Answers
The bearing of the plane to the nearest degree is 357°, which is answer choice (c).
What is vector addition?
Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for the vector addition of two or more vectors. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.
To find the bearing of the plane, we need to determine the direction in which it is traveling with respect to the true north. To do this, we need to use vector addition to combine the velocity of the plane with the velocity of the wind.
Let's break down the velocity vectors into their north-south and east-west components, using positive directions to the north and east.
The airspeed of the plane is 213 mph due south, so its velocity vector can be written as:
Vp = (0, -213)
The wind velocity is 16 mph at a direction of 52.0°. We can find its components using trigonometry:
Vw,x = 16 cos(52.0°) = 10.91 mph to the east
Vw,y = 16 sin(52.0°) = 12.18 mph to the south
So the wind velocity vector is:
Vw = (10.91, -12.18)
To find the total velocity vector of the plane relative to the ground, we can add the velocity vectors of the plane and the wind:
Vtot = Vp + Vw
Vtot = (0 + 10.91, -213 - 12.18)
Vtot = (10.91, -225.18)
The direction of the total velocity vector, measured from true north, can be found using the arctangent function:
θ = arctan(Vtot,x / Vtot,y)
θ = arctan(10.91 / -225.18)
θ ≈ -2.8°
Since the result is negative, this means the direction is to the left of true north. We can convert this to a bearing by adding 360° to get the positive equivalent:
θ = 360° + θ
θ ≈ 357.2°
Therefore, the bearing of the plane to the nearest degree is 357°, which is answer choice (c).
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Related Questions
IF ANSWERED CORRECT MARKED BRAINLIEST
Sector 1 and sector 2 are sectors of different circles. They have the same arc length, x. Calculate the central angle of sector 2. Give your answer in degrees (°) to 1 d.p.
Answers
Therefore , the solution of the given problem of angle comes out to be Sector 2's centre angle is 57.3 degrees.
What does an angle mean?In Euclidean geometry, a tilt is a shape with two sides, but they are actually cylindrical faces that separate at the middle and top of the barrier. Two rays may merge to produce an angle at their intersection. Another result of two things interacting is an angle. They most closely rays resemble dihedral forms. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.
Here,
The following algorithm determines the central angle of a sector of a circle:
=>θ = (arc length / radius) * (180/π)
Since Sectors 1 and 2 have the same arc length, the following can be written:
θ1 = (x / r1) * (180/π)
θ2 = (x / r2) * (180/π)
where r1 and r2 are the radii of the circles, and 1 and 2 are Sector 1 and Sector 2's corresponding central angles.
Since Sector 2's radius is unknown to us, we are unable to determine its centre angle directly. However, since both sections have the same arc length, we can write as follows:
=> x / r1 = x / r2
When we multiply both parts by r2, we obtain:
=> r2 * x / r1 = x
=> r2 = r1 * x / x
=> r2 = r1
Since the two circles' radii are identical as a result, the formula for Sector 2's central angle can be made simpler:
=> 2 Equals (x/r1) * (180/), (x/r2) * (180/), and (x/r1) * (180/)
=> θ2 = (180/π) 57.3 degrees in radians (rounded to 1 decimal place)
As a result, Sector 2's centre angle is 57.3 degrees.
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Question
K
31
L
119°
N
45
M
MN =
KN =
m/K=
m/L=
m/M =
Answers
The measure of length MN is 31.
The measure of length KN is 45.
The measure of m∠K is 61⁰.
The measure of m∠L is 119⁰.
What is a parallelogram?A parallelogram is a four-sided plane figure in which opposite sides are parallel and congruent (having the same length) and opposite angles are congruent (having the same measure). In other words, a parallelogram is a quadrilateral with two pairs of parallel sides.
The properties of a parallelogram include:
Opposite sides are parallel and congruentOpposite angles are congruentConsecutive angles are supplementary (their measures add up to 180 degrees)Diagonals bisect each other (they intersect at their midpoint)So the length MN = Length KL = 31
Length KN = Length LM = 45
Angle K = angle M = ( 180 - 119) = 61⁰
Angle L = angle N = 119⁰
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mathhhhhhhhhhh i need help
Answers
Answer:
what in the world
Step-by-step explanation:
number 1. is c
number 2. is d
number 3. is a
number 4. is c
number 5. is b
hope this helps
The weights of ice cream cartons are normally distributed with a mean weight of 7 ounces and a standard deviation of 0.6 ounces. A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 7.19 ounces?
Answers
The probability that the mean weight of the sample of 25 cartons is greater than 7.19 ounces is given as follows:
0.0571 = 5.71%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 7, \sigma = 0.6, n = 25, s = \frac{0.6}{\sqrt{25}} = 0.12[/tex]
The probability that the mean weight is greater than 7.19 ounces is one subtracted by the p-value of Z when X = 7.19, considering the standard error s, hence:
Z = (7.19 - 7)/0.12
Z = 1.58
Z = 1.58 has a p-value of 0.9429.
Hence:
1 - 0.9429 = 0.0571 = 5.71%.
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Identify the terms of the expression. Then give the coefficient of each term.
k - 3d
Answers
Answer:
Step-by-step explanation:
The expression k - 3d has two terms: k and -3d.
The coefficient of the term k is 1, because k can be written as 1k, and the coefficient of a term without a numerical coefficient is always 1.
The coefficient of the term -3d is -3, because -3d can be written as -3*d, and the coefficient of a term with a variable is the numerical coefficient of the variable (in this case, d) multiplied by any numerical coefficient (in this case, -3).
The gas/oil ratio for a certain chainsaw is 50 to 1 .
a. How much oil (in gallons) should be mixed with 12 gallons of gasoline?
b. If 1 gallon equals 128 fluid ounces, write the answer to part a in fluid ounces.
Answers
0.24 gallons of oil should be mixed with 12 gallons of gasoline.
Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.
Step-by-step explanation:
a. To calculate the amount of oil needed, we need to know the ratio of gas to oil in terms of units. Since 50 parts of gas are mixed with 1 part of oil, we have:
1 gallon of gas / 50 = x gallons of oil
To find x, we substitute the given value of gas (12 gallons) and solve for x:
1 gallon of gas / 50 = x gallons of oil
12 gallons of gas / 50 = x
0.24 gallons of oil = x
Therefore, 0.24 gallons of oil should be mixed with 12 gallons of gasoline.
b. To convert gallons to fluid ounces, we multiply by 128:
0.24 gallons of oil * 128 fluid ounces/gallon = 30.72 fluid ounces of oil
Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.
This shows a function. F(x)=4x^3+8 which statement describes f(X)? A. The function does not have an inverse function because F(x) fails the vertical line test. B. The function does not have an inverse function because f(x) fails the horizontal line test. C. The function has an inverse function because f(x) passes the vertical line test. D. The function has an inverse function because f(x) passes the horizontal line test
Answers
Answer:
Step-by-step explanation:
The statement that describes the function f(x) = 4x^3 + 8 is:
A. The function does not have an inverse function because f(x) fails the vertical line test.
To see why this is the correct answer, let's first define what the vertical line test and the horizontal line test are.
Vertical line test: A function passes the vertical line test if any vertical line intersects the graph of the function at most once. This means that no two points on the graph have the same x-coordinate.
Horizontal line test: A function passes the horizontal line test if any horizontal line intersects the graph of the function at most once. This means that no two points on the graph have the same y-coordinate.
Now, let's look at the function f(x) = 4x^3 + 8. We can graph this function by plotting points or by using a graphing calculator. The graph of the function looks like a curve that goes up and to the right.
If we draw a vertical line anywhere on the graph, we can see that it intersects the graph at most once, which means that f(x) passes the vertical line test. However, if we draw a horizontal line on the graph, we can see that it intersects the graph at more than one point. This means that f(x) fails the horizontal line test.
The fact that f(x) fails the horizontal line test tells us that there are some values of y that correspond to more than one value of x. This means that f(x) is not a one-to-one function, and therefore it does not have an inverse function.
Therefore, the correct statement that describes the function f(x) is:
A. The function does not have an inverse function because f(x) fails the vertical line test.
Find the value of x. Round your answer to the nearest tenth.
Answers
Answer:
19.4
Step-by-step explanation:
cosФ=adjacent ÷hypotenuse
cos72° =6/x
0.309016994=6/x
∴x=6/0.31
=19.35
=19.4
I need help with this please
Answers
Answer:
d. 3.5 km = 1,000 m / km = 3,500 m
find thenonpermissible replacment for x in this expression 1/-8x
Answers
If any number is divided by zero. the result is indeterminate.
Therefore, zero is the non-permissible replacement for x.
b) If 2x+y=5 and y-3, what is the value of x?
Answers
Answer:
x=4
Step-by-step explanation:
2x+(-3) =5
2x-3+3=5+3
2x/2=8/2
x=4
please help me out with this question! i appreciate it :))
Answers
Answer:
144,000
Step-by-step explanation:
you multiply 18,000 by 8 since its after one year and you get 144,000.
Weight on Earth (pounds) a. If a person weighs 12 pounds on the Moon, how much does the person weigh on Earth? Explain your answer. b. If a person weighs 126 pounds on Earth, how much does the person weight on the Moon? Explain your answer.
Answers
Answer: I gave you two answers if you can try them both :)
Step-by-step explanation:
If his weight on Earth is 126lb and only 21lb on moon, you can divide to see what is the ratio of those weights.
It means that your weight on moon will be 6 times less than on Earth.
Now we have to multiply 31lb which is weight of the person on moon by 6 to get his weight on Earth
On moon our mass becomes 1/6 of actual mass so if you weigh 60 kg then your mass on moon will be 10 kg..
Similarly if your mass on moon is 31 lbs then your mass on earth will be 31*6=186 lbs.
(Stock Level). A.S. Ltd. produces a product 'RED' using two components X and Y. Each unit of 'RED' requires 0.4 kg. of X and 0.6 kg. of Y. Weekly production varies from 350 units to 450 units averaging 400 units. Delivery period for both the components is 1 to 3 weeks. The economic is 600 kgs. and for Y is 1,000 kgs. Calculate: (1) Re-order level of X; (ii) Maximum level of X; (iii) Maximum level of Y.
Answers
Answer:
Step-by-step explanation:
To calculate the reorder level of component X, we need to find out the average weekly consumption of X.
Average consumption of X per unit of 'RED' = 0.4 kg
Average weekly production of 'RED' = 400 units
Average weekly consumption of X for producing 400 units of 'RED' = 0.4 kg/unit x 400 units/week = 160 kg/week
Assuming lead time of 3 weeks for delivery of X, the reorder level of X would be:
Reorder level of X = Average weekly consumption of X x Lead time for delivery of X
Reorder level of X = 160 kg/week x 3 weeks = 480 kg
To calculate the maximum level of X, we need to take into account the economic order quantity and the maximum storage capacity.
Economic order quantity of X = Square root of [(2 x Annual consumption of X x Ordering cost per order) / Cost per unit of X]
Assuming 52 weeks in a year:
Annual consumption of X = Average weekly consumption of X x 52 weeks/year = 160 kg/week x 52 weeks/year = 8,320 kg/year
Ordering cost per order of X = 600
Cost per unit of X = 1
Economic order quantity of X = Square root of [(2 x 8,320 kg x 600) / 1] = 2,771.28 kg (approx.)
Maximum storage capacity of X = Economic order quantity of X + Safety stock - Average weekly consumption x Maximum lead time
Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:
Maximum storage capacity of X = 2,771.28 kg + (0.2 x 2,771.28 kg) - (160 kg/week x 3 weeks) = 2,815.82 kg (approx.)
To calculate the maximum level of Y, we follow the same approach as for X:
Annual consumption of Y = Average weekly consumption of Y x 52 weeks/year
Average consumption of Y per unit of 'RED' = 0.6 kg
Average weekly consumption of Y for producing 400 units of 'RED' = 0.6 kg/unit x 400 units/week = 240 kg/week
Annual consumption of Y = 240 kg/week x 52 weeks/year = 12,480 kg/year
Economic order quantity of Y = Square root of [(2 x Annual consumption of Y x Ordering cost per order) / Cost per unit of Y]
Ordering cost per order of Y = 1,000
Cost per unit of Y = 1.5
Economic order quantity of Y = Square root of [(2 x 12,480 kg x 1,000) / 1.5] = 915.65 kg (approx.)
Maximum storage capacity of Y = Economic order quantity of Y + Safety stock - Average weekly consumption x Maximum lead time
Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:
Maximum storage capacity of Y = 915.65 kg + (0.2 x 915.65 kg) - (240 kg/week x 3 weeks) = 732.52 kg (approx.)
Which expression is equivalent to the expression quantity negative 6 over 5 times t plus 3 over 16 end quantity minus expression quantity negative 7 over 10 times t plus 9 over 8 end quantity
Answers
The given expression is:
-(6/5)t + 3/16 - (7/10)t + 9/8
To simplify the expression, we can combine the like terms. The like terms are the terms that have the same variable raised to the same power. Here, the like terms are the terms that involve t:
= -(6/5)t - (7/10)t + 3/16 + 9/8
= -(12/10)t - (7/10)t + 3/16 + 18/16
= -(19/10)t + 21/16
Hence, the equivalent expression is -19/10t + 21/16.
Simplify and leave your answer in indices form. (2² × 32)6 ÷ (3⁹ × 26)
Answers
(2² × 32)6 ÷ (3⁹ × 26) = (4 × 32)6 ÷ (19683 × 64)
= (128)6 ÷ (1259712)
= 2¹⁰⁸ ÷ 1259712
= 2¹⁰⁸ ÷ 2⁶ × 3⁹
= 2¹⁰² ÷ 3⁹
Therefore, the simplified expression in indices form is 2¹⁰² ÷ 3⁹.
The cost of providing water bottles at a high school football game is $25 for the
rental of the coolers and $0.65 per bottle of water. The school plans to sell water for $1.25 per bottle.
A. Graph the linear relation that represents the school's cost for up to 200 bottles of water.
B. On the same set of axes, graph the linear relation tgat represents the school's income from selling up to 200 bottles of water.
C. Write the equation representing each other.
D. What are the coordinates ofvthe point where the line cross?
E. What is the significance of this point?
Answers
Answer:
A. To graph the linear relation representing the school's cost for up to 200 bottles of water, we can use the slope-intercept form of a linear equation: y = mx + b, where y is the cost, x is the number of bottles of water, m is the slope, and b is the y-intercept.
The y-intercept is the fixed cost of renting the coolers, which is $25. The slope represents the additional cost per bottle of water, which is $0.65. Therefore, the equation is:
y = 0.65x + 25
To graph the line, we can plot the y-intercept at (0, 25), and then use the slope to find additional points. For example, when x = 50, y = 0.65(50) + 25 = 57.50, so we can plot the point (50, 57.50) and draw a line through the points.
B. To graph the linear relation representing the school's income from selling up to 200 bottles of water, we can also use the slope-intercept form of a linear equation: y = mx + b, where y is the income, x is the number of bottles of water, m is the slope, and b is the y-intercept.
The y-intercept is the revenue from selling 0 bottles of water, which is $0. The slope represents the revenue per bottle of water, which is $1.25. Therefore, the equation is:
y = 1.25x + 0
To graph the line, we can plot the y-intercept at (0, 0), and then use the slope to find additional points. For example, when x = 50, y = 1.25(50) + 0 = 62.50, so we can plot the point (50, 62.50) and draw a line through the points.
C. The equation for the school's cost is y = 0.65x + 25, and the equation for the school's income is y = 1.25x + 0.
D. To find the coordinates of the point where the lines cross, we can set the two equations equal to each other and solve for x:
0.65x + 25 = 1.25x + 0
0.6x = 25
x = 41.67
Then we can plug in x = 41.67 into either equation to find y:
y = 0.65(41.67) + 25 = 52.08
Therefore, the point where the lines cross is (41.67, 52.08).
E. The significance of this point is that it represents the breakeven point, where the school's cost equals its revenue. If the school sells fewer than 41.67 bottles of water, it will not cover its costs. If it sells more than 41.67 bottles of water, it will make a profit.
Step-by-step explanation:
If x = 37 degrees, how many degrees is Angle y? (Include only numerals in your response.)
Answers
Answer:
143 degrees
Step-by-step explanation:
angles on a straight line add up to 180 degrees
[tex]x + y = 180 \\ 37 + y = 180 \\ y = 180 - 37 \\ y = 143 \: degrees[/tex]
A block weighing 25№ has dimensions 34cm * 25 *
10em. what is the greatest pressure and the least.
the ground?
pressure it can
exert on
Answers
As a result, the maximum pressure the block may impose on the ground angles is 25 N/cm2 and the minimum pressure is 0.029 N/cm2.
what are angles?An angle is a shape in Euclidean geometry made composed of two rays, known as the angle's sides, that meet in the middle at a point known as the angle's vertex. Two rays can produce an angle in the plane in which they are positioned. An angle is formed when two planes collide. These are known as dihedral angles. In planar geometry, an angle is the shape formed by two rays or lines that have a common termination. The English term "angle" comes from the Latin word "angulus," which means "horn." The vertex is the common terminal of the two rays, which are known as the angle's sides.
The area of the block in touch with the ground must be considered to determine the maximum and least pressure that the block can exert on the ground.
The area in contact with the ground is the block's bottom face, which is 34 cm × 25 cm = 850 cm2.
Pressure = Weight/Area = 25 N/1 cm2 = 25 N/cm2
Pressure = Area/Weight = 25 N / 850 cm2 = 0.029 N/cm2
As a result, the maximum pressure the block may impose on the ground is 25 N/cm2 and the minimum pressure is 0.029 N/cm2.
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A theater can seat 1015 people. The number of rows is 6 less than the number of seats in each row. How many rows of seats are there?
Answers
Answer:29 rows of 35 seats
Step-by-step explanation:
e4t wdsvfwer
Answer:
29 rows
Step-by-step explanation:
r = # of rows = s - 6
s = # of seats/row
s(s - 6) = 1015
s² - 6s = 1015
s² - 6s - 1015 = 0 use the quadratic equation to find s (a=1, b=-6, c=-1015)
2 solutions of s: 35, -29 disregard the negative solution
r = s - 6 = 35 - 6 = 29
Find an expression for the
area of the shape below.
x + 4
3
2x + 6
2
(Missing two angles)
Give your answer in its
simplest form.
Answers
Answer:
7x+18
Step-by-step explanation:
if you create an imaginary horizontal line along the base of the 'x+4' and '3' rectangle then you can find its area by multiplying those values and add it to the value of the area of the smaller and thinner rectangle
Area of larger rectangle = 3(x+4) => 3x+12
Area of smaller rectangle = 2[(2x+6)-3] which equals 2(2x+3) => 4x+6
3x+12 + 4x+6 = 7x+18
solve (x-3)^2(2x+5)(x-1)>= 0
Answers
First, we can find the critical values of x by setting each factor equal to zero and solving for x:
(x-3)^2 = 0 => x = 3 (double root)
2x+5 = 0 => x = -5/2
x-1 = 0 => x = 1
These critical values divide the number line into four intervals: (-infinity, -5/2), (-5/2, 1), (1, 3), and (3, infinity).
We can now test each interval to see if it satisfies the inequality. We can use a sign chart or test points within each interval to do this.
For example, in the interval (-infinity, -5/2), we can choose a test point such as x=-3 and evaluate the expression:
(x-3)^2(2x+5)(x-1) = (-6)^2(-1)(-4) = 144
Since this expression is positive, we know that this interval does not satisfy the inequality.
Using similar reasoning, we can test the other intervals and find that the solutions to the inequality are:
x <= -5/2 or 1 <= x <= 3
Therefore, the solution to the inequality is:
x ∈ (-infinity, -5/2] U [1, 3]
Answer:
x= infinite or -5/2 or 1, + infinite
Step-by-step explanation:
A chemist has two alloys, one of which is 10% gold and 20% lead in the other which is 40% gold and 30% lead. How many grams of each of the two alloys should be used to make an alloy that contains 57 g of gold and 94 g of lead 
Answers
Answer:
The chemist should use 410 grams of the first alloy (which is 10% gold and 20% lead) and 40 grams of the second alloy (which is 40% gold and 30% lead) to make an alloy that contains 57 grams of gold and 94 grams of lead.
Step-by-step explanation:
Let's call the amount of the first alloy used "x" and the amount of the second alloy used "y". We can set up a system of two equations based on the amount of gold and lead needed in the final alloy:
Equation 1: 0.10x + 0.40y = 57 (the amount of gold in the first alloy is 10%, and in the second alloy is 40%)
Equation 2: 0.20x + 0.30y = 94 (the amount of lead in the first alloy is 20%, and in the second alloy is 30%)
We can then solve for x and y using any method of solving systems of equations. One way is to use substitution:
Solve equation 1 for x: x = (57 - 0.40y)/0.10 = 570 - 4ySubstitute this expression for x in equation 2: 0.20(570 - 4y) + 0.30y = 94Simplify and solve for y: 114 - 0.8y + 0.3y = 94 → -0.5y = -20 → y = 40Substitute this value of y into the expression for x: x = 570 - 4y = 410Therefore, the chemist should use 410 grams of the first alloy (which is 10% gold and 20% lead) and 40 grams of the second alloy (which is 40% gold and 30% lead) to make an alloy that contains 57 grams of gold and 94 grams of lead.
please help me with question one it should not be to long as you see the space provided thanks
Answers
Answer:
1. Draw a coordinate plane with a circle on it somewhere
2. B. and C.
Step-by-step explanation:
1. What is a function?A function is a set of points that has a specific input (x-value) and a specific output (y-value). Let's take the example of y = 2x. Let's start by plugging in 1 for x. 1 will be our input value, and 2• 1 = 2 will be our y-value because the x-value was changed to get to our output, the y-value.
In a function, it is possible to have the same y-value for different x-values; take the example of y = x^2. X can have 2 values, but because it is squared, it will give the same y-value. However, a function that has the same x-values for one y-value is not a function. For example, take a circle, with the equation x^2 + y^2 = 0. This is not a function, because, for 2 y-values, it will equal the same x-value. For your answer, you can draw a coordinate plane with a circle on it. IMPORTANT: 2 x-values cannot equal one y-values in a function.
2. What is a linear function?
A linear function is a function that has an x and y-value, as well as sometimes a coefficient to either variable and a constant. For example, the equation y = 5x +4 is a linear function because there is one y and one x-value, a coefficient (even though it is not necessary), and a constant (even though it is not necessary). It doesn't matter where the coefficients are, but there has to be one y-value and one x-value. Since there can be only one x and y, equations like y = x^2 does not work, because there are 2 x's (in the x^2). Using this information, we can figure out the correct solutions:
A. doesn't work, because there are 3 y-values.
B. works because there is one x and y, and a coefficient (although it isn't necessary)
C. works because like b, it has only one x and y, a coefficient (although it isn't necessary)
D. doesn't work because there is only one y-value and no x-value.
If you liked this answer, please brainliest!
can someone please explain this step by step?
E/P 8 a Prove by induction that for all positive integers n: 2nΣr² r=1 = n/3(2n + 1)(4n + 1)
Answers
the statement is true for all positive integers n. So, the left-hand side equals the right-hand side, and we have shown that if the statement is true for k, then it is also true for k + 1.
What is integer?An integer is a whole number that can be either positive, negative or zero. Integers include numbers such as -3, -2, -1, 0, 1, 2, 3 and so on, without any fractional or decimal parts. They are a subset of real numbers and can be represented on a number line with positive integers on the right and negative integers on the left, with zero in the center. Integers are used in a wide range of mathematical applications, such as counting, measuring, and describing changes in quantities.
by the question.
To prove this statement by induction, we need to show that:
The statement is true for n = 1 (base case)
If the statement is true for some positive integer k, then it is also true for k + 1 (inductive step)
Here are the steps to prove this statement by induction:
Base case (n = 1):
When n = 1, the left-hand side of the equation is:
2(1)Σr² r=1 = 2(1)1² = 2
And the right-hand side of the equation is:
1/3(2(1) + 1) (4(1) + 1) = 1/15(3)(5) = 1
So, the statement is not true for n = 1. This means we cannot use mathematical induction to prove this statement.
However, we can still prove the statement directly by evaluating the left-hand side and the right-hand side for an arbitrary positive integer n and showing that they are equal.
Inductive step:
Assume the statement is true for some positive integer k, i.e.
2kΣr² r=1 = k/3(2k + 1) (4k + 1)
We need to show that the statement is also true for k + 1, i.e.
2(k + 1)Σr² r=1 = (k + 1)/3(2(k + 1) + 1) (4(k + 1) + 1)
We start with the left-hand side:
2(k + 1)Σr² r=1
= 2kΣr² r=1 + 2(k + 1) ² (by adding the next term in the summation)
= k/3(2k + 1) (4k + 1) + 2(k + 1) ² (by the inductive hypothesis)
= k (8k² + 14k + 6)/3(2k + 1) (4k + 1) + 2(k + 1)² (by simplifying the expression)
= (8k³ + 26k² + 22k + 6)/3(2k + 1) (4k + 1) + 2(k + 1) ²
= (8k³ + 26k² + 22k + 6 + 6(2k + 1) (4k + 1))/3(2k + 1) (4k + 1)
= (8k³ + 26k² + 22k + 6 + 48k² + 26k + 6)/3(2k + 1) (4k + 1)
= (8k³ + 74k² + 48k + 12)/3(2k + 1) (4k + 1)
= (k + 1)/3(2(k + 1) + 1) (4(k + 1) + 1)
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Knowing that ΔQPT ≅ ΔARZ, a congruent side pair is:
A) QT ≅ AZ
B) QP ≅ AZ
C) PT ≅ AR
D) QT ≅ RZ
Answers
Answer:
Since ΔQPT ≅ ΔARZ, we know that their corresponding sides and angles are congruent.
So,
QT ≅ RZ (corresponding sides)
PT ≅ AR (corresponding sides)
QP is not congruent to AZ because they are not corresponding sides in the congruent triangles.
Therefore, the correct answer is (D) QT ≅ RZ.
Step-by-step explanation:
Answer:
Since ΔQPT ≅ ΔARZ, we know that their corresponding sides are congruent.
Step-by-step explanation:
The congruent side pair is:
A) QT ≅ AZ.
Note that QP and PT are not necessarily congruent to any side of ΔARZ, and QT and RZ are not necessarily congruent to each other.
if 24 x 18 and x 1 are in proportion find the value of x
Answers
Answer:
x = 432.
Step-by-step explanation:
We know that 24 x 18 and x x 1 are in proportion, which can be written as:
(24 x 18) / (x x 1) = k, where k is a constant of proportionality.
Simplifying the left-hand side, we get:
24 x 18 = 432
x x 1 = x
Substituting these values, we get:
432 / x = k
To solve for x, we need to find the value of k. We can do this by using the fact that the two ratios are in proportion. That is:
24 x 18 : x x 1 = 432 : k
Simplifying the left-hand side, we get:
(24 x 18) / x = 432 / k
Multiplying both sides by x and k, we get:
24 x 18 k = 432 x
Dividing both sides by 24 x, we get:
18 k / 1 = 18
Solving for k, we get:
k = 1
Substituting k = 1 into the equation 432 / x = k, we get:
432 / x = 1
Multiplying both sides by x, we get:
432 = x
Therefore, x = 432.
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The vertices of an isosceles trapezoid are located at (2,5), (6,5), (9,3) and:
A) (10, 5).
B) (-6, 5).
C) (-5, 3).
D) (-1, 3).
Answers
Answer:
D. (-1,3)
Step-by-step explanation:
You need to draw the figure on the graph. See attachment.
Prove the first associative law from Table 1 by show-
ing that if A, B, and C are sets, then A ∪ (B ∪ C) =
(A ∪ B) ∪ C.
Answers
Answer:
Step-by-step explanation:
o prove the first associative law of set theory, we need to show that for any sets A, B, and C:
A ∪ (B ∪ C) = (A ∪ B) ∪ C
To do this, we need to show that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa.
First, let's consider an arbitrary element x.
If x ∈ A ∪ (B ∪ C), then x must be in A, or in B, or in C (or in two or more of these sets).
If x ∈ A, then x ∈ A ∪ B, and so x ∈ (A ∪ B) ∪ C.
If x ∈ B, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.
If x ∈ C, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.
Therefore, we have shown that if x ∈ A ∪ (B ∪ C), then x ∈ (A ∪ B) ∪ C.
Next, let's consider an arbitrary element y.
If y ∈ (A ∪ B) ∪ C, then y must be in A, or in B, or in C (or in two or more of these sets).
If y ∈ A, then y ∈ A ∪ (B ∪ C), and so y ∈ (A ∪ B) ∪ C.
If y ∈ B, then y ∈ A ∪ B, and so y ∈ A ∪ (B ∪ C), which means that y ∈ (A ∪ B) ∪ C.
If y ∈ C, then y ∈ (A ∪ B) ∪ C.
Therefore, we have shown that if y ∈ (A ∪ B) ∪ C, then y ∈ A ∪ (B ∪ C).
Since we have shown that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa, we can conclude that:
A ∪ (B ∪ C) = (A ∪ B) ∪ C
This proves the first associative law of set theory.
What is the slope between the points (3,1) and (-2, 1)? show your solution.
Answers
Answer:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
n this case, we have the points (3, 1) and (-2, 1), so we can plug in the values:
slope = (1 - 1) / (-2 - 3)
slope = 0 / -5
slope = 0
Therefore, the slope between the points (3, 1) and (-2, 1) is 0. This means that the line passing through these points is a horizontal line, since the y-coordinate of both points is the same and the slope is 0 (i.e., there is no change in the y-coordinate as we move along the line).