Answers
Answer:
x≥2 and x<2 : ∅
x≥2 or x<2 : All real numbers
x≤2 and x≥2 : 2
Step-by-step explanation:
the first one must follow both conditions, so no number would work.
the second one works with any number, so all real numbers.
the third one has only one condition that works, 2
Related Questions
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Answers
Identify the matrix A: C. A is a 3 × 3 square matrix.
The negative (additive inverse) of A is: -A = [tex]\left[\begin{array}{ccc}1&0&-5\\-3&-6&1\\4&7&-1\end{array}\right][/tex]
How to determine the type of matrix?In Mathematics and Geometry, a square matrix can be defined as a type of matrix that is composed of an equal number of both rows and columns. Generally speaking, m × m matrix is typically referred to as a square matrix of order m.
In this context, we can reasonably infer and logically deduce that the number of rows in matrix A is the same as the number of columns in matrix A;
3 rows = 3 columns;
m × m = 3 × 3
From additive inverse postulate, we have the following:
A + (-A) = 0
[tex]\left[\begin{array}{ccc}-1&0&5\\3&6&-1\\-4&-7&1\end{array}\right]+\left[\begin{array}{ccc}1&0&-5\\-3&-6&1\\4&7&-1\end{array}\right]=0[/tex]
-A = [tex]\left[\begin{array}{ccc}1&0&-5\\-3&-6&1\\4&7&-1\end{array}\right][/tex]
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There arw 8 social studies books on the back table. This is 1/3 of the total number of social studies books in the classroom. Write the total number of Social studies books in the classroom.
Answers
Answer:
24 u jus gotta multiply by 3 cuz it is 1 out of 3
Step-by-step explanation: hi :)
this distance between two floors is 9'0 1/2". if 14 raisers are to be used in a set of stairs, what is the height of each raiser?
Answers
If the total height between two floors is 9'0 1/2" and 14 risers are to be used in a set of stairs, the height of each riser would be approximately 7.75 inches.
To find the height of each riser in a set of stairs given the total height between two floors, we need to divide the total height by the number of risers.
First, let's convert the total height to a consistent unit. The distance between two floors is given as 9'0 1/2". We can convert this to inches by multiplying the feet by 12 and adding the remaining inches:
9 feet = 9 * 12 = 108 inches
0 1/2 inch = 0.5 inch
Total height = 108 + 0.5 = 108.5 inches
Next, we divide the total height by the number of risers (14) to find the height of each riser:
Height of each riser = Total height / Number of risers
Height of each riser = 108.5 inches / 14
Using a calculator, we can compute:
Height of each riser ≈ 7.75 inches
Therefore, the height of each riser in the set of stairs would be approximately 7.75 inches.
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The members of the given set in this problem are given as follows:
X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}
How to obtain the union and intersection set of two sets?The union and intersection sets of multiple sets are defined as follows:
The union set is composed by the elements that belong to at least one of the sets.The intersection set is composed by the elements that belong to at all the sets.The intersection of the sets Y and Z for this problem is given as follows:
Y ∩ Z = {0, 6, 23, 26}
(which are the elements that belong to both of the sets).
The union of the above set with the set X is given as follows:
X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}
(elements that belong to at least one of the sets).
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K
Suppose a business purchases equipment for $12,500
and depreciates it over 5 years with the straight-line
method until it reaches its salvage value of $2500 (see
the figure below). Assuming that the depreciation can be
for any part of a year, answer the questions to the right.
A Dollars
15,000+
12,500
10,000+
5000
10,500
8500
6500
4500
2500
Years
Q
...
Answers
Q1- The annual depreciation for the equipment is $2,000.
Q2- The book value of the equipment at the end of Year 3 is $6,500.
Q1: What is the annual depreciation for the equipment?
To calculate the annual depreciation, we need to determine the difference between the initial value and the salvage value, and divide it by the number of years.
Initial value = $12,500
Salvage value = $2,500
Number of years = 5
Annual depreciation = (Initial value - Salvage value) / Number of years
= ($12,500 - $2,500) / 5
= $10,000 / 5
= $2,000
Therefore, the annual depreciation for the equipment is $2,000.
Q2: What is the book value of the equipment at the end of Year 3?
The book value of the equipment at the end of a specific year can be calculated by subtracting the accumulated depreciation from the initial value.
Initial value = $12,500
Annual depreciation = $2,000
Number of years = 3
Accumulated depreciation = Annual depreciation * Number of years
= $2,000 * 3
= $6,000
Book value at the end of Year 3 = Initial value - Accumulated depreciation
= $12,500 - $6,000
= $6,500
Therefore, the book value of the equipment at the end of Year 3 is $6,500.
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-) Find the equation of the line that passes through (1,0) and (3,6).
Answers
The equation of the line that passes through the points (1,0) and (3,6) is y = 3x - 3.
What is the equation of the line that passes through (1,0) and (3,6)?The formula for equation of line is expressed as:
y = mx + b
Where m is slope and b is the y-intercept.
Given that, the line passes through points (1,0) and (3,6).
First, we determine the slope:
[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{6 - 0}{3 - 1} \\\\Slope\ m = \frac{6}{2} \\\\Slope\ m = 3[/tex]
Now we plug the slope m = 3 and one point (1,0)into the point-slope form to find the equation:
( y - y₁ ) = m( x - x₁ )
( y - 0 ) = 3( x - 1 )
y = 3x - 3
Therefore, the equation of the line is y = 3x - 3.
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Consider the chart of LCD Television sets and population below. Round your ratio as a decimal to 6 places. Round the Owners per 100 to one decimal.
City
Number of Owners
Total Population
Ratio as decimal
Owners per 100
Indianapolis
6,245
0.90 million
New York
911,216
18.6 million
Cairo
10,598
19.1 million
Beijing
959,611
21.2 million
Tokyo
1,700,510
26.5 million
Answers
Indianapolis: Ratio as decimal: 0.006939, Owners per 100: 0.7
New York: Ratio as decimal: 0.049018, Owners per 100: 4.9
Cairo: Ratio as decimal: 0.000554, Owners per 100: 0.1
Beijing: Ratio as decimal: 0.045336, Owners per 100: 4.5
Tokyo: Ratio as decimal: 0.064198, Owners per 100: 6.4
To calculate the ratio as a decimal and the owners per 100 for each city, we need to divide the number of owners by the total population and perform some additional calculations.
Let's calculate the ratio as a decimal for each city:
For Indianapolis:
Number of Owners: 6,245
Total Population: 0.90 million
Ratio as decimal: 6,245 / 0.90 million
= 6,245 / 900,000
= 0.006939
For New York:
Number of Owners: 911,216
Total Population: 18.6 million
Ratio as decimal: 911,216 / 18.6 million
= 911,216 / 18,600,000
= 0.049018
For Cairo:
Number of Owners: 10,598
Total Population: 19.1 million
Ratio as decimal: 10,598 / 19.1 million
= 10,598 / 19,100,000
= 0.000554
For Beijing:
Number of Owners: 959,611
Total Population: 21.2 million
Ratio as decimal: 959,611 / 21.2 million
= 959,611 / 21,200,000
= 0.045336
For Tokyo:
Number of Owners: 1,700,510
Total Population: 26.5 million
Ratio as decimal: 1,700,510 / 26.5 million
= 1,700,510 / 26,500,000
= 0.064198
Now, let's calculate the owners per 100 for each city by multiplying the ratio as a decimal by 100:
Owners per 100 for Indianapolis: 0.006939 * 100 = 0.6939
Owners per 100 for New York: 0.049018 * 100 = 4.9018
Owners per 100 for Cairo: 0.000554 * 100 = 0.0554
Owners per 100 for Beijing: 0.045336 * 100 = 4.5336
Owners per 100 for Tokyo: 0.064198 * 100 = 6.4198
Therefore, rounding the ratio as a decimal to 6 places, and the owners per 100 to one decimal, we have:
Indianapolis: Ratio as decimal: 0.006939, Owners per 100: 0.7
New York: Ratio as decimal: 0.049018, Owners per 100: 4.9
Cairo: Ratio as decimal: 0.000554, Owners per 100: 0.1
Beijing: Ratio as decimal: 0.045336, Owners per 100: 4.5
Tokyo: Ratio as decimal: 0.064198, Owners per 100: 6.4
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PLS HELP ME
The function f(x) = -3(2)²+¹ +90 represents the number of tokens a child has x hours after arriving at an arcade.
What is the practical domain and range of the function?
Enter your answer by filling in the boxes to correctly complete the statements. If necessary, round to the nearest hundrea
The practical domain of the situation is x
Basic
The practical range of the situation is 90
A
O
Answers
Answer:
Practical domain: 0 ≤ x ≤ 3.907Practical Range: 0 ≤ y ≤ 84 where y is an integer, so we have the set {0,1,2,...,83,84}The 3.907 is approximate.
====================================
Explanation:
x = number of hours that elapse
y = f(x) = number of tokens
If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907
At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.
The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907
------------
Plug in x = 0 to find y = 84. This is the largest value in the range.
The smallest value is y = 0.
The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84
Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.
The x value can be fractional because 3.907 hours for instance is valid.
------------
Extra info:
The function is decreasing. It goes downhill when moving to the right.The points (0,84) and (1,78) and (2,66) and (3,42) are on this exponential curve.A point like (2,66) means x = 2 and y = 66. It indicates: "after 2 hours, they will have 66 tokens remaining".O 2. Draw two more arrangements with dots to form the sequence: 1; 3; 6; 10; 15;... ล th th 3. How many dots will there be in the 9 and 10" arrangements? Explain how you got your answer. (3) 4. What do you observe if you take any two consecutive arrangements and add the number of dots? (2) [19]
Answers
The 9th arrangement will have 36 dots, the 10th arrangement will have 45 dots, and when adding the number of dots in any two consecutive arrangements, the result will be the number of dots in the next arrangement.
To determine the number of dots in the 9th and 10th arrangements, we need to understand the pattern in the given sequence: 1, 3, 6, 10, 15, ...
To find the pattern, we can observe the differences between consecutive terms: 2, 3, 4, 5, ...
We notice that these differences increase by 1 each time. This indicates that the sequence is formed by adding consecutive positive integers to the previous term.
Using this pattern, we can determine the 9th and 10th arrangements as follows:
9th arrangement:
Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.
Therefore, the 9th arrangement will have 36 dots.
10th arrangement:
Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.
Therefore, the 10th arrangement will have 45 dots.
Now, let's address the observation when we take any two consecutive arrangements and add the number of dots.
If we take the nth arrangement and the (n+1)th arrangement, we can observe that the number of dots in the (n+1)th arrangement will be the sum of the number of dots in the nth arrangement and the number of dots added in the (n+1)th step.
For example, let's consider the 2nd and 3rd arrangements:
2nd arrangement: 3 dots
3rd arrangement: 3 + 3 (adding 2, the next positive integer) = 6 dots
This pattern holds true for any two consecutive arrangements in the sequence.
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The number of subsets in the given set is as follows:
128.
How to obtain the number of subsets in a set?Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:
[tex]2^n[/tex]
The set in this problem is composed by integers between 2 and 8, hence it has these following elements:
{2, 3, 4, 5, 6, 7, 8}.
The set has four elements, meaning that n = 7, hence the number of subsets is given as follows:
[tex]2^7 = 128[/tex]
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Two sides of a triangle have lengths 43 and 67. The angle included between these sides measures 27degrees°. To the nearest hundreth, what is the length of the third side?
Answers
To the nearest hundredth, the third side of the triangle is 62.74.
To find the length of the third side of the triangle, we can use the Law of Cosines, which relates the lengths of the sides and the cosine of an angle in a triangle. The formula is as follows:
[tex]c^2[/tex] = [tex]a^2[/tex] + [tex]b^2[/tex] - 2ab*cos(C)
Where:
c = length of the third side,
a and b = lengths of the other two sides, and
C = included angle.
Given that the lengths of the two sides are 43 and 67, and the included angle is 27 degrees, we can substitute these values into the formula:
[tex]c^2[/tex] = [tex]43^2[/tex] + [tex]67^2[/tex] - 2 * 43 * 67 * cos(27°)
Now we can calculate the value of c:
[tex]c^2[/tex] ≈ 1849 + 4489 - 2 * 43 * 67 * 0.8910065242
[tex]c^2[/tex] ≈ 1849 + 4489 - 5946.654213618
[tex]c^2[/tex] ≈ 3931.345786382
Taking the square root of both sides to isolate c, we get:
c ≈ √3931.345786382
c ≈ 62.74
Therefore, to the nearest hundredth, the length of the third side of the triangle is approximately 62.74.
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Monthly deposits of $480 were made at the end of each month for eight years. If interest is 4.5% compounded semi-annually, what amount can be withdrawn immediately after the last deposit?
Answers
The amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.
To solve this problemWe can use the formula for the future value of an ordinary annuity. The formula is given by:
[tex]FV = P * [(1 + r/n)^(^n^t^) - 1] / (r/n)[/tex]
Where
Future value is represented by FVmonthly deposit amount by Pannual interest rate by rnumber of compounding periods by n years by tGiven:
P = $480 (monthly deposit)r = 4.5% = 0.045 (annual interest rate)n = 2 (compounded semi-annually)t = 8 yearsPlugging in the values, we have:
[tex]FV = 480 * [(1 + 0.045/2)^(^2*^8^) - 1] / (0.045/2)[/tex]
Calculating the expression inside the brackets
[tex](1 + 0.045/2)^(^2^*^8^) = 1.0225^1^6[/tex]≈ 1.4197
Substituting this value back into the formula:
FV = 480 * (1.4197 - 1) / (0.045/2)
FV = 480 * 0.4197 / 0.0225
FV ≈ $8,876.80
So, the amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.
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Which tables could be used to verify that the functions they represent are inverses of each other? Select two options.
2
-6-10-14
0
0
0
0
X
Y
X
y
-5 -3
4
0
X
y
-14-10-6
0
-4 -2 0 3
X
-5
y -14 -10 -6
X -14
y 4
-5
-4
0
-10
2
-3 0 3 9
0
4
-3
0
4
4
5
-6
4
0 -3 -5
0 2
4
6 10
Answers
Answer:
A, D
Step-by-step explanation:
You want to identify the tables that represent inverse functions.
Inverse functionFor every ordered pair (x, y) of a function, there is an ordered pair (y, x) of its inverse function.
ApplicationThe first table shown has an ordered pair (x, y) = (4, -14). That means its inverse function must have the ordered pair (-14, 4). The two tables with that characteristic are shown in the attachment.
<95141404393>
The length of a classroom is 34 feet. What is this measurement in yards and feet?
Answers
Answer:
11 yards and 3 feet
Help pleaseeee!
30d = i
How many inches would the plant grow in 14 days?
Answers
The amount of inches that the plant grows in 14 days is given as follows:
420 inches.
How to model the situation?The proportional relationship that models the situation is given as follows:
i = 30d.
This means that the plant grows by 30 inches every day.
After 14 days, we have that d = 14, hence the size of the plant after 14 days is given as follows:
i = 30 x 14
i = 420 inches.
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A delivery driver makes $78 each day that he works and makes approximately $10 in tips for each delivery that he makes. If he wants to make at least $238 in one day, at least how many deliveries does he need to make?
Answers
Answer:
16 deliveries
Step-by-step explanation:
We can model the situation using a linear inequality. Since we're told that the driver makes $10 in tips for each delivery.Thus, this is the slope.Since he makes $78 each day, this number is a constant and he makes it even when no deliveries are made. Thus, this is the y-interceptSince he wants to make at least #238, we want to find a value of d (number of deliveries) which would cause his wages to equal #238. Thus, we can use the following equation to find:238 ≤ 10d + 78
160 ≤ 10d
16 ≤ d
Thus, he needs to make at least 16 deliveries to make at least $238 in one day. Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.
The graph of the function f(x) = 1/x+6 + 15 is a transformation of the graph of the function g(x) = 1/x by
Answers
The transformation of g(x) to f(x) is g(x) is shifted up 15 units and shifted left by 16 units
Describing the transformation of g(x) to f(x).From the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
Where, we have
f(x) = 1/(x + 16) + 15
g(x) = 1/x
From the above, we have
Horizontal difference = 16 - 0 = 16
Vertical difference = 15 - 0 = 15
This means that the transformation of g(x) to f(x) is g(x) is shifted up 15 units and shifted left by 16 units
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The mean age of 7 boys is 12yrs. What is the total age of the boys?
Answers
Answer:
total age = 84 years
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{total}{count}[/tex]
here count = 7 and mean = 12 , then
[tex]\frac{total}{7}[/tex] = 12 ( multiply both sides by 7 )
total = 7 × 12 = 84 years
A handrail, 5.4m long on a staircase is inclined at 40° to the horizontal .if the lower end of the handrail is 0.7m high, calculate the height of the upper end above the floor
Answers
The height of the upper end of the handrail above the floor is approximately 3.467726 meters.
To calculate the height of the upper end of the handrail above the floor, we can use trigonometry and the given information about the length of the handrail and the angle of inclination.
Let's break down the problem into two right triangles:
The first right triangle is formed by the handrail, the floor, and a vertical line connecting the lower end of the handrail to the floor. The vertical line represents the height of the lower end above the floor, which is given as 0.7m.
The second right triangle is formed by the handrail, the floor, and a horizontal line parallel to the floor, connecting the upper end of the handrail to the floor. This horizontal line represents the height we need to calculate.
Now, let's apply trigonometric ratios to find the height of the upper end of the handrail above the floor.
In the first right triangle:
Opposite side = height of the lower end = 0.7m
Hypotenuse = length of the handrail = 5.4m
Using the sine function:
sin(angle) = Opposite / Hypotenuse
sin(40°) = 0.7 / 5.4
Now, let's solve for the sin(40°):
sin(40°) ≈ 0.64279
Multiplying both sides of the equation by 5.4:
0.64279 * 5.4 ≈ 3.467726
So, the length of the vertical line in the second right triangle (representing the height of the upper end of the handrail above the floor) is approximately 3.467726 meters.
Therefore, the height of the upper end of the handrail above the floor is approximately 3.467726 meters.
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100 Points! Geometry question. Find x and y. Please show as much work as possible. Photo attached. Thank you!
Answers
Answer: x=2, y=4
Step-by-step explanation:
Since the lines are parallel, we can say that the larger triangle and the smaller triangle are similar. Thus. x+3/(2y-1) = (3/2x+2)/(3y-5). Also, note that there are hash lines, telling us that 2y-1 and 3y-5 are equal. Thus 2y-1=3y-5, and y=4. Plugging y=4 into the first equation yields: (x+3)/(7)=(3/2x+2)/(7), or x+3=3/2x+2. Then 1/2x=1, x=2.
Thus: x=2, and y=4
Answer:
x = 2
y = 4
Step-by-step explanation:
If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.
As the line bisects the side of the triangle with the y-variables, then the line is the midsegment of the triangle. This means that the line also bisects the side of the triangle with the x-variables.
Therefore, the two expressions with the x-variable are equal.
Similarly, the two expressions with the y-variable are equal.
Solving for x:
[tex]\boxed{\begin{aligned}\dfrac{3}{2}x+2&=x+3\\\\\dfrac{3}{2}x+2-x&=x+3-x\\\\\dfrac{1}{2}x+2&=3\\\\\dfrac{1}{2}x+2-2&=3-2\\\\\dfrac{1}{2}x&=1\\\\2 \cdot \dfrac{1}{2}x&=2 \cdot 1\\\\x&=2\end{aligned}}[/tex]
Solving for y:
[tex]\boxed{\begin{aligned}3y-5&=2y-1\\\\3y-5-2y&=2y-1-2y\\\\y-5&=-1\\\\y-5+5&=-1+5\\\\y&=4\end{aligned}}[/tex]
NO LINKS!! URGENT HELP PLEASE!!!
12. y = -2(x + 3)^3 + 1
1a. What type of function?
2b. How did you translate the parent function to produce the equation?
Answers
Answer:
polynomial; left 3 right 1
Step-by-step explanation:
The type of function is a polynomial.
The parent function is translated by moving -2x^3 to the left 3 and right 1.
Answer:
The function is a quadratic function.
Series of transformations:
Horizontal translation of 3 units left.Vertical stretch by a factor of 2.Reflection in the x-axis.Vertical translation of 1 unit up.Step-by-step explanation:
A quadratic function is a polynomial function of degree 2 (the highest exponent of the variable is 2).
Therefore, the given equation, y = -2(x + 3)² + 1, represents a quadratic function as the term (x + 3)² indicates that the highest power of the x-variable is 2.
[tex]\hrulefill[/tex]
The parent function of a quadratic function is y = x².
To translate the parent function to produce the given equation, we need to apply this series of transformations:
1. Horizontal translation
When "a" is added to the x-variable, the graph is shifted "a" units to the left. Therefore, the addition of 3 inside the parentheses shifts the graph horizontally to the left by 3 units.
2. Vertical Stretch
The coefficient in front of the squared term (x + 3)² indicates a vertical stretch or compression. In this case, since the coefficient greater than 1, it stretches the graph vertically, making it narrower compared to the parent function.
3. Reflection
As the stretch coefficient is negative, the graph is reflected across the x-axis, meaning the parabola opens downwards.
4. Vertical translation
When "a" is added to the function, the graph is shifted "a" units up. Therefore, the addition of 1 to the function shifts the graph vertically up by 1 unit.
In summary, the series of transformations that maps the parent function to the given function is:
Horizontal translation of 3 units left.Vertical stretch by a factor of 2.Reflection in the x-axis.Vertical translation of 1 unit up.Practical Exercise 2.5 Use the information from various financial statements prepared in this class as well as the records from Practical Exercise 2.2 to prepare a July 31 Balance Sheet for Academic Learning Services. Identify how much of the assets held by Academic Learning Services are financed by debt.
Answers
To prepare a July 31 Balance Sheet for Academic Learning Services, you would need access to the financial statements and records provided in the class, as well as the information from Practical Exercise
The Balance Sheet is a financial statement that presents the company's assets, liabilities, and shareholders' equity at a specific point in time. By examining the assets section of the Balance Sheet, you can identify how much of the company's assets are financed by debt. This can be determined by analyzing the liabilities portion, which includes any loans, credit lines, or other forms of debt. Subtracting the total liabilities from the total assets will give you the equity portion, representing the assets financed by sources other than debt. By comparing the two, you can ascertain the proportion of assets held by Academic Learning Services that are financed by debt.For such more question on liabilities
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9. Find the equation of the PARABOLA with a vertex at (-2, 6) and passing through the point (1, -3)
Answers
Answer:
y= -x²-4x+2
Step-by-step explanation:
write in vertex form
a(x-h)²+k
in our case h = -2 and k= 6
y=a(x+2)²+6
now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a
-3= a(1+2)²+6
-9=9a
a= -1
thus the formula is -(x+2)²+6
generally, teachers want things in standard form, so expand the exponent and simplify.
-(x²+4x+4)+6
y= -x²-4x+2
Answer:
[tex]y = -x^2 - 4x + 2[/tex]
Step-by-step explanation:
The equation of a parabola in vertex form is:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola.
In this case, the vertex is (-2, 6), so h = -2 and k = 6.
We also know that the parabola passes through the point (1, -3).
Plugging these values into the equation, we get:
[tex]-3 = a(1 - (-2))^2 + 6[/tex]
[tex]-3 = a(3)^2 + 6[/tex]
-9 = 9a
a = -1
Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:
[tex]y = -1(x + 2)^2 + 6[/tex]
This equation can also be written as:
[tex]y = -x^2 - 4x -4+6\\y=x^2-4x+2[/tex]
To factor 4x^2-25, you can first rewrite the expression as:
a. (2x-5)^2
b. (2x)^2-(5)^2
c. (x)^2-(2)^2
d. None of the above
Answers
To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).
In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:
b. (2x)^2 - (5)^2
Using the difference of squares formula, we can factor it as follows:
(2x + 5)(2x - 5)
Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.
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Work out the area of the trapezium below.
20 cm
16 cm
19 cm
10 cm
Answers
The area of the trapezium with bases 20cm and 10cm and a height of 16cm is 240 square centimeters.
What is the area of the trapezium?A trapezium is simply a two-dimensional quadrilateral that has one pair of parallel sides.
The area of a trapezium is expressed as:
Area = 1/2 × ( a + b ) × h
Where a and b are the base measure and h is the height.
From the diagram:
Base a = 20 cm
Base b = 10 cm
Height h 16 cm
Area = ?
Plug the values into the above formula and solve for the area:
Area = 1/2 × ( a + b ) × h
Area = 1/2 × ( 20 + 10 ) × 16
Area = 1/2 × ( 30 ) × 16
Area = 15 × 16
Area = 240 cm²
Therefore, the area of the trapezium is 240 square centimeters.
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What was the average speed in miles; per minute, during the interval of 30 and 40? Step by step.
Answers
The average speed in miles per minute during the interval of 30 and 40 is -1.5 miles per minute
How to determine the average speed in miles per minuteFrom the question, we have the following parameters that can be used in our computation:
The graph
During the interval of 30 and 40, we have
Distances = 15 and 0
So, we have
Average speed = (15 - 0)/(30 - 40)
Evaluate
Average speed = -1.5
Hence, the average speed in miles per minute is -1.5
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what is the equasion for this line
Answers
The equation of the line in the graph that passes through (0,1) and (4,0) is [tex]y = -\frac{1}{4}x + 1[/tex].
What is the equation of the line?The equation of line is expressed as:
y = mx + b
Where m is slope and b is the y-intercept.
From the image, the graph passes through points (0,1) and (4,0).
First, we calculate the slope (m) using the formula:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = \frac{0 - 1 }{4 - 0} \\\\m = -\frac{1 }{4 }[/tex]
Next, plug the slope m = -1/4 and one point (0,1) into the point-slope form and simplify:
( y - y₁ ) = m( x - x₁ )
[tex]y - 1 = -\frac{1}{4}( x - 0 ) \\\\y - 1 = -\frac{1}{4}x\\\\y = -\frac{1}{4}x + 1[/tex]
Therefore, the equation of the line is [tex]y = -\frac{1}{4}x + 1[/tex].
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Find a transformation T that maps the unit square to a figure with an area of 24 and a vertex at (5,3).
One such transformation is
T=
Answers
The transformation T maps the unit square to a figure with an area of 24 and a vertex at (5,3) which gives: T(x, y) = (6x + 5, 8y + 3).
How to Find a Transformation?To find a transformation T that maps the unit square to a figure with an area of 24 and a vertex at (5,3), we can use a combination of scaling and translation.
Let's denote the unit square as S, and the transformed figure as F.
To obtain a rectangle with an area of 48 and a vertex at (5,3), we can scale the unit square by multiplying the x-coordinates by 6 and the y-coordinates by 8, and then translate the scaled rectangle by adding (5,3) to the coordinates of each point.
Therefore, the transformation T can be expressed as:
T(x, y) = (6x + 5, 8y + 3)
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Decide whether the rates are equivalent. Maria saves $50 in 4 months.
Ralph saves $60 in 5 months
Answers
Answer:
The rates are not equivalent since Maria saves $0.50 more per month than Ralph.
Step-by-step explanation:
We can determine if two rates are equivalent by comparing the rates at which they save per month.
Maria's savings per month:
Both 50 and 4 can be divided by 2, which gives us 25/2. As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.
Ralph's savings per month:
Both 60 and 5 can be divided by 5, which gives us 12. Thus, Ralph saves $12 per month.
Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
(A) AA similarity
Step-by-step explanation:
In ΔABC,
∠A + ∠B + ∠C = 180
∠A + 27 + 90 = 180
∠A = 180 - 90 - 27
∠A = 63
Comparing ΔABC and ΔMNP,
∠A = ∠M = 63
∠C = ∠P = 90
Therfore, by AA property, the two triangles are similar