The sum of the two integers is -23.
Let the two negative integers be x and y where x is less than y. We know that their difference is 5 units apart. This means:
y - x = 5, or y = 5 + x
Also, we know that the product of the two integers is 126.
Therefore: x * y = 126
Substituting y in terms of x:x(5 + x) = 126
Simplifying: x² + 5x - 126 = 0(x + 14)(x - 9) = 0
Taking the negative root since the integers are negative:
x = -14, y = -9
The sum of the two integers is:-14 + (-9) = -23
Therefore, the sum of the two integers is -23.
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Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation. y"(θ)+3y'(θ)-y(θ)=secθ
The method of undetermined coefficients cannot be applied to find a particular solution of the given equation y''(θ) + 3y'(θ) - y(θ) = sec(θ) since sec(θ) is not an elementary function that fits the criteria for the method.
To determine whether the method of undetermined coefficients can be applied to find a particular solution for the given equation y''(θ) + 3y'(θ) - y(θ) = sec(θ), we need to consider the nature of the non-homogeneous term on the right-hand side (sec(θ)) and the compatibility with the method.
The method of undetermined coefficients is applicable when the non-homogeneous term is a linear combination of elementary functions such as polynomials, exponential functions, sine, cosine, and their linear combinations.
However, the term sec(θ) does not fall into this category.
Secant (sec(θ)) is not an elementary function. It is the reciprocal of the cosine function and has a non-trivial behavior. The method of undetermined coefficients relies on the assumption that the particular solution can be expressed as a sum of specific functions, each corresponding to the elementary functions in the non-homogeneous term.
Since sec(θ) does not fit this criterion, the method of undetermined coefficients cannot be directly applied to find a particular solution.
In this case, an alternative approach, such as variation of parameters or integrating factors, may be more appropriate for finding a particular solution for the given equation.
These methods are used to handle non-elementary non-homogeneous terms by introducing additional parameters or transforming the equation.
Therefore, in the given equation y''(θ) + 3y'(θ) - y(θ) = sec(θ), the method of undetermined coefficients cannot be directly applied to find a particular solution.
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HELP
The dot plot below represents how long it takes students in a 9th grade math class to get to school every morning.
How many students take 35 minutes to get to school?
The answer of the given question based on the Statistics the answer is only one student takes 35 minutes to get to school.
What is Horizontal axis?In mathematics, horizontal axis is reference line used in coordinate systems to plot the points and graph the functions. It is usually denoted as x-axis and is oriented horizontally, running from left to right.
In two-dimensional coordinate system, horizontal axis is perpendicular to vertical axis, which is usually denoted as y-axis and runs vertically from bottom to top. Together, x-axis and y-axis divide coordinate plane into four quadrants.
Based on the dot plot, it appears that there is only one dot that falls on the value of 35 on the horizontal axis. Therefore, only one student takes 35 minutes to get to school.
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Which values are solutions to ka? >-2? Select two options.
k= -10
k=-7
k=-5
k=-1
k=0
Answer:
The two options would be k = -10 and k = -7.
Step-by-step explanation:
Technically k = -5 and k = -1 are possible too, since if you multiply all of the above by -1 as a then all of them will be over -2. Even k = 0 would work, as all numbers multiplied by 0 are 0 and 0 > -2.
Hope this helped!
This measure of central tendency can be considered the most precise.
a. mode
b. median
c. mean
d. average
This measure of central tendency can be considered the most precise in option c. mean
The mean is a measure of central tendency that calculates the average of a set of values. It is often considered the most precise measure because it takes into account all the values in the dataset and provides a balanced representation.
The mean is calculated by summing all the values and dividing by the total number of values. Unlike the mode, which only identifies the most frequently occurring value, and the median, which represents the middle value, the mean incorporates all the values and provides a comprehensive summary of the dataset.
However, it is important to note that the mean can be sensitive to extreme values or outliers in the data.
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19. Find the slope of the line graphed below.
Answer: \(\frac{3}{4}\)
Step-by-step explanation:
Choose two points on the line, \(\frac{rise}{run}\) fraction, we get: the slope of the line is \(\frac{3}{4}\)
Answer:
answer is 3/14hhhytt
Step-by-step explanation:
1v1 Ttd
15 +(12+18a) simplify the expression
I NEED THE ANSWER ASAP PLEASE
Answer:
27+18a
Step-by-step explanation:
If ZMK APY, m M = 112 ° , m Y = 41 ° , m K = (13x 37) ° , and m A = (2y + 7) ° , find the values of x and y.
need a answer asap
Answer
13x-37=112
13x =149
X=11.4
2y+7=41
Y=24
The value of x and y respectively will be 13° and 17°.
Based on the equation that's given in the question, the value of x will be found thus:
13x - 37 = 112
Collect like terms
13x = 112 + 37
13x = 149
x = 149/13
x = 13
Also, note that 2y + 7 = 41, therefore, the value of y will be:
2y = 41 - 7
2y = 34
y = 34/2 = 17°
Therefore, the value of x and y respectively will be 13° and 17°.
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two carts, a and b, are connected by a rope 39 ft long that passes over a pulley p. the point q is on the floor 12 ft directly beneath p and between the carts. cart a is being pulled away from q at a speed of 2 ft/s. how fast (in ft/s) is cart b moving toward q at the instant when cart a is 5 ft from q? (round your answer to two decimal places.)
The velocity of the cart b is found as 20/23 ft/s over the pulley.
What is defined as the rate of change?The momentum of a variable is represented by the rate of change, which is used to mathematically define the percentage change in value over such a defined period of time.For the given data in the question.
q's velocity is 2 feet per second.
Rope length is 39 feet.
Assume x is the distance between A and Q. (refer the image).
Assume y is the distance between Q and B. (refer the image).
As a result of the image,
x² + 12² = L²
Now, with respect to time t, differentiate the above equation.
2x(dx/dt) + 0 = 2L.(dL/dt)
For x = 5 ft and L = 13 ft
dL/dt = (5×2)/13 = 10/13
In the case of B,
y² + 12² = (39 - L)² ; from diagram.
Differentiating now,
2y(dy/dt) + 0 = -2(39 - L).(dL/dt)
At x = 5 ft and y = 23 ft.
dy/dy = -20/23
(A negative sign indicates the opposite direction)
Thus, the velocity of cart b is found as 20/23 ft/s.
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Line segment JM has endpoints with coordinates 0 and 25 on a number line. Points K and L are on segment JM. K has a coordinate of 5 and point L has a coordinate of 12. Find the probability that a point on JM is placed first on JL and a second point is not placed on KL.
Answer:
D. 216/625Step-by-step explanation:
The length of the segment JM is 25 units.The segment JL is between 0 and 12, so is 12 units.The segment KL is between 5 and 12, so is 7 units.The probabilities for each point:
P(point on JL) = 12/25P(point not on KL) = 1 - 7/25 = 18/25Required probability:
P = 12/25*18/25 = 216/625Correct choice is D
12. The net for a right
triangular prism is shown
below.
136.5
square
units
6.5
4
4.
o
57.5
square
units
3
3
3
90 square
units
What is the total surface
area of the prism?
O
39 square
units
CLEAR ALL
Answer:
Basic Of Algebra. Basics of Algebra cover the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables. For example, x+10 = 0. This introduces an important algebraic concept known as equations.Step-by-step explanation:
Your neighbor goes to the post office once a month and picks up two checks, one for $11,000 and one for $3,400. The larger check takes four days to clear after it is deposited; the smaller one takes five days. Assume 30 days in a month.
a. What is the total float for the month?
b. What is the average daily float?
c-1. What are the average daily receipts?
c-2. What is the weighted average delay?
Answer/explanation:
a. The total float for the month can be calculated as follows:The delay for the larger check is 4 days, and the delay for the smaller check is 5 days, therefore the float is 4 + 5 = 9 days.The total float for the month is $14,400 ($11,000 + $3,400).Thus, the total float for the month is $14,400 for a period of 9 days.
b. The average daily float can be calculated as follows:Average daily float = Total float / Number of days in the periodAverage daily float = $14,400 / 30 daysAverage daily float = $480
Therefore, the average daily float is $480.
c-1. The average daily receipts can be calculated as follows:The total receipts for the month are $14,400, so the average daily receipts are:Average daily receipts = Total receipts / Number of days in the periodAverage daily receipts = $14,400 / 30 daysAverage daily receipts = $480
Therefore, the average daily receipts are $480.
c-2. The weighted average delay can be calculated as follows:Weighted average delay = (Delay for larger check * Amount of larger check + Delay for smaller check * Amount of smaller check) / Total amountWeighted average delay = (4 days * $11,000 + 5 days * $3,400) / $14,400Weighted average delay = $77,600 / $14,400Weighted average delay = 5.39 days (rounded to two decimal places)
Therefore, the weighted average delay is 5.39 days.
Is the function y = -x5 - 5 linear or nonlinear?
18 cm
28°
х
The value of x is approximately:
B) 20.39 cm
A) 8.45 cm
C) 33.85 cm
D) 38.34 cm
Answer:
c lolhahahahahahahahahahahahahahahahahahahahaha
Answer: c
Step-by-step explanation:
8.45 cm – 3.55 cm
how is the number e defined? (b) what is an approximate value for e? (c) what is the natural exponential function?
b) An approximate value for e is 2.71828,
c) The natural exponential function is eˣ
The number e is a mathematical constant that is closely related to the exponential function. It is one of the most important and widely used numbers in mathematics and science.
The number e is defined as the limit of the sequence of numbers
=> (1 + 1/n)ⁿ
as n approaches infinity.
In other words, it is the unique number that satisfies the equation
=> eˣ = lim(n→∞) (1 + x/n)ⁿ.
This equation states that as n increases, the value of the exponential function of x approaches eˣ.
The approximate value of e is 2.71828, but it can be calculated to an infinite number of decimal places.
The natural exponential function is a mathematical function that is defined by
=> eˣ
It is used to model real-world situations that involve exponential growth or decay, such as the growth of a population or the decay of a radioactive substance.
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Find the slope of the line through each pair of points.
(8,10), (7, 14)
What is the direction of the resultant velocity relative to the south riverbank?
Answer:
On occasion objects move within a medium that is moving with respect to an observer. For example, an airplane usually encounters a wind - air that is moving with respect to an observer on the ground below. As another example, a motorboat in a river is moving amidst a river current - water that is moving with respect to an observer on dry land. In such instances as this, the magnitude of the velocity of the moving object (whether it be a plane or a motorboat) with respect to the observer on land will not be the same as the speedometer reading of the vehicle. That is to say, the speedometer on the motorboat might read 20 mi/hr; yet the motorboat might be moving relative to the observer on shore at a speed of 25 mi/hr. Motion is relative to the observer. The observer on land, often named (or misnamed) the "stationary observer" would measure the speed to be different than that of the person on the boat. The observed speed of the boat must always be described relative to who the observer is.
Find
sin 22 1/2
°
please help
Answer:
0.69465837 is the answer
19 > y/5 - 9 Solve the inequality for y.
Simplify your answer as much as possible.
Answer:
140 > y
Step-by-step explanation:
19 >y/5 - 9
19+9 > y/5
28 >y/5
cross multiply
28×5 > y×1
140 > y
Write an equation in slope-intercept form of the line that passes through (−2, 5) and (−4, −5).
y=☐
y = − 1 /8x - 19/4
i think
Simplify (-12x+(-13))-(10x+(-12))
Answer:
-22x - 1
Step-by-step explanation:
(-12x+(-13)) - (10x+(-12))
(-12x-13) - (10x-12) Take away the plus sign since addition of a negative is the same as subtraction.
(-12x-10x) + (-13+12) Put like terms together.
-22x - 1 Simplify
Answer:the answer is -22x-1 hope that helps
Step-by-step explanation:
A scientist uses a submarine to study ocean life.
. She begins at sea level, which is an elevation of o feet.
. She descends 44.7 feet.
. She then travels directly up 20.7 feet.
. Next, she travels down a second time, 44.5 feet.
How many feet must she now ascend to get back to sea level?
Solve the simultaneous equations
4x+5y=−19
6x−3y=24
Help me please I need to pass
solve the system of equations. 2x + 7y =3
x = -4y
x =
y =
Answer:
x = 3/2−7y/2
Step-by-step explanation:
hope this is correct
Which graph shows a function AND it’s inverse.
Answer:
c
Step-by-step explanation:
they are linear functions and if you were to flip they mirror each other
WILL GIVE 50 POINTS
Which statement can be used to prove that the two triangles are congruent? the SAS Postulate the SSS Postulate the HL Theorem the ASA Postulate
Answer:
the HL Postulate
Step-by-step explanation:
The diagram gives us the information that 2 sides and 1 angle are congruent. Since the sides we know are a leg and the hypotenuse, and it is a right angle- we know to use the HL (Hypotenuse-Leg) Postulate.
If the angle given was the angle between the hypotenuse and the leg, we could use the SAS (Side-Angle-Side) Postulate. But, since it is the right angle instead- we know to use the HL Postulate!
Please can someone solve thiss !!! T~T
I have no idea what its saying and Im AlMosT doNE :(
Please help , it would mean so much
Answer:
y=2x
Step-by-step explanation:
Answer:
y=2x
is the answer answer
If researchers report that the results from their study were significant, p< .05, this means that:
A.) If they conducted the study over they would get the same results less than 5 times in 100.
B.) The results are untrustworthy
C.) We would expect the results to occur by chance less than 95 times out of 100
D.) We would expect the results to occur by chance less than 5 times out of 100.
If researchers report that the results from their study were significant, p < .05, this means that we would expect the results to occur by chance less than 5 times out of 100.
What does it indicate when researchers report results with p < .05?When researchers report that the results from their study were significant, p < .05, it means that we would expect the results to occur by chance less than 5 times out of 100. This threshold is commonly used in statistical hypothesis testing.
In statistical hypothesis testing, the p-value represents the probability of obtaining results as extreme as the observed results, assuming that the null hypothesis is true. If the p-value is less than the predetermined significance level of .05 (or 5%), it is considered statistically significant. This means that the observed results are unlikely to have occurred by chance alone, and there is evidence to support the alternative hypothesis.
Therefore, option D, "We would expect the results to occur by chance less than 5 times out of 100," is the correct interpretation of reporting significant results with p < .05.
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Please someone help me! If sinα*cosα=-0.5 then what's the value of sin^4α+cos^4α and sin^6α+cos^6α?
A line with a slope of -5 passes through the point (-3, 1). Write the
equation of the line in slope-intercept form.
Answer:
1/2
Step-by-step explanation: