Answer:
the solution would be X=3 as 3.1 represents 3×1.
35-14÷2 +8²
What’s the answer
Answer:
93
Step-by-step explanation:
Remember PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction)
35 - 12 : 2 + 8² =
35 - 6 + 64 =
93
6
Dani makes a picture of a tree.
The tree is made up of a green triangle,
two congruent green trapeziums
and a brown square.
Find the area of the green part of the tree.
12 cm
6 cm
4 cm
7 cm
cm²
The area of the green part of the tree is 55. 5cm²
How to determine the areaThe formula for area of a triangle is given as;
Area = 1/2bh
Substitute the values, we have;
Area = 1/2 × 6 × 7
Area = 21cm²
Area of trapezium is expressed as;
Area = a + b/2 h
Substitute the values, we have;
Area = 5 + 7/2 (3) + 4 + 7/2 (3)
expand the bracket, we have;
Area = 18 + 16.5
Area = 34.5 cm²
Total area = 34.5 + 21 = 55. 5cm²
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What is the value of this expression
please help
Answer:
a+2bc/3a....4+2(--5×--7)/3(4)....4+2(35)/12.....4+70/12...74/12..answer =6⅙..option C
The table below shows y, the distance an athlete runs during x seconds.
Time (x seconds) Distance (y meters)
50
100
150
7.5
15.0
22.5
30.0
37.5
200
250
The pairs of values in the table form points on the graph of a linear
function. What is the approximate slope of the graph of that function?
The approximate slope of the graph of the linear function is 0.15.
To find the approximate slope of the graph of the linear function, we can choose two points from the table and calculate the slope using the formula:
slope = (change in y) / (change in x)
Let's select the points (50, 7.5) and (250, 37.5) from the table.
Change in y = 37.5 - 7.5 = 30
Change in x = 250 - 50 = 200
slope = (change in y) / (change in x) = 30 / 200 = 0.15
Note: A linear function is a mathematical function that represents a straight line.
It can be written in the form:
f(x) = mx + b
where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis).
The slope (m) determines the steepness or slant of the line.
A positive slope indicates an upward-sloping line, while a negative slope indicates a downward-sloping line.
The slope represents the rate of change of the function.
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Please awnser asap I will brainlist
The transformed matrix, after interchanging R1 and R2, is:
2 9 4 5
8 -2 1 7
1 4 -4 9
To interchange rows R1 and R2, we swap the positions of the first and second rows in the matrix. This operation can be performed by physically swapping the rows or by using the properties of matrix operations. Let's apply this row operation to the given matrix:
Original matrix:
8 -2 1 7
2 9 4 5
1 4 -4 9
Interchanging R1 and R2, we get:
2 9 4 5
8 -2 1 7
1 4 -4 9
After switching R1 and R2, the modified matrix is:
2 9 4 5
8 -2 1 7
1 4 -4 9
In the transformed matrix, the original first row (8 -2 1 7) becomes the second row, and the original second row (2 9 4 5) becomes the first row. The remaining rows (R3) remain unchanged.
Therefore, R1 and R2 are switched, and the resulting matrix is:
2 9 4 5
8 -2 1 7
1 4 -4 9
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NO LINKS!! URGENT HELP PLEASE!!
Please help me with #31 & 32
Answer:
31. m∠E = 56.1°
32. c = 24.9 inches
Step-by-step explanation:
Question 31The Law of Sines relates the lengths of the sides of a triangle to the sines of its angles. It states that the ratio of the length of a side of a triangle to the sine of the opposite angle is constant for all three sides of the triangle.
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
Given values of triangle DEF:
m∠D = 81°d = 25e = 21To find m∠E, substitute the values into the Law of Sines formula and solve for E:
[tex]\dfrac{\sin D}{d}=\dfrac{\sin E}{e}[/tex]
[tex]\dfrac{\sin 81^{\circ}}{25}=\dfrac{\sin E}{21}[/tex]
[tex]\sin E=\dfrac{21\sin 81^{\circ}}{25}[/tex]
[tex]E=\sin^{-1}\left(\dfrac{21\sin 81^{\circ}}{25}\right)[/tex]
[tex]E=56.1^{\circ}\; \sf(nearest\;tenth)[/tex]
Therefore, the measure of angle E is 56.1°, to the nearest tenth.
See the attachment for the accurate drawing of triangle DEF.
[tex]\hrulefill[/tex]
Question 32The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
From inspection of triangle ABC:
C = 125°a = 13 inchesb = 15 inchesTo find the length of side c, substitute the values into the Law of Cosines formula and solve for c:
[tex]c^2=a^2+b^2-2ab \cos C[/tex]
[tex]c^2=13^2+15^2-2(13)(15) \cos 125^{\circ}[/tex]
[tex]c^2=169+225-390 \cos 125^{\circ}[/tex]
[tex]c^2=394-390 \cos 125^{\circ}[/tex]
[tex]c=\sqrt{394-390 \cos 125^{\circ}}[/tex]
[tex]c=24.8534667...[/tex]
[tex]c=24.9\; \sf inches\;(nearest\;tenth)[/tex]
Therefore, the length of side c is 24.9 inches, to the nearest tenth.
22. In a study was done on 136 subjects with syncope or near syncope were studied. Syncope is the temporary loss of consciousness due to a sudden decline in blood flow to the brain. Of these subjects, 75 also reported having cardiovascular disease. Construct a 90,95, 99 percent confidence interval for the population proportion of subjects with syncope or near syncope who also have cardiovascular disease.
The main answer is that the confidence intervals for the population proportion of subjects with syncope or near syncope who also have cardiovascular disease, at 90%, 95%, and 99% confidence levels, are as follows:
90% Confidence Interval: Approximately 51.84% to 70.53%
95% Confidence Interval: Approximately 49.77% to 72.60%
99% Confidence Interval: Approximately 46.48% to 76.89%
In the study, out of the 136 subjects with syncope or near syncope, 75 reported having cardiovascular disease.
To construct the confidence intervals, we can use the formula for a proportion's confidence interval. The formula is based on the normal distribution assumption when sample size is large enough, which is satisfied here.
By plugging in the sample proportion (75/136) and the appropriate critical values based on the desired confidence level (1.645 for 90%, 1.96 for 95%, and 2.576 for 99%), we can calculate the lower and upper bounds for each confidence interval.
These confidence intervals provide an estimate of the likely range within which the true population proportion lies.
For example, with 95% confidence, we can say that we are 95% confident that the true proportion of subjects with syncope or near syncope who also have cardiovascular disease falls between approximately 49.77% and 72.60%.
The wider the confidence interval, the lower the precision of the estimate, but the higher the level of confidence.
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Find the domain and range of function
Domain: (-∞, ∞) - all real numbers Range: (-∞, 2] - all real numbers less than or equal to 2.
To find the domain and range of the function 2 - |x - 5|, we need to consider the possible values for the input variable (x) and the corresponding output values.
Domain:
The domain of a function represents the set of all possible input values for which the function is defined. In this case, the function 2 - |x - 5| is defined for all real numbers. There are no restrictions or limitations on the values that x can take. Therefore, the domain is (-∞, ∞), which means that the function is defined for all real numbers.
Range:
The range of a function represents the set of all possible output values that the function can produce. To determine the range, we consider the possible values of the function for different input values.
The expression |x - 5| represents the absolute value of the quantity (x - 5). The absolute value function always produces non-negative values. So, |x - 5| will always be non-negative or zero.
When we subtract |x - 5| from 2, we have 2 - |x - 5|. The resulting values will range from 2 to negative infinity (2, -∞).
Therefore, the range of the function 2 - |x - 5| is (-∞, 2].
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Note the complete questions is
Find the domain and range of function 2 - |x - 5| ?
state five features of tropical rainfall
Answer: none
Step-by-step explanation:
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2AI + 3H₂SO4
To show that the reaction conserves matter, how many hydrogen (H) atoms
will the right side of the equation need to have?
A. 6
B. 3
C. 2
OD. 5
Answer:
A. 6
Step-by-step explanation:
You have 3 molecules of H2SO4, each molecule has two atoms of H and you have 3 molecules, so 3*2=6 atoms of H
The numbers 1
through 15
were each written on individual pieces of paper, 1
number per piece. Then the 15
pieces of paper were put in a jar. One piece of paper will be drawn from the jar at random. What is the probability of drawing a piece of paper with a number less than 9
written on it?
There is a 53.33% chance of drawing a piece of paper with a number less than 9 from the jar.
To calculate the probability of drawing a piece of paper with a number less than 9 written on it, we need to determine the number of favorable outcomes (pieces of paper with a number less than 9) and divide it by the total number of possible outcomes (all 15 pieces of paper).
In this case, the favorable outcomes are the numbers 1 through 8, as they are less than 9. There are 8 favorable outcomes.
The total number of possible outcomes is 15 since there are 15 pieces of paper in the jar.
Therefore, the probability of drawing a piece of paper with a number less than 9 is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 8 / 15
Simplifying the fraction, we find that the probability is approximately:
Probability ≈ 0.5333 or 53.33%
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6. A rock outcrop was found to have 89.00% of its parent U-238 isotope remaining. Approximate the age of the outcrop. The half-life of U-238 is 4.5 billion years old. 12 million years 757 million years 1.2 billion years 37 million years
The approximate age of the rock outcrop is 1.2 billion years.
To approximate the age of the rock outcrop, we can use the concept of radioactive decay and the half-life of the U-238 isotope.
The half-life of U-238 is 4.5 billion years, which means that after each half-life, the amount of U-238 remaining is reduced by half.
We are given that the rock outcrop has 89.00% of its parent U-238 isotope remaining.
This means that the remaining fraction is 0.8900.
To find the number of half-lives that have elapsed, we can use the following formula:
Number of half-lives = log(base 0.5) (fraction remaining)
Using this formula, we can calculate:
Number of half-lives = log(base 0.5) (0.8900)
≈ 0.1212
Since each half-life is 4.5 billion years, we can find the approximate age of the rock outcrop by multiplying the number of half-lives by the half-life duration:
Age of the rock outcrop = Number of half-lives [tex]\times[/tex] Half-life duration
≈ 0.1212 [tex]\times[/tex] 4.5 billion years
≈ 545 million years
Therefore, the approximate age of the rock outcrop is approximately 545 million years.
Based on the answer choices provided, the closest option to the calculated value of 545 million years is 757 million years.
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Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with x-axis labeled study time in hours and y-axis labeled grade percent. Points are plotted at 1 comma 50, 2 comma 50, 2 comma 60, 2 comma 70, 3 comma 70, 3 comma 80, 4 comma 85, and 4 comma 90, and a line of fit drawn passing through the points 0 comma 30 and 2 comma 60
Determine the equation of the line of fit.
y = 15x + 60
y = 15x + 30
y = 30x + 60
y = 30x + 30
The equation of the line of fit is y = 15x + 30.
To determine the equation of the line of fit, we can use the given data points (0,30) and (2,60). We can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Using the two data points, we can calculate the slope (m) as the change in y divided by the change in x:
m = (60 - 30) / (2 - 0) = 30 / 2 = 15
Now that we have the slope, we can substitute one of the data points into the equation to solve for the y-intercept (b). Let's use the point (0,30):
30 = 15(0) + b
30 = 0 + b
b = 30
Therefore, the equation of the line of fit is y = 15x + 30. This means that for every additional hour of study time (x), the grade percent (y) increases by 15, and the line intersects the y-axis at 30.
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Measurement techniques used to measure extent of skewness in data set values are called
Select one:
a. Measure of skewness
b. Measure of median tail
c. Measure of tail distribution
d. Measure of distribution width
e. Measure of peakdness
Note: Answer C is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answer:
a. Measure of skewness
Step-by-step explanation:
Skewness is a measure of the asymmetry of a probability distribution. It quantifies the extent to which a dataset's values deviate from a symmetric distribution. Various measures of skewness exist, including the Pearson's skewness coefficient, the Bowley skewness coefficient, and the moment coefficient of skewness. These measures provide a numerical indication of the skewness present in the dataset.
. Mira bought $300 of Freerange Wireless stock in
January of 1998. The value of the stock is expected
to increase by 7.5% per year. Use a graph to predict
the year the value of Mira's stock will reach $650.
Question 5(Multiple Choice Worth 1 points)
(01.07 MC)
Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points and E. They are also intersected by transversal EC. Angle ABC measures 70 degrees. Angle CED measures 30 degrees.
Given: line BC is parallel to line ED
m∠ABC = 70°
m∠CED = 30°
Prove:m∠BEC = 40°
Statement Justification
line BC is parallel to line ED Given
m∠ABC = 70° Given
m∠CED = 30° Given
m∠ABC = m∠BED Corresponding Angles Theorem
m∠BEC + 30° = 70° Substitution Property of Equality
m∠BEC = 40° Subtraction Property of Equality
Which of the following accurately completes the missing statement and justification of the two-column proof?
m∠BEC + m∠CED = m∠BED; Definition of a Linear Pair
m∠ABC + m∠BEC = m∠BED; Angle Addition Postulate
m∠ABC + m∠BEC = m∠BED; Definition of a Linear Pair
m∠BEC + m∠CED = m∠BED; Angle Addition Postulate
Answer:
m∠BEC + m∠CED = m∠BED; Angle Addition Postulate
Step-by-step explanation:
You need to show that <BED is made up of angles BEC and CED by the Angle Addition Postulate.
m∠BEC + m∠CED = m∠BED; Angle Addition Postulate
Let the variance of Y is 4x^2. What is the standard deviation of Y?
Select one:
a. none of the above
b. Square root of 4x^2
c. 2
d. 2x^2
e. x
Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
The correct answer is option (b): Square root of 4x^2.
The standard deviation of a random variable Y is the square root of its variance. In this case, the variance of Y is given as 4x^2. Taking the square root of 4x^2, we get the standard deviation of Y as 2x.
Therefore, the correct answer is the square root of 4x^2, which is the standard deviation of Y.
The following pie chart shows the number of rabbits, sheep, cattle, pigs on a farm rabbits 900 sheep 700 cattle 300 Pig 500 a. How many animals are on the farm? b.What represents the number of sheep on the farm c. what percentage of the total number of animals are rabbits d. Calculate the angle that represents number of pigs
a) There are 2400 animals on the farm.
b) The number of sheep on the farm is 700.
c) The percentage of rabbits in relation to the total number of animals is 37.5%.
d) The angle that represents the number of pigs is 75 degrees.
a) To determine the total number of animals on the farm, we add up the number of rabbits, sheep, cattle, and pigs:
Total number of animals = 900 (rabbits) + 700 (sheep) + 300 (cattle) + 500 (pigs) = 2400 animals.
b) The number of sheep on the farm is given as 700.
c) To calculate the percentage of rabbits in relation to the total number of animals, we divide the number of rabbits by the total number of animals and multiply by 100:
Percentage of rabbits = (900 / 2400) * 100 = 37.5%.
d) To calculate the angle that represents the number of pigs, we need to find the proportion of the total number of animals that pigs make up, and then convert it to an angle on the pie chart.
Proportion of pigs = 500 / 2400 = 0.2083.
To find the angle in degrees, we multiply the proportion by 360 degrees:
Angle representing pigs = 0.2083 * 360 = 75 degrees.
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When the sun’s angle of depression is 36 degrees, a building casts a shadow of 44 m. To the nearest meter, how high is the building? Enter a number answer only.
The height of the building is approximately 32 meters.
To determine the height of the building, we can use the tangent function, which relates the angle of depression to the height and the length of the shadow.
Let's denote the height of the building as h.
Given that the angle of depression is 36 degrees and the length of the shadow is 44 m, we can set up the following trigonometric equation:
tan(36°) = h / 44
Now, we can solve for h by multiplying both sides of the equation by 44:
h = 44 * tan(36°)
Using a calculator, we find that tan(36°) is approximately 0.7265.
Substituting the value, we get:
h = 44 * 0.7265
Calculating the value, we find:
h ≈ 32 meters
Consequently, the building stands about 32 metres tall.
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Please help me out with this question.
Answer:
Assuming options are independent or not independent/dependent, it would be not independent
Step-by-Step:
Probability of (A given B) = Probability(A)
P(A & B) divided by P(B) = P(A)
(1/9)/(1/15) = 2/5
5/3 = 2/5
Since 5/3 doesn't equal 2/5, the events if A and B are not independent
the table shows how the distance traveled by a dogsled is changing over time
what value is missing from the table
The missing value in the table is 64 miles.The correct answer is option C.
To determine the missing value in the table, we can observe the pattern in the given data. Looking at the time values, we can see that they are increasing by a constant interval of 2 hours: 2, 4, 6, 8, 10. The corresponding distances traveled are 16, 32, 48, ?, 80.
By examining the distances, we can see that they are increasing by a constant interval of 16 miles. The first distance is 16 miles when the time is 2 hours, and it increases by 16 miles for every 2-hour increment.
To find the missing value, we need to determine the distance traveled at 8 hours. Since the interval is 16 miles for every 2 hours, the distance traveled at 8 hours can be calculated by multiplying the interval by the number of 2-hour increments from the first data point: 16 miles * (8 hours / 2 hours) = 16 miles * 4 = 64 miles.
Therefore, the missing value in the table is 64 miles, which corresponds to option C.
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The probable question may be:
The table shows how the distance traveled by a dogsled is changing over time.
Time (in hours) :- 2,4,6,8,10.
Distance Traveled (In miles) :- 16,32,48,?,80.
What value is missing from the table?
A. 50.
B. 68.
C. 64.
D. 60.
Pls help pls help help help help
Answer:
The correct answer is
A. [tex]pq^4r^4[/tex]
Step-by-step explanation:
The statement of cash flows for Baldwin shows what happens in the cash account during the year. It can be seen as a summary of the sources and uses of cash. Pleas answer which of the following is true if Baldwin issues bonds
(-7,3))
10
Mark this and return
8
(-2,5) 6-
4-
(-2,1) 2-
12-10-8 -6 - -2
-2-
2
(3,3)
Which equation represents the hyperbola shown in the
graph?
O
O
O
(x - 2)² (v+3)² = 1
25
O
(x + 2)²
ܕ ܬܒܐ ܙ
(x + 2)²
25
(x - 2)²
25
(y-3)² 1
25
Save and Exit
(y - 3)²
4
(y + 3)²
Next
Submit
The equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.
From the given options, the equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.
To determine the equation of a hyperbola, we examine the standard form:
For a hyperbola centered at (h, k), with vertical transverse axis, the standard form is:
(y - k)²/a² - (x - h)²/b² = 1
From the given graph, we can observe that the center of the hyperbola is (-2, 3). This corresponds to the values of (h, k) in the standard form.
Next, we need to determine the values of a and b, which are the lengths of the transverse and conjugate axes, respectively. Looking at the graph, we see that the transverse axis has a length of 2a = 4, so a = 2. The conjugate axis has a length of 2b = 10, so b = 5.
Plugging these values into the standard form, we obtain:
(y - 3)²/4 - (x + 2)²/25 = 1
The equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.
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The correct equation representing the hyperbola shown in the graph is:
(x + 2)²/25 - (y - 3)²/4 = 1.
The equation that represents the hyperbola shown in the graph is:
(x + 2)²/25 - (y - 3)²/4 = 1
Let's analyze the options provided:
(x - 2)²(v + 3)² = 1:
This equation is not a valid representation of a hyperbola because it contains a term (v + 3)², which is not consistent with the variable used in the graph.
(x + 2)²/25:
This equation represents a horizontal parabola, not a hyperbola.
(x - 2)²/25:
This equation represents a horizontal parabola, not a hyperbola.
(y - 3)²/1:
This equation represents a vertical line, not a hyperbola.
(y - 3)²/4:
This equation represents a hyperbola with a vertical transverse axis and a conjugate axis length of 2b = 4 (b = 2).
The equation is in the standard form for a hyperbola with a vertical transverse axis.
The equation is provided as a standard form assuming the given coordinates and graph match the standard form representation of a hyperbola.
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what is the slope of the line that contains these points?
The slope remains constant and equal to 0.2 between all pairs of consecutive points, we can conclude that the slope of the line that contains all the given points is 0.2.
To calculate the slope of the line that contains the given points (-4, -3), (1, -2), (6, -1), and (11, 0), we can use the formula for slope, which is defined as the change in y divided by the change in x between any two points on the line.
Let's calculate the slope between the first two points (-4, -3) and (1, -2):
Slope = (change in y) / (change in x)
= (-2 - (-3)) / (1 - (-4))
= (-2 + 3) / (1 + 4)
= 1 / 5
= 0.2
Now, let's calculate the slope between the next two points (1, -2) and (6, -1):
Slope = (change in y) / (change in x)
= (-1 - (-2)) / (6 - 1)
= (-1 + 2) / (6 - 1)
= 1 / 5
= 0.2
Similarly, let's calculate the slope between the last two points (6, -1) and (11, 0):
Slope = (change in y) / (change in x)
= (0 - (-1)) / (11 - 6)
= (0 + 1) / (11 - 6)
= 1 / 5
= 0.2
Since the slope remains constant and equal to 0.2 between all pairs of consecutive points, we can conclude that the slope of the line that contains all the given points is 0.2.
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An office manager needs to cover the front face of a rectangular box with a label for shipping. the vertices of the face are (-5, 8), (3, 8), (-5, -4), and (3, -4). what is the area, in square inches, of the label needed to cover the box?
98 in2
48 in2
40 in2
20 in2
The area of the label needed to cover the box is 96 square inches. None of the provided answer options (98 in², 48 in², 40 in², or 20 in²) match the calculated area of 96 in².
We must determine the area of the rectangle formed by the provided vertices in order to determine the size of the label required to completely cover the front face of the rectangular box.
Let's label the vertices as follows:
A = (-5, 8)
B = (3, 8)
C = (-5, -4)
D = (3, -4)
The formula to calculate the area of a rectangle given the coordinates of its vertices is:
Area = |(x2 - x1) * (y2 - y1)|
Using the given coordinates, we can calculate the area:
Area = |(3 - (-5)) * (8 - (-4))|
Simplifying the expression:
Area = |(3 + 5) * (8 + 4)|
Area = |8 * 12|
Area = 96 square units
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How do you find the approximate circumference of a circle with a diameter of 6 inches.use 3.14 as estimate of tt that is correct to two decimal places.
Answer:
18.84 in
Step-by-step explanation:
The circumference of a circle = pi * diameter = 6*3.14 = 18.84 in.
Your firm has the option of making an investment in new software that will cost $172,395 today, but will save the company money over several years. You estimate that the software will
provide the savings shown in the following table over its 5-year life, . Should the firm make this investment if it requires a minimum annual return of 8% on all investments?
The present value of the stream of savings estimates is $ (Round to the nearest dollar)
The present value of the stream of savings estimates is approximately $200,256.
To determine whether the firm should make the investment in new software, we need to calculate the present value of the stream of savings estimates and compare it to the cost of the software.
The present value (PV) of the savings estimates can be calculated using the formula:
[tex]PV = C1/(1+r)^1 + C2/(1+r)^2 + ... + Cn/(1+r)^n[/tex]
Where C1, C2, ..., Cn represent the savings in each year, r is the minimum annual return required (8% or 0.08), and n is the number of years (5).
Given the savings estimates in the table, we have:
C1 = $35,000
C2 = $45,000
C3 = $50,000
C4 = $55,000
C5 = $60,000
Plugging these values into the present value formula and using the minimum annual return rate of 8% (0.08), we can calculate:
[tex]PV = 35000/(1+0.08)^1 + 45000/(1+0.08)^2 + 50000/(1+0.08)^3 + 55000/(1+0.08)^4 + 60000/(1+0.08)^5[/tex]
Evaluating this expression, we find that the present value of the stream of savings estimates is approximately $200,256.
Since the present value of the savings estimates is greater than the cost of the software ($172,395), the firm should make this investment. The investment is expected to provide a return greater than the minimum required annual return of 8%.
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The present value of the stream of savings estimates is $149,622.
To determine if the firm should make the investment, we need to calculate the present value of the stream of savings estimates and compare it to the initial cost of the software.
The present value (PV) of the savings estimates can be calculated using the formula:
PV = C1/(1+r)¹ + C2/(1+r)² + ... + Cn/(1+r)ⁿ
Where:
PV = Present value
C1, C2, ..., Cn = Cash flows in each period
r = Discount rate (minimum annual return)
Given the savings estimates in the table over a 5-year period and a minimum annual return of 8% (0.08), we can calculate the present value as follows:
PV = $15,000/(1+0.08)¹ + $35,000/(1+0.08)² + $50,000/(1+0.08)³ + $45,000/(1+0.08)⁴ + $40,000/(1+0.08)⁵
PV = $13,888.89 + $30,864.20 + $41,152.46 + $34,682.34 + $29,034.09
PV = $149,621.98 (rounded to the nearest dollar)
The present value of the savings is higher than the initial cost of the software ($172,395), the firm should make this investment if it requires a minimum annual return of 8% on all investments.
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Triangles J K L and M N R are shown. In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS? ∠J ≅ ∠M ∠L ≅ ∠R ∠K ≅ ∠N ∠R ≅ ∠K
To show that ΔJKL ≅ ΔMNR by SAS (Side-Angle-Side), we need the additional information that the lengths of the corresponding sides JK and MN are equal.
To prove ΔJKL ≅ ΔMNR using the SAS congruence criterion, we need to establish that two corresponding sides and the included angle of the triangles are congruent.
1. Given information:
- KL ≅ NR (corresponding sides)
- JL ≅ MR (corresponding sides)
- ∠J ≅ ∠M (included angle)
- ∠L ≅ ∠R (corresponding angles)
- ∠K ≅ ∠N (corresponding angles)
- ∠R ≅ ∠K (corresponding angles)
2. Additional information needed:
- We need to know if JK ≅ MN (corresponding sides) to establish the SAS congruence criterion.
3. Possible scenarios:
- If JK ≅ MN, then we can establish that ΔJKL ≅ ΔMNR by SAS.
- If JK is not equal to MN, then we cannot apply the SAS congruence criterion, and additional information or a different congruence criterion would be needed to prove the triangles congruent.
In summary, the lengths of the corresponding sides JK and MN need to be equal to prove ΔJKL ≅ ΔMNR by SAS. Without this information, we cannot conclude the congruence of the triangles using the SAS criterion alone.
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Find the dy/dx of the implicit x - 2xy + x^2y + y = 10.
The derivative dy/dx of the implicit equation[tex]x - 2xy + x^2y + y = 10[/tex] is given by[tex]\frac{(2y - 2 + 2xy)}{(-2x + x^2 + 1)}[/tex]
To find the derivative dy/dx of the implicit equation [tex]x - 2xy + x^2y + y =[/tex]10, we will use the implicit differentiation technique.
Step 1: Differentiate both sides of the equation with respect to x.
For the left-hand side:
[tex]d/dx (x - 2xy + x^2y + y) = d/dx (10)[/tex]
Taking the derivative of each term separately:
[tex]d/dx (x) - d/dx (2xy) + d/dx (x^2y) + d/dx (y) = 0[/tex]
Step 2: Apply the chain rule to the terms involving y.
The chain rule states that if we have y = f(x), then dy/dx = dy/du * du/dx, where u = f(x).
For the term 2xy, we have y = f(x) = xy. Applying the chain rule, we get:
[tex]d/dx (2xy) = d/dx (2xy) * dy/dx[/tex]
= 2y + 2x * dy/dx
Similarly, for the term x^2y, we have [tex]y = f(x) = x^2y.[/tex]Applying the chain rule:
[tex]d/dx (x^2y) = d/dx (x^2y) * \frac{dx}{dy} \\= 2xy + x^2 * \frac{dx}{dy}[/tex]
Step 3: Substitute the derivatives back into the equation.
[tex]d/dx (x) - (2y + 2x * dy/dx) + (2xy + x^2 * dy/dx) + d/dx (y) = 0[/tex]
Simplifying the equation:
[tex]1 - 2y - 2x * \frac{dx}{dy} + 2xy + x^2 * \frac{dx}{dy} + \frac{dx}{dy} = 0[/tex]
Step 4: Group the terms involving dy/dx together and solve for dy/dx.
Combining the terms involving dy/dx:
[tex]-2x * \frac{dx}{dy} + x^2 * \frac{dx}{dy} + dy/dx = 2y - 1 + 2xy - 1[/tex]
Factoring out dy/dx:
[tex](-2x + x^2 + 1) * \frac{dx}{dy} = 2y - 1 + 2xy - 1[/tex]
[tex]dy/dx = \frac{(2y - 2 + 2xy)}{(-2x + x^2 + 1)}[/tex]
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