The coordinates of the points dividing the line in 5:3 is (3/2, 3)
What is section formula?The section formula gives the coordinates of a point which divides the line joining two points in a ratio, internally or externally.
Given a line LM, passing through points (-1,-2) and (3,6) a point is dividing it in a ratio of 5:3
According to section formula,
(x, y) = (5*3 - 3*1)/8, (5*6 - 3*2)/8
(x, y) = (3/2, 3)
Hence, The coordinates of the points dividing the line in 5:3 is (3/2, 3)
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evaluate the integral. check your result by differentiation. (remember the constant of integration.) (x2 4)32x dx
The solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]
Given;
To evaluate the value of a given integral;
[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex]
Let;
[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex]
Now, assume u = x² + 4
→ [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex] = [tex]2\cdot \int \frac{u^3}{2}du[/tex]
→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]
→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]
→ [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]
By adding constant C;
[tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]+ C
Hence, the solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]
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What is "-1/6" as a whole number
Answer:
-0.16
Step-by-step explanation:
Divide the answer :)
if a coin with a date on it is found in a sealed archaeological deposit, we know that the deposit can be no older than the date on the coin. in that situation the date on the coin represents group of answer choices
Using the theories of archaeology, we got that date on the coin represents
a terminus post quem if a coin with a date on it is found in a sealed archaeological deposit.
Potassium-argon dating: This absolute dating method was actually developed by the A.E. Douglass, an American astronomer, chiefly from work he conducted at the Pueblos of American Southwest tree-ring dating Layers of the sediments resulting from the melting of ice sheets and deposited in the lakes on an annual basis are known as varves
Hence, if a coin with a date on it is found in a sealed archaeological deposit, and we know that the deposit can be no older than the date on the coin. in that situation the date on the coin represents a terminus post quem.
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help me guys ..........
Answer:
here you go....
Step-by-step explanation:
M(3,-2) is reflected in the line y=5?
The coordinates of the image of reflecting (3, -2) across the line y = 5 are (3, 12)
What is the image of the point after the reflection?
When we reflect a point (x, y) across a horizontal line of the form:
y = a
The coordinates of the image after the reflection are:
(x, 2a - y)
In this case we have the point (3, -2), and we reflect this across the line y = 5, then the new coordinates are:
(3, 2*5 - (-2))
(3, 10 + 2)
(3, 12)
The coordinates after the image are (3, 12)
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Figure JKLMN is reflected across the y-axis to form figure J'K'L'M'N'.
What are the coordinates of the vertices of figure J'K'L'M'N'?
Decide if each statement describing figures JKLMN and J'K'L'M'N' is true or false. Choose True or False for each statement.
a. L' is located at (-3, 4).
b. M' is located 4 units left of the y-axis.
c. The y-coordinate of N' is the opposite of the y-coordinate of N.
d. J'K' = JK
e. M' is located at (-4, 1).
The co-ordinates of J'K'L'M'N' are (0,5), (-2,3), (-3,4), (-4,1), (-1,2)
What is Co-ordinate Geometry?
Coordinate geometry is a field of mathematics that assists in displaying geometric forms on a two-dimensional plane and learning the attributes of these figures.
Solution:
The co-ordinates of J'K'L'M'N' are (0,5), (-2,3), (-3,4), (-4,1), (-1,2)
From the figure it can be clearly observed that
a) L' is located at (-3,4) - True
b) M' is located 4 units left of the y - axis - True
c) The y - co ordinate of zN' is the opposite of the y - co ordinate of N - False
d) J'K' = JK - False
e) M' is located at (-4,1) - True
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(a) A(-1,4)and B(3,2) are the end points of a line segment AB. Determine (i) The gradient of AB. (ii) The coordinates of the midpoint of AB. (iii) The equation of the perpendicular bisector of AB.
The slope of the line is -1/2, the coordinates of midpoint is (1,3) and the equation of perpendicular bisector is y = 2x + 1
What is slope?The slope of a line is a measure of its steepness.
Given that, a line segment has end points = A(-1,4) and B(3,2)
(i) Slope = (y2 - y1)/(x2 - x1) = -1/2
(ii) Coordinates of the midpoint of a line = (Xm, Ym) = (x₁ + x₂)/2, (y₁ + y₂)/2
(Xm, Ym) = (-1+3)/2, (4+2)/2 = (1,3)
(iii) The slope of the two lines perpendicular to each other are negative reciprocal of each other, so, slope of the line perpendicular to the given line is = 2
Standard equation of a line = y = mx + c
Since the line is the perpendicular bisector of AB, it will pass through (1,3)
Solving for c,
3 = 2*1 + c
c = 1
Therefore, the equation of the of line perpendicular to AB is
y = 2x + 1
Hence, the slope of the line is -1/2, the coordinates of midpoint is (1,3) and the equation of perpendicular bisector is y = 2x + 1
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The floor of a canyon has an elevation of −14. 5 feet. Erosion causes the elevation to change by −1. 5 feet per year. How many years will it take for the canyon floor to have an elevation of −31 feet?.
It will take 11 years for the canyon floor to have an elevation of −31 feet.
Define equation.A mathematical statement known as an equation makes two expressions' values equal. It is a mathematical statement that says "this is equivalent to that," in other words. The left side appears to be a mathematical expression, the centre appears to be an equal sign, and the right side is another mathematical expression. The right side of the equation frequently has a value of zero.
Given,
The first step in this situation is to define the variables.
So, we have:
x: the age in years
y: height in feet
The equation used to model the issue is then written.
So, we have:
y = 1.5x - 14.5
Then, at a -31 foot elevation, we have:
-31 = 1.5x - 14.5
For years,
x = -16.5/1.5
x = 11
In 11 years it will take for the canyon floor to have an elevation of −31 feet.
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Given: AB || CE
Find: ED
Answer:
49
Step-by-step explanation:
18/42=21/ED
18 ED=882
ED=49
Select the correct answer. The table shows the balance of an investment account at the beginning of each year the account was held. Assuming that no other deposits have been made to the account, which statement describes the account's growth?
Year/////Account Balance
1: $500.00
2: $510.00
3: $520.20
○The account is growing linearly at an annual interest rate of 4.04%.
○The account is growing exponentially at an annual interest rate of 4.04%. MUTAT
○The account is growing linearly at an annual interest rate of 2.00%.
○The account is growing exponentially at an annual interest rate of 2.00%.
The statement that describes the account growth is D. The account is growing exponentially at an annual interest rate of 2.00%.
How to calculate the growth?From the information, the table shows the balance of an investment account at the beginning of each year the account was held.
The percentage change for the second year will be:
= (510 - 500) / 500 × 100
= 10/500 × 100
= 2%
The percentage change for the third year will be:
= (520.20 - 510) / 510 × 100
= 10.20/510 × 100
= 2%
Therefore, there's. 2% growth.
The correct option is D.
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Answer:
D
Step-by-step explanation:
Can u help me please
The slope of the line as shown in the diagram is 4/3.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount.
To calculate the slope from the diagram, we use the formula below.
Formula:
S = Δy/Δx........... Equation 1Where:
S = Slope.From the graph,
At x = 30, y = 20
And at x = 60, y = 60
Therefore,
Δy = 60-20 = 40Δx = 60-30 = 30Substitute these values into equation 1
S = 40/30S = 4/3Hence, the slope of the is 4/3.
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When b is 9 what is 24/b + 8? In my homework, it says it is not 10, 11, 10.6 or 10.666.
Answer:
10.7
Step-by-step explanation:
The only thing I can think of is 10.7. Because when you do this problem you get 10.6666666667. So I'm assuming you're to round it. There is no other way to solve the problem that wouldn't get you either 10.6666666667 or 10.7.
Answer:
10.66
Step-by-step explanation:
[tex]\frac{24}{9}[/tex] + [tex]\frac{8}{1}[/tex]
[tex]\frac{24}{9}[/tex] + [tex]\frac{72}{9}[/tex]
[tex]\frac{96}{9}[/tex]
10.666...
Which of the following functions is graphed below?
Answer: B
Step-by-step explanation:
Answer:
Your answer is B
Step-by-step explanation:
It takes 5 minutes for your printer to print 40 papers
How long does it take for your printer to print 12 papers?
Answer:
1.5 minutes (or 1 minute and 30 seconds)
Step-by-step explanation:
5 : 40 = x : 12
x = (5 * 12)/40
x = 12/8
x = 1.5 minutes
Answer: 1 min and 50 seconds
Step-by-step explanation:
first, you have to find the unit rate of how many papers the printer can make in a min which is 40 divided by 5 which gets you a unit rate of 8 for every minute then you take your 12 paper and divide it by your unit rate of 8 per minute which gets you how long it would take to print 12 papers which equal 1.5
(13.4-0.896 and 8.6 + 9.16 pls help thx
The simplified terms are 12.504 and 17.76 when the terms are in decimal.
Given that,
The numbers are 13.4-0.896 and 8.6 + 9.16
We have to simplify the terms.
We know that,
When a full number and a fraction are combined, decimals are used. The "." symbol, often known as a decimal point, will be used to demarcate the entire number from the fraction in this instance.
Take the numbers,
13.4-0.896
Subtracting the terms
12.504
Take the numbers,
8.6 + 9.16
Adding the terms
17.76
Therefore, The simplified terms are 12.504 and 17.76 when the terms are in decimal.
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Seema used compatible numbers to estimate the product of (–25. 31)(9. 61). What was her estimate? –250 –240 240 250.
Estimate product of (-25.31) (9.61) using compatible numbers is equal to -250.
As given in the question,
Given expression is equal to :
( -25.31 ) ( 9.61 )
Compatible numbers to calculate the estimate product we have,
Compatible number for ( -25.31 ) is equal to ( -25 ) .
-25 > -25.31 > -26
-25.31 is more nearer to -25 .
Now, 9 < 9.61 < 10
Compatible number for 9.61 is equal to 10 as 9.61 is more close to 10.
( -25.31 ) × ( 9.61 )
= ( -25 ) × (10)
= 250
Therefore, estimate product of (-25.31) (9.61) using compatible numbers is equal to -250.
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Find the equation of the exponential function represented by the table below:
x. Y
0 0.01
1. 0.04
2 0.16
3 0.64
The equation of the exponential function represented by the table y = 0.12x + 0.01
From the table choose two points
The first point = (1, 0.04)
The second point = (2, 0.16)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (0.16 - 0.04) / (2-1)
= 0.12/1
= 0.12
From the table we can see that at x = 0 the value of y = 0.01, then the value of y intercept is 0.01
The slope intercept form is
y = mx + b
Substitute the values in the equation
y = 0.12x + 0.01
Hence, the equation of the exponential function represented by the table y = 0.12x + 0.01
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what is the linear equation to
x=-3x+8
The linear equation is equal to
y = -3x + 8
m = slope
x = input variable
c = 8
What is linear function ?The given equation is linear function or linear equation
A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
Definition of variables to suit the problem to be solved
y = output variable
m = slope
x = input variable
c = y intercept
In comparison, to the linear equation given as equal to
y = -3x + 8
m = -3
x = input variable
c = 8
putting the input variables gives out put accordingly
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Conider the polynomial function []
p
given by p(x)=5x38x2−3x1
A(x). Evaluate the function at x=−2
x
The polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 value at x = -2 is -1
given that
polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 at x=-2
To find the value of a function at x = -2, put in all the places of in the function.
Polynomial is made up of two words, poly, and nomial. "Poly" means many, and "nomial" means the term, and hence when they are combined, we can say that polynomials are "algebraic expressions with many terms".
Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants.
Here,
p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 put x =-2
p(-2) = 5[tex](-2)^{3}[/tex]+8[tex](-2)^{2}[/tex] - 3(-2)+1
p(-2) = 5(-8) + 8(4) + 6+1
p(-2) = -40+32+6+1
p(-2) = -40+39
p(-2) =-1
At So, the value of the function at x= -2 is -1
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Create the graph of this quadratic function below please!
x2+3x-108
Make sure to have the two roots and axis of symmetry AKA the vertex.
The graph of this quadratic function (x² + 3x - 108) is shown in the image attached below. Also, the two roots of this quadratic equation (x² + 3x - 108) are -12 and 9, while the axis of symmetry (vertex) is equal to -1.5.
What is a quadratic function?In Mathematics, a quadratic function is a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph.
Mathematically, the graph of every quadratic functions is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function would always form a parabolic curve. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.
Next, we would determine the axis of symmetry (vertex) of this quadratic function:
Axis of symmetry (vertex), Xmax = -b/2a
Axis of symmetry (vertex), Xmax = -3/2(1)
Axis of symmetry (vertex), Xmax = -1.5.
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Factor: 4x + 18 =
I don't understand Pre-algebra
Answer:
2(2x+9)
Step-by-step explanation:
Just break each number up
2 X 2 = 4
2 X 9 = 18
2(2x+9)
Answer:
-4.5
......
......
six ants simultaneously stand on the six vertices of a regular octahedron, with each ant at a different vertex. simultaneously and independently, each ant moves from its vertex to one of the four adjacent vertices, each with equal probability. what is the probability that no two ants arrive at the same vertex?
The probability that no two ants will reach the same vertex is 5/256.
Plane, point B and attention. Ants that move to D can come from either E or C. Ants moving to E can come from either B or D of points A and F of the octahedron. Therefore, there are 2 degrees of freedom to decide which ants move to D, 2 degrees of freedom to decide which ants move to E, and 2 degrees of freedom to decide which ants move to A.
So there are 2× 2× 2=8 ways an ant can move to different points.
There are 8 ways for ants to move to different points.
Points B, there are a total of 8 + 4 + 8 = 16 ways Ant can move to her different points. Aligned the square so that point B is defined as point where the ant moved from point A.
An ant can actually move from point A to 4 different points, so there are a total of 4×20=80 ways an ant can move to different points.
Each ant acts independently and has 4 different points to choose from.
So each ant has a 1/4 chance of moving to the desired location. Since he has 6 ants, the probability of appearance is
= 1/4096
So, the desired answer is 80/4096
= 5/256
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An expression is shown.
m² = 9+55
What is the positive value of m?
Answer: 8
[tex]m^{2} = 9+55\\m^{2} = 64\\m=8[/tex]
Answer: m = 8
9 + 55 = 64
[tex]\sqrt{64}[/tex] = 8
[tex]8^{2}[/tex] = 64
A. Solve for x. B. Is the triangle equilateral?
Answer:
x=8
No it’s not an equilateral
Step-by-step explanation:
Since side AB is about the same length as BC we can set them equal to each other
x-1=7
+1 +1
x=8
This is not an equilateral because if you fill in X for the third side you will get 5
8-3=5
Lance recieved 10 more sweets than Randal and Rema recieved three times the amount that was given to Lance and handal. The total number of sweets that was shared is 120. How many did Rema recieve?
Answer:
Rema receives 90 sweets
Step-by-step explanation:
See attached image
For her softball uniform,Meredith has a green,white,or striped jersey.She also has white or green shorts.If Meredith chooses a jersey and shorts randomly ,what is the probability that she will go to softball practice ima striped jersey and green shorts?
Answer: Give me brainliest or your mean.
Step-by-step explanation: 1/3 jersey 1/2 short. 1/3 x 1/2 = 1/6 possibility.
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.
The probability of a type I error is 0.022.
Given,
In the question;
It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested receive an incorrectly positive response because they do not have the condition.
The null hypothesis is given as "the individual does not have the disease".
We have to find the probability of type l error if the new blood test is used;
Here,
A: The individual does not have the disease
B: The individual does have the disease
We know that,
Type I Error is rejecting the true null hypothesis
Then, probability;
P (Type I Error) = P(Positive reaction to an individual who does not have the disease) = 0.022
Hence, The probability of a type I error is 0.022.
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helene was paid a total of $33.00 for the 6 hours she worked. she continues to be paid at the same rate. how long would it take her to earn $165.00 for working?
The number of hours that helena need to work to generate 165 dollars is
33 hours.
Helena has to work hours to earn $165. 33
Algebraic equations are equations with
unknown variables. The alphabet letters are used to represent algebraic equations.
Total $33.00 in her 6 hours she worked.
This question should find out how long it takes her to earn her $165.00 in that job.
let x hours be required work hours to earn $165.00 ..
This can be expressed in algebraic equations as:
x= 6× 165/33
x= 990/33
x= 30
Hence, helna have to work thirty hours to earn $165.00 ..
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What is the decimal value of 5/6? Show your work using long division.
Answer:
0.83 repeating 3
Step-by-step explanation:
5 goes in the box and 6 goes outside. you can't put 6 into 5 so you would put a 0 on the top and a decimal point. now you would write a 0 next to the 5 and you would do 6×8=48 and so put 8 next to the 0 and the decimal point. then subtract 50-48 which will be 2. Put another 0 next to the 50 and bring it down. you will have 20 which you do 6×3=18. and so put a 3 next to 0.8 and you will subtract 20-18=2. It will be repeating so put a line at the top of 3 to show that it's repeating.
Find the value of x.
a
x = [?]
x
In the given circle the length of the chord marked x is
We know that the length of the chord is bisected by the perpendicular from the center of the circle.
Therefore the length of the chord is 7 × 2 = 14 units.
Again from the chord properties of a circle we know that, chords that are equidistant from the center are equal.
Since both the chords are at a distance of 9 units hence both chord lengths
Hence the length of the other chord = 14 units.
∴ x = 14
The segment of a line that joins any two points on a circle's circumference is known as the chord. It must be emphasized that its longest chord is its diameter, which runs through the center of the circle.
The circle and its chord are depicted in the diagram below. In the center of the circle, equal-length chords subtend equal angles.
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