The area of the cross-section is 16 sq. cm. Thus, option C is the correct answer.
Vertices sides = 2, 3, 6, and 7
Divide part face = parallel to the face of vertices
It is given that a square face is present in the middle of the cube. The area of the cross-section of the cube results from the plane and cube intersection.
To find the distance between the square face of the cube and the length of the side:
distance = [tex]\sqrt{[(x^{2} - x1)^2 + (y^{2} - y1)^2 + (z^{2} - z1)^2]}[/tex]
we can use the coordinates of any two adjacent sides to find the distance.
distance = [tex]\sqrt{[(3-2)^2 + (3-2)^2 + (3-1)^2] }[/tex]
distance = [tex]\sqrt{11}[/tex]
To calculate the area of the face of the cube:
area = [tex]side^{2}[/tex]
area = [tex]\sqrt{(11)^2}[/tex]
area = 11
The area of the cross-section can be estimated as:
area = (1/2) x 11 x 4) + 5 vertices of plane
area = 16 sq. cm
Therefore we can infer that the area of the cross-section is 16 sq. cm
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What is the product of the expression, 5x(x2)? (1 point)
25x2
10x
5x3
5x2
The product of the expression 5x(x²) is 5x³.
1. Write down the given expression: 5x(x²)
2. Apply the distributive property, which states that a(b + c) = ab + ac. In this case, we have a single term inside the parentheses, so the expression becomes: 5x * x²
3. Multiply the coefficients (numbers) together: 5 * 1 = 5
4. Multiply the variables together, which means adding the exponents since they have the same base (x): x¹* x² = x⁽¹⁺²⁾ = x³
5. Combine the result from steps 3 and 4: 5x³
The product of the expression 5x(x²) can be found by multiplying the coefficients (numbers) and adding the exponents of the variables (letters). In this case, we have 5 times x times x squared.
5 times x equals 5x, and x squared means x times x, so we can rewrite the expression as:
5x(x²) = 5x(x*x) = 5x³
So, the product of the expression 5x(x²) is 5x³.
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Select all of the following that represent the part of the grid that is shaded.
A ten-by-ten grid has 7 columns shaded.
A.
70
100
B.
7
10
C.
70
10
D.
0. 07
E.
0. 7
A ten-by-ten grid has 7 columns shaded. All of the following that represent the part of the grid that is shaded are : The correct answer is (A) 70 and (B) 7.
The information given in the problem tells us that a ten-by-ten grid has 7 columns shaded. Since there are a total of 10 columns in the grid, this means that 7/10 of the columns are shaded.
To express this as a percentage, we can divide 7 by 10 and multiply by 100:
(7/10) x 100 = 70%
Therefore, 70 represents the percentage of columns that are shaded in the grid. Option (A) is correct.
Alternatively, we can express the same proportion as a decimal by dividing 7 by 10:
7/10 = 0.7
Therefore, 0.7 represents the proportion of columns that are shaded in the grid. Option (E) is incorrect because it shows 0.7 as a fraction instead of a decimal.
Option (B) is also correct because it correctly identifies the number of shaded columns as 7. Option (C) is incorrect because it includes both the percentage and the number of shaded columns, which is redundant. Option (D) is incorrect because it shows the proportion of shaded columns as a decimal with an extra zero.
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I Need help with this math problem
The value of angle x = 114°.
How to find angle x?From the figure, it is clear that The interior angle of a triangle is 39°, by the law of opposite angle.
The sum of the interior angle of a triangle is 180°
37° + 39° + ∠unknown1 = 180°
∠unkonown1 = 180° - 37° - 39°
∠unknown1 = 104°
The sum of the exterior angle and the interior angle is 180°.
∠unknown2+ ∠unknown 1= 180°
∠unknown2 = 180° - 104°
∠unknown2 = 76°
The sum of the interior angle of a triangle is 180°
∠unknown3 + ∠unknown2 + 38 = 180
∠unknown3 + 76° + 38 = 180
∠unknown3= 66°
The sum of the exterior angle and the interior angle is 180°.
∠X + <unknown3 = 180°
∠X = 180° - 66°
∠X = 114°
The value of the angle x is 114°.
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In the last 215 days, builders have completed 700 m2 of the alligator habitat that will eventually be 1,200 m2. How much longer will it take to complete the alligator habitat?
In the last 215 days, builders have completed 700 m2 of the alligator habitat that will eventually be 1,200 m2.
It will take approximately 153 days to complete the remaining part of the alligator habitat.
Determine how much longer it will take to complete the alligator habitat, first, we need to find the rate at which the builders are working.
Calculate the work rate
The builders have completed 700 m2 of the 1,200 m2 alligator habitat in 215 days.
Work rate = (completed work) / (number of days)
Work rate = 700 m2 / 215 days = 3.26 m2/day (approximately)
Calculate the remaining work
The total area of the alligator habitat is 1,200 m2, and 700 m2 has been completed.
Remaining work = Total area - Completed work
Remaining work = 1,200 m2 - 700 m2 = 500 m2
Calculate the time to complete the remaining work
Time to complete = (remaining work) / (work rate)
Time to complete = 500 m2 / 3.26 m2/day ≈ 153.37 days
It will take approximately 153 days to complete the remaining part of the alligator habitat.
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It will take approximately 394 more days to complete the alligator habitat.
We can start by finding the proportion of the habitat that has already been completed:
proportion completed = 700 m^2 / 1200 m^2 = 0.5833
This means that there is still 1 - 0.5833 = 0.4167 (or 41.67%) of the habitat left to complete.
Next, we can use a proportion to find out how long it will take to complete the remaining 41.67% of the habitat:
215 days / 0.5833 = x days / 0.4167
Solving for x, we get:
x = 215 days * 0.4167 / 0.5833 ≈ 153 days
Therefore, the total time it will take to complete the alligator habitat is approximately 215 + 153 = 368 days, or about 394 more days from the start.
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Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options
The quadratic equation where the squares had been completed is:
(x + 2)² = 27/5
How to complete squares?Remember the perfect square trinomial:
(a + b)² = a² + 2ab + b²
now we have the quadratic equation:
5x² + 20x - 7 = 0
If we divide it all by 5, we will get.
x² + 4x - 7/5 = 0
Now we can rewrite this as:
(x² + 2*2*x ) - 7/5 = 0
Now we need to add 2² in both sides, we will get:
(x² + 2*2x + 2²) - 7/5 = 2²
(x + 2)² = 4 + 7/5
(x + 2)² = 27/5
There the square is completed.
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Use the figure below to determine the value of the variable and the
lengths of the requested segments. Your answers may be exact or
rounded to the nearest hundredth. The figure may not be to scale.
Using tangents theorem, we can find the value of the missing length,
n = 18.7units.
Define a tangent?"To touch" is how the word "tangent" is defined. The same idea is conveyed by the Latin word "tangere". A tangent, in general, is a line that, while never entering the circle, precisely touches it at one point on its circumference. A circle has a number of tangents. They make a straight angle with the radius.
Here in the diagram,
We can see that as per the central angle and tangent theorem,
AB/BC = ED/DC
⇒ 17/10 = n/11
Cross multiplying:
⇒ 17 × 11 = n × 10
⇒ 10n = 187
⇒ n = 187/10
⇒ n = 18.7
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Show that the two straight lines through the origin which make an angle 45° with the line px + qy + r = 0 are given by the equation (p²-q)(x² - y²) + 4pqxy = 0.
The equation of the two straight lines through the origin making an angle of 45° with the line px + qy + r = 0 is (p²-q)(x² - y²) + 4pqxy = 0.
How to show the equation for the two straight lines passing through the origin and making a 45° angle with the line px + qy + r = 0?To prove that the equation of the two straight lines through the origin, making an angle of 45° with the line px + qy + r = 0, is given by (p²-q)(x² - y²) + 4pqxy = 0, we can use the concept of slopes and trigonometric identities.
Let's consider the line px + qy + r = 0. The slope of this line is given by -p/q.
Now, the lines making an angle of 45° with this line will have slopes equal to tan(45°), which is 1.
Using the formula for the tangent of the sum of angles, we have:
tan(45°) = (m - (-p/q))/(1 + m(-p/q)), where m represents the slope of one of the lines.
Simplifying the equation, we get:
1 = (mq + p)/(q - mp)
Cross-multiplying and rearranging the terms, we obtain:
(p² - q)(m² - 1) + 2pqm = 0
Since these lines pass through the origin (0,0), we can replace m with y/x. Substituting y/x for m in the equation above, we get:
(p² - q)(x² - y²) + 2pqxy = 0
Further simplifying the equation, we arrive at:
(p² - q)(x² - y²) + 4pqxy = 0
Hence, we have proven that the equation of the two straight lines through the origin, making an angle of 45° with the line px + qy + r = 0, is given by (p²-q)(x² - y²) + 4pqxy = 0.
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help please ill give brainliest
In the given circle, measure of angle m is 44° and the measure of angle n is 39°. Thus, the value of m is 44 and the value of n is 39
Circle Geometry: Calculating the values of m and nFrom the question, we are to determine the values of m and n in the given circle
From one of the circle theorems, we have that
The angles at the circumference subtended by the same arc are equal. That is, angles in the same segment are equal.
In the given diagram,
Angle m is in the same segment as the angle that measures 44°
Since angles in the same segment are equal,
Measure of angle m = 44°
Also,
Angle n is in the same segment as the angle that measures 39°
Since angles in the same segment are equal,
Measure of angle n = 39°
Hence,
m ∠m = 44°
m ∠n = 39°
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12
Find the first and second derivatives. S = 15 + 344 - 1 15 S' = S'' =
The first derivative of S is S' = 1/15.
The second derivative of S is S'' = 0.
To find the first derivative (S'):
Starting with the given equation S = 15 + 344 - 1 15, we can simplify it to S = 344 + 15.
We can take the derivative of each term separately since they are added together.
The derivative of a constant (15 and 344) is always 0, so we only need to take the derivative of 1/15.
S' = d/dx (344 + 15)
= d/dx (359)
= 0 + 0 + (d/dx (1/15))
= 1/15
Therefore, the first derivative of S is S' = 1/15.
To find the second derivative (S''):
We need to take the derivative of the first derivative (S').
Since the derivative of a constant is always 0,
we only need to take the derivative of 1/15.
S'' = d/dx (S')
= d/dx (1/15)
= 0
Therefore, the second derivative of S is S'' = 0.
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A survey was taken by students in 6th, 7th, and 8th grade to determine how many first cousins they have. The results are shown in the box plots below. Use these box plots to answer the questions.
Suppose that in 1682, a man bought a diamond for $32. Suppose that the man had instead put the $32 in the bank at 3% interest compounded continuously. What would that $32 have been worth in 2003? In 2003, the $32 would have been worth $ (Do not round until the final answer. Then round to the nearest dollar as needed.)
If a man bought a diamond for $32 in 1682 and the man had instead put the $32 in the bank at 3% interest compounded continuously, then the value of the diamond in 2003 would be $554,311.
The given problem is related to exponential growth. In this problem, the continuous compounding formula will be used to find the value of $32 in 2003.
The formula for continuous compounding is given by:
A = Pert Where,
P is the principal amount,
r is the annual interest rate,
e is the Euler's number which is approximately 2.71828, and
t is the time in years.
Using the formula, we get:
A = 32e^(0.03 x 321)
A = 32e^9.63
A = 32 x 17322.23
A = $ 554311.36
Thus, $32 invested at 3% compounded continuously from 1682 to 2003 would be worth $554,311.
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Find the solution and also verify your answer , under root 12 x 12 x - 4 is equals under root 4 x + 8
The solution to the given equation is x = -3/4 or x = 1.
What values of x satisfy the equation √(12x² - 4) = √(4x + 8)?In order to find the solution, we start by squaring both sides of the equation to eliminate the square roots:
12x² - 4 = 4x + 8
Next, we simplify the equation by moving all the terms to one side:
12x² - 4x - 12 = 0
Now we can factor the quadratic equation:
4x² - x - 3 = 0
By factoring or using the quadratic formula, we find that the equation can be written as:
(4x + 3)(x - 1) = 0
Setting each factor equal to zero gives us the solutions:
4x + 3 = 0 or x - 1 = 0
Solving for x in each equation yields:
x = -3/4 or x = 1
Therefore, the solution to the given equation is x = -3/4 or x = 1.
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Roxie plans on purchasing a new desktop computer for $1250. Which loan description would result in the smallest monthly payment when she pays the loan back?
12 months at 6. 25% annual simple interest rate
18 months at 6. 75% annual simple interest rate
24 months at 6. 5% annual simple interest rate
30 months at 6. 00% annual simple interest rate
The loan with the smallest monthly payment is the 30-month loan at 6% annual simple interest rate, with a monthly payment of $45.83.
To determine the loan with the smallest monthly payment, we need to calculate the monthly payment for each loan option and compare them.
We can use the formula for monthly payment on a simple interest loan:
monthly payment = (principal + (principal * interest rate * time)) / total number of payments
where:
principal is the amount borrowed (in this case, $1250)interest rate is the annual simple interest rate divided by 12 to get the monthly ratetime is the length of the loan in monthsWe can compute the monthly payments for each loan choice using this formula:
1. 12 Monthly interest rate = 0.0625/12 = 0.00521, monthly payment = (1250 + (1250 * 0.00521 * 12)) / 12 = $107.35
2. 18 months at 6.75%: monthly interest rate = 0.0675/12 = 0.00563, monthly payment = (1250 + (1250 * 0.00563 * 18)) / 18 = $81.96
3. 24 months at 6.5%: monthly interest rate = 0.065/12 = 0.00542, monthly payment = (1250 + (1250 * 0.00542 * 24)) / 24 = $66.14
4. 30 months at 6%: monthly interest rate = 0.06/12 = 0.005, monthly payment = (1250 + (1250 * 0.005 * 30)) / 30 = $45.83
Based on these calculations, the loan with the smallest monthly payment is the 30-month loan at 6% annual simple interest rate, with a monthly payment of $45.83.
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The width of the large size is 9.9 cm and its height is 19.8 cm.
The width of the small size bottle is 4.5 cm.
hcm
h =
4.5 cm
Calculate the height of the small bottle.
19.8 cm
9.9 cm
+
cm
Answer and Explanation:
The height of the small bottle can be calculated using the ratio of the width of the large and small bottles.
Ratio of width = Large bottle width / Small bottle width
Ratio of width = 9.9 cm / 4.5 cm
Ratio of width = 2.2
Therefore, the height of the small bottle can be calculated by multiplying the ratio of width with the height of the large bottle.
Height of small bottle = Ratio of width x Height of large bottle
Height of small bottle = 2.2 x 19.8 cm
Height of small bottle = 43.56 cm
The length of a rectangle is 6 ft longer than its width. if the perimeter of the rectangle is 64 ft, find its length and width
The length of the rectangle is 19 feet and its width is 13 feet.
Let's denote the width of the rectangle by w. Then, according to the problem statement, the length of the rectangle is 6 feet longer, which means it is equal to w + 6.
The perimeter of a rectangle is given by the formula:
perimeter = 2 × length + 2 × width
Substituting the expressions for length and width that we have just found, we get:
64 = 2 × (w + 6) + 2w
Simplifying the right-hand side:
64 = 2w + 12 + 2w
64 = 4w + 12
52 = 4w
w = 13
So the width of the rectangle is 13 feet. Using the expression for the length we found earlier, the length is:
length = w + 6 = 13 + 6 = 19
Therefore, the length of the rectangle is 19 feet and its width is 13 feet.
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HELP!! Which statements describe the end behavior of f(x)?f(x)?
Select two answers.
Answer:
As x approaches ∞, y approaches -∞
As x approaches -2.5, y approaches ∞
Step-by-step explanation:
A portion of an electrical circuit is displayed next. the switches operate independently of each other, and the probability that each relay closes when the switch is thrown is displayed by the switch. what is the probability that current will flow from s to t when the switch is thrown
If you provide me with a specific circuit diagram and the relevant details, I would be happy to help you determine the probability of current flowing from s to t when the switch is thrown.
What is the probability of current flowing from s to t when the switch is thrown?I apologize, but it seems that the circuit diagram you mentioned is not displayed here. Without the circuit diagram, it is not possible for me to provide a specific answer to your question.
However, in general, the probability of current flowing from s to t in an electrical circuit depends on several factors such as the voltage level, the resistance of the circuit components, and the state of the switches. If the switches are all closed, then the probability of current flowing from s to t will depend on the overall resistance of the circuit.
If you provide me with a specific circuit diagram and the relevant details, I would be happy to help you determine the probability of current flowing from s to t when the switch is thrown.
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Ten sixth-grade students reported the hours of sleep they get on nights
before a school day. Their responses are recorded in the dot plot. Looking
at the dot plot, Lin estimated the mean number of hours of sleep to be 8. 5
hours. Noah's estimate was 7. 5 hours. Diego's estimate was 6. 5
hours. Which estimate do you think is best? Solve for the mean to figure out
who was closer. *
Lin
ООО
Noah
Diego
Noah's estimate of 7.5 hours is closest to the actual mean number of hours of sleep reported by the ten sixth-grade students.
We have,
Compare the estimates given by Lin, Noah, and Diego.
Lin's estimate is 8.5 hours.
Noah's estimate is 7.5 hours.
Diego's estimate is 6.5 hours.
The average of these three estimates:
(8.5 + 7.5 + 6.5) / 3
= 22.5 / 3
= 7.5
It appears that Noah's estimate of 7.5 hours is the closest.
Therefore,
Noah's estimate of 7.5 hours is closest to the actual mean number of hours of sleep reported by the ten sixth-grade students.
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The complete question:
Which estimate of the mean number of hours of sleep reported by the ten sixth-grade students is closest to the actual mean: Lin's estimate of 8.5 hours, Noah's estimate of 7.5 hours, or Diego's estimate of 6.5 hours?
do you believe your children will have a higher standard of living than you have? this question was asked of a national sample of american adults with children in time/cnn poll. sixty-three percent answered in the affirmatve, with a margin of error or plys or minus 3%. assume that the true percentage of all american adults who beleive their children with have a hgiehr standard of living is .60
True percentage of all American believes that their children have higher standard of living with confidence interval of 95% is between 60% and 66% .
CI is the confidence interval
Answered in the affirmative = 63%
p is the sample proportion =0.63
z is the critical value from the standard normal distribution at the desired confidence level
Using attached z-score table,
95% confidence level corresponds to z=1.96
n is the sample size
Use the margin of error ,
Calculate a confidence interval for percentage of American adults who believe their children will have a higher standard of living.
A margin of error of plus or minus 3% means ,
95% confident that the true percentage falls within 3% of the sample percentage.
Using the formula for a confidence interval for a population proportion,
CI = p ± z×√(p(1-p)/n)
Plugging in the values, we get,
⇒ CI = 0.63 ± 1.96√(0.63(1-0.63)/n)
Solving for n, we get,
n = (1.96/0.03)^2 × 0.63(1-0.63)
⇒ n = 994.87
Rounding up to the nearest whole number, sample size of at least 995.
⇒ CI = 0.63 ± 1.96√(0.63(1-0.63)/995)
⇒CI = 0.63 ± 0.02999
95% confidence interval for the true percentage is,
⇒CI = 0.63 ± 0.03
⇒CI = (0.60, 0.66)
Therefore, 95% confidence interval that between 60% and 66% of all American adults with children believe that their children will have a higher standard of living.
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Find the line of tangency to the circle defined by (x-3)^2 + (y-7)^2 = 169 at the point (15,2).
first off, let's look at the equation of the circle
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{}{h}~~,~~\underset{}{k})}\qquad \stackrel{radius}{\underset{}{r}} \\\\[-0.35em] ~\dotfill\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})=169\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})=\stackrel{ r }{13^2}[/tex]
so we have a circle centered at (3 , 7) with a radius of 13, Check the picture below.
so the line we want is the line in purple, which is tangential to the circle and therefore perpendicular to the blue line.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the blue line
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{3}}} \implies \cfrac{ -5 }{ 12 } \implies - \cfrac{5 }{ 12 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-5}{12}} ~\hfill \stackrel{reciprocal}{\cfrac{12}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{12}{-5} \implies \cfrac{12}{ 5 }}}[/tex]
so we're really looking for the equation of a line whose slope is 12/5 and it passes through (15 , 2)
[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{12}{5} \\\\\\ \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{12}{5}}(x-\stackrel{x_1}{15}) \\\\\\ y-2=\cfrac{12}{5}x-36\implies {\Large \begin{array}{llll} y=\cfrac{12}{5}x-34 \end{array}}[/tex]
Quadrilateral FGHJ was dilated with the origin as the center of dilation to create quadrilateral F' G′ H′ J′.
Which rule best represents the dilation that was applied to quadrilateral FGHJ to create quadrilateral F' G′ H′ J′?
A. (x, y) à (5/7x, 5/7y)
B. (x, y) à (1. 4x , 1. 4y)
C. (x, y) à (x + 1, y + 2)
D. (x, y) à (x - 2, y + 1)
Which rule best represents the dilation that was applied to quadrilateral FGHJ to create quadrilateral F' G′ H′ J′?
The rule that best represents the dilation that was applied to quadrilateral FGHJ to create quadrilateral F'G'H'J' is option B, which is (x, y) à (1.4x, 1.4y).
What is the dilation rule used to create quadrilateral F'G'H'J' from FGHJ?A dilation is a transformation that changes the size of an object without changing its shape. It is performed by multiplying the coordinates of each point by a scale factor.
In this case, the center of dilation is the origin, which means that the coordinates of each point are multiplied by the same scale factor in both the x and y directions.
The scale factor can be found by comparing the corresponding side lengths of the two quadrilaterals. In this case, the scale factor is 1.4, which means that the lengths of the sides of F'G'H'J' are 1.4 times the lengths of the corresponding sides of FGHJ.
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If one line passes through the points (-3,8) & (1,9), and a perpendicular line passes through the point (-2,4), what is another point that would lie on the 2nd line. Select all that apply.
One point that would lie on the second line is (0,-4). Another possible point on the 2nd line is (0, 12).
To find the equation of the first line, we can use the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. The slope of the line passing through (-3,8) and (1,9) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
m = (9 - 8) / (1 - (-3))
m = 1/4
Using one of the points and the slope, we can find the y-intercept:
8 = (1/4)(-3) + b
b = 9
So the equation of the first line is:
y = (1/4)x + 9
To find the equation of the second line, we need to use the fact that it is perpendicular to the first line. The slopes of perpendicular lines are negative reciprocals, so the slope of the second line is:
m2 = -1/m1 = -1/(1/4) = -4
Using the point-slope form, we can write the equation of the second line:
y - 4 = -4(x + 2)
y - 4 = -4x - 8
y = -4x - 4
To find a point that lies on this line, we can plug in a value for x and solve for y. For example, if we let x = 0, then:
y = -4(0) - 4
y = -4
So the point (0,-4) lies on the second line.
Therefore, another point that would lie on the second line is (0,-4).
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The table displays data collected, in meters, from a track meet.
14
3
624
What is the median of the data collected?
2 19
332
2.5
02
4.5
03
€
To find the median of the data, we first need to arrange the numbers in order from smallest to largest:
3, 14, 624
Since we have an odd number of data points, the median is the middle number. In this case, the median is 14.
Therefore, the median of the data collected is 14 meters.
Consider the initial value problem for function y, y (0) = 4. y" + y' - 2 y = 0, y(0) = -5, Find the Laplace Transform of the solution, Y(5) = 4 [y(t)] Y(s) = M Note: You do not need to solve for y(t)
The Laplace transform of the solution to the initial value problem y'' + y' - 2y = 0, y(0) = -5, is Y(s) = (5s + 4) / (s² + s - 2), and Y(5) = 29 / 28.
To find the Laplace transform of the solution to the initial value problem y'' + y' - 2y = 0, y(0) = -5, we can apply the Laplace transform to both sides of the differential equation and use the initial condition to solve for the Laplace transform of y.
Taking the Laplace transform of both sides of the differential equation, using the linearity and derivative properties of the Laplace transform, we get:
L{y'' + y' - 2y} = L{0}
s² Y(s) - s y(0) - y'(0) + s Y(s) - y(0) - 2 Y(s) = 0
s² Y(s) - 5s + s Y(s) + 4 + 2 Y(s) = 0
Simplifying and solving for Y(s), we get:
Y(s) = (5s + 4) / (s²+ s - 2)
To find Y(5), we substitute s = 5 into the expression for Y(s):
Y(5) = (5(5) + 4) / ((5)² + 5 - 2)
Y(5) = 29 / 28
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Please help with the 2nd one
Answer:
Step-by-step explanation:
1807
After simplifying, which expressions are equivalent? select three options. (3.4a – 1.7b) (2.5a – 3.9b) (2.5a 1.6b) (3.4a 4b) (–3.9b a) (–1.7b 4.9a) –0.4b (6b – 5.9a) 5.9a – 5.6b
(3.4a – 1.7b) and (–1.7b 4.9a) and (5.9a – 5.6b) are equivalent expressions.
Which expressions are equivalent after simplification?
The question presents a list of six expressions. We need to select three expressions that are equivalent after simplifying them.
One of the expressions is (3.4a - 1.7b), and another is (-1.7b + 4.9a). These two expressions can be simplified to 2.4a - 1.7b.
Another expression is (2.5a - 3.9b), and another is (-3.9b + a). These two expressions can be simplified to 3.5a - 3.9b.
The third expression is 5.9a - 5.6b, which cannot be simplified further.
The three expressions that are equivalent after simplifying are (3.4a - 1.7b) and (-1.7b + 4.9a), (2.5a - 3.9b) and (-3.9b + a), and 5.9a - 5.6b.
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Now that you have chosen your mode of transportation, use your choice to answer the questions that follow.
What would the cost of your transportation be if you drove:
a. 10 miles? b. 25 miles? c. 42 miles? d. 68 miles?
Make sure to list your chosen mode of transportation and then answer all parts and show your work
(a) The cost of City Bus for driving 10 miles = $3.
(b) The cost of City Bus for driving 25 miles = $7.5.
(c) The cost of City Bus for driving 42 miles = $12.6.
(d) The cost of City Bus for driving 68 miles = $20.4.
We previously choose City Bus as our mode transport since the per mile cost for City Bus is less.
Let the model for City Bus be f(x) = cx + d, where f(x) is total cost and x is number of miles.
From the table of Taxi we get, f(2) = 0.60; f(4) = 1.20; f(6) = 1.80 and f(8) = 2.40.
So, 2a + b = 0.60 and 4a + b = 1.20
(4a + b) - (2a + b) = 1.20 - 0.60
2a = 0.60
a = 0.60/2 = 0.30
Now, f(8) = 2.40
8*0.30 + b = 2.40
2.40 + b = 2.40
b = 2.40 - 2.40 = 0
So the function rule for City Bus is, f(x) = 0.3x.
(a) Total cost to drive 10 miles is,
f(10) = 0.3*10 = 3
(b) Total cost to drive 25 miles is,
f(25) = 0.3*25 = 7.5
(c) Total cost to drive 42 miles is,
f(42) = 0.3*42 = 12.6
(d) Total cost to drive 68 miles is,
f(68) = 0.3*68 = 20.4
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900,000=x+y+z
79,750=0. 08x+0. 09y+0. 01z
2x=z
Answer:
since 2x = z
replace z with 2x
900000 = x+y+z
900000 = x+y+2x
900000 = 3x+y - eqn (1)
79750= 0.08x +0.09y+0.01z
79750 = 0.08x +0.09y+0.01(2x)
79750 = 0.08x+0.09y+0.02x
79750 = 0.10x +0.09y - eqn(2)
from eqn(1)
900000 = 3x + y
y = 900000-3x - eqn(3)
substitute eqn(3) in eqn(2)
79750 = 0.1x +0.09y
79750=0.1x + 0.09(900000-3x)
79750=0.1x+ 81000 - 0.27x
collect like terms
79750 -81000 = 0.1x-0.27x
-1250 = -0.17x
to find x divide both sides by -0.17
x = -1250/-0.17 ~= 7353
since 2x = z
2*7353 = 14706
in eqn(3)
y = 900000-3x
y= 900000-3(7353)
y = 900000-22059
y = 877941
x =7353,y= 877941,z=14706
(n+3)!/(n+1)! please help immediately
Answer:
(n + 3)(n + 2) or n² + 5n + 6------------------
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n:
n! = n × (n - 2) × (n - 3) × ... × 2 × 1As per above mentioned definition we see that:
(n + 3)! = (n + 3) × (n + 2) × (n + 1)!Hence the quotient of (n + 3)! and (n + 1)! is:
(n + 3)(n + 2) or n² + 5n + 6Solve x∕3 < 5 Question 12 options: A) x < 15 B) x ≥ 15 C) x ≤ 15 D) x > 15
Answer:
A) x < 15
Step-by-step explanation:
You want the solution to x/3 < 5.
InequalityThe steps to solving an inequality are basically identical to the steps for solving an equation. There are a couple of differences:
the direction of the inequality symbol must be respectedmultiplication/division by negative numbers reverses the inequality symbol1-stepIf this were and equation, it would be a "one-step" equation. That step is to multiply both sides by the inverse of the coefficient of x.
The coefficient of x is 1/3. Its inverse is 3. Multiplying both sides by 3, we have ...
3(x/3) < 3(5)
x < 15 . . . . . . . . . simplify
Note that 3 is a positive number, so we leave the inequality symbol pointing the same direction.
__
Additional comment
We can swap the sides of an equation based on the symmetric property of equality:
a = b ⇔ b = a
When we swap the sides of an inequality, we need to preserve the relationship between them. (This is the meaning of "respect the direction of the inequality symbol".)
a < b ⇔ b > a
Besides multiplying and dividing by a negative number, there are other operations that affect the order of values.
-2 < 1 ⇔ 2 > -1 . . . . . multiply by -12 < 3 ⇔ 1/2 > 1/3 . . . . . take the reciprocal (same signs)a < b ⇔ cot⁻¹(a) > cot⁻¹(b) . . . . use function having negative slopeNote that the 1/x function is another one that has negative slope, which is why it reverses the ordering for values with the same sign. (It has no effect on ordering of values with opposite signs.)
