The solution set for the equation 1/2 = 1/3 - |(x-3/6)+x| is {1/12, -1/12}.
How to Solve Absolute Value Equations?To solve the equation 1/2 = 1/3 - |(x-3/6)+x|, we need to isolate the absolute value expression and solve for x in two cases.
Case 1: (x-3/6)+x is nonnegative, which means the absolute value can be removed.
1/2 = 1/3 - (x-3/6)-x
1/2 = 1/3 - 2x + 1/2
2x = 1/6
x = 1/12
Case 2: (x-3/6)+x is negative, which means the absolute value must be flipped.
1/2 = 1/3 + (x-3/6)+x
1/2 = 1/3 + 2x - 1/2
2x = -1/6
x = -1/12
Therefore, the solution set is {1/12, -1/12}.
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Nosaira solved an equation. her work is shown below: 3(2x 1 ) = 2(x 1) 1 6x 3 = 2x 2 1 6x 3 = 2x 3 4x = 0 x = 0 she determines the equation has no solution. which best describes nosaira’s work and answer? her work is correct, but there is one solution rather than no solution. her work is correct and her interpretation of the answer is correct. her work is incorrect. she distributed incorrectly. her work is incorrect. she moved terms across the equals sign incorrectly.
Nosaira's work is incorrect. Her mistake is in the step where she simplifies the expression 2x+1 on the left side of the equation by multiplying it with 3. She distributed the 3 only to the 2x term, but forgot to distribute it to the 1 term as well.
So, the correct expression on the left side should be 6x+3 instead of 6x+1. This mistake leads to the wrong equation 6x+3=2x^2-1, and when she tries to solve for x, she ends up with the equation 4x=0, which only has one solution, x=0.
Therefore, Nosaira's interpretation of the answer as having no solution is incorrect. The original equation actually does have a solution, which is x=1/2. If we correct the mistake in her work, we can see that the equation becomes [tex]6x+3=2x^2-1[/tex], which simplifies to [tex]2x^2-6x-4=0[/tex]. We can then factor out 2 to get [tex]x^2-3x-2=0[/tex], which can be factored further into (x-2)(x+1)=0. Therefore, the solutions are x=2 and x=-1, but we need to reject the negative solution as it does not satisfy the original equation.
In conclusion, Nosaira made a mistake in distributing the coefficient 3, which led to an incorrect equation and an incorrect interpretation of the answer. It is important to be careful and check our work, especially when dealing with algebraic expressions and equations.
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Suppose f'(x) = 833 + 12x + 2 and f(1) = -4. Then f(-1) equals (Enter a number for your answer)
To find f(-1), we can use the fact that the derivative of a function f(x) gives us the slope of the tangent line to the graph of f(x) at any point x. We can use this information along with the given value of f(1) to find the equation of the tangent line at x=1, and then use that equation to find the value of f(-1).
First, we find the equation of the tangent line at x=1:
- The slope of the tangent line at x=1 is f'(1) = 833 + 12(1) + 2 = 847
- The point (1, f(1)) lies on the tangent line, so we can use the point-slope form of the equation of a line to write the equation of the tangent line:
y - (-4) = 847(x - 1)
y + 4 = 847x - 847
y = 847x - 851
Now we can use this equation to find f(-1):
- The point (-1, f(-1)) also lies on the tangent line, so we can substitute x=-1 and solve for y:
f(-1) + 4 = 847(-1) - 851
f(-1) + 4 = -1698
f(-1) = -1702
Therefore, f(-1) = -1702.
To find f(-1), we first need to determine the function f(x). We know f'(x) = 833 + 12x + 2. To find f(x), we need to integrate f'(x) with respect to x:
∫(833 + 12x + 2) dx = 833x + 6x^2 + 2x + C
Now, we use the given condition f(1) = -4 to find the constant C:
-4 = 833(1) + 6(1)^2 + 2(1) + C
Solve for C:
C = -4 - 833 - 6 - 2 = -845
Now we have the function f(x) = 833x + 6x^2 + 2x - 845. To find f(-1), plug in x = -1:
f(-1) = 833(-1) + 6(-1)^2 + 2(-1) - 845
f(-1) = -833 + 6 - 2 - 845
f(-1) = -1674
So, f(-1) equals -1674.
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Write a derivative formula for the function.
f(x) = 12.7(4.1^x) / x^2
The answer is:
[tex]f'(x) = 12.7(4.1^x)(ln(4.1)/x - 2/x^2)[/tex]
What is quotient rule?The derivative of f(x), we can use the quotient rule. Let's define
[tex]u(x) = 12.7(4.1^x)[/tex]. [tex]v(x) = x^2[/tex]Then:
[tex]f(x) = u(x)/v(x) = (12.7(4.1^x))/x^2[/tex][tex]f'(x) = [v(x)u'(x) - u(x)v'(x)]/v(x)^2[/tex][tex]f'(x) = [(x^2)(12.7(4.1^x)ln(4.1)) - (12.7(4.1^x))(2x)]/x^4[/tex]Simplifying this expression gives:
[tex]f'(x) = 12.7(4.1^x)(ln(4.1)/x - 2/x^2)[/tex]To find the derivative of f(x), we used the quotient rule, which states that the derivative of a quotient of two functions is equal to (the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator) divided by the denominator squared.
In our case, we defined u(x) and v(x) as the numerator and denominator, respectively, and used the formula to find the derivative of f(x).The derivative of u(x) is found using the chain rule and the derivative of [tex]4.1^x[/tex], which is [tex]4.1^x[/tex] times the natural logarithm of 4.1.
The derivative of v(x) is simply 2x. We then substitute these values into the quotient rule formula and simplify the resulting expression to get the final derivative formula:
[tex]f'(x) = 12.7(4.1^x)(ln(4.1)/x - 2/x^2)[/tex]This formula tells us the slope of the tangent line to the graph of f(x) at any given point x.
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Lines AC←→
and DB←→
intersect at point W. Also, m∠DWC=138°
.
The measure of the angles are m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°
How do we calculate?The Vertical angle theorem states that if two lines intersect at a point then vertically opposite angles are congruent.
To find the measure of all the angles:
∠AWB and ∠DWC are vertically opposite angles.
Therefore, ∠AWB = ∠DWC
⇒ ∠AWB = 138°
we know that the Sum of all the angles in a straight line = 180°
⇒ ∠AWD + ∠DWC = 180°
⇒ ∠AWD + 138° = 180°
⇒ ∠AWD = 180° – 138°
⇒ ∠AWD = 42°
Since ∠AWD and ∠BWC are vertically opposite angles.
Therefore, ∠AWD = ∠BWC
⇒ ∠BWC = 42°
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#complete question:
Lines AC←→ and DB←→ intersect at point W. Also, m∠DWC=138° .
Enter the angle measure for the angle shown.
see attached image:
The Greens bought a condo for $110,000 in 2005. If its value increases at 6% compounded annually, what will the value be in 2020?
Answer:
$264,000
Step-by-step explanation:
PV = $110,000
i = 6%
n = 15 years
Compound formula:
FV = PV (1 + i)^n
FV = 110,000 (1 + 0.06)^15
FV = 110,000 · 2.40(rounded) = $264,000
What is the exact circumference of a circle with a radius of 15 cm?
Responses
10π cm
10 pi, cm
15π cm
15 pi, cm
30π cm
30 pi, cm
60π cm
Answer:
30π cm
Step-by-step explanation:
if r = 15 cm
circumference = π2r
= π × 2 × 15
= 30π cm
#CMIIWPythagorean Theorem help quickly please
Using the Pythagorean theorem, the height of the ramp in the given diagram is 8.9 ft
Pythagorean theorem: Calculating the height of the ramp
From the question, we are to determine how high the ramp is
From the Pythagorean theorem which states that "in a right triangle, the square of the longest side, that is hypotenuse, equals sum of squares of the two other sides".
In the given diagram,
We have a right triangle
The measure of the hypotenuse is 21 ft
One of of the side measures 19 ft
Now, we will calculate x
By the Pythagorean theorem, we can write that
h² + 19² = 21²
h² = 21² - 19²
h² = 441 - 361
h² = 80
h = √80
h = 8.94427 ft
h ≈ 8.9 ft
Hence, the ramp is 8.9 ft high
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how many shortest lattice paths start at (2, 2) and
a) end at (11, 11) and pass through (8, 10)?
b) end at (11,11) and avoid (8,10)
A. The number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.
B. The number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.
What is combinatorics?
Combinatorics is a branch of mathematics that deals with counting and arranging the possible outcomes of different arrangements and selections of objects.
For part (a), the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is given by the product of the number of shortest lattice paths from (2, 2) to (8, 10) and from (8, 10) to (11, 11).
To find the number of shortest lattice paths from (2, 2) to (8, 10), we can count the number of ways to choose 6 steps up out of 8 total steps (the remaining 2 steps are to the right), which is 8 choose 6 = 28.
Similarly, the number of shortest lattice paths from (8, 10) to (11, 11) is the number of ways to choose 1 step up out of 4 total steps (the remaining 3 steps are to the right), which is 4 choose 1 = 4.
Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.
b) To find the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10), we can use the principle of inclusion-exclusion.
Let's first count the number of shortest lattice paths from (2, 2) to (11, 11) without any restrictions. Since we can only move up or to the right, the number of such paths is the number of ways to choose 9 steps up out of 18 total steps (the remaining 9 steps are to the right), which is 18 choose 9 = 48620.
Next, we count the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10). Using the method described in part (a), we found that the number of such paths is 28 * 4 = 112.
Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.
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Next Problem (1 point) Suppose f"(x) = -(sin(x)), f'(0) = 0, and f(0) = -3. - Find f(1/4). f(1/4) = 1
f(1/4) is approximately equal to -2.9974. The problem states that f"(x) = -(sin(x)), which means that the second derivative of the function f(x) is equal to the negative of the sine of x. We are also given that f'(0) = 0 and f(0) = -3.
To find f(1/4), we need to use the information given to us and apply the process of integration. We know that the first derivative of f(x) is f'(x), so we need to integrate f"(x) to find f'(x). Integrating the negative sine function will give us the cosine function, so:
f'(x) = -cos(x) + C
Where C is a constant of integration. To find the value of C, we use the fact that f'(0) = 0:
0 = -cos(0) + C
C = 1
So now we have:
f'(x) = -cos(x) + 1
Next, we integrate f'(x) to find f(x):
f(x) = -sin(x) + x + D
Where D is another constant of integration. We can find the value of D by using the fact that f(0) = -3:
-3 = -sin(0) + 0 + D
D = -3
So finally, we have:
f(x) = -sin(x) + x - 3
Now we can find f(1/4):
f(1/4) = -sin(1/4) + (1/4) - 3
f(1/4) = -0.2474 + 0.25 - 3
f(1/4) = -2.9974
Therefore, f(1/4) is approximately equal to -2.9974.
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Find the mass of a ball of radius R if the mass density is proportional to the product of the distance to the origin multiplied the distance to an equatorial plane. Note that: (ib A ball is a solid whose edge is a sphere. (ii) An equatorial plane is any plane that contains the center of the sphere. (iii) It is convenient to look for a coordinate system that facilitates the task. By For example, the center of the ball can be placed at the origin. And the equatorial plane? (iv) What type of coordinates is the most suitable for problem?
The mass density is proportional to the product of the distance to the origin multiplied the distance to an equatorial plane.The center of the ball can be placed at the origin.
The mass of ball is M = (2/5)MR^2
Process of finding mass:
To find the mass of a ball of radius R with a mass density that is proportional to the product of the distance to the origin multiplied by the distance to an equatorial plane, we need to first find the equation for the mass density.
In spherical coordinates, a point is described by its distance from the origin (r), its polar angle (θ), and its azimuthal angle (φ).
Using this coordinate system, we can write the mass density as:
ρ(r,θ,φ) = k r^2 sinθ
where k is a constant of proportionality.
To find the mass of the ball, we need to integrate the mass density over the entire volume of the ball. The volume element in spherical coordinates is given by:
dV = r^2 sinθ dr dθ dφ
Integrating the mass density over this volume gives us:
M = ∫∫∫ ρ(r,θ,φ) dV
= k ∫0^R ∫0^π ∫0^2π r^4 sin^3θ dr dθ dφ
= 2πk/5 R^5
where R is the radius of the ball.
To find the value of k, we can use the fact that the total mass of the ball is given by:
M = (4/3)πρavg R^3
where ρavg is the average mass density of the ball. From this equation, we can solve for k:
k = (3/4πρavg) = (3/4πR^3)M
Substituting this value of k into our expression for the mass of the ball, we get:
M = (2/5)MR^2
Therefore, the ball's mass is proportional to its radius's square.
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John rides his bike 68 km south and then 6 km went. How far is he from his starting point?
John is approximately 68.26 km away from his starting point after riding 68 km south and then 6 km west.
To find out how far John is from his starting point after riding 68 km south and then 6 km west, we will use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we will consider the 68 km south as one side, and the 6 km west as the other side, with the distance from the starting point being the hypotenuse.
Step 1: Square the lengths of the two given sides.
68^2 = 4624
6^2 = 36
Step 2: Add the squared values together.
4624 + 36 = 4660
Step 3: Find the square root of the sum to get the length of the hypotenuse (distance from the starting point).
√4660 ≈ 68.26 km
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A taxi drives at a speed of 40 kilometers (km) per hour. How far does it travel in 210 minutes?
The taxi travels 140 kilometers in 210 minutes at a speed of 40 km/h.
Let's calculate the distance a taxi travels in 210 minutes at a speed of 40 km/h.
Convert minutes to hours
Since the speed is given in km/h, we need to convert 210 minutes into hours.
There are 60 minutes in an hour, so divide 210 by 60:
210 minutes ÷ 60 = 3.5 hours
Calculate the distance
Now that we have the time in hours, we can use the formula for distance:
Distance = Speed × Time
In this case, the speed is 40 km/h, and the time is 3.5 hours.
Plug these values into the formula:
Distance = 40 km/h × 3.5 hours
Compute the result
Multiply the speed by the time to find the distance:
Distance = 140 km.
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The height of the carton is 7 inches. It is made out of a piece of specialized cardboard. It
requires approximately 349 square inches of specialized cardboard to make a carton.
3. How much specialized cardboard will be needed to make just one of the larger faces of the
carton?
square inches
Show how you figured it out.
The amount of cardboard needed to make just one of the larger faces of the carton is 62.72 square inches.
To find out the amount of cardboard needed to make just one of the larger faces of the carton, we need to first determine the dimensions of the face. Since we know the height of the carton is 7 inches, we need to figure out the length and width of the face.
Assuming the carton is rectangular, we can use the formula for the surface area of a rectangular prism to find the total amount of specialized cardboard needed for the entire carton. The formula is:
Surface area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
We know that the carton requires approximately 349 square inches of specialized cardboard to make, so we can set up the equation:
349 = 2lw + 2lh + 2wh
Since we are only interested in finding the amount of cardboard needed for one of the larger faces, we can assume that one of the dimensions (either length or width) is equal to the height of the carton (7 inches). Let's say that the other dimension is the length (l). Then we can rewrite the equation as:
349 = 2(7)(l) + 2(7)(h) + 2wh
349 = 14l + 14h + 2wh
Now we can substitute the value of h (7) into the equation:
349 = 14l + 14(7) + 2w(7)
349 = 14l + 98 + 14w
251 = 14l + 14w
251/14 = l + w
We don't know the exact dimensions of the face, but we do know that the sum of the length and width is 251/14 inches. Since the face is rectangular, we can assume that the length and width are equal (otherwise it would be a different shape). Therefore, each dimension would be half of 251/14 inches:
l = w = (251/14)/2 = 8.96 inches (rounded to two decimal places)
Now we can use the formula for the area of a rectangle to find the amount of specialized cardboard needed for one face:
Area = length x width
Area = 8.96 x 7
Area = 62.72 square inches
Therefore, approximately 62.72 square inches of specialized cardboard will be needed to make just one of the larger faces of the carton.
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I know its not alot of point but please help me and no essay you will get brainliest if ur answer was first and correct
A 100 g blackbird is flying with a speed of 12 m/s directly toward a 30 g bluebird, who is flying in the opposite direction at a speed of 40 m/s
Answer: 0 g * m/s
Step-by-step explanation:
You first want to multiply 100g, by 12 m/s. This gives you the momentum of the first bird, the answer being 1200 g * m/s
Second, You was to multiply 30g, by 40 m/s. This gives you the momentum of the second bird, The answer also being 1200 g * m/s.
Then, subtract The final answers, and you get 0 g * m/s.
=(100 g)(12 m/s)+(30 g)(−40 m/s)
=1200 g⋅ m/s+(−1200 g⋅ m/s)
=0 g⋅ m/s
I am not an expert, so I may have gotten some things incorrect.
If this doesn't make sense please consult an expert :,)
The relative speed of the birds is 52 m/s.
We are given that;
Number of blackbirds= 100g
Speed= 12m/s
Now,
The relative speed of the blackbird as seen by the bluebird is:
vblackbird relative to bluebird=vblackbird−vbluebird
vblackbird relative to bluebird=−12−40
vblackbird relative to bluebird=−52 m/s
This means that the blackbird is moving to the left at 52 m/s as seen by the bluebird. The relative speed of the bluebird as seen by the blackbird is:
vbluebird relative to blackbird=vbluebird−vblackbird
vbluebird relative to blackbird=40−(−12)
vbluebird relative to blackbird=52 m/s
This means that the bluebird is moving to the right at 52 m/s as seen by the blackbird. The relative speed of either bird is equal to the magnitude (absolute value) of their relative velocity.
Therefore, by the speed the answer will be 52 m/s.
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SOMEONE HELPP!! giving brainlist to anyone who answers
Answer:
Rahul:
[tex]53000( {1.02875}^{7} ) = 64631.59[/tex]
Layla:
[tex]53000 {e}^{.0225 \times 7} = 62040.78[/tex]
$64,631.59 - $62,040.78 = $2,590.81
After 7 years, Rahul's account will have $2,591 more than Layla's account.
Solve the following inequality for r. Write your answer in simplest form. -5r - 2(-10r - 9)<=-6r + 8 - 9
Distribute on the left side:-5r + 20r + 18 ≤ -6r - 1
Combine like term on the left side:15r + 18 ≤ -6r -1 (Add 6 to both sides)21r + 18 ≤ -1 (Subtract 18 from both sides)21r ≤ -1921r/21 ≤ -19/21 (Divide by 21)Get Solution r ≤ -19/21Solution:r ≤ -19/21
In the figure, is tangent to the circle at point U. Use the figure to answer the question.
Hint: See Lesson 3. 09: Tangents to Circles 2 > Learn > A Closer Look: Describe Secant and Tangent Segment Relationships > Slide 4 of 8. 4 points.
Suppose RS=8 in. And ST=4 in. Find the length of to the nearest tenth. Show your work.
1 point for the formula, 1 point for showing your steps, 1 point for the correct answer, and 1 point for correct units.
If you do not have an answer please dont comment
The length of UT, to the nearest tenth, is approximately 10.5 inches.
How long is segment UT?
To find the length of UV, we can use the tangent-secant theorem, which states that the square of the length of the tangent segment (UV) is equal to the product of the lengths of the secant segments (RS and ST).
First, we need to find the length of RS + ST:
RS + ST = 8 in + 4 in = 12 in
Next, we can use the formula for the tangent-secant theorem:
[tex]UV^2 = RS * ST[/tex]
[tex]UV^2 = 8 in * 4 in[/tex]
[tex]UV^2 = 32 in^[/tex]
To find the length of UV, we take the square root of both sides:
[tex]UV = √32 in[/tex]
Calculating the square root, we get:
UV ≈ 5.7 in (rounded to the nearest tenth)
Therefore, the length of UV is approximately 5.7 inches.
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.PLEASEEEEEEEEEEEEEE
Answer:
#1 (176 - x)°
#2 m∠3 = m∠4 = 90°
Step-by-step explanation:
If a pair of parallel lines are cut by a transversal, there are several angles that are either equal to each other or are supplementary(angles add up to 180°).
For the specific questions...
For #1.
Angles ∠1 and ∠2 are supplementary angles since they are adjacent to each other and lie on the same straight line
Therefore
m∠1 + m∠2= 180°
Given m∠1 = (x + 4)° this becomes
(x + 4)° + m∠2 = 180°
m∠2 = 180° - (x + 4)°
= 180° - x° - 4°
= (176 - x)°
For #2
∠3 and ∠4 are supplementary angles so m∠3 + m∠4 = 180°
If m∠3 = m∠4 each of these angles must be half of 180°
So
m∠3 = m∠4 = 180/2 = 90°
QUESTION IN PHOTO I MARK BRAINLIEST
The value of x for the circle is,
⇒ x = 13.2
We have to given that;
In circle Y,
m arc WX = 142°
m ∠WZX = (8x - 35)°
Since, angle WZX is half the measure of arc WX,
Hence, We get;
⇒ (8x - 35)° = 142 / 2
⇒ 8x - 35 = 71
⇒ 8x = 35 + 71
⇒ 8x = 106
⇒ x = 13.2
Thus, The value of x for the circle is,
⇒ x = 13.2
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someone help please!! very confusing
The most goals scored by the team as shown on the box plot, in a game was 8 goals.
How to find the most goals scored ?The uppermost value in a box plot is depicted by the upper whisker, and it stretches from the 3rd quartile (Q3) all the way to the maximum data point within 1.5 times the span between the first and third quartiles (IQR) above Q3.
What this means therefore, is that the most goals scored by the team would be 8 goals as this is the point on the box plot that is at the maximum level.
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In building a brick staircase, we need 200 bricks for the bottom step and 84 bricks for the top step. If, beginning with the bottom step, each successive step requires four fewer bricks, how many bricks will be required to build the staircase?
The number of bricks that will be required to build the staircase is: 30 bricks
How to find the nth term of an arithmetic sequence?An arithmetic sequence is defined as one where you get the next term by adding a constant, called the common difference, to the previous term. A lot of formulas come from this simple fact. and they allow us to solve for any term in the sequence and even the sum of the first few terms.
The formula for the nth term of an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
where:
a₁ is first term
d is common difference
n is nth term
We are given:
a₁ = 200
d = -4
aₙ = 84
Thus:
84 = 200 + (n - 1)(-4)
84 - 200 = -4n + 4
-4n = -120
n = 30
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In parallelogram best, diagonals bs and et bisect each other at o.
1. if es = 10cm, how long is bt?
2. if be = 13cm, how long is ts?
3. if eo = 6cm and so = 7cm, what is the length of et? bs?
4. if et + bs = 18cm and so = 5cm, find et and bs.
When the parallelogram, diagonals bs and et bisect at each other at o, we get the following answers:
1. In a parallelogram, the diagonals bisect each other. So, if ES = 10 cm, then EO = OS = 5 cm. Since EO and OS are half of the diagonal ET, then ET = EO + OS = 5 cm + 5 cm = 10 cm. Similarly, diagonal BT will also be equal to 10 cm, as it has the same length as diagonal ET.
2. In a parallelogram, opposite sides are equal. So, if BE = 13 cm, then TS = 13 cm, as they are opposite sides.
3. If EO = 6 cm and SO = 7 cm, then the length of diagonal ET is EO + OS = 6 cm + 7 cm = 13 cm. Since the diagonals of a parallelogram are equal, the length of diagonal BS will also be 13 cm.
4. If ET + BS = 18 cm and SO = 5 cm, we can use the fact that diagonals bisect each other to find ET and BS. Let EO = x cm. Then, ET = 2x cm and BS = 2(5-x) cm. Now, we can set up the equation: 2x + 2(5-x) = 18. Solving for x, we get x = 4 cm. So, ET = 2x = 8 cm and BS = 2(5-x) = 10 cm.
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Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1). Determine the image coordinates of K′ if the preimage is translated 6 units up.
A. K′(−10, 0)
B. K′(−4, −6)
C. K′(−4, 6)
D. K′(2, 0)
The coordinates of the images after the translation are K' (-4, 6).
Finding the coordinates of the image of points K'To find the image coordinates of K', we need to translate the coordinates of K 6 units up.
This can be done by adding 6 to the y-coordinate of K.
So, the y-coordinate of K' will be:
y-coordinate of K' = y-coordinate of K + 6
= 0 + 6
= 6
To find the x-coordinate of K', we just need to keep the x-coordinate of K the same, since the translation is only in the vertical direction.
Therefore, the image coordinates of K' are (-4, 6).
So, the correct answer is C. K′(−4, 6).
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Ethan goes to the park. The park is 85km away from his house towards south. After 2. 00 minutes,Wthan is 195km away from his house towards west. Find Ethans velocity
If after 2.00 minutes, Ethan is 195km away from his house towards west, Ethan's velocity is approximately 6393 km/h.
To find Ethan's velocity, we need to first determine the distance he traveled and the time he spent traveling.
Given:
1. Initial position: Ethan's house
2. Distance to park: 85 km south
3. Final position: 195 km west from house after 2 minutes
To find the total distance, we can use the Pythagorean theorem, as the path forms a right triangle:
Distance = √(85² + 195²) = √(7225 + 38025) = √(45250) ≈ 212.72 km
Now, let's convert the time from minutes to hours:
2 minutes = 2/60 hours ≈ 0.0333 hours
Finally, we can calculate Ethan's velocity:
Velocity = Distance / Time = 212.72 km / 0.0333 hours ≈ 6393 km/h
Ethan's velocity is approximately 6393 km/h.
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at the three points 1. Sketch the vector field 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2)
The vector field for 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be plotted with arrows with magnitude 4 at point (1,3), magnitude 3 at point (-1,2), and magnitude 3 at point (3,-2).
The given vector field 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be drawn by plotting arrows at each point (x,y) in the plane with the direction and magnitude of each arrow presented by the vector
7 (x,y) = xî + xyî.
over point (1,3),
the vector is 7(1,3) = 1î + 3î = 4î.
over point (-1,2),
the vector is 7(-1,2) = -1î - 2î = -3î.
Over point (3,-2),
the vector is 7(3,-2) = 3î - 6î = -3î.
The vector field for 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be plotted with arrows with magnitude 4 at point (1,3), magnitude 3 at point (-1,2), and magnitude 3 at point (3,-2).
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The value of the limit lim x->2 | (x-2)(x+2)/(x^2-4) is
The value of the limit lim x->2 | (x-2)(x+2)/(x^2-4) is undefined. This is because as x approaches 2, the denominator (x^2-4) approaches 0, which means that the fraction as a whole is undefined. Therefore, there is no value that the limit can approach.
The value of the limit lim x->2 | (x-2)(x+2)/(x^2-4) is:
Step 1: Recognize that the given expression can be simplified. Notice that the denominator, x^2 - 4, is a difference of squares, so it can be factored as (x-2)(x+2).
Step 2: Simplify the expression by canceling the common factors in the numerator and the denominator: (x-2)(x+2) / (x-2)(x+2) simplifies to 1, because the factors (x-2)(x+2) cancel each other out.
Step 3: Now that the expression is simplified, substitute x = 2 to find the value of the limit: lim x->2 | 1 = 1.
Your answer: The value of the limit lim x->2 | (x-2)(x+2)/(x^2-4) is 1.
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There’s are 12 levels in Kianah’s new video game. If he plays the same number of levels each day, what are all the possibilities for the number of days he could doesn’t playing the game without repeating a level
Kianah can finish the game in 1, 2, 3, 4, 6, or 12 days, depending on how many levels he plays each day.
To find all the possibilities for the number of days Kianah can play the game without repeating a level, we need to find all the factors of 12. The factors of 12 are 1, 2, 3, 4, 6, and 12. These are all the possible numbers of levels Kianah can play each day without repeating a level.
If Kianah plays 1 level each day, he will finish the game in 12 days. If he plays 2 levels each day, he will finish in 6 days. If he plays 3 levels each day, he will finish in 4 days. If he plays 4 levels each day, he will finish in 3 days. If he plays 6 levels each day, he will finish in 2 days. And if he plays all 12 levels each day, he will finish in 1 day.
Therefore, Kianah can finish the game in 1, 2, 3, 4, 6, or 12 days, depending on how many levels he plays each day. It's important to note that these possibilities assume that Kianah is able to complete all the levels he plays each day without getting stuck or repeating any levels.
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Triangle abc lies on the plane such that point b is at b(-8,-4). the midpoint of side ac is m with coordinates m(7,5). if a segment from a was drawn to the midpoint of side bc then where would it intersect bm
If a segment from a was drawn to the midpoint of side AB then where would it intersect BM is AN = 2.5cm and MN = 3.5cm.
A midpoint is a point in the midway of a line connecting two locations. The two reference points are the line's ends, and the midpoint is located between the two. The midway splits the line connecting these two places in half. Furthermore, a line drawn to bisect the line connecting these two points passes through the midpoint.
The midpoint formula is used to locate the midway between two places with known coordinates. If we know the coordinates of the other endpoint and the midpoint, we can apply the midpoint formula to obtain the coordinates of the endpoint.
ΔAMN = ΔABC (Corresponding angles)
ΔANM = ΔACB (Corresponding angles)
ΔAMN ≈ ΔABC (By AA similarity test)
[tex]\frac{AM}{AB} =\frac{AN}{AC} =\frac{MN}{BC}[/tex] (CPST)
Since, M is mid-point of AB,
AM = 1/2AB, or, AM/AB = 1/2
AM/AB = AN/AC = 1/2.
AN/AC = 1/2
AN/5 =1/2 [AC = 5cm]
MN/7 =1/2 [BC = 7cm]
MN = 7/2 = 3.5
AN = 2.5cm and MN = 3.5cm.
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What is the area of a circle with a diameter of 80m? (hint : you have to find the radius first)
Answer:
A = 5026.548246 m²
Step-by-step explanation:
Equation for Area of a Circle: A = πr² where r is the radius.
The radius of a circle is always half the diameter. Since we know the diameter is 80m, we can divide by 2 to find our radius.
80/2 = 40m
Now that we have found our radius, we can plug the value into r and solve.
A = π(40)² = 5026.548246 m²