Answer:
(3,4,5)
(6,8,10)
(5,12,13)
(8,15,17)
(12,16,20)
(7,24,25)
(10,24,26)
(20,21,29)
(16,30,34)
(9,40,41)
Just choose 2 numbers from {1,2,3,4,5,6,7,8,...} and make sure the one you input for x is larger.
Post the three in the comments and I will check them for you.
Step-by-step explanation:
We need to choose 2 positive integers for x and y where x>y.
Positive integers are {1,2,3,4,5,6,7,.....}.
I'm going to start with (x,y)=(2,1).
x=2 and y=1.
[tex](2^2+1^2)^2=(2^2-1^2)^2+(2\cdot2\cdot1)^2[/tex]
[tex](4+1)^2=(4-1)^2+(4)^2[/tex]
[tex](5)^2=(3)^2+(4)^2[/tex]
So one Pythagorean Triple is (3,4,5).
I'm going to choose (x,y)=(3,1).
x=3 and y=1.
[tex](3^2+1^2)^2=(3^2-1^2)^2+(2\cdot3\cdot1)^2[/tex]
[tex](9+1)^2=(9-1)^2+(6)^2[/tex]
[tex](10)^2=(8)^2+(6)^2[/tex]
So another Pythagorean Triple is (6,8,10).
I'm going to choose (x,y)=(3,2).
x=3 and y=2.
[tex](3^2+2^2)^2=(3^2-2^2)^2+(2\cdot3\cdot2)^2[/tex]
[tex](9+4)^2=(9-4)^2+(12)^2[/tex]
[tex](13)^2=(5)^2+(12)^2[/tex]
So another is (5,12,13).
I'm going to choose (x,y)=(4,1).
[tex](4^2+1^2)^2=(4^2-1^2)^2+(2\cdot4\cdot1)^2[/tex]
[tex](16+1)^2=(16-1)^2+(8)^2[/tex]
[tex](17)^2=(15)^2+(8)^2[/tex]
Another is (8,15,17).
I'm going to choose (x,y)=(4,2).
[tex](4^2+2^2)^2=(4^2-2^2)^2+(2\cdot4\cdot2)^2[/tex]
[tex](16+4)^2=(16-4)^2+(16)^2[/tex]
[tex](20)^2=(12)^2+(16)^2[/tex]
We have another which is (12,16,20).
I'm going to choose (x,y)=(4,3).
[tex](4^2+3^2)^2=(4^2-3^2)^2+(2\cdot4\cdot3)^2[/tex]
[tex](16+9)^2=(16-9)^2+(24)^2[/tex]
[tex](25)^2=(7)^2+(24)^2[/tex]
We have another is (7,24,25).
You are just choosing numbers from the positive integer set {1,2,3,4,... } and making sure the number you plug in for x is higher than the number for y.
I will do one more.
Let's choose (x,y)=(5,1).
[tex](5^2+1^2)^2=(5^2-1^2)^2+(2\cdot5\cdot1)^2[/tex]
[tex](25+1)^2=(25-1)^2+(10)^2[/tex]
[tex](26)^2=(24)^2+(10)^2[/tex]
So (10,24,26) is another.
Let (x,y)=(5,2).
[tex](5^2+2^2)^2=(5^2-2^2)^2+(2\cdot5\cdot2)^2[/tex]
[tex](25+4)^2=(25-4)^2+(20)^2[/tex]
[tex](29)^2=(21)^2+(20)^2[/tex]
So another Pythagorean Triple is (20,21,29).
Choose (x,y)=(5,3).
[tex](5^2+3^2)^2=(5^2-3^2)^2+(2\cdot5\cdot3)^2[/tex]
[tex](25+9)^2=(25-9)^2+(30)^2[/tex]
[tex](34)^2=(16)^2+(30)^2[/tex]
Another Pythagorean Triple is (16,30,34).
Let (x,y)=(5,4)
[tex](5^2+4^2)^2=(5^2-4^2)^2+(2\cdot5\cdot4)^2[/tex]
[tex](25+16)^2=(25-16)^2+(40)^2[/tex]
[tex](41)^2=(9)^2+(40)^2[/tex]
Another is (9,40,41).
Complete the equation of the line through (-1,6)(?1,6)left parenthesis, minus, 1, comma, 6, right parenthesis and (7,-2)(7,?2)left parenthesis, 7, comma, minus, 2, right parenthesis. Use exact numbers. Y=y=y, equals
Answer:
y = -x +5
Step-by-step explanation:
The 2-point form of the equation of a line is useful for this.
y = (y2 -y1)/(x2 -x1)(x -x1) + y1 . . . 2-point form of equation for a line
y = (-2 -6)/(7 -(-1))/(x -(-1)) +6 . . . . substitute the give points
y = -8/8(x +1) +6 . . . . . . . . . . . . . . simplify a bit; next, simplify more
y = -x +5
The equation of the line passing through the point s (-1, 6) and (7, -2) is y = -x + 5
The formula for calculating the equation of a line is expressed as y = mx + b where;
m is the slope of the line
b is the y-intercept
Given the coordinate points (-1,6) and (7, -2)
Get the slope:
Slope = -2-6/7-(-1)
Slope = -8/8
Slope = - 1
Get the y-intercept:
-2 = -1(7) + b
-2 = -7 + b
b = -2 + 7
b = 5
Get the required equation:
Recall that y = mx + b
Substituting m = -1 and b = 5 into the equation:
y = -x + 5
Hence the equation of the line passing through the point s (-1, 6) and (7, -2) is y = -x + 5
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What is the radius of the following circle?
Answer:
The radius is: 1
Step-by-step explanation:
The equation of a circle in center-radius form is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where the center is at the point (h, k) and the radius is "r".
Given the equation of the circle:
[tex]x^2+y^2=1[/tex]
You can identify that:
[tex]r^2=1[/tex]
Then, solving for "r", you get that the radius of the circle is:
[tex]r=\sqrt{1}\\\\r=1[/tex]
Answer:
Radius = 1
Step-by-step explanation:
It is given that equation of a circle is x² + y² = 1
Points to remember
Equation of a circle with center(h, k) and radius r is given by,
(x - h)² + (y - k)² = r²
To find the radius of circle
Compare the two equations
x² + y² = 1 and (x - h)² + (y - k)² = r²
we get the center is (0, 0)
therefore we can write
r² = 1
r = 1
Therefore radius r = 1
Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and the leading coefficient. If the function is not a polynomial, state why.
Answer:
Please provide the polynomial to answer this question
Step-by-step explanation:
An expression will be said a polynomial if it contains variables like x, p , q, t etc etc.
They can be of any degree. like [tex]x^2[/tex] , [tex]y^3[/tex] , [tex]t^4[/tex] etc
The degree of a polynomial is the highest exponent of the variable we have in the polynomial
Example : Degree of polynomial [tex]x^3-1 = 3[/tex]
If it do not have any variable , it is not called a polynomial because it basically gives us a constant
The given function violates both conditions for a polynomial, the correct answer is B. This is not a polynomial function because the variable powers are not all non-negative integers, and the coefficients are not constants.
To determine if the given function is a polynomial, we need to check two things:
The variable powers should be non-negative integers (whole numbers).
The coefficients of each term should be constants.
Let's analyze the function f(x)=√x+1 · (x+2)
Variable powers: The variable powers in the function are 1/2 and 1. The power 1/2 (square root) is not a non-negative integer, and thus violates the first condition for a polynomial.
Coefficients: The coefficients in the function are (1/2) and 1, which are not constants, but rather they involve variables. This also violates the second condition for a polynomial.
Since the given function violates both conditions for a polynomial, the correct answer is:
B. This is not a polynomial function because the variable powers are not all non-negative integers, and the coefficients are not constants.
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The complete question is:
Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and the leading coefficient. If the function is not a polynomial, state why.
f(x)=√x+1 · (x+2)
A.This is not a polynomial function because there is no leading coefficient.
B. This is not a polynomial function because the variable powers are not all non-negative integers.
C. This is not a polynomial function because the factors are not all linear.
D. This is not a polynomial function because it is not written in the form f(x) = axⁿ + bxⁿ⁻¹ + ..... + rx² + sx + t.
what is the y intercept for f(x) = 5x +7
Answer:
7
Step-by-step explanation:
the slope intercept form is y=mx + b
where b is the y intercept,
and your question is y=5x + 7
so the y intercept form would equal to 7
Find all polar coordinates of point P where P = ordered pair 1 comma pi divided by 3.
Answer:
(1, π/3 +2kπ), (-1, 4π/3 +2kπ) . . . where k is any integer
Step-by-step explanation:
Adding any multiple of 2π to the angle results in the same point in polar coordinates.
Adding 180° (π radians) to the point effectively negates the magnitude. As above, adding any multiple of 2π to this representation is also the same point in polar coordinates.
There are an infinite number of ways the coordinates can be written.
Answer:
All the polar coordinates of point P are [tex](1,2n\pi+\frac{\pi}{3})[/tex] and [tex](-1,(2n+1)\pi+\frac{\pi}{3})[/tex], where n is an integer.
Step-by-step explanation:
The given point is
[tex]P=(1,\frac{\pi}{3})[/tex] .... (1)
If a point is defined as
[tex]P=(r,\theta)[/tex] .... (2)
then the polar coordinates of point P is defined as
[tex](r,\theta)=(r,2n\pi+\theta)[/tex]
[tex](r,\theta)=(-r,(2n+1)\pi+\theta)[/tex]
where, n is an integer and θ is in radian.
From (1) and (2) we get
[tex]r=1, \theta=\frac{\pi}{3}[/tex]
So, the polar coordinates of point P are
[tex](r,\theta)=(1,2n\pi+\frac{\pi}{3})[/tex]
[tex](r,\theta)=(-1,(2n+1)\pi+\frac{\pi}{3})[/tex]
Therefore all the polar coordinates of point P are [tex](1,2n\pi+\frac{\pi}{3})[/tex] and [tex](-1,(2n+1)\pi+\frac{\pi}{3})[/tex], where n is an integer.
I seriously need help with this question!! I'm not kidding! Please help me!!
Answer:
63
Step-by-step explanation:
The two tangents to a circle from the same point are the same length.
SD = SG
5x +18 = 8x -9
27 = 3x . . . . . . . . add 9-5x
9 = x . . . . . . . . . . divide by 3
SG = 8x -9 = 8·9 -9
SG = 63
A rectangle's width is one-fourth of its length. Its area is 9 square units. The equation l(l) = 9 can be used to find l, the length of the rectangle. What is the length of the rectangle? 0.75 units 1.5 units 3 units 6 units
Answer:
6 units
Step-by-step explanation:
A rectangle's width is one-fourth of its length.
w = 1/4 l
area is 9 square units
A = l*w = 9
Replacing w with 1/4l
l * (1/4l) = 9
1/4 l^2 = 9
Multiply each side by 4 to clear the fraction
4 * 1/4 l^2 = 4*9
l^2 = 36
Take the square root of each side
sqrt (l^2) = sqrt(36)
l =6
Answer:
6 units
Step-by-step explanation:
Let the length = L
Then the width = L/4
area = length * width
area = L * L/4 = 9
L^2/4 = 9
L^2 = 36
L = 6 or L = -6
Since we are dealing with a length, we eliminate the negative answer.
Answer: 6 units
P.S. Your equation is incorrect. L(L) = 9 would work for a square with 4 congruent sides and area 9. Here the sides have different lengths. The equation is L(L/4) = 9.
Cosella is conducting an experiment where she assesses how quickly teenagers can run a 100-meter race after consuming specific amounts of caffeine. She divides her sample up into three groups. Group 1 receives a glass of water with no caffeine added. Group 2 receives a glass of water with an amount of caffeine equivalent to that in one cup of coffee. Group 3 receives a glass of water with an amount of caffeine equivalent to that in two cups of coffee. Each participant is then timed as they run the course. In this study, the independent variable is
a. the previous running experience of each participant
b. the teenagers who are being studied
c. the time it takes to run the 100-meter race
d. the amount of caffeine being ingested
Answer:
c. the time it takes to run the 100-meter race
Step-by-step explanation:
An independent variable is the variable which is not being controlled and it does not depend on the other variables. This is the variable which is being studied/measured in the experiment.
Option a. The previous running experience is not being considered and is not a variable under study in this case. So this is not the answer.
Option b. The teenagers who are being studied constitute the sample. These are not the variables.
Option c. Time is the independent variable, as it is being measured during the experiment and the conclusion is being drawn based on it.
Option d. Amount of caffeine is being decided by Cosella and is therefore not the independent variable.
Therefore, the correct answer is option c
help your girl out !!
giving out 15 points plus brainliest
Eggs ares sold in boxes. A small box holds 6 eggs hina buys x small boxes of eggs write down in terms of x the total number of eggs in these small boxes
[tex]6x[/tex]
............................................
The variable z is inversely proportional to x. When x is 6, z has the value of 2. What is the value of z when x=13
Round to at least the thousandths place if needed
Answer:
[tex]z=0.923[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and z, represent an inverse variation if it can be expressed in the form [tex]z*x=k[/tex] or [tex]z=k/x[/tex]
step 1
Find the value of k
For x=6, z=2
[tex]z*x=k[/tex]
substitute
[tex]2*6=k[/tex]
[tex]k=12[/tex]
therefore
The equation of the inverse variation is equal to
[tex]z*x=12[/tex]
step 2
What is the value of z when x=13
substitute the value of x in the equation and solve for z
[tex]z*(13)=12[/tex]
[tex]z=12/13[/tex]
[tex]z=0.923[/tex]
Find the distance between the points (0, –1) and (3, –3).
A. 25
B. 5
C. √13
D. 13
Answer:
C. √13
Step-by-step explanation:
The distance between two points is given by
d =sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt( (3-0)^2 + (-3--1)^2)
= sqrt( 3^2 + (-3+1)^2)
= sqrt( 9+(-2)^2)
= sqrt( 9+4)
= sqrt(13)
To answer this, you basically use Pythagoras' Theroem, but instead of:
[tex]c = \sqrt{a^{2} + b^{2}}[/tex]
it will be :
[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2} }[/tex]
So you are finding the squareroot of the (difference in y coordinates)² plus (difference in x coordinates) ²:
x is the x-coordinate of (0, -1) (so x = 0)
y is the y-coordinte of (0, -1) ( so y = -1)
x1 is the x coordinate of (3, -3) ( so x1 = 3)
y1 is the y coordinate of (3, -3) (so y1 = -3)
--------------------------------------------------
Now, lets find the distance between the two points, by substituting all of this values into the equation at the top:
[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2} }[/tex] (substitute in values)
[tex]distance = \sqrt{( 0 -3)^{2} + (-1 - -3)^{2} }[/tex] (simplify: note -1 - - 3 = -1 + 3)
[tex]distance = \sqrt{( -3)^{2} + (-1 +3)^{2} }[/tex] (simplify)
[tex]distance = \sqrt{( -3)^{2} + (2)^{2} }[/tex] (now square the numbers)
[tex]distance = \sqrt{9 + 4 }[/tex] (simplify)
[tex]distance = \sqrt{13 }[/tex]
___________________________________________
Answer:C. [tex]\sqrt{13}[/tex]
What are the missing angle measures in parallelogram
RSTU?
A. MZR = 70°, mT = 110°, mzU = 110°
B. mZR = 110°, m_T = 110°, m_U = 70°
C. mZR = 110°, m_T = 70°, m_U = 110°
D. mZR = 70°, mZT = 110°, m_U = 70°
Based on the properties of a parallelogram, the missing angle measures are:
m∠U = 70°m∠R = 110°m∠T = 110°What are the Angles of a Parallelogram?The opposite angles of a parallelogram are defined as congruent angles, while the adjacent angles in a parallelogram are supplementary.
Thus:
m∠U = m∠S = 70°
m∠R = 180 - 70 = 110°
m∠T = m∠R =110°
Therefore, based on the properties of a parallelogram, the missing angle measures are:
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The missing angle measures are:
m∠U = 70°m∠R = 110°m∠T = 110°What are the Angles of a Parallelogram?A parallelogram's opposing angles are known as congruent angles, whilst its adjacent angles are known as supplementary angles.
So, by the property of parallelogram
m∠U = m∠S = 70°
m∠R = 180 - 70
m∠R = 110°
and, m∠T = m∠R =110°
Thus, by the properties of a parallelogram, the angle are:
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Can someone please help me with this math question
Answer:
C'(4,4)
Step-by-step explanation:
The dilation of quadrilateral ABCD over the origin by a scale factor of 2 has the rule
(x,y)→(2x,2y)
So,
A(-3,-1)→A'(-6,-2)B(-1,1)→B'(-2,2)C(2,2)→C'(4,4)D(3,-2)→D'(6,-4)Hence, the coordinates of the image point C' are (4,4) (see attached diagram for details)
Answer:
The coordinates of C' = (4,4)
Step-by-step explanation:
The coordinates of C can be found by looking at the graph,
Coordinates of C = (2,2)
ABCD is dilated by a factor of 2 to get A'B'C'D'.
So, the coordinates of C' will be found by multiplying the coordinates of C by 2.
C' = (2*2,2*2)
C' = (4,4)
So, The coordinates of C' = (4,4)
A Chi square test has been conducted to assess the relationship between marital status and church attendance. The obtained Chi square is 23.45 and the critical Chi square is 9.488. What may be concluded?
a. reject the null hypothesis, church attendance and marital status are dependent
b. reject the null hypothesis, church attendance and marital status are independent
c. fail to reject the null hypothesis, church attendance and marital status are dependent
d. fail to reject the null hypothesis, church attendance and marital status are independent
Answer: a. reject the null hypothesis, church attendance and marital status are dependent
Step-by-step explanation:
If the obtained chi-square value is greater than the critical chi square value then we reject the null hypothesis.Given : A Chi square test has been conducted to assess the relationship between marital status and church attendance. The obtained Chi square is 23.45 and the critical Chi square is 9.488.
Null hypothesis : There is no relationship between the variables.
Alternative hypothesis : There is a relationship between the variables.
Here we can see that the obtained chi-square (23.45) value is greater than the critical chi square value (9.488) , then we have to reject the null hypothesis.
So the correct answer is reject the null hypothesis, church attendance and marital status are dependent.
Given the obtained Chi-square 23.45 is greater than the critical Chi square 9.488, we reject the null hypothesis, implying there is a significant relation or dependence between marital status and church attendance.
Explanation:In a Chi square test, if the obtained Chi square value is higher than the critical Chi square value, it means that the observed data significantly deviates from what is expected under the null hypothesis. Therefore, in this case, where the obtained Chi square is 23.45 and the critical number is 9.488, we would reject the null hypothesis. Considering that the null hypothesis is generally posed under the assumption of no relation or independence between the variables being tested, rejecting it thus implies that there is a significant relationship or dependence between marital status and church attendance. Therefore, the correct answer to the question is a. reject the null hypothesis, church attendance and marital status are dependent
.
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which methods could you use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15)
Answer:
Option D. Divide 15 by 2
Step-by-step explanation:
we know that
To find the y-coordinate of the midpoint of a vertical line, adds the y-coordinates of the endpoints and divide by two
we have the endpoints
(0,0) and (0,15)
The y-coordinate of the midpoint is (0+15)/2=15/2=7.5
therefore
Divide 15 by 2
Answer:
the answer is to count by hands ( A ) and divide 15 by 2 ( D )
Step-by-step explanation:
What is the complementary event to drawing a blue marble? (check all that apply)
drawing a red marble
drawing a green marble
drawing a red or green marble
not drawing a blue marble
PLZ hurry I give brainly
The complementary event to drawing a blue marble includes any outcome other than drawing a blue marble. Therefore, drawing a red marble, a green marble, a red or green marble, or not drawing a blue marble, all are complementary events.
Explanation:In probability, the complementary event of an event represents all outcomes not covered by the original event. In this case, the original event is 'drawing a blue marble'. Thus, the complementary event would include any outcome other than drawing a blue marble.
Based on the options given:
Drawing a red marbleDrawing a green marbleDrawing a red or green marbleNot drawing a blue marbleAll these are complementary events to drawing a blue marble, as they all represent outcomes other than 'drawing a blue marble'.
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Tyler and Katie started a lemonade stand to raise money. They donated \dfrac{2}{10} 10 2 ? start fraction, 2, divided by, 10, end fraction of their profits to their school library, \dfrac{1}{10} 10 1 ? start fraction, 1, divided by, 10, end fraction to the animal shelter, and \dfrac{4}{10} 10 4 ? start fraction, 4, divided by, 10, end fraction to the food bank. They saved the rest to buy materials for their next project. What fraction of their profits did Tyler and Katie donate?
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
Fraction of the amount donated to school library = [tex]\frac{2}{10}[/tex]
Fraction of the amount donated to animal shelter = [tex]\frac{1}{10}[/tex]
Fraction of the amount donated to food bank = [tex]\frac{4}{10}[/tex]
The rest of the amount was saved for next project.
Thus, the total fraction of the amount donated will be the sum of fractions of amount donated to school library, animal shelter and food bank.
i.e.
Fraction of the amount donated = [tex]\frac{2}{10}+\frac{1}{10}+\frac{4}{10} = \frac{7}{10}[/tex]
This means, Tyler and Katie donated [tex]\frac{7}{10}[/tex] of their profits.
Answer:−1.825
Step-by-step explanation:
A man buys 52 coconuts, but some are lost on his way home. If he evenly divides the amount of coconuts he has left among four people, 3 coconuts are left. If he divides the coconuts among three people, 2 remain. And if he divides the coconuts among five people, he's left with 2 coconuts. How many coconuts did he lose on his way home?
Answer:
4 coconuts
Step-by-step explanation:
52-x/4+3+5
52-x/12
13-x/3
4
Answer:
5 coconuts
Step-by-step explanation:
If there were no loss , and 52 coconuts were distributed among 4 people, the number of coconuts each one would have obtained would be 13. Now as few coconuts are spoiled, the each one of those 4 people can get
1) 12 coconuts , and as per condition given there will be 3 more coconuts left. Hence total number of coconuts would be 12*4+3=48+3=51
Hence 1 coconuts would have been spoiled. Now let us see if this satisfies the second condition too.
If 51 coconuts are distributed equally among 3 people , each one gets 17 coconuts and none is left. But the condition says that 2 coconuts are left. Hence
Our assumption of loss of coconut was wrong.
2) 11 coconuts, as per condition given there will be 3 more coconuts left. Hence total number of coconuts would be 11*4+3=44+3=47
Hence 52-47=5 coconuts would have been spoiled. Now let us see if this satisfies the second condition too.
If 47 coconuts are distributed equally among 3 people , each one gets 15 coconuts and 2 coconuts are left. Hence it satisfies the second condition also. Let us see, if it satisfies third condition too.
If 47 coconuts are distributed among 5 people , each one gets, 9 cocnuts and coconuts left will be 2. Hence it satisfies the third condition also.
Hence , there were 5 coconuts spoiled.
I need help with this transformation.
Answer:
So a translation and a rotation and that is it.
D.
Step-by-step explanation:
There is no reflection.
If we had a negative in front of the x there would have been a reflection.
We can definitely tell the graph was translated 3 units up because of the +3.
There are other ways to look at a translation of a line but it has been translated for sure.
It has also been rotated because of the factor of 1/9 in front of x.
Let me show you a graph.
Comparing to y=mx+b where m is slope and b is y-intercept, we see the slope of f(x)=x is 1 and the y-intercept of f(x)=x is 0 while
the slope of g(x)=(1/9)x+3 is (1/9) and y-intercept of g(x)=(1/9)x+3 is 3.
I drew them here on the graph.
I also drew y=x+3 which has slope 1 and y-intercept 3.
So I just wanted to show you have we translate y=x up to y=x+3, you still don't have the same line. But notice if you rotate y=x+3 using the (0,3) as the center of rotation you could get the green line to lay on the orange line.
Is this supposed to be multiple choice? If so it's a terrible question as the answer is all of the above. I'll sketch out the transformations, avoiding details.
Transform y=x to y=x/9 + 3
a. using rotation and reflection
Rotate around the origin to get y=-x/9 and reflect in y=3/2 to get y=x/9 +3
b. using translation, reflection, rotation
Translate to y = x - 3, reflect in the x axis to get y = x + 3 and rotate around (0,3) to get the result.
c. using translation and reflection.
Translate to y = x + 3 and reflect along the line which bisects the angle at (0,3).
d. rotation and translation
Rotate to a slope of 1/9 and translate up 3 units.
You have a 10 by 24 piece of cardboard. You are going to cut squares of equal size from each corner, and fold up the sides to make an open box as shown below. Write an expression for the width of the box.
Answer:
10-2x
Step-by-step explanation:
If x is the length of one side of the square, the total width of the cardboard has two squares cut from it. The amount of width remaining is the width of the box. Since the original width of the cardboard is 10, the width of the box is ...
10 -2x
Over twenty years, it was found that the number of doctors of medicine, MD (in thousands), in the United States can be approximated by MD=(28,390+693t)/(85-t) where t=0 represents 1980. The number of doctors of osteopathy, DO (in thousands), can be approximated by DO=(776-12t)/(65-2t) .
Write an expression for the total number I of doctors of medicine (MD) and doctors of osteopathy (DO). Simplify the result.
How many MDs did the United States have in 2010? How many MDs did the United States have in 2010?
Answer:
16. the expression below.
17. about 470,933 MD's and about 18,743 DO's
The expression for the total number of doctors is [tex]\frac{-1374t^2+43192.22t+67805.35}{(65-2t)(85-t) }[/tex]
We have to write an expression for the number of MD and DO
a. MD + DO
[tex]\frac{28390+693t}{85-t} +\frac{776-12t}{65-2t}[/tex]
This can be simplified as
[tex]\frac{(28390+693t)(65-2t)+(776-12t)(85-t) }{(85-t)(65-2t) }[/tex]
[tex]= \frac{-1374t^2+43192.22t+67805.35}{(65-2t)(85-t) }[/tex]
b. If t = 0 in 1980, in 2010, t = 30
The number of MD would be
[tex]\frac{28390+693*30}{85-30} \\= 379[/tex]
The number of DO would be
[tex]\frac{776-12*30}{65-2*30}\\\\= 83[/tex]
Read more on mathematical expressions here: https://brainly.com/question/723406
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What is cos3phi= 1/2??? Please help and explain!
Answer:
[tex]\large\boxed{\Phi=\dfrac{\pi}{9}+\dfrac{2k\pi}{3}\ or\ \Phi=-\dfrac{\pi}{9}+\dfrac{2k\pi}{3}}[/tex]
Step-by-step explanation:
[tex]\cos3\Phi=\dfrac{1}{2}\qquad\text{substitute}\ 3\Phi=\theta\\\\\cos\theta=\dfrac{1}{2}\iff\theta=\dfrac{\pi}{3}+2k\pi\ or\ \theta=-\dfrac{\pi}{3}+2k\pi\qquad k\in\mathbb{Z}\\\\\text{We're going back to substitution:}\\\\3\Phi=\dfrac{\pi}{3}+2k\pi\ or\ 3\Phi=-\dfrac{\pi}{3}+2k\pi\qquad\text{divide both sides by 3}\\\\\Phi=\dfrac{\pi}{9}+\dfrac{2k\pi}{3}\ or\ \Phi=-\dfrac{\pi}{9}+\dfrac{2k\pi}{3}[/tex]
Please help prove these identities!
We have the following expression:
[tex]tan(\theta)cot(\theta)-sin^{2}(\theta)=cos^2(\theta)[/tex]
We know that:
[tex]cot(\theta)=\frac{1}{cot(\theta)}[/tex]
Therefore, by substituting in the original expression:
[tex]tan(\theta)\left(\frac{1}{tan(\theta)}\right)-sin^{2}(\theta)=cos^2(\theta) \\ \\ \\ Simplifying: \\ \\ 1-sin^2(\theta)=cos^2(\theta)[/tex]
We know that the basic relationship between the sine and the cosine determined by the Pythagorean identity, so:
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]
By subtracting [tex]sin^2(\theta)[/tex] from both sides, we get:
[tex]\boxed{cos^2(\theta)=1-sin^2(\theta)} \ Proved![/tex]
PART b)We have the following expression:
[tex]\frac{cos(\alpha)}{cos(\alpha)-sin(\alpha)}=\frac{1}{1-tan(\alpha)}[/tex]
Here, let's multiply each side by [tex]cos(\alpha)-sin(\alpha)[/tex]:
[tex](cos(\alpha)-sin(\alpha))\left(\frac{cos(\alpha)}{cos(\alpha)-sin(\alpha)}\right)=(cos(\alpha)-sin(\alpha))\left(\frac{1}{1-tan(\alpha)}\right) \\ \\ Then: \\ \\ cos(\alpha)=\frac{cos(\alpha)-sin(\alpha)}{1-tan(\alpha)}[/tex]
We also know that:
[tex]tan(\alpha)=\frac{sin(\alpha)}{cos(\alpha)}[/tex]
Then:
[tex]cos(\alpha)=\frac{cos(\alpha)-sin(\alpha)}{1-\frac{sin(\alpha)}{cos(\alpha)}} \\ \\ \\ Simplifying: \\ \\ cos(\alpha)=\frac{cos(\alpha)-sin(\alpha)}{\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)}} \\ \\ Or: \\ \\ cos(\alpha)=\frac{\frac{cos(\alpha)-sin(\alpha)}{1}}{\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)}} \\ \\ Then: \\ \\ cos(\alpha)=cos(\alpha).\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)-sin(\alpha)} \\ \\ \boxed{cos(\alpha)=cos(\alpha)} \ Proved![/tex]
PART c)We have the following expression:
[tex]\frac{cos(x+y)}{cosxsiny}=coty-tanx[/tex]
From Angle Sum Property, we know that:
[tex]cos(x+y)=cos(x)cos(y)-sin(x)sin(y)[/tex]
Substituting this in our original expression, we have:
[tex]\frac{cos(x)cos(y)-sin(x)sin(y)}{cosxsiny}=coty-tanx[/tex]
But we can also write this as follows:
[tex]\\ \frac{cosxcosy}{cosxsiny}-\frac{sinxsiny}{cosxsiny}=coty-tanx \\ \\ Simplifying: \\ \\ \frac{cosy}{siny}-\frac{sinx}{cosx} =coty-tanx \\ \\ But: \\ \\ \frac{cosy}{siny}=coty \\ \\ \frac{sinx}{cosx}=tanx \\ \\ Hence: \\ \\ \boxed{coty-tanx=coty-tanx} \ Proved![/tex]
PART d)We have the following expression:
[tex]\ln\left|1+cos \theta\right|+\ln\left|1-cos \theta\right|=2\ln\left|sin \theta\right|[/tex]
By Logarithm product rule, we know:
[tex]log_{b}(x.y) = log_{b}(x) + log_{b}(y)[/tex]
So:
[tex]\ln\left|1+cos \theta\right|+\ln\left|1-cos \theta\right|=\ln\left|(1+cos \theta)(1-cos \theta)\right|[/tex]
The Difference of Squares states that:
[tex]a^2-b^2=(a+b)(a-b) \\ \\ So: \\ \\ (1+cos \theta)(1-cos \theta)=1-cos^2 \theta[/tex]
Then:
[tex]\ln\left|(1+cos \theta)(1-cos \theta)\right|=\ln\left|1-cos^{2} \theta\right|[/tex]
By the Pythagorean identity:
[tex]sin^2(\theta)+cos^2(\theta)=1 \\ \\ So: \\ \\ sin^2 \theta = 1-cos^2 \theta[/tex]
Then:
[tex]\ln\left|1-cos^{2} \theta\right|=\ln\left|sin^2 \theta|[/tex]
By Logarithm power rule, we know:
[tex]log_{b}(x.y) = ylog_{b}(x)[/tex]
Then:
[tex]\ln\left|sin^2 \theta|=2\ln\left|sin \theta|[/tex]
In conclusion:
[tex]\boxed{\ln\left|1+cos \theta\right|+\ln\left|1-cos \theta\right|=2\ln\left|sin \theta\right|} \ Proved![/tex]
Please help me with this story problem.
Answer:
Step-by-step explanation:
We know that the function is measured in terms of time. And the constant distance traveled in 50 miles. The inverse of the function is supposing say t(d) which measures the function in terms of distance traveled. The inverse of the function is obtained by dividing the distance by 50 as in the original function then the function is multiplied by 50. So the inverse of function obtained is: t(d) = d/50
Steps: d(t) = 50t
t = d/50
t(d) = d/50
I hope this helps!
What is the measure of x? Help me on this Geometry question.
Answer:
21°
Step-by-step explanation:
the angles of triangle abc has to = 180 so subtract the known angles to get 21
angles bca and daf have to be the same so its 21
Answer:
[tex]x=21[/tex]
Step-by-step explanation:
We have been given an image of two parallel lines cut by a transversal. We are asked to find the measure of x.
We know that corresponding angles of two parallel lines are equal. We can see that angle BCA and angle DAF are corresponding angles.
Let us find measure of angle BCA using angle sum property.
[tex]54^{\circ}+105^{\circ}+m\angle BCA=180^{\circ}[/tex]
[tex]159^{\circ}+m\angle BCA=180^{\circ}[/tex]
[tex]159^{\circ}-159^{\circ}+m\angle BCA=180^{\circ}-159^{\circ}[/tex]
[tex]m\angle BCA=21^{\circ}[/tex]
Therefore, the value of x is 21 degrees.
Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample. If you have a gerbil, then you are a pet owner
Answer: The contrapositive statement :"If you do not have a gerbil, then you are not a pet owner.”
It is false.
Counter example : If you have a dog, then you are a pet owner.
Step-by-step explanation:
We know that the contrapositive of a statement of the form " If a then b" is "If not a then not b.
Given: The conditional statement is "If you have a gerbil, then you are a pet owner.”
Then the contrapositive statement will be "If you do not have a gerbil, then you are not a pet owner.”
The contrapositive statement is false.
Counter example : If you have a dog, then you are a pet owner.
Means if you area pet owner then it can be any pet not just gerbil.
Answer:
The contrapositive is false.
Step-by-step explanation:
Given conditional statement is :
If you have a gerbil, then you are a pet owner (conditional statement is in the form of if p, then q)
The contrapositive is represented as (if not q, then not p)
So, the contrapositive sentence will be :
If you are not a pet owner, then you do not have a gebril.
This statement is false as if you are not a pet owner then you will not have any animal with you and not only gebril.
Find the slope of the function f ( x ) = 5x/2 + 3, by the definition of limit. Express answer as a fraction using the "/" key as the fraction bar.
[tex]\huge{\boxed{\frac{5}{2}}}[/tex]
Slope-intercept form is [tex]f(x)=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
[tex]\frac{5x}{2}=\frac{5}{2}x[/tex], so change the equation to represent this. [tex]f(x)=\frac{5}{2}x+3[/tex]
Great! Now the function is in slope-intercept form, so we can just see that [tex]m[/tex], or the slope, is equal to [tex]\boxed{\frac{5}{2}}[/tex]
An engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 130lb and 171lb. The new population of pilots has normally distributed weights with a mean of 137lb and a standard deviation of 28.9lb. If a pilot is randomly selected find the probability that his weight is between 130lb and 171lb
Answer: 0.4758
Step-by-step explanation:
Given : Mean : [tex]\mu=137\text{ lb}[/tex]
Standard deviation : [tex]\sigma =28.9\text{ lb}[/tex]
Also, the new population of pilots has normally distributed .
The formula to calculate the z-score :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x=130 lb .
[tex]z=\dfrac{130-137}{28.9}=-0.2422145\approx-0.24[/tex]
For x=171lb.
[tex]z=\dfrac{171-137}{28.9}=1.1764705\approx1.18[/tex]
The p-value =[tex]P(-0.24<z<1.18)=P(z<1.18)-P(z<-0.24)[/tex]
[tex]=0.8809999-0.4051651=0.4758348\approx0.4758348\approx0.4758[/tex]
Hence, the required probability : 0.4758
CAN SOMEONE HELP ME FIND THE CIRCUMFERENCE
Answer:
51.496 miles
Step-by-step explanation:
circumference of circle= 2pir
here we will tale radius as 8.2 because 16.4 is diameter of circle.
2*3.14*8.2=
6.28*8.2=51.496 miles