Answer:
55 degrees
Step-by-step explanation:
sin Φ = cos 35
sin Φ = .81915
Φ = arc sin (.81915) = 55 degrees
Or you could just know that the cos of an angle is equal to the sin of its comeplement
A man sets out to travel from A to C via B. From A he travels a distance of 8km on a bearing N30degreesE to B. From B he travels further 6km due east. Calculate how far is north of A, east of A
The displacement of the man from Noth east of A from C is 12.2 km.
What is the displacement of the man?
The displacement of the man is the distance between his initial position at A and final position at C.
The angle formed at position B is calculated as follows;
θ = 30⁰ + 90⁰
θ = 120⁰
The displacement of the man is calculated by applying cosine rule as follows;
d² = 8² + 6² - 2(8 x 6) cos (120)
d² = 148
d = √148
d = 12.2 km
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Algebra 1. please help!!
Answer: f(t) = 2.4t - 500
Step-by-step explanation:
So first of all, we need how much she actually profits from each taco. She charges $3.25 per taco, but we cannot forget that it is not free to make a taco in the first place. It costs her $0.85 to make a taco. This means we have to subtract the 85 cents from the 3 dollars 25 cents, which means it ends up being $2.40, or as the answer choices have it, 2.4.
So now we know what the number of tacos is being multiplied by: 2.4.
2.4t is now the profit per taco multiplied by the number of tacos.
But we're not quite done yet.
She has a fixed expense of $500 a month, which means this has to be subtracted from her taco profits to find her true profit.
Putting all of this together, we get f(t)=2.4t - 500.
(t)= (profit per taco)(amount of tacos sold) - (fixed expenses)
PLS HELP ME WITH THIS 2. QUESTIONS, 50 POINTS
( The first 2 images are from the first question, the other one is from the second)
Answer: B g(x)=1/4f(x) odd
Step-by-step explanation:
First Page:
Points from the graph
Points from f(x) points from g(x)
(1,2) (1, 1/2)
(4, 16) (4, 4)
f(x) was multiplied by 1/4 to get to g(x)
Second Page:
Even functions are symmetrical about the y-axis: . Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x).
lets test for even: does f(x)=f(-x) => f(1)=f(-1) no -2[tex]\neq[/tex]2
see image for plotted points
lets test for odd: does f(x)= -f(-x) => f(1) = -f(-1) yes -2 = -2
Answer:
[tex]\textsf{B)} \quad g(x)=\dfrac{1}{4}f(x)[/tex]
[tex]\textsf{B)} \quad \textsf{odd}[/tex]
Step-by-step explanation:
Functions f(x) and g(x) are exponential functions.
From inspection of the given points on both graphs:
f(4) = 16g(4) = 4When x = 4, the y-value of function f(x) is four times the y-value of function g(x). Therefore, function g(x) is ¹/₄ of function f(x):
[tex]g(x)=\dfrac{1}{4}f(x)[/tex]
[tex]\hrulefill[/tex]
And even function is symmetric about the y-axis:
f(x) = f(-x) for all values of x.According to the table, f(3) = -4 and f(-3) = 4.
Therefore, as f(x) ≠ f(-x), the function is not even.
An odd function is symmetric about the origin:
f(-x) = -f(x) for all values of x.According to the table, f(-3) = 4 and f(3) = -4. So -f(3) = -(-4) = 4.
Therefore, as f(-3) = -f(3), the function is odd.
[tex]\hrulefill[/tex]
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a city department of transportation studied traffic congestion on a certain highway. to encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2 . the probability distribution of the number of people in passenger cars on the highway is shown in the table. number of people 1 2 3 4 5 probability 0.56 0.28 0.08 0.06 0.02 based on the probability distribution, what is the mean number of people in passenger cars on the highway?
The mean number of people in passenger cars on the highway is 1.7 (approximately 2).
The mean of a probability distribution function is also known as Expectation of the probability distribution function.
The mean number of people in passenger cars (or expectation of number of people in passenger cars ) on the highway can be denoted as E(x) where x is the number of people in passenger cars on the highway.
Thus E(x) can be calculated as,
E(x) = ∑ [tex]x_{i} p_{i}[/tex] ∀ i= 1,2,3,4,5
where, [tex]p_{i}[/tex] is the probability of number of people in passenger cars on the highway
⇒ E(x) = (1)(0.56) + (2)(0.28) + (3)(0.08) + (4)(0.06) + (5)(0.02)
⇒ E(x) = 1.7
Hence the mean number of people in passenger cars on the highway is 1.7, which is less than 2.
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A 6 in.
D
X
F 6 in. G
The calculated value of x in the right triangle is 6
Calculating the value of xfrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where we have
x/6 = 6/x
To solve this equation, we can use the property of cross-multiplication.
So for the equation x/6 = 6/x, we can cross-multiply as follows:
x/6 = 6/x
x * x = 6 * 6
x^2 = 36
To solve for x, we need to take the square root of both sides of the equation:
√(x^2) = √36
x = 6
The value of x is 6
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A triangular prism is 36 millimeters long and has a triangular face with a base of 36 millimeters and a height of 24 millimeters. The other two sides of the triangle are each 30 millimeters. What is the surface area of the triangular prism?
The surface area of the triangular prism is
5752 square millimetersHow to find the surface area of the triangular prismThe surface area of the triangular prism is
= area of the two side rectangles + area of the base rectangles + area of the 2 triangles
= 2 * 36 * 30 + 36 * 36 + 2 * 1/2 * 36 * 24
= 2160 + 1296 + 1296
= 5752 square millimeters
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1. Mrs. Zimmerman is interested in learning about how much time seventh grade students at our school spend outdoors on a typical school day.
Select all the samples that are a part of the population. Justify your reasoning.
. The 20 students in a seventh grade math class.
B. The first 20 students to arrive at school on a particular day.
C. The seventh grade students participating in a science fair put on by the four middle schools in a school district.
D. The 10 seventh graders on the school soccer team.
E. The students on the school debate team.
A, c, D
Step-by-step explanation:
A) we can sample these 7th graders as we are looking to study 7th graders.
b) The first 20 students could be from any grade and so this option wouldn't work.
c) Involves 7th graders.
d) involves 7th graders
E) The students could be any grade level on the debate team so, this option wouldn't work.
Calculate the derivative of the following function, 4 y=sin(cos (8x)) ) Find the critical points of the following function f(x) = xVx+6"
The critical points of f(x) are x = -3 and x = 4.
Derivative of 4y = sin(cos(8x)):
We can find the derivative of the given function using the chain rule of differentiation. Let u = cos(8x), then we have:
y = sin(u)
dy/du = cos(u) (derivative of sin(u))
du/dx = -8sin(8x) (derivative of cos(8x) using chain rule)
dy/dx = dy/du * du/dx = cos(cos(8x)) * (-8sin(8x))
Therefore, the derivative of 4y = sin(cos(8x)) is:
dy/dx = -32sin(8x)cos(cos(8x))
Critical points of f(x) = x√(x+6):
To find the critical points of f(x), we need to find where the derivative of the function is equal to zero or undefined.
f(x) = x√(x+6)
f'(x) = (√(x+6) + x/2√(x+6))
To find the critical points, we need to set f'(x) equal to zero and solve for x:
(√(x+6) + x/2√(x+6)) = 0
Multiplying both sides by 2√(x+6), we get:
2x + 6 = -x√(x+6)
Squaring both sides, we get:
4[tex]x^2[/tex] + 24x + 36 = [tex]x^3[/tex] + 6[tex]x^2[/tex]
Rearranging, we get:
[tex]x^3[/tex] + [tex]2x^2[/tex] - 24x - 36 = 0
We can solve this cubic equation using numerical methods or by factoring.
By testing values, we can see that x = -3 is a root of the equation. Dividing the equation by (x+3), we get:
[tex]x^2[/tex]- x - 12 = 0
This quadratic equation can be factored as (x-4)(x+3) = 0.
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Help with problem in photo
Check the picture below.
A company manufactures and sells x microwaves per month. The monthly price-demand equation is: p(x) = 280 – 0.4z (a) Assuming that the manufacture would like to charge between $100 and $500 for microwaves, find the price that maximizes the revenue. (b) What is the maximum revenue from selling microwaves?
The price that maximizes revenue for the given monthly price-demand equation with price range between $100 and $500 is $220.
(b) The maximum revenue from selling microwaves can be found by multiplying the price that maximizes revenue by the corresponding quantity of microwaves sold. Using the price-demand equation p(x) = 280 - 0.4x, we can find the quantity that corresponds to the price that maximizes revenue as follows:p(x) = 280 - 0.4x220 = 280 - 0.4x0.4x = 60x = 150Therefore, the quantity that corresponds to the price that maximizes revenue is x = 150. The maximum revenue can be found by multiplying the price and quantity:Revenue = Price * QuantityRevenue = $220 * 150Revenue = $33,000Therefore, the maximum revenue from selling microwaves is $33,000.
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80.0% complete
question
a customer wants you to enlarge a photo to 234 its current height. the photo’s current height is 314 inches. what should its enlarged height be, in inches?
If the photo’s current height is 314 inches, the enlarged height should be approximately 547.6 inches (rounded to one decimal place), which is 80.0% larger than the current height.
To calculate the enlarged height, you need to find out the percentage increase in height from the current height to the desired height.
The desired height is 234 inches, which is 234/314 = 0.744 or 74.4% of the current height.
To find the actual enlarged height, you need to increase the current height by 74.4%.
Enlarged height = current height + (current height x percentage increase)
Enlarged height = 314 + (314 x 0.744)
Enlarged height = 314 + 233.616
Enlarged height = 547.616
Therefore, the enlarged height should be approximately 547.6 inches (rounded to one decimal place), which is 80.0% larger than the current height.
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Norma and david crawled to the barn and then hopped back to the house. they crawled at 300 centimeters per minute and hopped at 400 centimeters per minute. if round took 7 minutes, hiw long did they crawl
Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.
Find time Norma and David spent crawling to barn if the round trip took 7 minutes. They crawled at 300 cm/min hopped back at 400 cm/min.Let x be the time (in minutes) that Norma and David spent crawling to the barn, and y be the time (in minutes) they spent hopping back to the house. We know that:
x + y = 7 (the total time they spent on the round trip was 7 minutes)
300x + 400y = distance to the barn and back (since their speeds are given in centimeters per minute, the product of their speeds and the time spent crawling or hopping gives the distance in centimeters)
We want to find x, the time they spent crawling to the barn. We can solve for x by rearranging the first equation as x = 7 - y, and substituting into the second equation:
300(7 - y) + 400y = distance to the barn and back
2100 - 300y + 400y = distance to the barn and back
100y = distance to the barn and back - 2100
y = (distance to the barn and back - 2100)/100
Now we need to find the distance to the barn and back. They crawled to the barn at 300 cm/min, so the distance they crawled is 300x cm. They hopped back to the house at 400 cm/min, so the distance they hopped is 400y cm. The total distance to the barn and back is:
distance to the barn and back = 300x + 400y
= 300x + 400[(distance to the barn and back - 2100)/100] (substituting the expression we found for y)
= 300x + 4(distance to the barn and back - 2100)
Simplifying and solving for distance to the barn and back, we get:
distance to the barn and back = 5400/7 cm
Finally, we can substitute this value into the expression we found for y, and solve for x:
y = (distance to the barn and back - 2100)/100
= (5400/7 - 2100)/100
= 24/7
x = 7 - y
= 7 - 24/7
= 37/7
Therefore, Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.
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How do I solve a Pythagorean triangle of 7 squared + 2 squared and then the number after what would it be when u square root it
To solve a Pythagorean triangle of 7 squared + 2 squared, you need to use the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the unknown side, which we'll call x. So, we have:
7² + 2² = x²
Simplifying this equation, we get:
49 + 4 = x²
53 = x²
To find the value of x, we need to take the square root of both sides:
√53 = x
So the answer to the problem is √53. When you square root it, you get a decimal approximation of approximately 7.28.
In summary, to solve a Pythagorean triangle, you need to use the Pythagorean theorem and find the square root of the sum of the squares of the other two sides to find the length of the unknown side.
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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 13)(0,13) and (5, 416)(5,416)
The exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].
To write an exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416), follow these steps:
1. Use the point (0, 13) to determine the value of a. Since the x-coordinate is 0, we have y = a * b⁰, which simplifies to y = a. Therefore, a = 13.
2. Use the point (5, 416) to determine the value of b. Plug in the values for x and y, as well as the value of a we just found: 416 = 13 * b⁵.
3. Solve for b: b⁵ = 416 / 13 = 32. Taking the fifth root of both sides, we get b = 2.
So, the exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].
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The diagonals of quadrilateral ABCD intersect at E(0,2). ABCD has vertices at A(1,6) and B(-2,4). What must be the coordinates of C and D to ensure that ABCD is
a parallelogram?
Answer:
C = (-1, -2)
D = (2, 0)
Step-by-step explanation:
You want the coordinates of points C and D in parallelogram ABCD such that point E(0, 2) is the intersection of the diagonals. Given points are A(1, 6) and B(-2, 4).
ParallelogramThe diagonals of a parallelogram bisect each other. This means the point of intersection of the diagonals is the midpoint of each:
E = (A +C)/2 . . . . . . . . . . . . . . . E is the midpoint of AC
C = 2E -A = 2(0, 2) -(1, 6)
C = (-1, -2)
and
D = 2E -B = 2(0, 2) -(-2, 4) . . . . . using the same pattern
D = (2, 0)
HELPPPPP FAST PLEASEEEE
Answer:
AEC is similar to BDC in terms of the type of triangle
That's all I can really say
I hope this helps :)
(3^6-3^8)/(9^4 -9^2)
Answer:
Step-by-step explanation:
First, let's simplify the numerator:
3^6 - 3^8 = 729 - 6561 = -5832
Now, let's simplify the denominator:
9^4 - 9^2 = 6561 - 81 = 6480
So, the expression simplifies to:
(-5832) / 6480 = -0.9
In which of the following situations does order matter? Select all that apply
Answer:
Locker and Phone number
Step-by-step explanation:
Gym student grouped together with no thought doesnt matter, lunch menu doesn't need order, and a classroom seating chart doesn't really matter
the line is parallel to the graph of y=-1/2x-1 and contains the point (-4, 5)
The equation of the line parallel to the graph of y = (-1/2)x - 1 and containing the point (-4, 5) is y = (-1/2)x + 3.
What is the equation of the parallel line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the graph
y = (-1/2)x - 1
The equation of a line parallel to the graph of y = (-1/2)x - 1 will have the same slope as the given line, which is -1/2.
Now. using the point-slope form, we can find the equation of the line that passes through the point (-4, 5) with slope -1/2:
y - y1 = m(x - x1)
y - 5 = (-1/2)(x - (-4))
y - 5 = (-1/2)x - 2
y = (-1/2)x + 3
Therefore, the equation of the parallel line is y = (-1/2)x + 3.
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A rectangular mural measures 1 meter by 3 meters. Rebekah creates a new mural that is 0. 5 meters longer. What is the perimeter of Rebekah's new mural?
The perimeter of Rebakh's new mural is 9 meters.
Rebakh has created a new mural which is a rectangle. It is a two-dimensional shape with length and breadth. The original rectangular mural was having dimensions of 1 meter by 3 meters, but the mural Rebekah created was 0.5 meters longer than the original one.
So, now the new mural created by Rebakh has a width of (3 + 0.5 ) = 3.5 meters and a length of 1 meter. The perimeter is defined as the total length of the four sides of the rectangle. To find the perimeter, we will add up the length and width of the rectangle and multiply it by 2. The perimeter of the new mural, in this case, is 1 + 1 + 3.5 + 3.5 = 9 meters.
Therefore, the perimeter of Rebakh's new mural is 9 meters.
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Bilquis is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 29 meters from the building. The angle of elevation from her eyes to the roof (point A) is 17°, and the angle of elevation from her eyes to the top of the antenna (point B) is 31º. If her eyes are 1. 51 meters from the ground, find the heigh[of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary.
The height of the antenna is approximately 17 meters.
To solve for the height of the antenna, we need to use trigonometry. Let's call the height of the antenna "h".
First, we need to find the distance from point A to point B. We can use the angle of elevation from her eyes to the roof (17°) and the horizontal distance from the building (29m) to find the height of the building.
tan(17°) = height of building / 29m
height of building = 29m * tan(17°)
height of building = 8.20m
Now we can use the height of the building and the angle of elevation from her eyes to the top of the antenna (31°) to find the distance from point A to point B.
tan(31°) = h / 29m + 8.20m
h = (29m + 8.20m) * tan(31°)
h = 15.51m
Finally, we need to add the height of Bilquis' eyes to the height of the antenna to find the total height.
total height = h + 1.51m
total height = 17.02m
Therefore, the height of the antenna is approximately 17 meters.
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Find the inverse for each relation: 4 points each 1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)}
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answer:
Inga can use the following steps to solve the quadratic equation 2x^2 + 12x - 3 = 0:
Divide both sides by 2 to simplify the equation: x^2 + 6x - 3/2 = 0.Add 3/2 to both sides to eliminate the constant term on the left-hand side: x^2 + 6x = 3/2.Complete the square by adding (6/2)^2 = 9 to both sides: x^2 + 6x + 9 = 3/2 + 9.Factor the left-hand side as a perfect square: (x + 3)^2 = 27/2.Take the square root of both sides, remembering to include both the positive and negative square roots: x + 3 = ±√(27/2).Simplify the square root: √(27/2) = (√27/√2) = (3√3/√2).Subtract 3 from both sides: x = -3 ± (3√3/√2).Rationalize the denominator by multiplying the numerator and denominator of the second term by √2: x = -3 ± (3√6/2).Therefore, the steps that Inga could use to solve the quadratic equation are:
2(x^2 + 6x + 9) = -3 + 2(9) (Option 1)
2(x^2 + 6x) = 3 (Option 2)
x + 3 = ±√(27/2) (Option 3)
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how many times can 2 go into 1742? please its for my homework due tomorrow
It costs $50 a year to be member of an online gaming service. The membership allows you to play games online for free; however, you will still need to purchase games for $60 each. If you can purchase up to 6 games a year, which are the domain and range of this linear function?
A. Domain: All real numbers
Range: All real numbers
B. Domain: {50, 110, 170, 230, 280, 340}
Range: {0, 1, 2, 3, 4, 5, 6}
C. Domain: {0, 1, 2, 3, 4, 5, 6}
Range: {50, 110, 170, 230, 290, 350, 410}
D. Domain: {0, 1, 2, 3, 4, 5, 6}
Range: {60, 160, 210, 270, 320, 380}
The correct answer is C.
The cost of membership is fixed at $50 per year, and the cost of purchasing games is $60 each. If you purchase up to 6 games a year, the cost of each purchase will be $60, and the total cost of membership and games will be $50 + ($60 x number of games purchased).
The function that relates the number of games purchased to the total cost is:
Total cost = 50 + 60(number of games purchased)
Now, let's consider the options provided:
A. Domain: All real numbers
Range: All real numbers
This is not a valid option since the domain and range are not restricted to the given context.
B. Domain: {50, 110, 170, 230, 280, 340}
Range: {0, 1, 2, 3, 4, 5, 6}
This option does not represent the relationship between the number of games purchased and the total cost correctly.
C. Domain: {0, 1, 2, 3, 4, 5, 6}
Range: {50, 110, 170, 230, 290, 350, 410}
This option correctly represents the relationship between the number of games purchased and the total cost. The domain represents the number of games purchased (up to 6), and the range represents the total cost (membership fee + cost of games).
D. Domain: {0, 1, 2, 3, 4, 5, 6}
Range: {60, 160, 210, 270, 320, 380}
This option represents the cost of games purchased only, and does not include the cost of membership.
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How much will 3. 75 kg of meat cost at ?190. 00 per kilogram?
a. ?71250 b. ?7. 125 0 c. ?712. 50 d. ?7125. 0
3.75 kg of meat will cost 712.50, The correct answer is option (c).To determine how much 3.75 kg of meat will cost at ?190.00 per kilogram, you'll need to perform a multiplication using the given weight and price per kilogram, we need to :
1. Identify the weight of the meat: 3.75 kg.
2. Identify the cost per kilogram: ?190.00.
3. Multiply the weight (3.75 kg) by the cost per kilogram (?190.00).
3.75 kg × ?190.00/kg = 712.50
So, 3.75 kg of meat will cost ?712.50, which corresponds to option (c) in your list of possible answers. Remember to always check your calculations and units when solving problems like this to ensure accuracy.
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are 4(5k – 3) and 14k – 8 equivalent
help please
Answer: No they are not
Step-by-step explanation:
Distribute the 4 from the left equation into the parenthesis.
you would get 20k - 12
that is not equivalent to 14k - 8
Larry sold 300 items in his sports memorabilia shop. 5 of the items sold 6 were football items. 20% of the other items sold were baseball items. What percent of the total items sold were baseball items?
Approximately 21.3 percent of the total items sold were baseball items.
Out of the 300 items sold, 5 of them were football items, so the number of non-football items sold is:
300 - 5 = 295
We know that 20% of the non-football items sold were baseball items, so the number of baseball items sold is:
0.20 * 295 = 59
Therefore, the total number of baseball and football items sold is:
59 + 5 = 64
The percentage of total items sold that were baseball items is:
(64 / 300) * 100% = 21.3%
Therefore, approximately 21.3 percent of the total items sold were baseball items.
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Please help me with this question. I need a detailed explanation if possible. I am offering 25 points.
1. (x⁻²y⁵)²*(x⁻³y⁸/x⁻⁶y⁻²), the power and multiplication law is not used correctly.
2. (y⁵/x²)*(y¹⁰/x³), the power and multiplication law is not used correctly.
3. y⁷/x⁴ * y¹⁰/x³, the multiplication law is not used correctly.
What is the simplification of the exponents?The exponents are simplified as follows; (using power exponents)
1. (x⁻²y⁵)²*(x⁻³y⁸/x⁻⁶y⁻²)
= (x⁻⁴y¹⁰)*(x⁻⁹y¹⁰)
= x⁻¹³y²⁰
2. (y⁵/x²)*(y¹⁰/x³) (simplify using multiplication and division rule)
(y⁵/x²)*(y¹⁰/x³)
= (y⁵x⁻²)*(y¹⁰x⁻³)
= y¹⁵x⁻⁵
3. y⁷/x⁴ * y¹⁰/x³ (simplify using multiplication and division rule)
y⁷/x⁴ * y¹⁰/x³
= (y⁷x⁻⁴)(y¹⁰x⁻³)
= y¹⁷x⁻⁷
4. y¹⁷/x⁷ (This expression is simplified correctly)
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The sum of twice a nuber,n, and 14 is 30.
2x+14=30
2x =30-14
2x=16
x =8
Answer:
8
Step-by-step explanation:
Twice means 2 so twice a number,n, means 2 times n thus 2n
sum means add so, 2n + 14
"is" means equal so 2n + 14 = 30
Solve for n:
2n=16
N=8
