Answer:
y - 2 = -⁶/₅xStep-by-step explanation:
The point-slope form of the equation of the line passing point (x₁, y₁) and with the slope of m is: y - y₁ = m(x - x₁)
m = -⁶/₅
Y-Intercept = 2 ⇒ point (0, 2) ⇒ x₁ = 0, y₁ = 2
Point-Slope Form: y - 2 = -⁶/₅(x - 0)
Seth is using a large shoe box to store his baseball cards. The length of the box is 12 inches, and the height is 6 inches. If the volume of Seth's box is 288 cubic inches, how wide is the box?
Step-by-step explanation: *First, decide which volume formula to use: v = lwh
*Next, substitute in for what you do know (leave variable for unknown): 288 = 12 · w · 6
*Then simplify the side of the equation with the variable: 288 = 72 · w
*Now divide each side of the equation by 72 to solve for w:
288 ÷ 72 = w
4 in = w
A helicopter hovers 1150 feet above a small island. The figure shows that the angle of depression from the helicopter to point P is 39° How far off the coast to the nearest foot is island?
Show explicitly that the following functions: (a) (x+at)², (b) 2e-(x-at) ², 7 satisfy the wave equation J²u(x, t) Ət² = (c) 5 sin[3 (x - at)] + (x + at). ₂d²u(x, t) dx²
Each satisfies the wave equation.
We are given the functions as follows:
(a) (x+at)², (b) 2e-(x-at) ², 7 satisfy the wave equation J²u(x, t) Ət² = (c) 5 sin[3 (x - at)] + (x + at).
₂d²u(x, t) dx²
Let us prove that they satisfy the wave equation using the formula of the wave equation. Wave equation is given by;
J²u(x, t) Ət² = ₂d²u(x, t) dx²
Applying the partial derivative to
(a) with respect to time, t, we obtain:
2a(x+at)
The second partial derivative with respect to x is as follows:
2a
By substituting these results into the wave equation, we have:
J²u(x, t) Ət² = ₂d²u(x, t) dx²
(2a(x+at)) = 2aJ²u(x, t) Ət² = 2a
Ət² = 1/J².
Thus, (a) satisfies the wave equation.
For part (b), let us begin by taking the partial derivative of the function with respect to time, t. This is given by:
-4a e^-(x-at) ²
By taking the second partial derivative with respect to x, we get:4a e^-(x-at) ²
Similar to above, we substitute these results into the wave equation as follows:
J²u(x, t) Ət² = ₂d²u(x, t) dx²
-4a e^-(x-at) ² = 4aJ²u(x, t) Ət² = -4a e^-(x-at) ²/J²
Ət² = -1/J²e^-(x-at) ².
Thus, (b) satisfies the wave equation.
For part (c), let us calculate the partial derivative with respect to t as follows:
5a cos[3(x-at)] + a
The second partial derivative with respect to x is given by:-
15a sin[3(x-at)]
By substituting these results into the wave equation, we have:
J²u(x, t) Ət² = ₂d²u(x, t) dx²
(5a cos[3(x-at)] + a) = -15a
sin[3(x-at)]J²u(x, t) Ət² = -15a
sin[3(x-at)]/(5a cos[3(x-at)] + a)
Ət² = -3 sin[3(x-at)]/(cos[3(x-at)] + 1/5).
Thus, (c) satisfies the wave equation.
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Similar Polygons
DEFG is similar to HJKL. What is the length of LK?
A) 5
B)21
C) 80/3
D) 60
Answer:
I think it's 21. .........
A sofa is 7 feet 5 inches long. How many inches is the sofa?
89 inches!
Because each foot is 12 inches and 12*7=84 and 84+5=89!
The table shows the scores of students recent test. Find the mean of the scores and round to the nearest hundredth
Answer:
Answer and work is in the pdf
Step-by-step explanation:
75+75+80+80+80+80+80+80+85+85+90+90+90+90+90+90+95+95+95+100+100+100+100+100+100
=2,425
2+6+2+6+3+8
=27
2,425/27=89.81
The mean is 89.81
Given the functions f(n)=11 and g(n)=((3)/(4))^(n-1), combine them to create a geometric sequence, a_(n), and solve for the 9 th term.
The given functions f(n) = 11 and g(n) = (3/4)^(n-1) can be combined to create a geometric sequence. The nth term of a geometric sequence is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the first term is given as 11, and the common ratio is (3/4).
The nth term of a geometric sequence is calculated using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the position of the term. By substituting the values into the formula, we can find the 9th term.
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PLEASE HELP!! I'll make brainliest
i need help please thanks
Answer:
33
Step-by-step explanation:
6 * 3 = 18
8-3 = h
h = 5
A = 5 * 3 = 15
Combined:
15 + 18
33
pleaseeeeeeeeeeee heeellllpppppppp i’ll mark u
Answer:
Add up all of the numbers, and divide by the number of digits. To put it another way, the total is divided by the count.
Step-by-step explanation:
so ... 2,4,4,2
2+4+4+2= 12
12 divided by 4=3
i think 3 is the mean....
hope this helps.....
A wheel of the given radius is rotating at the indicated rate. radius 9 in., 2100 rpm (a) Find the angular speed (in radians per minute). radians per minute (b) Find the linear speed of a point on the circumference (in ft/min). (Round your answer to the nearest whole number.) ft/min
The linear speed of a point on the circumference is approximately 9895 feet per minute.
(a) To find the angular speed in radians per minute, we need to convert the given rotational speed from rpm (revolutions per minute) to radians per minute. Since there are 2π radians in one revolution, we can use the conversion factor:
Angular speed (in radians per minute) = Rotational speed (in rpm) * 2π
Given that the rotational speed is 2100 rpm, we can calculate the angular speed:
Angular speed = 2100 rpm * 2π ≈ 13194 radians per minute
Therefore, the angular speed of the wheel is approximately 13194 radians per minute.
(b) To find the linear speed of a point on the circumference in feet per minute, we can use the formula:
Linear speed = Angular speed * Radius
Given that the radius of the wheel is 9 inches, we need to convert it to feet:
Radius = 9 inches * (1 foot / 12 inches) = 0.75 feet
Now, we can calculate the linear speed:
Linear speed = 13194 radians per minute * 0.75 feet ≈ 9895 feet per minute
Therefore, the linear speed of a point on the circumference is approximately 9895 feet per minute.
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BRAINLY TO WHOEVER HELPS AND GETS IT RIGHT
~no links pls~
Answer: A
Step-by-step explanation:
Find the equation in slope-intercept form for the line with a slope of 5/4 and passes through the point (8, 2)
Answer:
92/37
Step-by-step explanation:
Yasmin ordered 20 sandwiches for the STEM club's after school meeting. Some were turkey and some were ham sandwiches. Turkey sandwiches cost $5.50 and ham costs $4.50. The total bill was $97. How many turkey sandwiches were ordered?
7 TURKEY AND 13 HAM
I USED CALCULATOR BTW
a restaurant used 6.5 ounces of cheese to make 5 slices of pizza. if each slice had the same amount of cheese, how much was on each slice?
Answer:
1.3 ounces, 1.3*5 =6.5
Which correctly describes this rotation?
A. a counterclockwise rotation of 30° about point A
B. a counterclockwise rotation of 45° about point A
c. a counterclockwise rotation of 90° about point A
D. a counterclockwise rotation of 180° about point A
Patrick left an $7 tip on a $53 restaurant bill. What percent tip is that?
The percent tip is 13.2%.
To find out what percentage Patrick gave as tip, we need to divide the tip amount by the total bill amount and then convert the result into a percentage.
For this question:
Patrick left an $7 tip on a $53 restaurant bill. What percent tip is that?
Solution:The percentage of tip can be found using the following formula:
% = (Tip amount / Total bill amount) x 100
Plugging in the given values we get:
% = (7 / 53) x 100% = 0.132 x 100% = 13.2 %
Therefore, Patrick gave a 13.2% tip on his restaurant bill.
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trigonometry question
Answer:
Step-by-step explanation:
x = 87.2ft
Hope that helps :)
Compare lengths. Select >, <, or = .
900 cm _ 9 m
Answer:
900 cm = 9 m
Step-by-step explanation:
9 m = 900 cm
Therefore, 9 m equals 900 cm.
Michael's dog stands 10 feet from a table, and notices a plate resting on the edge of the table. The height from the ground to the top of the table is 4 feet, and his dog's eyes are 1 foot above the ground. What is the angle of elevation from Michael's dog to the plate? Round your answer to the nearest whole degree.
Answer:
The angle of elevation is 17°.
Step-by-step explanation:
Let's draw the scenario to better understand the problem:
Focusing on the right triangle formed, it appears that we get measures of the two sides of the right triangles.
Opposite Side = 3 Ft.
Adjacent Side = 10 Ft.
To find the angle of elevation, we will be using the Targent Function:
[tex]targent \: 0 = \frac{opposite \: side}{adjacent \: side} \\ targent \: 0 = \frac{3}{10} \\ 0 = {targent}^{ - 1} ( \frac{3}{10} ) \\ 0 = 16.69924423399 = 17[/tex]
Therefore, the angle of elevation is 17°.
The number of bagels sold daily for two bakeries is shown in the table.
Bakery A Bakery B
53 34
52 40
50 36
48 38
53 41
47 44
55 40
51 39
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Why? Select the correct answer below. (5 points)
Mean for both bakeries because the data is symmetric
Mean for Bakery B because the data is symmetric; Median for Bakery A because the data is not symmetric
Mean for Bakery A because the data is symmetric; Median for Bakery B because the data is not symmetric
Median for both bakeries because the data is not symmetric
Answer:
“Mean for both bakeries because the data is symmetric.”
Step-by-step explanation:
This is correct because the numbers shown in this problem is all in the same range. Meaning that on bakery A and B there are no stray numbers, also known as outliers. No outliers means that the data is symmetric. If you search up, you can see that when the data is symmetric, you use “mean.”
also I got it right on my test
Answer:
Mean for both bakeries because the data is symmetric.
Step-by-step explanation:
i need the prosces plis is for tomorrow
Answer:
p) = 17/30 or 0.56
q) = 191/60 or 3 11/60
Use Cramer's rule to solve the following equation systems A2 JA A VAL 8x1 + 9x2 + 413 = 2 11 +212 + 313 = 3 711 + 6x2 + 5/3 = 1 The solutions are x; = 4,15 = , and ; = What are All, a; and|A3/? 1. |4,1 = -60, x) = -1, and |A3= -60 2. [A1] = -78, 3) = -0.7, and |A3] = 28 3. |A1 = -60, ; = 1, and A3] = 36 4. |A 1 = -78, x = 1.25, and |A3| = 52 2. Given the function y = f(r) = 57- 4r. (a) Find the difference quotient as a function of and Ar. 1. 10.r - 4 2. 5.r? - 4r 3. 5(Ar)? - 4A: 4. 10.r + 5Ar - 4 (b) Find f'(-1) and f'(5). 1. S'(-1) = 9 and f'(5) = 105 2. f'(-1) = -14 and f'(5) = 46 3. $'(-1) = -14 and f'(5) = 105 4. f'(-1) = -19 and f'(5) = 71
1) The solutions to the equation system are x₁ = 11/39 and x₂ = -7/39.
2) The difference quotient as a function of Δr is -4.
3) f'(-1) = -4 and f'(5) = -4.
To solve the equation system using Cramer's rule, we need to find the determinant of the coefficient matrix A and the determinants of the matrices obtained by replacing each column of A with the column on the right-hand side.
The given equation system is:
8x₁ + 9x₂ = 2
11x₁ + 2x₂ = 3
7x₁ + 6x₂ = 1
Step 1: Calculate the determinant of the coefficient matrix A.
A = |8 9|
|11 2|
|7 6|
|A| = (8 * 2) - (9 * 11)
= -78
Step 2: Calculate the determinant of the matrix obtained by replacing the first column of A with the column on the right-hand side.
A₁ = |2 9|
|3 2|
|1 6|
|A₁| = (2 * 2) - (9 * 3)
= -22
Step 3: Calculate the determinant of the matrix obtained by replacing the second column of A with the column on the right-hand side.
A₂ = |8 2|
|11 3|
|7 1|
|A₂| = (8 * 3) - (2 * 11)
= 14
Step 4: Calculate the solutions x₁ and x₂ using Cramer's rule.
x₁ = |A₁| / |A|
= -22 / -78
= 11/39
x₂ = |A₂| / |A|
= 14 / -78
= -7/39
Therefore, the solutions to the equation system are x₁ = 11/39 and x₂ = -7/39.
Now, let's move on to the second part of your question regarding the function f(r) = 57 - 4r.
(a) To find the difference quotient as a function of Δr (Δr represents the change in r):
Difference quotient = (f(r + Δr) - f(r)) / Δr
Expanding and simplifying the expression:
Difference quotient = (57 - 4(r + Δr) - (57 - 4r)) / Δr
= (57 - 4r - 4Δr - 57 + 4r) / Δr
= -4Δr / Δr
= -4
Therefore, the difference quotient as a function of Δr is -4.
(b) To find f'(-1) and f'(5), we need to find the derivative of f(r) with respect to r.
f'(r) = d/dx (57 - 4r)
= -4
Substituting r = -1 and r = 5 into f'(r), we get:
f'(-1) = -4
f'(5) = -4
Therefore, f'(-1) = -4 and f'(5) = -4.
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Given the points A(-2, 0), B(6, 16), C(1, 4), D(5, 4), E(2,2)2
,2
)), and F(32,−4232
,−42
), find the position vector equal to the following vectors.
AB⃗
AB
This indicates that vector 2AB has a length of 165.
Given the points A(-2, 0), B(6, 16), C(1, 4), D(5, 4), and E, let's determine the length of the vector 2AB. To begin, we must determine the distance that separates points A and B. The distance formula is as follows: Equation for distance: We can calculate d as [(x2 - x1)2 + (y2 - y1)2] using the distance formula: Spot = [(6 - (- 2))2 + (16 - 0)2] = [(6 + 2)2 + (16)2] = [(8)2 + (16)2] = [(64 + 256) = 320 = 8] Now, we can deduct the directions of point A from guide B toward decide the vector Stomach muscle:
To find 2AB, simply multiply each part of AB by 2: AB = (6 - (-2)i + (16 - 0)j = 8i + 16j 2AB = 2(8i + 16j) = 16i + 32j. Last but not least, we must ascertain the magnitude of 2AB. The extent recipe is as per the following: Size formula: Using the magnitude formula, we get: ||v|| = (v12 + v22). ||2AB|| = (162 + 322) = (256 + 1024) = (1280 + 165). This indicates that vector 2AB has a length of 165.
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Reagan rides on a playground roundabout with a radius of2.5 feet. To the nearest foot, how far does Reagan travel over an angle of 4π/3 radians?
Answer:
10 feets
Step-by-step explanation:
Given that:
Angle, θ = 4π/3
Radius, r = 2.5 feets
To obtain how Far Reagan traveled, we calculate the Length of the arc, s
s = r*θ
s = 2.5 feets * 4π/3
s = 10π/3
s = 10.4719
To the nearest foot ; distance traveled by Reagan is 10 feets
Liz flips a coin 80 times. The coin lands heads up 32 times and tails up 48 times. Complete each statement. The theoretical probability of the coin landing heads up is 50%. (Type an integer or a decimal.) Based on Liz's results, the experimental probability of the coin landing heads up is
Answer:
40%
Step-by-step explanation:
Answer: 50, 60, Less.
Step-by-step explanation: The theoretical probability of the coin landing heads up is 50%
Based on Liz's results, the experimental probability of the coin landing heads up is 60
The theoretical probability is less than the experimental probability in this experiment.
Hope this helped have a nice day!
Which of the following are among the five basic postulates of Euclidean geometry? Check all that apply.
A. All circles have 360 degrees
B. A straight line segment can be drawn between any two points.
C. A straightedge and compass can be used to create a triangle.
D. Any straight line segment can be extended indefinitely.
Answer:
B and D.
Step-by-step explanation:
A p e x
The following are among the five basic postulates of Euclidean geometry
A straight line segment can be drawn between any two points.Any straight line segment can be extended indefinitely.The five basic postulates of Euclidean geometry
The five (5) basic postulates are:
Any segment of a straight line connecting any two points can be drawn.You can draw and stretch any straight line to any finite length.Given a centre and radius, circles are drawn.Congruent angles are always right angles.There is a line that is parallel to the given line if a given point is not on the supplied line.Learn more about Euclidean Geometry here:
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What is the area of a parallelogram that has a base of 4 ½ inc. and a height of 2 ¼ in. ?
Answer:
4.5
Step-by-step explanation:
At a birthday party pizzas and sodas were purchased for the kids. The number of sodas bought was two more than three times the number of pizzas. Pizzas cost $9.50 each and sodas cost $1.25 each. (ANSWER A AND B PLEASEEEEEEE I REALLY NEED HELP!!!!)
A). If 8 pizzas were bought, how many sodas were bought?
B). How much was the total money would be spent on the pizza and sodas from (A)?
THANK YOU SOOOOO MUCH!!!! :))))))
Answer:
61
Step-by-step explanation:
Givens
Let the pizzas = x
Let the sodas = y
Equation
y = 3x + 2
Part A
y = 3*8 + 2
y = 24 + 2
y = 26
Part B
Sodas = 26* 1.25 = 32.50
Pizzas =9.50 * 3 = 28.50
Total for both = 32.50 + 28.50 = 61
Please help and explain, please no links, thank you
Answer:
The two triangles are related by angles, so the triangles are similar but not proven to be congruent.
Step-by-step explanation:
Because the triangles have the same angles, they are congruent. The definition of congruence is if you take a shape and scale it up or down (or keep it the same) therefore, they are congruent.
Hope this helped, have a nice day
EDIT: I screwed up, I thought it was supposed to be similar. These triangles are SIMILAR not congruent. The actual answer is they are related by AAA similarity but they are similar, but they are not proven to be congruent. Hope this clears it up, and sorry.
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