1) Find AB
B
A 9 in
Use the Law of
Sines:
SinA
a
(0) 8 in
A
54°
11 in
D 7 in
5 in
SinB
b
12
31 in
SinC
C
Remember
Answers
Check the picture below.
[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(54^o)}{31}=\cfrac{\sin(12^o)}{AB}\implies AB\sin(54^o)=31\sin(12^o) \\\\\\ AB=\cfrac{31\sin(12^o)}{\sin(54^o)}\implies AB\approx 8~in[/tex]
Make sure your calculator is in Degree mode.
Related Questions
The cost that a recycling company charges is directly proportional to the number of recycling bins collected. The cost is $33 for each bin.
A: Write a direct variation equation to represent the cost.
B: How many bins can a customer pay the company to collect the bins for $500? Write and solve the equation.
C: Suppose the customer plans to tip the recycling company $30, how many bins can the customer get removed for $500 now? Write and solve the equation.
Answers
a) The direct variation equation is y = 33x.
b) The customer can pay the company to collect 15 bins.
c) The customer can get approximately 16 bins (rounded to the nearest whole number) removed for $500 with a $30 tip included.
A) The direct variation equation to represent the cost would be y = kx, where y represents the cost, x represents the number of bins collected, and k is the constant of proportionality. In this case, since the cost is $33 for each bin collected, the value of k is 33. Therefore, the direct variation equation is y = 33x.
B) To find the number of bins a customer can pay the company to collect for $500, we can set the cost (y) equal to $500 and solve for x (the number of bins). Thus, we have:
y = 33x
500 = 33x
x = 500/33
x ≈ 15.15
Therefore, the customer can pay the company to collect 15 bins (rounded to the nearest whole number) for $500.
C) If the customer plans to tip the recycling company $30, the total cost would be $500 + $30 = $530. We can set the cost (y) equal to $530 and solve for x:
y = 33x + 30
530 = 33x + 30
500 = 33x
x ≈ 15.91
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The sum of two numbers exceeds a third number by four. If the sum of the three numbers is at least 20 and 28,find any three intgral values satisfying the inequality .
Answers
Answer:
Let the three numbers be x, y, and z.
We are given that x + y = z + 4.
We are also given that x + y + z >= 20 and x + y + z <= 28.
Combining these two inequalities, we get:
z + 4 + z >= 20
2z >= 16
z >= 8
Since z is an integer, z can be 8, 9, 10, 11, 12, 13, 14, 15, 16, or 17.
For each value of z, we can find the corresponding values of x and y using the equation x + y = z + 4.
For example, if z = 8, then x + y = 12.
So, the three integral values satisfying the inequality are 8, 4, and 0.
Another example is z = 15.
In this case, x + y = 19.
So, the three integral values satisfying the inequality are 15, 2, and 2.
There are many other possible solutions.
PLS REPLY FAST NO EXPLAINATION NEEDED
Tony solved the equation below by completing the square, but he got the incorrect solution. In which step did Tony first make an error?
Step 1 : x 2 + 4 x = 77
Step 2 : x 2 + 4 x + 4 = 81
Step 3 : ( x + 2 ) 2 = 81
Step 4 : x + 2 = ± 81
Step 5 : x = 79 , x = − 83
Answers
The error made by Tony is in Step 4, where he wrote "x + 2 = ± 81". The correct step should be:
Step 4: Take the square root of both sides to solve for x.
√((x + 2)^2) = √81
In this step, Tony should have taken the square root of both sides, but he made the mistake of only taking the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.
The correct step should be:
x + 2 = ±9
Step 5: Solve for x.
x + 2 = 9 or x + 2 = -9
Step 6: Subtract 2 from both sides to isolate x.
x = 9 - 2 or x = -9 - 2
This will give the correct solutions:
x = 7 or x = -11
So, the error made by Tony occurred in Step 4 where he only took the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.
Hope this helps!
Draw a bar chart to show how the price increased
Answers
The bar chart showing the growth of the price per tone of ground nut over the years is attached accordingly.
What is a bar chart?A bar chart, sometimes known as a bar graph, is a type of chart or graph that displays categorical data using rectangular bars with heights or lengths proportionate to the values they represent. The bars can be plotted horizontally or vertically. A vertical bar chart is also known as a column chart.
From the bar chart, is clarer to see that the price of ground nut per tone increased steadily year on year.
By the year 2008, it had hit record high of 100,000 per ton.
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Graph the function f(t)=e0.4t
Answers
Answer:
here is the graph for it
Step-by-step explanation:
A company reports the following beginning inventory and two purchases for the month of January on January 26th the company says $420 units ending inventory at January 31st totals $170 units assume the Perpetual inventory system is used determine the cost to assigned to the ending inventory will cost or assigned based on the lifo method
Answers
The cost assigned to the ending inventory will cost or assigned based on the lifo method is attached.
What is the inventory about?Denoting the valuation of inventories a business owns at the completion of any accounting term – be it monthly, quarterly, or annually – ending inventory speaks to the cost of items that have yet to be sold or used in the creation of goods and services.
Checking a company's economic performance is contingent on examining its ending inventory since this element impacts cost of goods sold (COGS) substantially; many corporations' COGS are worked out by subtracting the cost of goods distributed over a period from the overall cost of goods available for sale during that same interval.
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Denzel used the spinner shown below to compare theoretical probability and experimental probability. He spun the spinner 180 times and recorded the letter that it landed on each time. The results are shown in the table..
Which statement correctly compares the theoretical probability and experimental probability for one of the letters on the spinner?
A. The theoretical probability of landing on a C is greater than the experimental probability of landing on an C.
B. The theoretical probability of landing on a D is greater than the experimental probability of landing on an D.
C. The theoretical probability of landing on a B is less than the experimental probability of landing on an B.
D. The theoretical probability of landing on an A is less than the experimental probability of landing on an A.
Answers
Answer:
C
Step-by-step explanation:
The theoretical probability of landing on A, B, C, or D is all 1/4. This would also mean the theoretical probability is 45/180. Statement C is the only one that is true.
Which graph represents the function f(x) = 2^x-1 + 2?
Answers
The graph that represents the exponential function f(x) = 2^(x - 1) + 2 is given as follows:
Graph A.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function for this problem is defined as follows:
f(x) = 2^(x - 1) + 2
It has an horizontal asymptote at y = 2, which removes the option C.
The parameter b is of b = 2, meaning that the function is increasing, which removes option D.
The numeric value of the function when x = 0 is given as follows:
f(0) = 2^(0 - 1) + 2
f(0) = 1/2 + 2
f(0) = 5/2
f(0) = 2.5.
Hence graph A is correct.
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Sonic Corporation purchased and installed electronic payment equipment at its drive-in restaurants in San Marcos, TX, at a cost of $37,800. The equipment has an estimated residual value of $2,400. The equipment is expected to process 261,000 payments over its three-year useful life. Per year, expected payment transactions are 62,640, year 1; 143,550, year 2; and 54,810, year 3.
Complete a depreciation schedule for each of the alternative methods.
1. Straight-line.
2. Units-of-production.
3. Double-declining-balance.
Answers
Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year
Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit
Depreciation rate = 2 / 3 = 0.667 or 66.7%
Complete a depreciation schedule for each of the alternative methods.Method of the straight line:
Annual depreciation = (Cost - Residual value) / Useful life
Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year
Schedule of depreciation: shown in the below table
Units-of-production method:
Depreciation per unit = (Cost - Residual value) / Total units of production
Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit
Depreciation schedule:
Double-declining-balance method:
Depreciation rate = 2 / Useful life
Depreciation rate = 2 / 3 = 0.667 or 66.7%
Depreciation schedule: shown in the below table
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Write an expression in factored form for the polynomial of least possible degree graphed below.
Answers
An expression in factored form for the polynomial of least possible degree is y(x) = (x-2)(x+2).
What is polynomial?
Polynomials can be represented in various forms, including standard form, factored form, and expanded form. Standard form is where the polynomial is written with the terms in descending order of degree, with coefficients in front of each term. Factored form is where the polynomial is written as a product of linear factors, and expanded form is where the polynomial is written out in full, with all the terms multiplied together.
A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using addition, subtraction, and multiplication operations. The variables are raised to non-negative integer powers, and the highest power of the variable is called the degree of the polynomial.
For example, the polynomial 2x³ + 3x³ - 4x + 1 has degree 3, as the highest power of x is 3. The coefficients in this polynomial are 2, 3, -4, and 1.
Here, the curve touch two points (-2,0) and (2,0).
So, we can say (-2) and 2 are the root of the polynomial.
We know of a and b are two root of any polynomial then the polynomial will be (x-a)(x-b).
So, the expression is y(x) = (x-2)(x+2).
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matrix A = 2 -7 matrix B = -9 5
6 1 1 -1
If X - A = B, what is X?
Answers
X - A + A = B + A
Simplifying the left side, we get:
X = B + A
To add two matrices, we add their corresponding elements. Thus:
X = [-9+2, 5-7; 6+1, 1-1]
X = [-7, -2; 7, 0]
Therefore, X is the matrix [-7, -2; 7, 0].
Function f has a vertex. Can the function be increasing over its entire domain? Can it be decreasing over its entire domain? Explain.
Choose the correct answer below.
A. A function with a vertex is always increasing if the y-coordinate of the vertex is positive and is always decreasing if the y-coordinate of the vertex is negative.
B. A function with a vertex is constant. So, the function can neither be increasing nor decreasing.
C. A function with a vertex must switch from increasing to decreasing or vice versa at the vertex. So, the function cannot be only increasing or only decreasing over its
entire domain.
D. A function with a vertex can be always increasing as long as the function approaches positive infinity in both directions and can be always decreasing as long as the
function approaches negative infinity in both directions.
Answers
A function with a vertex must switch from increasing to decreasing or vice versa at the vertex. So, the function cannot be only increasing or only decreasing over its entire domain.
Given data ,
A function with a vertex, also known as a vertex form of a quadratic function, is a function of the form f(x) = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. The vertex is the point on the parabola where it changes direction from increasing to decreasing or vice versa.
It is impossible for a function with a vertex to increase continuously if its whole domain shows an increase in the function. Similar to the last example, a function with a vertex cannot decrease throughout its whole domain because that would imply that the function is constantly decreasing.
Hence , a function with a vertex must switch from increasing to decreasing or vice versa at the vertex, and it cannot be only increasing or only decreasing over its entire domain.
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What is the solution to the system of equations graphed below?
3
2
68 x
Answers
The solution of the system of equations is given by the point of intersection of all the equations that compose the graph.
How to obtain the solution to the system of equations?In this problem, the graph of the system of equations is given, hence we use it to obtain the solution.
The solution of the system of equations is given by the point of intersection of all the equations that compose the graph, that is, the point where all the curves cross each other.
The point of intersection represents the solution of the system of equations as it is the input values for which all the equations have the same output value.
Missing InformationThe problem is incomplete, hence the procedure to obtain the solution of the system of equations from the graph is presented.
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The probability that a certain state will be hit by a major tornado (category F4 or F5) in any single year is
parts (a) through (d) below.
1/20
Complete
(Simplify your answer. Round to five decimal places as needed.)
- What is the probability that the state will be hit by a major tornado in three consecutive years?
(Simplify your answer. Round to five decimal places as needed.)
What is the probability that the state will not be hit by a major tornado in the next ten years?
(Round to three decimal places as needed.)
What is the probability that the state will be hit by a major tornado at least once in the next ten years?
(Round to three decimal places as needed.)
Answers
the probability of a major tornado in three consecutive years is 1/8000. the probability of not having a major tornado in the next ten years is approximately 0.328. he probability of having at least one major tornado in the next ten years is approximately 0.672.
How to the probabilities in the question(a) The probability of a major tornado in any single year is 1/20. To find the probability of a major tornado in three consecutive years, we multiply the probabilities together:
P(major tornado in 3 consecutive years) = (1/20) * (1/20) * (1/20) = 1/8000
So the probability of a major tornado in three consecutive years is 1/8000.
(b) The probability of not having a major tornado in any single year is 19/20. To find the probability of not having a major tornado in the next ten years, we raise this probability to the power of 10:
P(no major tornado in next 10 years) = (19/20)^10 ≈ 0.328
So the probability of not having a major tornado in the next ten years is approximately 0.328.
(c) To find the probability of having at least one major tornado in the next ten years, we can subtract the probability of having no major tornadoes in the next ten years from 1:
P(at least one major tornado in next 10 years) = 1 - P(no major tornado in next 10 years)
P(at least one major tornado in next 10 years) = 1 - (19/20)^10 ≈ 0.672
So the probability of having at least one major tornado in the next ten years is approximately 0.672.
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Tom and Philip were given the graph of a linear function and asked to find the slope. Tom says that the slope is 12 while Philip says that the slope is 2.
Which reason correctly justifies Tom's answer?
Answers
Since there is no graph or equation I can only tell you Tom and Philip need to use rise over run to find slope on a graph.
If they have points on the graph or points on a table, they can use slope formula
y2 - y1 over x2 - x1
A triangle has a base of 12 cm and an area of 18 cm².
Find the height of the triangle:
Height = cm
Answers
Answer:
3cm
Step-by-step explanation:
triangle formula is height times base divided by two and divide base by two. then its 6 and divide 6 from 18. so the answer is 3cm
trell is working in a lab testing bacteria populations. After starting out with a population of 404 bacteria, he observes the change in population and notices that the The population doubles every 36 minutes. tep 1 of 2: Find the equation for the population P in terms of time t in minutes.
Answers
We can actually see here that the equation for the population P in terms of time t in minutes will be: P = 404 × 2^(t/36).
How we arrived at the solution?We can see here that looking at the change in population, we can use the following:
P = P₀ × 2^(t/Δt).
Where:
P₀ = initial population = 404 bacterias
t = time elapsed (in minutes).
Δt = time it takes for the population to double (36 minutes).
Thus, we see that substituting this, we have:
P = 404 × 2^(t/36).
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2.2.3 quiz: angle theorems what is the value of y? OA.50
Answers
its c please mark me as a brainliest
answer this please and thank you
Answers
Answer:
2800=1.4tons
Step-by-step explanation:
2000Ib=1ton
Quadrilateral EFGH is a rhombus which addition fact would prove that EFGH is a square
the answer choices are in the photo below I will give brainlyest to right answer
Answers
Option C) EG bisects ZFEH would prove that EFGH is a square.
What is quadrilateral?In geometry, a quadrilateral is a polygon with four sides and four vertices (corners). It is a two-dimensional shape with four straight sides, and the sum of its interior angles is equal to 360 degrees. Some common types of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. Each type of quadrilateral has its own unique set of properties, such as congruent sides and angles, parallel sides, or perpendicular diagonals. Quadrilaterals are used in many areas of mathematics, as well as in engineering, architecture, and other fields.
Here,
A rhombus has opposite sides congruent, but its angles are not necessarily right angles. However, if the diagonals of a rhombus are perpendicular bisectors of each other, then the rhombus is a square.
If EG bisects ZFEH, then the opposite angles of the rhombus are congruent and the diagonals of the rhombus are perpendicular bisectors of each other. This means that EFGH is a square, and all its sides and angles are congruent.
Options A), B), and D) do not provide any information about the shape of EFGH.
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If the difference of two numbers is less than the sum of the numbers, which of the following must be true.
F. Neither number is positive
G. At least one of the number is positive
H. Exactly one of the number is positive
J. Both numbers are positive
K. None of these statement must be true
Answers
True, option (G) is which is - at least one of the numbers is positive.
Define term positive integer number?A positive integer is a whole number greater than zero, i.e., any number that can be expressed without fractions or decimals, and is greater than zero.
If the difference of two numbers is less than the sum of the numbers, it is always true that at least one of the numbers is positive. As a result, "At least one of the numbers is positive" is the response, which is (G).
Here we assume that x and y are two numbers. The difference between the two numbers is |x - y|, which is always positive.
Now, according to the given condition:
|x - y| < x + y
Simplifying this inequality, we get:
-x + y < x + y
2y > 0
Dividing both sides by 2, we get:
y > 0
Therefore, we can conclude that at least one of the numbers (y) is positive. Note that it is possible for both numbers to be positive or for one number to be positive and the other to be zero.
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What is the vertex form of function f? f (x) = 2x^2 + 6x + 5
Answers
Answer:
y = 2(x + 1.5)² + 0.5
Step-by-step explanation:
"To convert the standard form y = ax² + bx + c to vertex form:
Extract a from the first two terms: y = a[x² + (b/a)x] + c.
Add and subtract (b/(2a))² inside the bracket: y = a[x² + (b/a)x + (b/(2a))² - (b/(2a))²] + c.
Use the short multiplication formula: y = a[(x + b/(2a))² - (b/(2a))²] + c.
Expand the bracket: y = a(x + b/(2a))² - b²/(4a) + c.
This is your vertex form with h = -b/(2a) and k = c - b²/(4a)."
^^ not my explanation!!
Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.
y = 11.46 e1.107x
y = 0.45x1.903
y = –109.41 + 14.59x
y = –477.38 + 237.66 ln x
Answers
The regression equation that fits the scenario will be y = 11.46 e1.107x
How to explain the equationUtilizing this method with the provided information, we attain the regression equation:
ln y = 2.4502 + 0.0515x
It should be noted that to find the exponential equation, we can elevate both sides of the equation:
y = e^(2.4502 + 0.0515x) = 11.46 * e^(1.107x)
Consequently, the mathematical model that is most suitable for the mentioned data is:
y = 11.46 * e^(1.107x)
The coefficient of determination (R-squared) for said model is 0.994, thus indicating an incredibly strong fit.
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a group of students was to clean up to two areas in their school. area a was 1 1 2 times of area b. in the morning (half of a day), the number of students cleaning area a was 3 times that of the number of students in area b. in the afternoon (another half of a day), 7 12 of the students worked in area a while the rest of them in area b. at the end of the day, area a was done, but area b still needed 4 students to work one more day before it was done. how many were there in this group of students?
Answers
the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students,
How to solve the problem?
Let's use the following variables to represent the unknowns in the problem:
Let A be the area of area A
Let B be the area of area B
Let x be the number of students working in area B in the morning
Let 3x be the number of students working in area A in the morning
Let y be the total number of students in the group
From the problem statement, we know that A = 1.5B (since area A is 1.5 times area B). We also know that in the morning, the number of students working in area A is 3 times the number of students working in area B. This can be expressed as:
3x = y/2 (since half of the students work in the morning)
In the afternoon, 7/12 of the students work in area A, so the number of students working in area B is:
(1-7/12)y = 5/12y
At the end of the day, area A is done and area B still needs 4 more students to work for another day. This means that the amount of work done by the students in area B is (y/2 - 3x) + (5/12y - 4B) = B, since the total work needed to be done in area B is B and the amount of work done by the students in area A is y/2 - 3x.
Substituting A = 1.5B and 3x = y/2, we can solve for y:
(y/2 - 3x) + (5/12y - 4B) = B
y/2 - 3(y/2)/3 + 5/12y - 4B = B
y/2 - y/2 + 5/12y = 5B
17/12y = 5B
y = (5/17)12B
Therefore, the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students, but we can say that the number of students is proportional to the area of area B. If we know the area of area B, we can use the equation above to find the total number of students in the group.
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If JK is tangent to circle L, find x.
x =
(60 POINTs will give BRAINIEST FOR EFFORT)
Answers
Answer:
x ≈ 11.87 units-----------------------
Tangent line is perpendicular to radius at the point of tangency.
Hence we have:
MJ ⊥ KJTherefore ΔMKJ is a right triangle.
Radius is 11, so diameter is 22, this is one of legs and its hypotenuse is 25 units.
Use Pythagorean theorem to find the missing leg:
x² = 25² - 22²x² = 141x = √141x ≈ 11.87 units (rounded)The accompanying data represent women's median earnings as a percentage of men's median earnings for recent years beginning with 1989. Is there a trend? How does it appear to affect women? Construct a time-series graph. Median Earnings Year Median Earnings 1989 1990 1991 1992 1993 1994 1995 1996 1997 59.2 60.1 62.3 61.7 62.5 61.7 61.7 65.0 67.0 Year 1998 1999 2000 2001 2002 2003 2004 2005 Median Earnings 65.6 62.9 63.3 61.5 65.2 63.9 66.7 68.8 Full data set 0 www X C. Median Earnings 70- 64- 584 1989 1997 Year 2005 Clear all Final check
Answers
Time Series Graph: Plot A
Based on the above plot, earnings first rise till 1997, and then start falling till 2001. After 2001, earnings start rising again. So overall there is an upward trend.
Why is option A the answer?Based on these observations, the answer is Option A, which says:
Option A: There is a general upward trend though there have benn some down years. An upward trend would be helpful to women so that their earnings become equal to those of men.
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I am confused on how to solve the table and find the velocity
Answers
Answer:
Step-by-step explanation:
y = 5x^3 - x
Slope of a secant
= (y2 - y1)/(x2-x1) where (x1, y1) and (x2, y2) are the 2 points.
Slope for the interval (1, 2)
= [5(2)^3 - 2)- (5(1)^3 - 1)] / (2-1)
= 34
Slope for interval (1, 1.5)
= [5(1.5)^3 - 1.5)- (5(1)^3 - 1)] / (1.5-1)
= 22.75
In the same way we get the slopes of the intervals:
(1, 1.1):- 15.55
(1, 1,01):- 15.15
(1, 1.001):- 15.015
So the answer is 15.
Given that a line has a slope of 1/2 and
its y-intercept is the point (0, 7), write
the equation of the line in slope-
intercept form, y = mx + b.
A. y= (1/2)x
B. 7 = (1/2)x+ 0
C. y= (1/2)x+ 7
D. y= 7x+ ½
Answers
Explanation:
The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
In this case, we are given that the slope of the line is 1/2, and the y-intercept is the point (0, 7). Therefore, we can substitute these values into the slope-intercept form to get:
y = (1/2)x + 7
So, the equation of the line in slope-intercept form is y = (1/2)x + 7.
sqrt y^6 where y is greater than or equal to 0
Answers
Simplifying the expression √y⁶ for y is y³
Simplifying the expression for yFrom the question, we have the following parameters that can be used in our computation:
sqrt y^6
Rewrite the expression using numbers and mathematical symbol
So, we have
√y⁶
Take the square root of both sides
So, we have
√y⁶ = y³
Hence, the solution to the expression √y⁶ is y³
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Probability problem pls help me
Answers
Where is the question?