Answer:
Step-by-step explanation:
To find the shortest length of cable needed, we can use trigonometry to calculate the length of the hypotenuse of a right triangle formed by the mountain, the cable car, and the ground.
Let's denote the height of the mountain as H = 3,400 feet and the horizontal distance from the base of the mountain to the point where the cable car will be installed as D = 940 feet.
In the right triangle, the vertical leg represents the height of the mountain, the horizontal leg represents the distance from the base to the point where the cable car is installed, and the hypotenuse represents the length of the cable.
We can use the sine function to relate the angle of inclination, the height, and the hypotenuse of the triangle:
sin(angle) = opposite/hypotenuse
In this case, the angle of inclination is 74 degrees, and the opposite side is the height of the mountain (H).
Therefore, we can write the equation as:
sin(74 degrees) = H/hypotenuse
Rearranging the equation, we have:
hypotenuse = H / sin(74 degrees)
Let's calculate the value of sin(74 degrees) and substitute the values to find the length of the hypotenuse:
sin(74 degrees) ≈ 0.9613
hypotenuse = 3,400 / 0.9613 ≈ 3,535.89 feet
Therefore, the shortest length of cable needed is approximately 3,535.89 feet when rounded to two decimal places.
there are 2 containers of beads. container a has 400 black beads and 250 white beads. container b has 200 black beads and 670 white beads. how many black and white beads must be transferred from b to a so that 50% of the beads in a are white and 25% of the beads in b are black?
Step-by-step explanation:
First box contains 8 black and 12 white beads Second box contains 9 black and 6 white beads.
(a) One black bead from each box is taken.
Number of such cases = 8×9=72
Total number of possibilities = 20×15=300
Probablity of getting both black beads =
300
72
=
25
6
(b) One black and one white bead is taken.
So if one black bead is taken from first box then one white bead is taken from second box and if one white bead is taken from first box then one black bead is taken from second box.
Number of such cases = 8×6+12×9=48+108=156
Total number of possibilities = 20×15=300
Probablity of getting one black and one white bead =
300
156
=
25
13
find the approximate area of the shaded region, given that the area of the sector is approximately 13.08 square units.
The area of the shaded region is 3915 units².
We have,
Area of the sector.
= 13.08 units²
Now,
To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.
Area = √[s(s - a)(s - b)(s - c)]
where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case,
The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:
Calculate the semi-perimeter:
s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units
Use Heron's formula to find the area:
Area = √[7(7 - 5)(7 - 5)(7 - 4)]
= √[7(2)(2)(3)]
= √[84]
≈ 9.165 units (rounded to three decimal places)
Now,
Area of the shaded region.
= Area of the sector - Area of the isosceles triangle
= 13.08 - 9.165
= 3.915 units²
Thus,
The area of the shaded region is 3915 units².
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A line passes through the point(-7,-4) and has a slope of 3
Answer:
[tex]y=3x+17[/tex]
Step-by-step explanation:
Use point-slope form
[tex]y-y_1=m(x-x_1)\\y-(-4)=3(x-(-7))\\y+4=3(x+7)\\y+4=3x+21\\y=3x+17[/tex]
a formula in the form y=mx+b models the cost, y, of four-year college x years after 2010. would you expect m to be positive, negative, or zero? explai your answer
we would expect m to be positive.
In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.
Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.
If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.
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Help me!!! absolutely dying rn 5 stars to anyone who helps
Answer:
11a)
A regular hexagon (6 sides) is given. Because it is regular, every interior angle has the same value.
We know that the sum of the interior angles of a triangle is 180°. Using this information, we can break this hexagon up into 4 triangles:
Given each triangle's interior angles sum to 180°, and we have 4 triangles, the total sum of the interior angles of the entire hexagon is
180*4 = 720
The sum of the interior angles of the hexagon is 720°.
11b)
The same idea can be applied:
This time a regular decagon (10 sides) is given. This shape can be broken up into 8 triangles (This value will always be the number of sides - 2).
We can now multiply to find the total sum of the interior angles.
180*8 = 1440
The sum of the interior angles of the decagon is 1440°.
(The formula to solve for interior angle sum of regular shapes is 180 * (number of sides - 2)
11c)
To find the measure of one interior angle of a regular octagon (8 sides), we must take the total sum of the interior angles and divide that by 8 (to find the value of 1 angle).
First, find the interior sum value using interior angle sum formula:
180 * (8-2) = 180 * 6 = 1080°
Now we can divide this by 8 to find the sum of one interior angle:
1080/8 = 135°
The value of one interior angle of a regular octagon is 135°.
(The formula to solve for one interior angle of a regular shape is
[180 * (number of sides - 2)] / number of sides
11d)
The sum of the exterior angles of any polygon is 360°.
An easy way to demonstrate this idea is with an equilateral triangle (every interior angle is 60°). If the interior angle is 60°, the exterior angle is 120° (supplemental theorem).
A triangle has 3 angles: 120 * 3 = 360°. The sum of exterior angles is 360°.
For a heptagon (7 sides), or any other polygon, the same result will be found.
(In order to algebraically solve this however, you would find the value of one interior angle using the formula above, subtract that value from 180 to find the value of one exterior angle, and then multiply the value of one exterior angle by 7 for a heptagon).
11e)
Given the sum of exterior angles is 360°, we can simply divide 360 by the number of sides to find the value of one exterior angle.
360 / 7 = 51.42857...
The measure of one exterior angle of the heptagon is about 51.4°.
The Peel Trading Company received an invoice dated September 20 for $ less 25%, 20%, terms 5/10, 2/30, n/60. Peel made a payment on September 30 to reduce the debt to $5000 and a payment on October 20 to reduce the debt by $3000.
(a)
What amount must Peel remit to pay the balance of the debt at the end of the credit period?
(b)
What is the total amount paid by Peel?
The Total amount paid by Peel is $8000. Peel must remit $13,333.33 to pay the balance of the debt at the end of the credit period.
(a) To determine the amount Peel must remit to pay the balance of the debt at the end of the credit period, we need to calculate the remaining balance after the two payments.
The original invoice amount is not given in the question, so we'll calculate it using the given discounts. Let's assume the original invoice amount is X dollars.
First, let's calculate the amount after a 25% discount:
Amount after 25% discount = X - 0.25X = 0.75X
Next, let's calculate the amount after a 20% discount:
Amount after 20% discount = 0.75X - 0.20(0.75X) = 0.75X - 0.15X = 0.60X
Now, let's consider the payment on September 30 to reduce the debt to $5000:
Remaining balance after September 30 payment = 0.60X - $5000
Finally, let's consider the payment on October 20 to reduce the debt by $3000:
Remaining balance after October 20 payment = (0.60X - $5000) - $3000
To find the amount Peel must remit to pay the balance, we set the remaining balance equal to zero and solve for X:
(0.60X - $5000) - $3000 = 0
Simplifying the equation:
0.60X - $8000 = 0
0.60X = $8000
X = $8000 / 0.60
X = $13,333.33
Therefore, Peel must remit $13,333.33 to pay the balance of the debt at the end of the credit period.
(b) To find the total amount paid by Peel, we sum the two payments made by Peel:
Total amount paid = $5000 + $3000
Total amount paid = $8000
Therefore, the total amount paid by Peel is $8000.
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According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this increased by approximately 0.6% per year. If this trend continues, in which year will 46% of babies be born out of wedlock?
Que número estoy pensando si al multiplicarlo por 4 y luego de sumarle 16 obtengo 8?
Para encontrar el número que estás pensando, podemos plantear una ecuación. Denotemos al número desconocido como "x". Según la información proporcionada, podemos escribir la ecuación:
4x + 16 = 8
Ahora resolvamos la ecuación para encontrar el valor de "x":
4x = 8 - 16
4x = -8
x = -8/4
x = -2
Entonces, el número que estás pensando es -2.
Melanie invested $2,500 at 5% for 15 years. Josiah invested $1,000 at 10% for five years. Who will earn the most money over time?
Answer:
Melaine
Step-by-step explanation:
[tex]\text{Melaine's Total Earnings}=\$2500(1.05)^{15}=\$5197.32\\\text{Josiah's Total Earnings}=\$1000(1.10)^{10}=\$2593.74[/tex]
Therefore, Melaine will earn the most money over time
Label each of the following scale factors based on whether they would cause an expansion or a contraction.
0.75
4/5
-7
11/9
-4.3
NO LINKS!
Answer:
0.75 = contraction
4/5 = contraction
-7 = expansion
11/9 = expansion
-4.3 = expansion
Step-by-step explanation:
The scale factor is a numerical value that expresses the proportional change in size between an original object or figure and a scaled version of it.
ExpansionIf the magnitude of the scale factor is greater than 1, it indicates an expansion, meaning the new size is larger than the original size.
ContractionIf the magnitude of the scale factor is between 0 and 1, it indicates a contraction, meaning the new size is smaller than the original size.
ReflectionIf the scale factor is negative, it indicates a reflection in addition to the expansion or contraction.
[tex]\hrulefill[/tex]
As 0.75 is between 0 and 1, the scale factor of 0.75 would cause a contraction.
As 4/5 is between 0 and 1, the scale factor of 4/5 would cause a contraction.
As the magnitude of -7 is 7, and 7 is greater than 1, the scale factor of -7 would cause an expansion.
As 11/9 is greater than 1, the scale factor of 11/9 would cause an expansion.
As the magnitude of -4.3 is 4.3, and 4.3 is greater than 1, the scale factor of -4.3 would cause an expansion.
Answer:
0.75: Contraction
4/5: Contraction
-7: Expansion
11/9: Expansion
-4.3: Expansion
Step-by-step explanation:
0.75: This scale factor is less than 1, indicating a decrease in size. It would cause a contraction.4/5: This scale factor is less than 1, indicating a decrease in size. It would cause a contraction.-7: This scale factor is negative, indicating a change in direction. It would cause an expansion.11/9: This scale factor is greater than 1, indicating an increase in size. It would cause an expansion.-4.3: This scale factor is negative, indicating a change in direction. It would cause an expansion.To win the jackpot, 4 different numbers are randomly selected from 1 to 45 and one number from 1 to 30. The order of the first 4 numbers does not matter. What is the probability of winning the jackpot on one try? type your answer as a fraction or in scientific notation
The probability of winning is given as P(winning) = 1 / 4,469,850
How to solve for the probabilityC(45, 4) = 45! / [4!(45-4)!]
= 45*44*43*42 / (4*3*2*1)
= 148995
So, the total number of possible outcomes is 148995 * 30 = 4,469,850.
Now, we have to figure out the number of winning outcomes. In a lottery, there's typically only one winning combination (the numbers drawn), so the number of winning outcomes is 1.
This is an incredibly small probability, indicating that the chances of winning this kind of lottery on a single ticket are extremely low.
P(winning) = 1 / 4,469,850
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The ages of members in a family are: 70, 42, 29, 64, 38, 35, 42, 34 What is the mean? What is de Median? What is de mode? What is de Range? What is the standard deviation?
The mean is 46.75, the median is 40, the mode is 42, the range is 41, and the standard deviation is approximately 13.12.
To find the mean, median, mode, range, and standard deviation of the given ages, let's organize the data in ascending order:
29, 34, 35, 38, 42, 42, 64, 70
Mean:
To find the mean, we sum up all the values and divide by the total number of values:
Mean = (29 + 34 + 35 + 38 + 42 + 42 + 64 + 70) / 8
= 374 / 8
= 46.75
Median:
The median is the middle value in a sorted dataset. In this case, we have an even number of values, so we take the average of the two middle values:
Median = (38 + 42) / 2
= 40
Mode:
The mode is the most frequently occurring value. In this case, the mode is 42 since it appears twice, more than any other value.
Range:
The range is the difference between the highest and lowest values:
Range = 70 - 29
= 41
Standard Deviation:
To find the standard deviation, we need to calculate the deviations from the mean, square them, take the average, and then find the square root:
Deviation from the mean: (29-46.75), (34-46.75), (35-46.75), (38-46.75), (42-46.75), (42-46.75), (64-46.75), (70-46.75)
Squared deviations: 339.2656, 167.5625, 122.0625, 71.0625, 21.0625, 21.0625, 340.5625, 527.0625
Average squared deviation: (339.2656 + 167.5625 + 122.0625 + 71.0625 + 21.0625 + 21.0625 + 340.5625 + 527.0625) / 8
= 172.6719
Standard Deviation: √172.6719 ≈ 13.12
Therefore, the mean is 46.75, the median is 40, the mode is 42, the range is 41, and the standard deviation is approximately 13.12.
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the population of a small town, P, as a function of time, t, in years past 1940 is given below.
P= 1304 + 300t
The population grew to 5650 in 13.48 years .
Given,
Population of town in 1940 is a function given by:
P= 1304 + 300t
Now,
Let total number of population after certain years be 5650.
Let t1 be the year in which the population reached a count of 5650. Solve for t1:
5650= 1304 + 300t1
t1 = 13.48 years
The population grew to the number 5650 in 13.48 years past 1940, approximately 1954 .
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is making a large table in the shape of a trapezoid, as shown. She needs to calculate the area of the table. She is making the longest side of the table twice as long as the table's width. Complete parts a and b below.
Answer:
Step-by-step explanation:
Answer:
Chloe is making a large table in the shape of a trapezoid, as shown. She needs to calculate the area of the table. She is making the longest side of the table twice as long as the table's width. Complete parts a and b below.
a) Write an expression for the area of the table in terms of the width x.
One possible expression is:
A = (x + 2x) * h / 2
where A is the area of the table, x is the width of the table, and h is the height of the table.
To get this expression, we use the formula for the area of a trapezoid :
A = (a + b) * h / 2
where a and b are the lengths of the parallel sides of the trapezoid. Since Chloe is making the longest side of the table twice as long as the width, we can write:
a = x
b = 2x
Substituting these values into the formula, we get:
A = (x + 2x) * h / 2
b) Simplify the expression and find the area of the table if x = 3 feet and h = 4 feet.
To simplify the expression, we can combine like terms and apply the order of operations:
A = (x + 2x) * h / 2
A = (3x) * h / 2
A = 3 * x * h / 2
To find the area of the table if x = 3 feet and h = 4 feet, we can plug in these values into the simplified expression:
A = 3 * x * h / 2
A = 3 * 3 * 4 / 2
A = 9 * 4 / 2
A = 36 / 2
A = 18
Therefore, the area of the table is 18 square feet.
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A bus is scheduled to leave the terminal at 10:15 in the morning and travel for 5 3/4 hours to Bally city. If the bus leaves the terminal 35 minutes late, when will it arrive in Bally city?
Answer:
Step-by-step explanation:
3/4 hours=3/4×60=45 minutes
10:15+5.45 hrs=16:00+0:35=16:35=4.35 pm
so C
Norma owns and operates an accounting business as a sole proprietor. She purchased several computers at a cost of $9,000 for use in her business. Her business produced $120,000 of net income. Assume that she purchased the computers (5-year property) and placed them into service on January 11th of the current year. What is the amount of the cost recovery deductions for the first 3 years under MACRS? [The MACRS Table is shown under Course Supplement Materials.] (Be sure to show your work). Calculate the cost recovery deduction for the first 3 years if Norma elects straight-line depreciation. (Show your work). What is the cost recovery deduction she can use for each year under Section 179?
The cost recovery deductions for the first 3 years under MACRS are as follows:
Year 1: $1,800
Year 2: $2,304
Year 3: $941 (rounded)
Let's determine the cost recovery deductions under MACRS for the first 3 years:
Lets determine the property class for the computers.
Since the computers are 5-year property, they fall under the "5-Year Property" class.
Now determine the MACRS depreciation percentages for the property class.
Referring to the MACRS table, the depreciation percentages for 5-Year Property are as follows:
Year 1: 20.00%
Year 2: 32.00%
Year 3: 19.20%
Calculate the cost recovery deduction for each year.
Year 1:
Cost Recovery Deduction = Cost of Computers × Depreciation Percentage for Year 1
= $9,000 × 20.00%
= $1,800
Year 2:
Cost Recovery Deduction = (Cost of Computers - Accumulated Depreciation)×Depreciation Percentage for Year 2
= ($9,000 - $1,800) ×32.00%
= $7,200× 32.00%
= $2,304
Year 3:
Cost Recovery Deduction = (Cost of Computers - Accumulated Depreciation) × Depreciation Percentage for Year 3
= ($9,000 - $1,800 - $2,304) × 19.20%
= $4,896 × 19.20%
= $940.99 (rounded to nearest dollar)
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I need some help if anyone sees this and knows how please lmk!!
The true statement are:
Both printers will print the same number of poster for $25.Poster Perfect cost less if you want to print more than 5 posters.Poster Perfect: Since Poster Perfect charges a setup fee of $10 plus $3 per poster, the total cost will increase linearly with the number of posters printed.
We can set up equation as
y= 10 + 3x where x is number of pieces
The graph will show a constant slope for PrintPro:
Since PrintPro charges a flat rate of $5 per poster with no setup fee, the total cost will increase at a constant rate as the number of posters printed increases.
We can set up equation as
y= 5x where x is number of pieces
For x = 5
Poster Perfect: y= 10+ 15 = $25
PrintPro: y = 25
and, for x= 6
Poster Perfect: y= 10 + 18 = $28
PrintPro: y = 30
So, the true statement are:
Both printers will print the same number of poster for $25.
Poster Perfect cost less if you want to print more than 5 posters.
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loan amount $17,000 simple interest 6.8% total interest $867 loan in months
The monthly payment on the loan would be approximately $2,023.52.
To calculate the loan in detail, we need to determine the time period and the monthly payment. Let's break down the given information:
Loan amount: $17,000
Simple interest rate: 6.8%
Total interest: $867
First, we can calculate the interest amount using the formula for simple interest:
Interest = Principal × Rate × Time
We know the interest amount is $867, and the principal (loan amount) is $17,000. Let's solve for time (in years):
867 = 17,000 × 0.068 × Time
Dividing both sides of the equation by (17,000 × 0.068), we get:
Time = 867 / (17,000 × 0.068)
Time ≈ 0.7596 years
Since the loan term is usually expressed in months, we multiply the above result by 12 to convert it to months:
Time in months = 0.7596 × 12
Time in months ≈ 9.1152 months
Now that we have the time period in months, we can calculate the monthly payment (P) using the formula:
P = (Principal + Total Interest) / Time in months
P = (17,000 + 867) / 9.1152
P ≈ 2,023.52
Therefore, the monthly payment on the loan would be approximately $2,023.52.
To summarize, for a loan amount of $17,000 with a simple interest rate of 6.8% and a total interest of $867, the loan term would be approximately 9.1152 months, and the monthly payment would be around $2,023.52.
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What percent of the 8th graders prefer comedies? Round your answer to the nearest whole number percent.
Answer:
Step-by-step explanation:
Thee percentage of 8th graders that prefer comedies is 44%
Probability of an eventpercentage is the ratio of required to the total number of samples in an experiment.
Here,
8th graders that prefer comedies = 18
Total number of 8th graders = (10+18+13) = 41
P(8th that prefer comedies) = (18/41) × 100% = 43.90
Therefore, the percentage of 8th graders that prefer comedies is 44%.
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What is the volume, in cubic in, of a rectangular prism with a height of 8in, a width of 13in, and a length of 18in?
Answer:
Step-by-step explanation:
V = width x length x height
= 13 x 18 x 8
= 1,872 in³
Answer:
A rectangular prism is a three-dimensional shape that has six rectangular faces. The volume of a rectangular prism is the amount of space inside it. To find the volume of a rectangular prism, we can use the formula: V = lwh, where l is the length, w is the width, and h is the height of the prism. In this case, we are given that the height is 8 in, the width is 13 in, and the length is 18 in. Plugging these values into the formula, we get:
V = lwh
V = (18)(13)(8)
V = 1872
Therefore, the volume of the rectangular prism is 1872 cubic inches.
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please help me it's due tomorrow
The value of sin θ is equal to 3/5.
We have,
Given that θ is the angle for which [tex]cos^{-1}(4/5)[/tex] is equal to, we can determine the value of sin θ using the trigonometric identity:
sin²θ + cos²θ = 1
To find sin θ, we can rearrange the identity as:
sin θ = √(1 - cos²θ)
Since θ satisfies the condition 0 < θ < π/2, we know that cos θ is positive, and thus we can directly substitute [tex]cos^{-1}(4/5)[/tex] into the equation:
sin θ = √(1 - (4/5)²)
sin θ = √(1 - 16/25)
sin θ = √(9/25)
Since 0 < θ < π/2, sin θ is positive.
Therefore:
sin θ = 3/5
Hence,
The value of sin θ is equal to 3/5.
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81a^2+5b^2
factor, but this is algebra and intro to pre-calc
The expression 81a² + 5b² cannot be factored
How to factor the expressionfrom the question, we have the following parameters that can be used in our computation:
81a² + 5b²
using the above as a guide, we have the following:
The terms of the expression cannot be factored
This is so because they do not have any common factor
Hence, the expression 81a² + 5b² cannot be factored
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If Sherry Smith received 820 votes, how many total votes were cast? Round your answer to the nearest whole number.
Sherry Smith received 820 votes, the total Number of votes cast was 1000.
The total number of votes cast if Sherry Smith received 820 votes, you need to be provided with information on the percentage of votes Sherry Smith won. This is because knowing the percentage of votes Sherry Smith won would enable you to calculate the total number of votes cast, as follows:
If Sherry Smith won x percent of the total votes cast, then the total number of votes cast would be:
A total number of votes cast = (820 ÷ x) × 100We can use the formula above to calculate the total number of votes cast as follows:
If Sherry Smith won 82 percent of the total votes cast, then the total number of votes cast would be: Total number of votes cast = (820 ÷ 82) × 100Total number of votes cast = 1000 votes
Therefore, Sherry Smith received 820 votes, and the total number of votes cast was 1000.
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The track below has two straight lengths and two curved ends. What is the distance around the track to the nearest tenth of a meter?
The Distance around the track is 400.4 meters
In order to determine the distance around a track with two straight sections and two curved ends,
we must first determine the lengths of each section.
Let us consider the given diagram.The distance of the straight section can be determined by adding the length of two opposite sides together. Let us assume that each side of the straight section measures 50 meters. Thus, the total length of the straight section is:50m + 50m = 100mTo calculate the length of the curved sections, we must first determine the radius of each section.
This can be done by dividing the diameter by 2, since the diameter is not given,
we can divide the total length of each curved section by pi (3.14) and then divide the answer by 2 to get the radius of each section.
Let's say the total length of each curved section is 150 meters, therefore, the radius is:150m / 3.14 / 2 = 23.89m (rounded to the nearest hundredth)
Therefore, the circumference of each curved section is:2πr = 2 x 3.14 x 23.89 = 150.18m (rounded to the nearest hundredth)
So, the total distance around the track is:100m + 150.18m + 150.18m = 400.36 meters (rounded to the nearest tenth).
Therefore, the distance around the track is 400.4 meters (rounded to the nearest tenth).
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The point A (p, -2) is mirrored in the point B (6,-q). The image is A'(4, -8). What is p and q?
Answer:
p =4
q = -2
Step-by-step explanation:
To mirror is to reflect. See the picture
Show your work please it’s due Tuesday please
let's convert all mixed fractions to improper fractions, then add them up.
[tex]\stackrel{mixed}{2\frac{1}{10}}\implies \cfrac{2\cdot 10+1}{10}\implies \stackrel{improper}{\cfrac{21}{10}}~\hfill \stackrel{mixed}{1\frac{2}{7}} \implies \cfrac{1\cdot 7+2}{7} \implies \stackrel{improper}{\cfrac{9}{7}} \\\\\\ \stackrel{mixed}{4\frac{9}{10}}\implies \cfrac{4\cdot 10+9}{10}\implies \stackrel{improper}{\cfrac{49}{10}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{21}{10}+\left(\cfrac{9}{7}+\cfrac{49}{10} \right)\implies \cfrac{21}{10}+\left(\cfrac{(10)9~~ + ~~(7)49}{\underset{\textit{using this LCD}}{70}} \right)\implies \cfrac{21}{10}+\left(\cfrac{90+343}{70} \right) \\\\\\ \cfrac{21}{10}+\left(\cfrac{433}{70} \right)\implies \cfrac{21}{10}+\cfrac{433}{70}\implies \cfrac{(7)21~~ + ~~(1)433}{\underset{\textit{using this LCD}}{70}}\implies \cfrac{147+433}{70} \\\\\\ \cfrac{580}{70}\implies \cfrac{58}{7}\implies 8\frac{2}{7}[/tex]
Step-by-step explanation:
[tex]2 \frac{1}{10} + (1 \frac{2}{7} + 4 \frac{9}{10} )[/tex]
[tex]2 \frac{1}{10} = \frac{21}{10} [/tex]
[tex]1 \frac{2}{7} = \frac{9}{7} [/tex]
[tex]4 \frac{9}{10} = \frac{49}{10} [/tex]
[tex] \frac{21}{10} + ( \frac{9}{7} + \frac{49}{10} )[/tex]
[tex]( \frac{9}{7} + \frac{49}{10} ) = \frac{90 + 343}{70} = \frac{433}{70} [/tex]
[tex] \frac{21}{10} + \frac{433}{70} = \frac{147 + 433}{70} = \frac{580}{70} = 8 \frac{2}{7} [/tex]
Solve the following system of equations with the substitution method:
y=3/5x-15
y=-3/4x+12
Answer:
x = 20, y = -3
Step-by-step explanation:
Set both equations equal to each other
[tex]\displaystyle y=\frac{3}{5}x-15\\\\y=-\frac{3}{4}x+12\\\\\\\\\frac{3}{5}x-15=-\frac{3}{4}x+12\\\\\frac{12}{20}x-15=-\frac{15}{20}x+12\\\\\frac{27}{20}x-15=12\\\\\frac{27}{20}x=27\\\\x=20\\\\y=\frac{3}{5}x-15\\\\y=\frac{3}{5}(20)-15\\\\y=\frac{60}{5}-15\\\\y=12-15\\\\y=-3[/tex]
Given the following definitions: U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7} How many elements are in A' ∩ B' ? Your Answer:
[tex]A'=\{3,6,7\}\\B'=\{2,4,6\}\\A'\cap B'=\{6\}[/tex]
Therefore, [tex]n(A'\cap B')=1[/tex].
Answer:
1 element
Step-by-step explanation:
A' means not A and B' means not B
∩ means both
so now we have how many elements are not in A and not in B
A has 1,2,4,5 so not A will be 3,6,7
B has 1,3,5,7 so not B will be 2,4,6
now we look at what not A and not B have together and that is 1 element {6}
find the equation of the line. the line passes through the points (5, 2) and (- 4, - 4)
to get the equation of any straight line, we simply need two points off of it.
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-4}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{5}}} \implies \cfrac{ -6 }{ -9 } \implies \cfrac{2}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{5}) \\\\\\ y-2=\cfrac{2}{3}x-\cfrac{10}{3}\implies y=\cfrac{2}{3}x-\cfrac{10}{3}+2\implies {\Large \begin{array}{llll} y=\cfrac{2}{3}x-\cfrac{4}{3} \end{array}}[/tex]
Triangles DEF and D'E'F' are shown on the coordinate plane below: H F D D' 2 -8-7--5-4-3-2-1 1 2 3 4 5 6 7 8 T 20 F CO What rotation was applied to triangle DEF to create triangle D'E'F'?
