By analytic geometry, the equation of the line y = - (1 / 12) · x + 11 is perpendicular to the line y = 12 · x + 3.
How to derive the equation of a line perpendicular to another line
In accordance with analytic geometry, lines are described by algebraic equations of the form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - InterceptThe relationship between the slopes of two perpendicular lines:
m · m' = - 1
First, write the original line:
y = 12 · x + 3
Second, write the slope and the intercept of the original line:
m = 12, b = 3
Third, the slope and the intercept of the perpendicular line:
m = - 1 / 12, b = 11
Fourth, write the equation of the perpendicular line:
y = - (1 / 12) · x + 11
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The technician at the store worked on the computer for 5.5 hours and charged him $109 for parts. The total was $576.50. What was the cost of labor, per hour?
Answer:
$85.00
Step-by-step explanation:
Let's first subtract the cost of the parts from the total to find the cost of the labor:
Cost of labor = Total cost - Cost of parts
Cost of labor = $576.50 - $109
Cost of labor = $467.50
We know that the technician worked for 5.5 hours, so we can find the cost of labor per hour by dividing the cost of labor by the number of hours:
Cost of labor per hour = Cost of labor / Number of hours
Cost of labor per hour = $467.50 / 5.5
Cost of labor per hour = $85
Therefore, the cost of labor per hour is $85.
Please help me with this question
The graph of the function is added as an attachment
How to determine the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
g(x) = 6, -7 < x ≤ -2
2, -2 < x ≤ 3
-2, 3 < x ≤ 8
The above is a piecewise function that has three linear functions, and three domains
Using the above as a guide, we have the following:
We plot each function in each domain
See attachment for the graph of the function
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simplify:(-8+35)+|-16+4| a.15 b.31 c.39d.55
c. 39
Step-by-step explanation:
the answer is 39
Explain the distinguishing feature of the distance between the foci and a point on the ellipse
The distinguishing feature of the distance between the foci and a point on the ellipse is that it is constant for all points on the ellipse.
What is an Ellipse?
In mathematics, an ellipse is a closed curve that is symmetrical about two perpendicular lines, called the major and minor axes.
The distinguishing feature of the distance between the foci and a point on the ellipse is that it is constant for all points on the ellipse. This distance is known as the focal length or eccentricity, and it is a measure of how much the ellipse deviates from a perfect circle. The sum of the distances from any point on the ellipse to the two foci is always equal to this constant distance, which can be calculated using the equation c² = a² - b², where c is the distance between the foci, and a and b are the lengths of the major and minor axes of the ellipse, respectively.
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Answer:
Step-by-step explanation:
The sum of the distances between the foci and any point on an ellipse is a constant sum. This sum is equal to the length of the major axis.
An ellipse is a set of all points in a plane so that the sum of the distances from two fixed points, called the foci, is constant. d1 + d2 = 2a = constant. An ellipse is what we commonly call an oval and looks like a squashed or flattened circle. In fact, a circle is a special kind of ellipse where the foci are located at the center of the circle. Two fixed points on the interior of an ellipse are given by (0, c) and (0, -c) for an ellipse with a vertical orientation and by (c, 0) and (-c, 0) for an ellipse with a horizontal orientation. The larger denominator is the major axis; therefore, if the larger denominator is under the x2, the ellipse will have a horizontal orientation. If the larger denominator is under the y2, the ellipse will be oriented vertically. Because both the vertices and foci lie on the major axis, they will both have the same y-coordinate (if the major axis is horizontal) or the same x-coordinate (if the major axis is vertical).
alex runs 5 miles in 40 minutes. if alex runs at the same rate how many miles can ge run in 120 minutes
Answer:
15 miles in 120 minutes
Step-by-step explanation:
We can start by using the unit rate of Alex's running speed:
5 miles / 40 minutes = 0.125 miles per minute
This means that Alex runs at a speed of 0.125 miles per minute.
To find out how many miles he can run in 120 minutes, we can multiply his speed by the number of minutes:
0.125 miles/minute × 120 minutes = 15 miles
Therefore, if Alex runs at the same rate, he can run 15 miles in 120 minutes.
how many ounces are there in 4 1
_
2 pounds show your work
Answer:
64 Ounces
Step-by-step explanation:
There are 64 ounces in 4 1/2.
4 1/2 = 4.5
4.5 x 16 = 72
72 ounces - 8 ounces = 64 ounces
Answer:64
Step-by-step explanation:
A fish and wildlife conservation release three bald eagles that have been rehabilitated. Before release, they measure the wingspan (in feet) and weight (in pounds) of each eagle.
The mean of the wingspans is 6 1/4 feet, the median is 6 feet, and the range is 1 3/4 feet.
The mean of the weights is 12.75 pounds, the media. is 12.75 pounds and the range is 5 pounds
a. What are the wingspan of the 3 bald eagles?
b. What are the weights of the 3 bald eagles?
Answer:
a. Since we know the mean and median of the wingspans, we can assume that the data is approximately normally distributed. We also know the range, which is the difference between the maximum and minimum values. From this information, we can set up two equations:
Mean = (Wingspan1 + Wingspan2 + Wingspan3)/3 = 6 1/4
Median = 6
We can use the second equation to eliminate one of the variables. If the median is 6, then the middle value must be 6 as well. Let's assume that Wingspan2 = 6. Then we have:
(Wingspan1 + 6 + Wingspan3)/3 = 6 1/4
Multiplying both sides by 3 and simplifying:
Wingspan1 + Wingspan3 = 18 3/4
We also know that the range is 1 3/4, so:
Wingspan3 - Wingspan1 = 1 3/4
Solving for Wingspan3 in terms of Wingspan1:
Wingspan3 = Wingspan1 + 1 3/4
Substituting this into the previous equation:
Wingspan1 + (Wingspan1 + 1 3/4) = 18 3/4
2Wingspan1 + 1 3/4 = 18 3/4
2Wingspan1 = 17
Wingspan1 = 8 1/2
Therefore, Wingspan3 = 10 1/4. So the three bald eagles have wingspans of 8 1/2 feet, 6 feet, and 10 1/4 feet.
b. Since the mean and median of the weights are the same, we can assume that the data is exactly normally distributed. We also know the range, which is the difference between the maximum and minimum values. From this information, we can set up two equations:
Mean = (Weight1 + Weight2 + Weight3)/3 = 12.75
Median = 12.75
We can use the second equation to eliminate one of the variables. If the median is 12.75, then the middle value must be 12.75 as well. Let's assume that Weight2 = 12.75. Then we have:
(Weight1 + 12.75 + Weight3)/3 = 12.75
Multiplying both sides by 3 and simplifying:
Weight1 + Weight3 = 38.25
We also know that the range is 5 pounds, so:
Weight3 - Weight1 = 5
Solving for Weight3 in terms of Weight1:
Weight3 = Weight1 + 5
Substituting this into the previous equation:
Weight1 + (Weight1 + 5) = 38.25
2Weight1 + 5 = 38.25
2Weight1 = 33.25
Weight1 = 16.625
Therefore, Weight3 = 21.625. So the three bald eagles have weights of 16.625 pounds, 12.75 pounds, and 21.625 pounds.
A savings account of $2500 earned $225 simple interest in 3 years. Find the
interest rate.
Answer:
Results
Interest Rate -61.911%
Total of 36 Monthly Payment of $8,100.00
Total Interest Paid $-16,900.00
Step-by-step explanation:
Answer:R= 3%/year
Step-by-step explanation:
r = 225 / (2500 x 3) = 0.03
r= 0.03
converting r decimal to a percentage
R = 0.03 * 100 = 3%/year
The interest rate required to accumulate simple interest of $225.00 from a principle of $2,500.00 over 3 years is 3% per year.
if a/5=60/4 what is the value of a
Answer:
a = 75
Step-by-step explanation:
f(x)=−5x3−4x2+8x and g(x)=−4x2+8, find (f−g)(x) and (f−g)(−2).
Answer:
(f-g)(x) = -5x^3 + 8x - 8.
(f-g)(-2) = 16.
Step-by-step explanation:
To find (f-g)(x), we need to subtract g(x) from f(x) and simplify:
(f-g)(x) = f(x) - g(x)
= (-5x^3 - 4x^2 + 8x) - (-4x^2 + 8)
= -5x^3 - 4x^2 + 8x + 4x^2 - 8
= -5x^3 + 8x - 8
Therefore, (f-g)(x) = -5x^3 + 8x - 8.
To find (f-g)(-2), we substitute x = -2 into the expression we just found:
(f-g)(-2) = -5(-2)^3 + 8(-2) - 8
= -5(-8) - 16 - 8
= 40 - 24
= 16
Therefore, (f-g)(-2) = 16.
Helpppp I need somthing quick question #4 pls or any of them
Answer:
4) No, It is not a right triangle
Step-by-step explanation:
12 is the hypotenuse which is the longest side of the triangle
6² + 8² = 12² （Pythagoras Theorem）
36 + 64 ≠ 144
Hence it is not a right triangle
A marine biologist was interested in seeing the relationship between a manatee's weight and height. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
The correct answer is a scatter plot, because it would show the association or relationship between two variables.
What is a scatter plot?A scatter plot is a graph that displays values of two variables on two axes. It is used to show the relationship between the two variables and how one variable affects the other. It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram. The points are plotted on a graph and can be used to identify patterns and trends in the data.
A scatter plot can be used to display the relationship between two variables, such as the weight and height of a manatee. The points on the scatter plot would represent each manatee's weight and height, and the pattern of the points can be used to see the overall relationship between the two variables. A line graph, on the other hand, is used to show how a variable changes over time between each data point given, and would not be suitable for this context as the data collected is not related to time.
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Find the value of the sphare
Answer:
[tex]2304[/tex][tex]\pi[/tex]
Step-by-step explanation:
V = [tex]\frac{4}{3} \pi r^{3}[/tex]
V = [tex]\frac{4}{3} *\pi * 12*12*12[/tex]
Use 3 to divide one of the 12 which will be equal to 4
V = [tex]4 *\pi *4*12*12[/tex]
V = [tex]2304\pi[/tex]
A marketing specialist at a large bank analyzes global commercial and residential real estate property indexes.
What inference can be drawn from these graphics?
A person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia.
The majority of individuals who purchased commercial real estate in the UK in 2004 and sold it in 2008 most likely suffered a huge loss.
If the trends shown in the graphics continued to the present day, a couple from the US who moves to France should expect to pay more for a similar home there.
Based on the trends shown, it is probable that since 2010 commercial real estate prices have increased in all countries except the UK, US, and Australia.
According to the graphs, the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia (option A).
How to select a suitable conclusion to the graphics?To select an appropriate conclusion that matches the information in the graphs we must carefully analyze the information in the graphs. Additionally, we can read each of the options and check them with the trends shown in the graphs.
In accordance with the above procedure, we can infer that the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia because the Residential real estate graph shows that In 2010 housing was more expensive in Australia than in Spain.
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14
20
K
22.4
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T
32
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Similar By:
S
Determine if the triangles are similar. If similar.state how and complete the similarity statement
Answer:
triangles, we can determine if these triangles can be proven similar by using the SSS Similarity ... use AA Similarity to prove the triangles are similar.
round to the nearest tenth solve for x, proofs needed
Using the Pythagorean theorem we can see that x = 9.3
How to find the value of x?Think of a right triangle with a hypotenuse of 16, a cathetus of 18 - 5 =13, and the other cathetus is x (we are ignoring the right part of the figure, only look at the triangle in the left)
Then we can use the Pythagorean theorem (the sum of the squares of the legs is equal to the square of the hypotenuse) to find the value of x.
x = √(16² - 13²) = 9.3
That is the value of x.
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x2/3 is the same as x^2/x^3
Answer:
Step-by-step explanation: true
Find the derivative of y=x^4sec(x^9)
Using the product rule and chain rule, we can find the derivative of y with respect to x as follows:
y = x^4sec(x^9)
y' = (4x^3)(sec(x^9)) + (x^4)(sec(x^9))(d/dx(tan(x^9)))
We can simplify the derivative using the identity d/dx(tan(u)) = sec^2(u)(du/dx), where u = x^9:
y' = (4x^3)(sec(x^9)) + (x^4)(sec(x^9))(sec^2(x^9))(9x^8)
Simplifying further, we get:
y' = 4x^3sec(x^9) + 9x^12sec(x^9)
Therefore, the derivative of y with respect to x is 4x^3sec(x^9) + 9x^12sec(x^9).
Jimmy cuts grass in the summertime to save money for college. This week, he was paid $50
on Monday, $70 on Tuesday, $25 on Wednesday, $45 on Thursday, and $50 on Friday. What
is the average amount that Jimmy was paid for each work day this week?
$45
A.
B. $48
C. $50
D. $70
Answer:
B. $48
Step-by-step explanation:
Average=sum of the numbers÷number of numbers you added
Average will now be $50+$70+$25+$45+$50= $240÷5= $48
If you were to reflect the coordinates (4,6), (12,2), and (-1,0) about the y-axis, what would
then be your new coordinates?
Answer:
Step-by-step explanation:
When reflecting coordinates about the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same.
So, for the point (4, 6), the new coordinates after reflection about the y-axis would be (-4, 6).
For the point (12, 2), the new coordinates would be (-12, 2).
For the point (-1, 0), the new coordinates would be (1, 0).
Therefore, the new coordinates after reflecting these points about the y-axis are (-4, 6), (-12, 2), and (1, 0).
Carlos evaluated 20-(2x6)+8 divided by 4 and got 29. Is his answer correct? if not, explain what Carlos did wrong and find the correct answer.
10 is the appropriate response to the expression.
Carlos gave the erroneous response of 29.
Carlos made the error of doing addition and subtraction operations prior to multiplication and division operations, as is evident.
What is an expression?Every mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Everything with a variable value is anything whose value changes over time. Typically, alphabetical letters like a, b, c, m, n, p, x, y, and z are used to denote expression variables. A combination of several variables and integers can be used to create a variety of expressions.
From the question:
We must assess the expression utilizing the PEMDAS order of operations and contrast the results:
20 - (2x6) + 8 ÷ 4
= 20 - 12 + 2
= 10
Carlos gave the erroneous response of 29. It seems that Carlos determined the expression to be: 20 - (2x6) + 8 ÷ 4 = 29
Carlos made the error of doing addition and subtraction operations prior to multiplication and division operations, as is evident. Multiplication and division must be done before addition and subtraction, per the PEMDAS order of operations.
Carlos ought to have determined the expression to be:
20 - (2x6) + 8 ÷ 4 = 20 - 12 + 2 = 10
Hence, 10 rather than 29 is the appropriate response to the expression.
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Wireless phone company A charges $20 per
month plus $0.12 per minute. Wireless phone
company B charges $50 per month plus $0.06
per minute. For how many minutes of calls will
the monthly bills be the same?
(A) 80 minutes
(B) 100 minutes
(C) 160 minutes
(D) 250 minutes
(E) 500 minutes
Answer:
E
Step-by-step explanation:
For Company A, the monthly cost y in dollars can be represented by:
y = 0.12x + 20
where x is the number of minutes used.
For Company B, the monthly cost y in dollars can be represented by:
y = 0.06x + 50
where x is the number of minutes used.
To find the number of minutes of calls where the monthly bills will be the same, we need to set the two equations equal to each other and solve for x:
0.12x + 20 = 0.06x + 50
0.06x = 30
x = 500
Therefore, the monthly bills will be the same for both companies when the number of minutes used is 500.
Answer: (E) 500 minutes
If f(x) = 2x(1-x)^2, then f(1) =
(A) 0
(B) 2
(c) 4
(D) 6
(E) 8
Answer:
0
Step-by-step explanation:
2(1)*(1-(1))²=0
plug in 0 for everywhere you see x
kim and courtney share a 20 ounce box of cereal. By the end of the week kim has eat 2/5 of the box and courtney has eaten 1/10 of the box of cereal what fraction of the box is left
Answer: 1/2
Step-by-step explanation:
Kim ate 2/5 which is also equal to 4/10 and Courtney has eaten 1/10
4/10 + 1/10 = 5/10 = 1/2
The state of Colorado is 4 centimeters long and 3 centimeters wide on a map. A cartographer wants to use a scale factor of 2.5 to enlarge the map. What is the area of the enlarged map?
12 cm2
30 cm2
35 cm2
75 cm2
The area of the enlarged map is 75 cm². Answer: (D) 75 cm².
What is scale ?
Scale refers to the ratio of distances or sizes on a map or drawing to the actual distances or sizes of the objects they represent in the real world. It is often expressed as a ratio, such as 1:10,000 or 1/4 inch = 1 foot, and is used to create maps and drawings that accurately represent real-world objects and distances. Scales can be used to enlarge or reduce the size of a map or drawing, making it easier to view and work with.
The original area of Colorado on the map is:
Area = length x width = 4 cm x 3 cm = 12 cm²
To enlarge the map with a scale factor of 2.5, we need to multiply the length and width by 2.5:
New length = 4 cm x 2.5 = 10 cm
New width = 3 cm x 2.5 = 7.5 cm
The area of the enlarged map is:
New area = new length x new width = 10 cm x 7.5 cm = 75 cm²
Therefore, the area of the enlarged map is 75 cm². Answer: (D) 75 cm².
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calculate 7 x 3 1/4 pleaseeee help
Answer:
7 x 3 1/4 = 91/4 or 22 3/4
Step-by-step explanation:
To calculate 7 x 3 1/4, we can first convert the mixed number 3 1/4 to an improper fraction:
3 1/4 = (3 x 4 + 1) / 4 = 13/4
Then, we can multiply 7 by 13/4 as follows:
7 x 13/4 = (7 x 13) / 4 = 91/4
Therefore, 7 x 3 1/4 = 91/4 or 22 3/4 (if we want to express the answer as a mixed number).
Answer:
22 3/4
Step-by-step explanation:
There are plenty of ways of solving this question. The improper fraction of 3 1/4 is 13/4.
7 · 3 1/4
[tex]\frac{7}{1}[/tex] x [tex]\frac{13}{4}[/tex] = [tex]\frac{91}{4}[/tex]
[tex]\frac{91}{4}[/tex] = 22.75 = 22 3/4
Help please and please explain how to solve this
Find the equivalent expression using the
same bases.
1080
Clear all
(21.15)⁹
Enter the correct answer.
000
DONE
(21)⁹ . (15)⁹ is the equivalent expression using the same bases.
What are power and exponent?
One can represent extremely big or extremely small numbers in a more straightforward fashion by using exponents and powers. For instance, we can write 3 x 3 x 3 x 3 as 34, where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner.
It is claimed that the entire statement 34 possesses power. How many times you should multiply a number depends on its power. Other names for powers include exponents and indices.
using (a.b )ⁿ = (a)ⁿ . (b)ⁿ
( 21.15)⁹ = (21)⁹ . (15)⁹
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suppose A and B are dependent events. If P(A)= 0.4 and P(B)= 0.9, what is P(AnB)
The value of the probability P(A n B) is 0.36
How to determine the value of the probabilityFrom the question, we have the following parameters that can be used in our computation:
A and B are dependent events.
P(A)= 0.4 and P(B)= 0.9
Using the above as a guide, we have the following:
P(A n B) = P(A) * P(B)
Substitute the known values in the above equation, so, we have the following representation
P(A n B) = 0.4 * 0.9
Evaluate
P(A n B) = 0.36
Hence, the solution is 0.36
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A basic set of drawing pencils costs $8.98. A professional set of drawing pencils costs $27.49. How much more does the professional set cost than the basic set?