Select the correct answer from each drop-down menu.
Point A is the center of this circle.
The ratio of the lengths of ____ and ____ is 2:1
First Choices : ( EF, BC )
Second Choice ( AD, IH )
Answers
The ratio of the lengths of EF and BC is 2:1. The correct answer is (EF, BC), where the length of EF is twice the length of BC.
The ratio of the lengths of two segments is given as 2:1. We can set up a proportion and find that the length of one segment is twice the length of the other.
In this question, the ratio of the lengths of two segments is given as 2:1. We are asked to find the lengths of the two segments, which are represented by two choices: (EF, BC) and (AD, IH). To solve this problem, we can set up a proportion. Let's assume that EF and BC represent the lengths of the segments, and we can write the proportion as:
[tex]\frac {EF}{BC} =\frac {2}{1}[/tex]
To solve for the lengths, we can cross multiply:
[tex]EF \times 1 = BC \times 2[/tex]
[tex]EF = 2 \times BC[/tex]
So, the length of EF is twice the length of BC. Therefore, the correct answer is (EF, BC), where the length of EF is twice the length of BC.
Final answer:
The student's question deals with the concept of ratios and similar triangles in High School level Mathematics. Without additional context to the specific figures and points mentioned, a precise answer cannot be given. Typically, in similar triangles, corresponding side lengths are proportional, allowing calculation of unknown lengths when a ratio is provided.
Explanation:
The question refers to finding a ratio of lengths related to geometrical figures. Since ratios and proportions frequently deal with lengths and geometry, and the provided examples reference triangles, circles, and other geometric shapes, this question is most closely related to the subject of Mathematics. The use of similar triangles to find unknown lengths is a typical high school-level geometry problem.
Based on the information given in the question, it seems we are required to use the property that states the ratios of corresponding sides of similar triangles are equal. To answer the student's question specifically, we'd need more context to the figures in question, such as circle C with center F and point F', or the configuration of the triangles abc and a'b'c'.
For instance, if we have two similar triangles, with corresponding side lengths in a ratio of 2:1, this means that if one triangle has a side length of 'x', the similar triangle's corresponding side length would be '2x'. To answer the student's query correctly, however, additional information on which particular sides of the named points are being inquired about is necessary.
Related Questions
Nathaniel writes the general form of the equation gm = cm + rg for when the equation is solved for m. He uses the general form to solve the equation –3m = 4m – 15 for m. Which expression shows what Nathaniel will actually evaluate? 4 + 15 – 3 4 – 15 + 3 –15 –
Answers
Answer:
The required expression is [tex]m=\frac{-15}{-3-4}[/tex].
Step-by-step explanation:
The general form of the equation is
[tex]gm=cm+rg[/tex] .... (1)
We need to solve this equation for m.
Subtract cm from both the sides.
[tex]gm-cm=rg[/tex]
Taking out the common factor.
[tex]m(g-c)=rg[/tex]
Divide both sides by (g-c).
[tex]\frac{m(g-c)}{g-c}=\frac{rg}{g-c}[/tex]
[tex]m=\frac{rg}{g-c}[/tex] ..... (2)
The given equation is
[tex]-3m=4m-15[/tex] ..... (3)
From (1) and (3), we get
[tex]g=-3,c=4,rg=-15[/tex]
Substitute g=-3, c=4, rg=-15 in equation (2).
[tex]m=\frac{-15}{-3-4}[/tex]
Therefore the required expression is [tex]m=\frac{-15}{-3-4}[/tex].
Answer:
the corect answer on edge is c
Step-by-step explanation:
Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has written \dfrac{1}{4}
4
1
start fraction, 1, divided by, 4, end fraction as many articles as Mustafa has. Gia has written \dfrac{3}{2}
2
3
start fraction, 3, divided by, 2, end fraction as many articles as Mustafa has.
Write an inequality to determine the number of articles, mmm, Mustafa could have written for the school newspaper.
What is the solution set of the inequality?
Answers
Answer:
m + m/4 + 3m/2 > 22m > 8 . . . . m restricted to multiples of 4, perhapsStep-by-step explanation:
Let m represent the number of articles Mustafa has written. Then the total number of articles written must satisfy the inequality ...
m +m/4 +3m/2 > 22
This has solution ...
(11/4)m > 22
m > (4/11)22
m > 8 . . . . . . . . the solution to the inequality
If all the numbers are integers, and the ratios are exact, then we must have m be a multiple of 4 (that is, 4 times the number of articles Heloise wrote).
The solution set will be ...
m ∈ {12, 16, 20, 24, ...} (multiples of 4 greater than 8)
Answer:
inequality - m+ 1/4m + 3/2m > 22
solution set - m>8
Step-by-step explanation:
i promise
I need help on understanding this one! Thank you!
Answers
Answer:
(6^⅕) (cos(-24°) + i sin(-24°))
Step-by-step explanation:
First, we convert from Cartesian to polar:
r = √((-3)² + (-3√3)²)
r = √(9 + 27)
r = 6
θ = atan( (-3√3) / (-3) ), θ in the third quadrant
θ = atan(√3)
θ = 240° + 360° k
Notice that θ can be 240°, 600°, 960°, etc.
Therefore:
-3 − 3√3 i = 6 (cos(240° + 360° k) + i sin(240° + 360° k))
Now we take the fifth root:
[ 6 (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕
(6^⅕) [ (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕
Applying de Moivre's Theorem:
(6^⅕) (cos(⅕ × 240° + ⅕ × 360° k) + i sin(⅕ × 240° + ⅕ × 360° k))
(6^⅕) (cos(48° + 72° k) + i sin(48° + 72° k))
If we choose k = -1:
(6^⅕) (cos(-24°) + i sin(-24°))
There are 24,000 square miles of forest in a western state. Forest fires decrease this area by 9.2% each year. The state needs to have more than 15,000 square miles of forest to keep their funding from a nonprofit wildlife organization.
Which inequality represents this situation, and if the fires continue to decrease the area of the forests at the same rate, will the state be able to keep their funding from the nonprofit wildlife organization in 5 years?
24,000(1.092)t > 15,000; no
24,000(0.092)t > 15,000; yes
24,000(0.908)t > 15,000; no
24,000(1.098)t > 15,000; yes
Answers
Answer:
24,000(0.908)^t > 15,000; no
Step-by-step explanation:
The multiplier each year is 100% - 9.2% = 90.8% = 0.908. There is only one answer choice with this as the yearly multiplier.
_____
In order to answer the yes/no question, we chose to rewrite the inequality as ...
24000·0.908^t -15000 > 0
The graph shows that is true for t < 4.87. In 5 years, the forest area will be below the minimum.
Suppose that the length of a certain rectangle is four centimeters more than three times its width. If the area of the rectangle is 95 square centimeters, find its length and width.
Answers
Answer: The length and width of the rectangle are 19 cm and 5 cm respectively.
Step-by-step explanation: Given hat the length of a rectangle is four centimeters more than three times its width and the area of the rectangle is 95 square centimeters.
We are to find the length and width of the rectangle.
Let W and L denote the width and the length respectively of the given rectangle.
Then, according to the given information, we have
[tex]L=3W+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Since the area of a rectangle is the product of its length and width, so we must have
[tex]A=L\times W\\\\\Rightarrow 95=(3W+4)W\\\\\Rightarrow 3W^2+4W-95=0\\\\\Rightarrow 3W^2+19W-15W-95=0\\\\\Rightarrow W(3W+19)-5(3W+19)=0\\\\\Rightarrow (W-5)(3W+19)=0\\\\\Rightarrow W-5=0,~~~~~3W+19=0\\\\\Rightarrow W=5,~-\dfrac{19}{3}.[/tex]
Since the width of the rectangle cannot be negative, so we get
[tex]W=5~\textup{cm}.[/tex]
From equation (i), we get
[tex]L=3\times5+4=15+4=19~\textup{cm}.[/tex]
Thus, the length and width of the rectangle are 19 cm and 5 cm respectively.
The length of the rectangle is 19 and the width is 5 and it can be determined by using the formula of area of the rectangle.
Given that,The length of a certain rectangle is four centimeters more than three times its width.
If the area of the rectangle is 95 square centimeters,
We have to determine,The length and width of the rectangle.
According to the question,Let the length of the rectangle be L,
And the width of the rectangle is W.
The length of a certain rectangle is four centimeters more than three times its width.
The perimeter of a square is the sum of the length of all its four sides.The perimeter formulas of different two-dimensional shapes:
Then,
[tex]\rm L = 3W+4[/tex]
And If the area of the rectangle is 95 square centimeters,
The area of any polygon is the amount of space it occupies or encloses.It is the number of square units inside the polygon.
The area is a two-dimensional property, which means it contains both length and width
[tex]\rm Area \ of \ the \ rectangle = length \times width\\\\L\times W = 95[/tex]
Substitute the value of L from equation 1,
[tex]\rm L\times W = 95\\\\(3W+4) \times W = 95\\\\3W^2+4W=95\\\\3W^2+4W-95=0\\\\3W^2+19W-15W-95=0\\\\W(3W+19) -5(3W+19) =0\\\\(3W+19) (W-5) =0\\\\W-5=0, \ W=5\\\\3W+19=0, \ W = \dfrac{-19}{3}[/tex]
The width of the rectangle can not be negative than W = 5.
Therefore,
The length of the rectangle is,
[tex]\rm L = 3W+4\\\\L = 3(5)+4\\\\L=15+4\\\\L=19[/tex]
Hence, The length of the rectangle is 19 and the width is 5.
To know more about Rectangle click the link given below.
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Elijah drove 45 miles to his job in an hour and ten minutes in the morning. On the way home: however, traffic was much heavier and the same trip took an hour and half. What was his average speed in miles per hour for the round trip?
Answers
Answer:
33.75
Step-by-step explanation:
You first need to determine the total distance of the round trip. This is twice the 45 mile trip in the morning, which is 90 miles. In order to determine the total amount of time spent on the round trip, convert the time travel to minutes.
1 hr + 10 mins = 70 mins
1hr + 30 = 90 mins
So his total travel time would equal to 90+70=160 minutes
his average speed is:
90mi/160min * 60min/1hr = 90*60/160
= 33.75
Elijah's average speed for the round trip is approximately 31.76 miles per hour.
To calculate the average speed for the round trip, we need to determine the total distance traveled and the total time taken.
In the morning, Elijah drove 45 miles in 1 hour and 10 minutes. To convert the minutes to hours, we divide 10 minutes by 60, which gives us 10/60 = 1/6 hours. Therefore, his morning travel time is 1 hour + 1/6 hour = 7/6 hours.
On the way home, the same trip took him 1 hour and 30 minutes. Converting the minutes to hours, we divide 30 minutes by 60, which gives us 30/60 = 1/2 hours. Therefore, his return travel time is 1 hour + 1/2 hour = 3/2 hours.
To calculate the total distance traveled, we sum the distance from the morning trip and the return trip: 45 miles + 45 miles = 90 miles.
The total time taken for the round trip is the sum of the morning travel time and the return travel time: 7/6 hours + 3/2 hours = 17/6 hours.
To calculate the average speed, we divide the total distance by the total time: 90 miles / (17/6 hours).
Dividing 90 miles by 17/6 hours is the same as multiplying 90 miles by 6/17, which gives us (90 * 6) / 17 = 540/17.
Therefore, Elijah's average speed for the round trip is approximately 31.76 miles per hour.
To know more about speed:
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You bought a guitar 6 years ago for $400. If its value decreases by
about 13% per year, how much is your guitar worth now?
$351.23
$226.55
$322
$173.45
Answers
Answer:
$173.45
Step-by-step explanation:
the beginning value is $400. if it loses 13%, that means it keeps 87% of its value. so you multiply by 0.87 6 times for each year
The variable z is inversely proportional to x. When x is 16, z has the value 0.5625. What is the value of z when x= 25?
Answers
Answer:
0.36
Step-by-step explanation:
z is inversely proportional to x:
z = k / x
When x is 16, z has the value 0.5625.
0.5625 = k / 16
k = 9
What is the value of z when x= 25?
z = 9 / 25
z = 0.36
Answer:
The answer is 9/25 or .36 if you prefer it in decimal form.
Step-by-step explanation:
inversely proportional means there is a constant that we are going to divide by.
So z is inversely proportional to x means z=k/x where k is a constant.
We are given when x=16, z=0.5625. This information will be used to find our constant value k.
0.5625=k/16
Multiply both sides by 16:
16(0.5625)=k
Simplify:
9=k.
This means no matter what (x,z) pair we have the constant k in z=k/x will always be 9.
The equation we have is z=9/x.
Now we want to find z when x=25.
z=9/25
z=.36
State the domain and range of the function f(x) =2[[x]]
A. reals Even integers.
B. reals odd integers.
C. reals all integers.
D. reals positive integers.
Just to let you guys know, people thought the answer was C, but the correct answer was A. i don't know why it is A, please explain:(
Answers
Answer:
A real Even integers
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
It's all down the the double parentheses. They mean 'round down to the nearest integer'. Also because of the 2 the integer will be even.
Tristan records the number of customers who visit the store each hour on a Saturday. His data representing the first seven hours are 15, 23, 12, 28, 20, 18, and 23. How many customers visited the store during the eighth hour if the median number of customers per hour did not change?Show all your work and explain how you arrived at your answer.
Answers
12, 15, 18, 20, 23, 23, 28
Median is the middle number of the list—20.
Answer:
20
Step-by-step explanation:
Given that Tristan records the number of customers who visit the store each hour on a Saturday.
His data representing the first seven hours are 15, 23, 12, 28, 20, 18, and 23.
There are 7 entries and if written in ascending order 12,15,18,20,23,23,28
Median = middle entry -20
If one more entry is added then we have two middle entries and median would be the average of the two.
Hence if median is to remain the same, eighth hour no of customers visited should be 20
Answer is 20
The edge of a cube was found to be 15 cm with a possible error in measurement of 0.4 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.)
Answers
The maximum error on volume = 270cm³
The relative error on the volume =0.08
The percentage error on volume = 8%.
How to calculate the volume of a given cube?
To calculate the volume of a given cube, the following steps should be taken as follows:
Formula for volume of a cube = a³
where;
a = 15 cm
Volume(V) = 15³ = 3375cm³
The maximum error on volume(dV);
= 3×side²×dx
= 3×15²×0.4cm
= 270cm³
The relative error on the volume;
= dV/V
= 270/3375
= 0.08
The percentage error on volume;
=Relative error × 100
= 0.08× 100
= 8%
You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 200 yards due west from your position and takes a bearing on the cabin of N 30.7°E. How far are you from the cabin?
Answers
Answer:
336.7 yards away from the cabin....
Step-by-step explanation:
The angle 30.7° is also the angle of the upper interior angle of the triangle (near the cabin)
Use the tan function:
opposite = 200 yards
adjacent = x
tan(30.7°) = (opposite / adjacent)
tan(30.7°) = 200 yards/x
x * tan(30.7°) = 200 yards
x = 200 yards/ tan(30.7°)
x= 200/ 0.594
x = 336.7 yards.
336.7 yards away from the cabin....
Answer: 337
Step-by-step explanation: you have to round up
A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.4,4.3). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?
Answers
Answer: 2.85
Step-by-step explanation:
Given : A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.4, 4.3) .
We know that the the confidence interval for population mean [tex]\mu[/tex] is given by :-
[tex]\mu\pm E[/tex], where E is the margin of error.
Lower limit of confidence interval = [tex]\mu-E=1.4[/tex] (1)
Upper limit of confidence interval = [tex]\mu+E=4.3[/tex] (2)
Adding (1) and (2), we get
[tex]2\mu=5.7\\\\\Rightarrow\ \mu=2.85[/tex]
Hence, the point estimator of the mean percentage of reservations that are canceled on the day of the flight = 2.85
The point estimator for the mean percentage of airline reservations being canceled on the day of the flight is 2.85%, found by averaging the lower and upper bounds of the given 90 percent confidence interval.
The point estimator of the mean percentage of reservations that are canceled on the day of the flight can be determined from the confidence interval given as (1.4, 4.3).
The point estimator is simply the mean of the lower and upper bounds of the confidence interval. To find this, we add the lower and upper limits together and divide by two.
The calculation is as follows:
[tex]\frac{1.4 + 4.3}{2} = 2.85[/tex]
Therefore, the point estimator for the mean percentage of airline reservations being canceled on the day of the flight is 2.85%.
The variable z is directly proportional to x, and inversely proportional to y. When x is 4 and y is 10, z has the value 0.8. What is the value of z when x= 13, and y= 18
Answers
Answer:
13/9
Step-by-step explanation:
Directly proportional means it will be multiply to our constant k.
Inversely proportional means it will divide our k.
So we are given z is directly proportional to x and inversely proportional to y.
This means:
[tex]z=k \cdot \frac{x}{y}[/tex].
We are given (x=4,y=10,z=0.8). We can use this to find k. The k we will find using the point will work for any point (x,y,z) since k is a constant. A constant means it is to remain the same no matter what.
[tex]0.8=k \cdot \frac{4}{10}[/tex]
[tex]0.8=k(.4)[/tex]
Divide both sides by .4:
[tex]\frac{0.8}{0.4}=k[/tex]
[tex]k=2[/tex]
The equation for any point (x,y,z) is therefore:
[tex]z=2 \cdot \frac{x}{y}[/tex].
We want to find z given x=13 and y=18.
[tex]z=2 \cdot \frac{13}{18}[/tex]
[tex]z=\frac{2 \cdot 13}{18}[/tex]
[tex]z=\frac{13}{9}[/tex]
Need help big time...please explain how you got the answer.
Answers
Answer:
Step-by-step explanation:
This is a right triangle with the 90 degree angle identified at D and the 60 degree angle identified at B. Because of the triangle angle sum theorem, the angles of a triangle all add up to equal 180 degrees, so angle C has to be a 30 degree angle.
There is a Pythagorean triple that goes along with a 30-60-90 triangle:
( x , x√3 , 2x )
where each value there is the side length across from the
30 , 60 , 90 degree angles.
We have the side across from the 90 degree angle, namely the hypotenuse. The value for the hypotenuse according to the Pythagorean triple is 2x. Therefore,
2x = 2√13
and we need to solve for x. Divide both sides by 2 to get that
x = √13
Now we can solve the triangle.
The side across from the 30 degree angle is x, so since we solved for x already, we know that side DB measures √13.
The side across from the 60 degree angle is x√3, so that is (√13)(√3) which is √39.
And we're done!
The product shown is a difference of squares. What is the missing constant term in the second factor?(–5x – 3)(–5x + )
Answers
Answer:
3
Step-by-step explanation:
the missing no is 3
I have answered ur question
Answer:
3
Step-by-step explanation:
To find the standard equation for a circle centered at the origin, we use the distance formula, since the radius measures? A. The distance from any point in the circle to the origin.B. The circumference c. The distance from any point inside the circle to the origin.D. The distance from the x-coordinate to the origin.
Answers
Answer:
A. The distance from any point in the circle to the origin
Step-by-step explanation:
The distance formula tells you that the distance (d) is related to the coordinates of two points (x1, y1) and (x2, y2) by ...
d² = (x2 -x1)² +(y2 -y1)²
For points (x, y) on the circle and (0, 0) at the origin, this becomes ...
d² = (x -0)² +(y -0)²
If we want the distance to the point (x, y) to be equal to the radius of the circle, this becomes ...
x² +y² = r² . . . . . . the standard equation of a circle centered at the origin
Answer: The distance from any point in the circle to the origin
Step-by-step explanation:
answer key
Solve 3x^2 + x + 10 = 0 round solutions to the nearest hundredth
A. X= -2.83 and x=0.83
B. No real solutions
C. X= -2.01 and x= 1.67
D. X= -1.67 and x=2.01
Answers
Answer:
C. X= -2.01 and x= 1.67
Step-by-step explanation:
[tex]3x {}^{2} + x + 10 = 0 \\ 3x {}^{2} + 6x - 5x + 10 = 0 \\ 3x(x + 2) - 5(x + 2) \\ (x + 2)(3x - 5 )\\ x + 2 = 0 \: \: or \: \: 3x - 5 = 0 \\ x = - 2 \: \: or \: \: x = \frac{5}{3} [/tex]
ANSWER
B. No real solutions
EXPLANATION
The given equation is
[tex]3 {x}^{2} + x + 10 = 0[/tex]
By comparing to
[tex]a {x}^{2} + bx + c= 0[/tex]
We have a=3,b=1 and c=10.
We substitute these values into the formula
[tex]D = {b}^{2} - 4ac[/tex]
to determine the nature of the roots.
[tex]D = {1}^{2} - 4(3)(10)[/tex]
[tex]D = 1 - 120[/tex]
[tex]D = - 119[/tex]
The discriminant is negative.
This means that the given quadratic equation has no real roots.
Draw a diagram for this statement.
one sixth of the 48 vegetable plants were tomato plants.
use your diagram to determine how many of the vegetable plants were tomato plants
Answers
Answer:
8
Step-by-step explanation:
one sixth of 48 is 8 therefore you have eight tomato plants
URGENT PLEASE HELP ME WITH THIS MATH QUESTION
Answers
Answer:
The image is (0 , -6)
Step-by-step explanation:
* Lets explain some important facts
- When a point reflected across a line the perpendicular
distance from the point to the line equal the perpendicular
distance from its image to the same line
- If the line of the reflection is horizontal then the perpendicular
distance between the point and the line is y - y1 , and the
perpendicular distance between the image and the line is y2 - y
- If point (x , y) reflected across the x- axis, then its image is (x , -y)
* Lets solve the problem
∵ Point (0 , 0) reflected across the line y = 3
∴ y = 3 and y1 = 0
∴ The distance between the point and the line is 3 - 0 = 3
∴ The distance between the image and the line also = 3
∴ y2 - 3 = 3 ⇒ add 3 to both sides
∴ y2 = 6
∴ The y-coordinate of the image is 6
∴ The image of point (0 , 0) after reflection across the line y = 3 is (0 , 6)
- The image of the point reflected across the x-axis, then change the
sign of the y-coordinate
∴ The final image of point (0 , 0) is (0 , -6)
* The image is (0 , -6)
What is the magnitude of the position vector whose terminal point is (-2, 4)?
Answers
Answer:
2√5
Step-by-step explanation:
The Pythagorean theorem tells you how to find the distance from the origin.
d = √((-2)² +4²) = √20 = 2√5
The vector's magnitude is 2√5 ≈ 4.47214.
Answer:
The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]
Step-by-step explanation:
Given : Vector whose terminal point is (-2, 4).
To find : What is the magnitude of the position vector?
Solution :
We have given, terminal point (-2,4)
The magnitude of the point x(a,b) is given by,
[tex]|x|=\sqrt{a^2+b^2}[/tex]
Let point x=(-2,4)
[tex]|x|=\sqrt{(-2)^2+(4)^2}[/tex]
[tex]|x|=\sqrt{4+16}[/tex]
[tex]|x|=\sqrt{20}[/tex]
Therefore, The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]
Please help will give the brainliest
Find the coordinates of the vertices formed by the system of inequalities.
X≤ 3
-x + 3y ≤ 12
4x + 3y ≥ 12
A (0, 3), (4, 0), (5, 3)
B (3, 0), (0, 4), (3, 5)
C (-3, 3), (1, 3), (0, 4)
D (3, -3), (3, 1), (4, 0)
2. At What point is the maximum value found in the system of inequalities graphed below for the function f(x, y) = x - 2y?
A (0, 3)
B (0, 0)
C (5, 0)
D (5, 3)
Answers
Final answer:
To find the vertices of the system of inequalities x ≤ 3, -x + 3y ≤ 12, and 4x + 3y ≥ 12, we can solve each pair of inequalities to find the intersection points. The vertices are the points where the lines intersect. The coordinates of the vertices are (3, 0), (0, 4), and (3, 5). For the function f(x, y) = x - 2y, the point where the maximum value is found in the system of inequalities is (5, 3).
Explanation:
To find the coordinates of the vertices formed by the system of inequalities x ≤ 3, -x + 3y ≤ 12, and 4x + 3y ≥ 12, we can solve each pair of inequalities to find the intersection points. The vertices are the points where the lines intersect.
The solution is (3, 0), (0, 4), and (3, 5), so the correct answer is B.
For the second question, to find the point where the maximum value is found for the function f(x, y) = x - 2y in the system of inequalities graphed below, we need to locate the highest point on the graph. From the given options, (5, 3) is the point where the maximum value is found, so the correct answer is D.
In the spinner below the large wedges are twice the size of the smaller ones. What is true about the probablilty of landing on 6 and the probability of landing on 5
Answers
Answer:
we need an image of the spinner to answer the question. are we supposed to just know what it looks like?
Step-by-step explanation:
flvs she cheating
Question about Radicals.
Answers
Answer:
Conjugate
Step-by-step explanation:
Those are conjugates. In factoring polynomials, if you have one with a + sign separating the a and the square root of b, you will ALWAYS have one with a - sign. They will always come in pairs. Same with imaginary numbers.
Find the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4).
A. (3.5, 7)
B. (-6.5, -9)
C. (-4, -6)
D. (-1.5, -1)
Answers
Answer:
The answer is A(3.5,7)
Point of partition refers that a point intersect a particular line or curve at a fixed ratio. The coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).
Given information-The coordinates of the A is (5,8).
The coordinates of the B is (-1,4).
P partitions the segment AB in the ratio 1:3.
Point of PartitionPoint of partition refers that a point intersect a particular line or curve at a fixed ratio.
When a point [tex]p(x,y)[/tex] intersect a line which has the coordinates [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] at a ratio l and m then this point can be represent as,
[tex]p(x,y)=\left ( \dfrac{lx_2+mx_1}{l+m} , \dfrac{ly_2+my_1}{l+m} \right )[/tex]
Put the values,
[tex]p(x,y)=\left ( \dfrac{1\times(-1)+3\times 5}{1+3} , \dfrac{1\times 4+3\times8}{1+3} \right )[/tex]
[tex]p(x,y)=\left ( \dfrac{-1+15}{4} , \dfrac{4+24}{4} \right )[/tex]
[tex]p(x,y)=\left ( \dfrac{14}{4} , \dfrac{28}{4} \right )[/tex]
[tex]p(x,y)=(3.5,7)[/tex]
Hence the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).
Learn more about the point of partitions of a line here;
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A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be three times the amount of vinegar. How much of each ingredient is needed in order to make 18 oz of furniture polish?
To make 18 oz of furniture polish, ___ oz of vinegar and
_______ oz of olive oil are needed.
Answers
Answer:
To make 18 oz of furniture polish, 4.5 oz of vinegar and 13.5 oz of olive oil are needed.
Step-by-step explanation:
The ratio of ingredients is ...
oil : vinegar = 3 : 1
So vinegar is 1 of the 3+1 = 4 parts of the polish mix. The amount of vinegar required for 18 oz of polish is ...
(1/4)×(18 oz) = 4.5 oz
The remaining quantity is olive oil:
18 oz - 4.5 oz = 13.5 oz
To make 18oz of furniture polish, 4.5 oz of vinegar and 13.5 oz of olive oil are needed. These quantities are found by setting up an equation based on the problem's conditions and solving for x.
Explanation:To begin solving the problem we need to understand that both the vinegar and the olive oil are together making up the 18oz of furniture polish. Since the amount of olive oil is three times the amount of vinegar, we can denote the quantity of vinegar as 'x'. Thus, the quantity of olive oil will be '3x'.
Adding these together gives us the total ounces, thus, we have our equation: x + 3x = 18. Solving this, we get 4x = 18. Dividing by 4 gives us x = 18/4 = 4.5.
Therefore, to make 18oz of furniture polish, you will need 4.5 oz of vinegar and 13.5 oz (3 times 4.5) of olive oil.
Learn more about Proportional Quantities here:https://brainly.com/question/33747792
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In a right triangle, the measure of one of the acute angles is 60 degrees more than the measure of the smallest angle. Find the measures of all three angles.
Answers
Answer:
90°, 75°, and 15°
Step-by-step explanation:
In a right triangle, one of the angles is 90°.
Let x = the smallest angle
Then 60 + x = the third angle
The sum of the three angles is 180°.
90 + 60 + x + x = 180
150 + 2x = 180
2x = 30
x = 15
Measure of right angle = 90°
Measure of smallest angle = x = 15°
Measure of third angle = 60 + x = 75°
The measures of the angles are 90°, 75°, and 15°.
Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm. The electric potential of the inner conductor, with respect to the outer conductor, is +600 V. An electron is released from rest at the surface of the outer conductor. What is the speed of the electron as it reaches the inner conductor?
Answers
Answer:
v = 1.45 × 10⁷ m/s
Step-by-step explanation:
Given:
Inner radius of the cylinder, r₁ = 20 mm = 0.2 m
outer radius of the cylinder, r₂ = 80 mm = 0.8 m
Potential difference, ΔV = 600V
Now, the work done (W) in bringing the charge in to the inner conductor
W = [tex]\frac{1}{2}mv^2[/tex]
where, m is the mass of the electron = 9.1 × 10⁻³¹ kg
v is the velocity of the electron
also,
W = qΔV
where,
q is the charge of the electron = 1.6 × 10⁻¹⁹ C
equating the values of work done and substituting the respective values
we get,
qΔV = [tex]\frac{1}{2}mv^2[/tex]
or
1.6 × 10⁻¹⁹ × 600 = [tex]\frac{1}{2}\times 9.1\times 10^{-31}v^2[/tex]
or
[tex]v = \sqrt\frac{2\times 600\times 1.6\times 10^{-19}}{9.1\times 10^{-31}}[/tex]
or
v = 14525460.78 m/s
or
v = 1.45 × 10⁷ m/s
Final answer:
The speed of the electron as it reaches the inner conductor is calculated using conservation of energy, giving a final speed of approximately 1.46 × 107 m/s.
Explanation:
Electron Velocity in Coaxial Conductors
An electron released from the outer conductor will be accelerated towards the higher potential inner conductor due to the electric field between them. To calculate the speed of the electron as it reaches the inner conductor, we use the concept of conservation of energy. The electrical potential energy lost by the electron as it moves from the outer to the inner conductor is converted into kinetic energy.
The initial potential energy (Ui) of the electron can be given by:
Ui = qVwhere q is the charge of the electron (q = -1.6 × 10-19 C) and V is the potential difference (V = 600 V).
The final kinetic energy (Kf) when the electron reaches the inner conductor is:
Kf = ½ [tex]mv^2[/tex]where m is the mass of the electron (m = 9.11 × 10-31 kg) and v is the final speed we want to find.
Using conservation of energy (Ui + Ki = Kf + Uf and noting that both the initial kinetic energy Ki and the final potential energy Uf are zero), we get:
qV = ½ [tex]mv^2[/tex](-1.6 × 10-19 C)(600 V) = ½ (9.11 × 10-31kg)[tex]v^2[/tex]Solving for v gives us the final speed of the electron:
v = √[(2qV)/m]v = √[(2(-1.6 × 10-19 C)(600 V))/(9.11 × 10-31kg)]v = 1.46 × 107 m/sThis is the speed of the electron when it reaches the inner conductor.
19. Solve sin O+ 1 = cos 20 on the interval 0≤x < 2xpi
Answers
Answer:
[tex]\theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{2\pi}{3},\frac{4\pi}{3}[/tex]
Step-by-step explanation:
If I'm interpreting that correctly, you are trying to solve this equation:
[tex]sin(\theta )+1=cos(2\theta)[/tex]
for theta. To do this, you will need a trig identity sheet (I'm assuming you got one from class) and a unit circle (ditto on the class thing).
We need to solve for theta. If I look to my trig identities, I will see a double angle one there that says:
[tex]cos(2\theta)=1-2sin^2(\theta)[/tex]
We will make that replacement, then we will have everything in terms of sin.
[tex]sin(\theta)+1=1-2sin^2(\theta)[/tex]
Now get everything on one side of the equals sign to solve for theta:
[tex]2sin^2(\theta)+sin(\theta)=0[/tex]
We can factor out the common sin(theta):
[tex]sin\theta(2sin\theta+1)=0[/tex]
By the Zero Product Property, either
[tex]sin\theta=0[/tex] or
[tex]2sin\theta+1=0[/tex]
Now look at your unit circle and find that the values of theta where the sin is 0 are located at:
[tex]\theta=\frac{\pi }{2},\frac{3\pi}{2}[/tex]
The next one we have to solve for theta:
[tex]2sin\theta+1=0[/tex] simplifies to
[tex]2sin\theta=-1[/tex] and
[tex]sin\theta=-\frac{1}{2}[/tex]
Look at the unit circle again to find the values of theta where the sin is -1/2:
[tex]\theta=\frac{2\pi}{3},\frac{4\pi}{3}[/tex]
Those ar your values of theta!
Which of the following statements is(are) NOT applicable to typologies? a. They are typically nominal composite measures. b. They involve a set of categories or types. c. They may be used effectively as independent or dependent variables. d. They are often used when researchers wish to summarize the intersection of two or more variables.e. All of these choices apply to typologies.
Answers
Answer: The following statements is not applicable to typologies, "They may be used effectively as independent or dependent variables."
Typology is a complex measurement that affect the categorization of observations in terms of their property on multiple variables.They are typically nominal composite measures.They involve a set of categories or types. They are often used when researchers wish to summarize the intersection of two or more variables.