=55^{\circ}[/tex]
Part 2
By the Law of Sines,
[tex]\frac{EF}{\sin 43^{\circ}}=\frac{15}{\sin 55^{\circ}}\\\\EF=\frac{15 \sin 43^{\circ}}{\sin 55^{\circ}}\\\\EF \approx 12.49[/tex]
Answer:
What is the measure of angle E?
m∠E =
✔ 55
°
What is the length of EF rounded to the nearest hundredth?
EF ≈
✔ 12.49
Step-by-step explanation:
Find a 49 of the sequence 70, 63, 56, 49,
Answer:
- 226
Step-by-step explanation:
ARITHMETIC SEQUENCE.
Number of term of an Arithmetic progressions has the formular.
Tn = a + ( n - 1 ) d
From the question,
First term ( a ) = 70
common difference = T2 - T1 = 63 - 70 = -7
For the 49th term
T49 = a + 48d
= 70 + 48 ( -7 )
= 70 - 336 = - 226
Which equation represents this number sentence?
Nine more than the quotient of a number and 3 is 21.
n3+9=21
fraction n over 3 end fraction plus 9 equals 21
3n+9=21
fraction 3 over n end fraction plus 9 equals 21
n+93=21
fraction numerator n plus 9 end numerator over 3 end fraction equals 21
9n+3=21
The equation which represents the number sentence given in the task content is; n/3 + 9 = 21.
Which equation correctly represents the number sentence?According to the task content, it follows that the sentence given is; Nine more than the quotient of a number and 3 is 21.
Since, the quotient of a number and 3 can be written as; n/3.
Consequently, the correct equation is; n/3 +9 = 21.
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The test scores of 1,200 students are normally distributed with a mean of 83 and a standard deviation of 5.5. Under which interval did approximately 978 students score?
Select one:
a. 72
b. 77.5
c. 83
d. 72
Using the Empirical Rule, it is found that the interval in which approximately 978 students scored was:
A. 72 < x < 88.5.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.The percentage that 978 is of 1200 is:
978/1200 x 100% = 81.5%.
Considering the symmetry of the normal distribution, two outcomes are possible involving 81.5% of the measures:
Between one standard deviation below the mean and two above, which in the context of this problem is between 77.5 and 94.Between two standard deviations below the mean and one above, which in the context of this problem is between 72 and 88.5, which is option A in this problem.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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35. A can of popcorn is to be packed in a box for shipping as shown. The can is 18 inches tall and has a radius of 7 inches. The box is 19 inches tall and has a square base with sides of length 15 inches. All empty space around the can is to be filled with packing material. How many cubic inches of packing material will be needed?
The amount of packing material is 1506 cubic inches
How to determine the amount of packing material?The given parameters are:
Can
Radius, r = 7 inches
Height, h = 18 inches
Box
Base dimension, l = 15 inches
Height, h = 19 inches
The volume of the can is:
[tex]V = \pi r^2h[/tex]
So, we have:
[tex]V_1 = 3.14 * 7^2 * 18[/tex]
[tex]V_1 = 2769[/tex]
The volume of the box is
[tex]V =l^2h[/tex]
So, we have:
[tex]V_2 =15^2 * 19[/tex]
[tex]V_2 =4275[/tex]
The amount of packing material is;
Amount = V2 - V1
This gives
Amount = 4275 - 2769
Evaluate
Amount = 1506
Hence, the amount of packing material is 1506 cubic inches
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which of thw following equations has roots x=-1, x=-2, and x=3i, and passes through the point (0,36)?
Answer:
C. f(x) = 2x⁴ +6x³ +22x² +54x +36
Step-by-step explanation:
You can use Descartes' rule of signs and the y-intercept to help you select the correct answer.
Y-interceptThe given point (0, 36) is the y-intercept of the function. This tells you 36 is the constant in the polynomial, eliminating choices A and B.
Rule of signsDescartes' rule of signs tells you the number of positive real roots will be less than or equal to the number of sign changes in the coefficients when the function is written in standard form. The number of negative real roots will be the number of sign changes after the signs of odd-degree terms are reversed.
Given rootsThe given real roots are both negative. There are zero positive real roots, so all of the signs of the coefficients in the function must be the same (no changes). This eliminates choice D, and tells you C is the correct answer.
f(x) = 2x⁴ +6x³ +22x² +54x +36
At 9am a car a began a journey from a point, travelling at 40 mph. at 10am another car b started travelling from the same point ai 60 mpb in the same direction as car a. at what time will car b pass car a?
Answer:
In 3h (12am)
Step-by-step explanation:
First car A Will by 10 am be 40 miles from staring point, then car B Will start going 60mph and by 11am car A Will be 80 miles from start, and car B Will be 60 miles from start in 12 am car A Will be at 120 miles and car B Will be also 120 miles
And answer is in 3h or in 12am
Which type of bacterial pneumonia is most often seen in children and young adults, is characterized by a persistent cough and low-grade fever, and is usually treated with tetracycline
The type of bacterial pneumonia is most often seen in children and young adults is; Pneumococcal infection.
What is the Type of Bacteria?The correct type of Bacterial pneumonia that is most often seen in children and young adult is called Pneumococcal infection. This is because it is a name for any infection caused by bacteria called Streptococcus pneumoniae, or pneumococcus.
Thus, we can conclude that the type of Bacterial pneumonia here is called Pneumococcal infection.
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find the volume of these rctangular prisms l=11.5cm w=2.5mm h=6cm
step by step pls
Answer:
172.5cm^3
Step-by-step explanation:
* = multiply or times
volume = length*width*height
Plug in the numbers: 11.5*2.5*6 = 172.5cm^3
There are 500 passengers on a train. 7/20 are men and 40% are women. the rest are children
On the train, there are a total of 125 children.
Calculating the number of childrenTotal number of passengers = 500
Out of 500 passengers, men =7/20
So, the number of men= 500* 7/20 = 175
Out of 500 passengers, women = 40%
So, the number of women passengers = 500*40/100 = 200
Therefore, the total number of men and women passengers= 175+200 = 375.
There are also children on the train. So, the rest number should be those children.
The rest number =children= 500- 375 = 125.
So, it is concluded from the above equation that there are 125 children on the train.
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Diagram 1 shows a tangent to a circle, centre O. Find x and y; 40° y Diagram 1
Answer:
x = 80 , y = 50
Step-by-step explanation:
the angle between the tangent and the radius at the point of contact is 90°
given the angle between the tangent and the chord is 40° , then
angle inside triangle = 90° - 40° = 50°
the triangle has 2 equal radii forming 2 sides thus is isosceles with 2 base angles being congruent, then
y = 50°
the sum of the 3 angles in the triangle = 180° , then
x = 180° - 50° - 50° = 180° - 100° = 80°
Answer:
x = 80°
y = 50°
Step-by-step explanation:
the legs of the inner triangle (tangent to O, and O to point with y angle) are equal because both are the radius of the circle.
that makes the inner triangle an isoceles triangle with both angles on the baseline (tangent to point with y angle) being equal.
the angle of the tangent to the leg "tangent to O" is per definition a right angle (90°). otherwise it would not be a tangent.
one post of the right angle is 40°, so the other part (the triangle inner angle at the tangent point) is then 90-40 = 50°.
since both leg angles must be equal (as described above), y = 50° too.
and as the sum of all angles in a triangle must be 180°, that gives us for x
180 = 50 + 50 + x
x = 180 - 50 - 50 = 80°
A scientist testing the effects of a chemical on apple yield (apples/acre) sprays an orchard with the chemical. A second orchard does not receive the chemical. In the fall, the yield is determined (number of apples harvested per acre). What is the dependent variable
Following are the dependent variables:
1. The amount of water that each orchard receives.
2. The species of trees in the orchard.
Reason:
The exercise scientist is looking for the effects of a chemical between an apple crop to which it is administered and another to which it is not, 4 options are presented, of which it is essential to count as a variable the amount of water each Orchard and tree species in the orchard, since they can generate alterations in the results, the other two variables of the exercise such as number of apples and size of the orchards are not significant and their variations do not affect the scientist's objective.
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2sin^2(x)+sin(2x)=2
please help!!
[tex]2sin {}^{2} (x) + sin(2x) = 2 \\ 2sin {}^{2} (x) + 2sin(x)cos(x) = 2 \\ sin {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\1 - cos {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\ - cos {}^{2} (x) + sin(x)cos(x) = 0[/tex]
[tex]cos(x)( - cos(x) + sin(x)) = 0[/tex]
[tex]cos(x) = 0 \\ x = \frac{\pi}{2} + k\pi \\ \\ sin(x) = cos(x) \\ x = \frac{\pi}{4} + k\pi[/tex]
What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}
The domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}
How to determine the domain?The function is given as
g(x) = –⌊x⌋ + 3
The above is a step function, and the domain is the set of input values it can accept
Step functions of the given form can accept any real value of x
Hence, the domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}
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Complete question
The graph of the step function g(x) = –⌊x⌋ + 3 is shown. What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}
Answer:
A
Step-by-step explanation:
WILL MAKE BRAINLIEST!! What type of angle is angle A?
Carson buys eggs and lemons at the store. he pays a total of $39.62. he pays $6.74 for the eggs. he buys 8 bags of lemons that each cost the same amount.
The algebraic equation is used to determine the costs of each bag of lemons is 8x = $39.62 - $6.74
According to the question,
Cost of 1 bag of lemons = $x
Cost of 8 bags of lemons = 8*x = 8x
Cost of 8 bags of lemons = Total cost - cost of the egg
8x = $39.62 - $6.74
Hence, the algebraic equation is used to determine the costs of each bag of lemons is 8x = $39.62 - $6.74.
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PLEASE HELP 80 POINTS !!!!!!!!
Answer:
Step-by-step explanation:
a) it is a reflection
b) it is vertex B"
The square root of the quantity 4 x minus 3 end quantity equals 5.
Answer:
The statement is false.
Step-by-step explanation:
Given,
[tex] \sqrt{4 \times - 3} = 5[/tex]
To Prove
Soln:
[tex] \sqrt{4 \times - 3} [/tex]=[tex]2i \sqrt{3} [/tex]
=>[tex]2i \sqrt{3} ≠5[/tex]
Hence, 2i√3 is not equal (≠) to 5.
Safety guidelines specify that a ladder should form an angle between 70° and 80° with the ground. If a ladder is 4 m long, determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines?
Answer:
Step-by-step explanation:
70 = x/4
x = 4 cos 70 = 1.37m
x = 4 cos 80 = 0.69m
The range is ( 0.69m, 1.37m)
The range of distances from the wall (x) that the foot of the ladder placed to fall within the safety guidelines is between 0.7052 meters and 1.456 meters.
To determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines, use trigonometry.
Let's assume the distance from the wall to the foot of the ladder is x meters the ladder is 4 meters long.
The angle between the ladder and the ground is given to be between 70° and 80°. Let's consider the extreme cases for each angle:
When the ladder makes an angle of 70° with the ground:
In this case, the angle between the wall and the ladder (θ) will be 90° - 70° = 20°.
When the ladder makes an angle of 80° with the ground:
In this case, the angle between the wall and the ladder (θ) will be 90° - 80° = 10°.
Now, use trigonometry to calculate the range of distances (x) from the wall:
For the first case (θ = 20°):
tan(20°) = Opposite / Adjacent
tan(20°) = x / 4
x = 4 × tan(20°)
For the second case (θ = 10°):
tan(10°) = Opposite / Adjacent
tan(10°) = x / 4
x = 4 × tan(10°)
Now, let's calculate the values:
x ≈ 4 × 0.3640 ≈ 1.456 meters (rounded to three decimal places) - for the first case.
x ≈ 4 × 0.1763 ≈ 0.7052 meters (rounded to four decimal places) - for the second case.
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20 points!
i need help with these rational numbers
The rational numbers are explained below.
What are rational numbers?The complete question can't he found. Therefore, an overview will be given. Rational numbers are the numbers that can be represented by the quotient p/q of two integers.
In this case, p and q are integers and p isn't equal to 0.
The examples include 1/5, 1/3, -2, 5, etc.
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Find the area of the figure
Answer:
36 in.
Step-by-step explanation:
find the area of the rectangle and triangle first
area of rectangle = length x height
aR = (6 + 6) x 5
aR = 12 x 5
aR = 60
area of triangle = base x height x 1/2
aT = (6 + 6) x 4 x 1/2
aT = 12 x 4 x 1/2
aT = 24
now, to find the area of the shaded area subtract the triangle from the rectangle
area = rectangle - triangle
a = 60 - 24
a = 36
Using the equation y = 2x - 3, what would the input need to be for an output of 7?
00
O 11
05
08