Exact value of the expression cos (2 [tex]tan^-^1 (\frac{4}{3})[/tex]) = -7/25 . which is the cosine of the value of an angle 2 [tex]tan^-^1 (\frac{4}{3})[/tex]) .
let [tex]tan^-^1 (\frac{4}{3})[/tex] = θ
so tan θ = 4/3
tan θ = p/b
Trignometic angle formula
so p= 4k and b= 3k where k is a constant value.
h = [tex]\sqrt{p^2+b^2}[/tex]
=> [tex]\sqrt{16k^2+ 9k^2}[/tex]
=> 25k^2
=> 5k
where p is perpendicular , b is base and h is hypotenuse
so h= 5k
sin θ = p/h
=> 4k/5k
=> 4/5
cos θ =b/h
=> 3k/5k
=> 3/5
and cos (2 [tex]tan^-^1 (\frac{4}{3})[/tex]) = cos (2θ)
cos (2θ) = 2 [tex]cos^2[/tex] θ -1
=> 2 * [tex]\frac{3}{5} ^2[/tex] - 1
=> 18/25 -1
=> -7/25
so value of cos (2 [tex]tan^-^1 (\frac{4}{3})[/tex]) = -7/25
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Which of the following best describes the solutions to the equation below?
3x+8=2(x+4)
A: x=1
B: x=0
C: inf solution
D: No Solution
Answer:
B
Step-by-step explanation:
3x + 8 = 2(x + 4) ← distribute parenthesis
3x + 8 = 2x + 8 ( subtract 2x from both sides )
x + 8 = 8 ( subtract 8 from both sides )
x = 0
B is the correct answer
Step-by-step explanation:
B is the correct answer
Find the value of each variable in the following parallelogram
Answer:
x= 92 degrees
Y=44 degrees
Write an equation of a line with a slope of 2/3 whose graph will cross the y-axis at the point (0, 12.65).
Therefore , the solution of the given problem of slope intercept comes out to be y = 0.66x +12.65.
What exactly is a slope-intercept form?The gradient intercept method can be used once you are satisfied that Y = mx + b holds true. The direction form can be used to illustrate a hypothesis for a line by focusing on a single point directly and its slope. The slope is determined by the increase across the run and is first represented by the point form (x,y). The slope can be determined using slope intercept method, which is y = mx + b. (0, b). The direct form is a method for formulating a prediction equation for a line by making just one precise declaration about a vector slope.
Here,
Given : slope = 2/3
and coordinates = (0 , 12.65)
Thus ,
the equation of the given line by using formula of slope intercept:
=> y- y1 = m(x-x1 ) + c
=> y - 12.65 = 2/3*x
=> y = 0.66x +12.65
Therefore , the solution of the given problem of slope intercept comes out to be y = 0.66x +12.65.
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Which expression simplifies to 5 radical 3?
The rational expression that simplifies to 5 square root of 3 is given as follows:
C. [tex]\sqrt{75}[/tex]
What is a rational expression?A rational expression is a term that involves a root in the expression.
The simplified rational expression for this problem is given as follows:
[tex]5\sqrt{3}[/tex]
The original expression, from which the simplified expression was obtained, can be obtained moving the number 5 back to the square root.
The number is moved back into the square root with an exponent of 2, hence the original expression is obtained as follows:
[tex]\sqrt{3 \times 5^2} = \sqrt{75}[/tex]
Which is the original expression, meaning that the correct option regarding which expression simplifies to five times the square root of three is given by option C.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Identify the elements of the range of the function shown in the graph.
Responses
6
3
1
5
2
-6
The range of the relation on the graph is:
R: {1, 2, 6}
How to identify the range on the graph?For a relation y = f(x), the range is defined as the set of the possible outputs of the function (the possible values of y).
Here we can see a graph of 3 points, such that the coordinates of these points (on the form (x, y)) is:
(3, 6), (5, 2) and (6, 1)
The range is the set of the second values of each of these pairs, so the range in this case is:
R: {1, 2, 6}
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How do you find the perpendicular distance between two lines in 3D?
To find the perpendicular distance between two lines in 3D, you can use the dot product of the vector joining the two lines and the cross product of the direction vectors of the two lines, divided by the length of the cross product vector.
To find the perpendicular distance between two lines in 3D, you can use the following method:
Write the parametric equations of the two lines: Line 1: x = x1 + tv, y = y1 + tw, z = z1 + tu and Line 2: x = x2 + sv, y = y2 + sw, z = z2 + su, where (x1,y1,z1), (x2,y2,z2) are the coordinates of the two lines, (v,w,u) and (s,t,r) is the direction vectors of the two lines respectively.Find the vector joining the two lines: (x2-x1, y2-y1, z2-z1)Find the cross product of the direction vectors of the two lines, this is the vector that is perpendicular to both lines.Take the dot product of the vector joining the two lines and the cross product of the direction vectors, and divide by the length of the cross product vector.The absolute value of the result obtained in step 4 is the perpendicular distance between the two lines.To learn more about 3-D Lines at
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Help pls I am struggling with this
Slope = 1/4. Now let's put it into point slope form to find out the y-intercept. Then convert it into y=mx+ b form, the standard slope intercept form
How to calculate the linear equation?
Step1:
(-4,-2) and (4,0)
y=1/4x-1
Let's find the slope first, with the two given ordered pairs.
Slope = 1/4.
Now let's put it into point slope form to find out the y-intercept.
Then convert it into y=mx+ b form, the standard slope intercept form.
y + 2 = 1/4(x+4)
Then we convert it into y=mx+ b form (our final answer);
y=1/4x-1
Step 2:
(0,1)and(5,3)
y=2/5x+1
the equation of a line in slope-intercept form is.
y=mmx+ b
where m is the slope and b the y-intercept
to calculate the slope use the gradient formula
m=y2-y1/x2-x1
(x1,y1)=(0,1) and (x2,y2)=(5,3)
m=3-1/5-0=2/5
using m=2/5 and b=1
y=2/5x+1
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(+6)-(-3) (+1)
That’s the first one then I have this one
(-3)-(-7)-(+8)
The integer value of both values is 10 and -4.
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
A positive integer and a negative integer cannot be multiplied. A pair of positive integers have a positive product. Two negative integers add up to a positive number. A positive integer and a negative integer do not add up to a positive number.
Positive and negative numbers are used differently in everyday life. Although positive numbers are frequently employed everywhere, negative integers are also used to measure temperature because it is possible for a city's temperature to be either -4°C or -10°C.
(+6)-(-3) (+1)
⇒ 6 + 3 + 1 [using rules of integers, (-)(-) yields (+)]
⇒ 9 + 1
⇒ 10
(-3)-(-7)-(+8)
⇒ -3 + 7 - 8 [using rules of integers, (-)(+) yields (-)]
⇒ -3 - 8 + 7
⇒ -11 + 7
⇒ -4 [As -11 is greater than 7]
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There are x sparrows in a tree. There are 50 sparrows on the ground beneath the tree. Let y represent the total number of sparrows in the tree and on the ground.
A. Express y in terms of x
B. Make a table to show the relationship between y and x. Use values of x=10,20,30,40, and 50 in your table
A. Using the given information, y expressed in terms of x is y = x + 50
B. The table that shows the relationship between y and x is
x y
10 60
20 70
30 80
40 90
50 100
Expressing y in terms of xFrom the question, we are to express y in terms of x
From the given information,
There are x sparrows in a tree and 50 sparrows on the ground beneath the tree
If y represent the total number of sparrows in the tree and on the ground,
Then,
We can write that
y = x + 50
B.
We are to make a table to show the relationship between y and x
Using the equation above
y = x + 50
When x = 10
y = 10 + 50
y = 60
When x = 20
y = 20 + 50
y = 70
When x = 30
y = 30 + 50
y = 80
When x = 40
y = 40 + 50
y = 90
When x = 50
y = 50 + 50
y = 100
Thus,
The table is:
x y
10 60
20 70
30 80
40 90
50 100
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Write an equation of a line in slope-intercept form that goes through the points (-13,0) and (-1, -6).
Answer: m = -1/2
Step-by-step explanation:
Bing bang boomarang i have no idea
Through the woods, hiker Eric comes upon a redwood tree. The sun casts shadows for both hiker Eric and the tree. Eric knows he is 6 feet tall and his shadow is 8 feet long. He is 496 feet away from the tree. How tall is the great redwood?
The height of the redwood has been calculated as 372 meters.
How to solve for the heightIn order to get the height of this tree, I would have to make use of the similar triangles method. The proportion is set as
tree height / tree shadow = Eric's height / Eric's shadow
Eric's height is 6 feet, his shadow is 8 feet
The proportion is 6 / 8
= 3 / 4
To get the height of the tree we have to multiply the proportion by the distance with which Eric is away from the tree
= 3 / 4 * 496
= 372 feet
The redwood is 372 feet
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help asap will give briniest.
3 seconds.
Step-by-step explanation:1. Identify the given values.The problem states that the ball was kicked from a height of 12 ft, this would be the initial height of the ball. Hence:
h₀= 12 ft
Also, initial velocity is 44ft/s. Hence:
v₀= 44ft/s
2. Substitute the variables by the given values in the formula.[tex]h(x)=-16x^{2} +v_{0} x+h_{0} \\ \\h(x)=-16x^{2} +(44ft/s) x+(12ft)[/tex]
3. Rewrite as a common mathematical equation.[tex]h(x)=-16x^{2} +44 x+12[/tex]
4. Solve for time (x).Since the height when the ball hits the ground is 0, we need to substitute the height value (h(x)) by 0, and then solve the equation for "x".
Using the quadratic formula (check the attached image) we can get the value of time.
Taking the coefficients:
A= -16
B= 44
C= 12
[tex]x_{1} =\frac{-(44)+\sqrt{(44)^{2}-4(-16)(12) } }{2(-16)}= -0.25s\\ \\x_{2} =\frac{-(44)-\sqrt{(44)^{2}-4(-16)(12) } }{2(-16)} =3s[/tex]
Since "x" is being used to represent time, and time is a variable that can only be positive, we're only taking the positive value.
Hence, we can conclude that after 3 seconds after being kicked, the ball wil hit the ground.
12 Sketch the graphs of the following equations on the same Cartesian coordinate plane
a) 2y + 7 = 3x
b) 1/2x + 4y = 6
Answer:
Step-by-step explanation:
2y+7=3x
-3x+2y=-7
1/2x+4y=6
x+8y=12
In graphing a linear equation using the slope-intercept method, plot the y-intercept then use the x-intercept to locate the second point. (PLEASE HELP)
The slope-intercept method is a way to graph a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept. This method allows you to find the slope and y-intercept of the line and use that information to graph the line.
An explanation graph is what?
A graph shows how two variables that are typically measured along one of a pair of axes at right angles relate to one another.
To graph a linear equation using the slope-intercept method, you can follow these steps:
Identify the y-intercept by looking for the constant term (b) in the equation. The y-intercept is the point where the line crosses the y-axis, so it will have an x-coordinate of 0.
Plot the y-intercept on the coordinate plane.
Identify the slope of the line by looking for the coefficient of the x-term (m) in the equation. The slope represents the steepness and direction of the line.
Using the slope and the y-intercept, pick a point on the x-axis and use the slope to find the corresponding point on the y-axis.
Plot the point found in step 4.
Plot the two spots and then draw a straight line through them.
Note that this method will work for any linear equation where y = mx + b, and can help you graph a line quickly.
Also note that there is another method to graph a linear equation, it's called the point-slope method which is starting from any point on the line and use the slope to locate the additional line points.
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In your school, a skating competition was organized and you were asked to find the best skater out of 5 participants of class 7 students.
Contestant A covered a distance 1100m within 40 minutes.
Contestant B covered a distance 1800m within 1 hour and 10 minutes.
Contestant C covered a distance 1000m within 60 minutes.
Contestant D covered a distance 900m within half an hour.
Contestant E covered a distance 1500m within 55 minutes.
Best saker out of 5 participants is Contestant D because his speed of skating is the highest. He has a speed 30 m/min.
what is skating?Skating is a kind of sports as well as exercise. It is such a sport in where a participant needs to move on skates.
Who is the best skater out of 5 participants?
Best skater is determined by the performance of each participant.
The performance can be detected by observing the speed of skater.
speed = distance travelled by skater / time
we notice from the above question that contestant A covered a distance 1100m within 40 minutes.
so, speed of A = 1100 m/ 40 min = 27.5 m/min
Contestant B covered a distance 1800m within 1 hour and 10 minutes.
speed of B contestant = 1800m/ 70 min= 25.71 m/min
Contestant C covered a distance 1000m within 60 minutes.
speed of contestant C = 1000m/ 60 min = 16.67 m/min
Contestant D covered a distance 900m within half an hour.
speed of D = 900m /30 min = 30 m/min
Contestant E covered a distance 1500m within 55 minutes.
speed of contestant E = 1500m/ 55 min = 27.27 m/min
from the above discussion, we find that contestant D has the highest speed among all other skaters.
speed of contestant D = 30 m/min
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FOR SOME WHO CAN ANSWER THESE 4 QUESTIONS!!!
The number and percentages of the parameters in the question are;
652 people make more than $60,000About 19.9% of all police officers make less than $40,000What is a percentage?A percentage is a representation of a part of a whole as a fraction with a hundred (100) as the denominator.
T
From the attached table in the question, we get;
The number of people that make more than $60,000 = 388 + 198 + 66 = 652
The number of people in the survey including the teachers, police officers and firefighters, that make more than $60,000 are 652 peopleThe number of police officers in the survey = 224 + 703 + 198 = 1125
The number of police officers that make less than $40,000 = 224
The percentage of police officers that make less than $40,000 is therefore;
(224 ÷ 1125) × 100 ≈ 19.9%The percentage of all police officers that make less than $40,000 is about 19.9%Other information obtainable from the table are as follows;
The number of police officers that make more than $40,000 = 703 + 198 = 901
The percentage of all police officers that make more than $40,000 is therefore;
(901 ÷ 1125) × 100 ≈ 80.09%
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Your younger brother is getting stickers from a vending machine at the local supermarket. A proportion of stickers have the phrase "Girls
Rule!" If there are 12 stickers with this message in a sample of 36 stickers, what is the 95% confidence interval for this proportion? (1 point)
O a (0.1764, 0.4836)
Ob(0.1793, 0.4873)
Oc (0.1676, 0.4724)
Od (0.1799, 0.4881)
The formulae that specify how much 8% solution in equation and how much 24% solution were utilized are x+ y=200 and x+3y=450.
What is an equation ?A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Let x and y be the volume of the 8% and 24% solutions, respectively, that were utilized.
The entire solution volume, as stated in the question, will be 200ml. The resulting equation is: x +y=200
Now that it has been stated that 8%, 18%, and 24% saline mixes would be employed as the solution, the following equation will be:
[tex]0.08x+ 0.24y=0.18*200\\8x/100+24/100=18/100*200\\8x+24y=3600\\\\8(x+3y)=3600\\ x+3y=450\\[/tex]
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On solving the provided question, we can say that For the specified percentage, the 95% confidence interval is (0.864, 0.3580).
A confidence interval is defined.A confidence interval in statistics expresses the probability that a population parameter would fall between a set of values for a specific percentage of the time. Analysts commonly utilize 95% or 99% confidence intervals for their predictions.
If total samples = E = 36, then
8 results were obtained.
Chance = p = 8/36 = 0.2222
Z value at 95% confidence level = 1.96
p = [tex]0.2222 + 1.96 ( \sqrt{ 0.2222() 1 - 0.2222) / 36 } ) = 0.3580[/tex]
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Find the hypotenuse use simplest radical form if necessary
The triangle's third side will measure 6.71 units in length.
What is meant by Pythagoras theorem?Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle. Use the Pythagoras theorem to find the third side of a right-angled triangle.The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c² = a² + b², where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.According to the Pythagorean theorem, two squares added together equal the square of the longest side.
The Pythagoras theorem's equation is as follows:
H² = P² + B²
The triangle's third side will be the following length:
Let x represent the triangle's third side's length. Next, we have
9² = 6² + x²
81 = 36 + x²
x² = 45
x = 6.708
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Factor completely. Drag the expressions into the box if they are part of the factored form of the polynomial. If the polynomial is not factorable,
drag prime.
8c^3-27d^3
Answer: prime
Step-by-step explanation:
there is no greatest common factor (GCF) of the coefficients: 8 and -27. And the variables: c and d, are different so the polynomial is in its prime form.
subtract -9x^2+4x from -8^2+8x-10
What do you divide 41/8 by to get the most simplest form
Answer:
The simplest form would be 5 1/8
Step-by-step explanation:
You don't have a common factor with 41 and 8, so the real reduced answer would just be mixed, as 5 1/8.
Judy measured the lengths of her flowers, in inches. The lengths are shown below.
1/4
1/2
3/4
1/4
1/4
1
1/4
1/2
3/4
1/2
The total length of the flowers that Judy measures will be the 1 3/4 inches.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
From the information, Judy measured the lengths of her flowers, in inches. The total length of the flowers will be the sum. This will be:
= 1/4 + 1/2 + 3/4 + 1/4
= 1 3/4 inches.
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Complete question
Judy measured the lengths of her flowers, in inches. The lengths are shown below.
1/4
1/2
3/4
1/4
What is the total length of the measurement?
Draw a line parallel to the line x=5 that intersects the x-axis at (1,0). What is the equation of this line?
So, on solving the provided question, we cans ay that new slope interest equation is y = 3x +c
what is slope intercept?In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.
given, x = 5, that is lope
coordinates = (1,0)
new slope interest equation is
y = 3x +c
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The correct question is -
Draw a line parallel to the line x=5 that intersects the x-axis at (1,0). What is the equation of this line?
10. The table below shows the changes in value for a share of stock that
started at $37.69 on Monday.
Changes in the Value
of Stock by Day
C. $37.79
D. $39.71
Day of
the Week
Tuesday
Wednesday
Thursday
Friday
Changes in
Stock Value
$ 0.69
-$ 0.82
$ 0.37
-$ 0.14
What is the value of the stock at the end of the day on Friday?
A $35.67
B. $37.71
On solving the provided question we can say that the equation will be -
37.79x + 39.71y = 0.69 = 75.4 +75.4 = 150.8
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
the equation will be -
37.79x + 39.71y = 0.69
x = 2
y = 2
75.4 +75.4 = 150.8
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Draw a net for a cube with a edge length x centimeters? What is the surface area of this cube? What is the volume of this cube?
The net of the cube is attached to this answer, and;
a. The surface area of the cube = 6X^2 squared centimeters
b. The volume of the cube = x^3 cubic centimeters
What is a net of a given shape?The net of a shape or figure is the shape gotten when it is opened through its edges and spread out on a flat surface. If this shape is folded with respect to its edges, the original shape would be reproduced.
The net of the given cube is attached to this answer.
a. To determine surface area of the cube, we have;
surface area of a cube = 6*length*length
= 6l^2
Given that the length of the sides of the cube is x centimeters,
area of the cube = l^2
= x^2
surface area of the cube = 6x^2
b. The volume of a cube = length^3
= l^3 ;l
The volume of the cube = x^3
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Rebecca
pays $3.50 per gallon for 12 gallons of gas.
How much did Rebecca pay in all for the gas?
Answer:
3.50 × 12 = 42
Therefore, she spent 42 dollars.
Use a trigonometric ratio to solve for c. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
Which of the following is not a pythagorean triplet a) 3,4,5 b) 6,8,10c) 5,12,13d) 2,3,4
D) 2, 3, 4 is not a pythagorean triplet.
Pythagoras theorem is in the form of;
a²+b²=c²
Applying this formula to the given options we get'
a) 3, 4, 5 is a Pythagorean triplet because 3^2 + 4^2 = 9 + 16 = 25 = 5^2
b) 6, 8, 10 is not a Pythagorean triplet because 6^2 + 8^2 = 36 + 64 = 100 = 10^2
c) 5, 12, 13 is a Pythagorean triplet because 5^2 + 12^2 = 25 + 144 = 169 = 13^2
d) 2, 3, 4 is not a Pythagorean triplet because 2^2 + 3^2 = 4 + 9 = 13 ≠ 4^2
In other words the pythagorean theorem states that in a right angled triangle, the square of the hypotenuse is the sum of the squares of the other 2 sides.
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The points L ( 1 , 8 ) (1,8), M ( 0 , 0 ) , and N ( − 8 , 1 ) (−8,1) form a triangle. Plot the points then click the "Graph Triangle" button. Click on the graph to plot a point. Click a point to delete it. L M N Find the desired slopes and lengths, then fill in the words that characterize the triangle. slope of LM = slope of MN = slope of NL = length of LM = length of MN = length of NL =
For a triangle with vertices L (1 , 8),, M (0 , 0) , and N (-8 , 1) the plot is plotted and the slope and lengths are
slope of LM = 8
slope of MN = 8
slope of NL = 7/9
length of LM = √65
length of MN = √65
length of NL = √130
How to find the slope and length of the lineThe slope, m of the lines is calculated the formula
m = (y₀ - y₁) / (x₀ - x₁)
where
m = slope
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
Slope of LM L (1 , 8), M (0 , 0)
m = (8 - 0) / (1 - 0)
m = (8) / (1)
m = 8
Slope of LM L (1 , 8), M (0 , 0)
m = (8 - 0) / (1 - 0)
m = (8) / (1)
m = 8
Slope of NL, N (-8 , 1), L (1 , 8)
m = (1 - 8) / (-8 - 1)
m = (-7) / (-9)
m = 7/9
The length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
For LM L (1 , 8), M (0 , 0)
d = √{(1 - 0)² + (8 - 0)²}
d =√{1 + 64}
d = √65
For MN M (0, 0) N (-8 , 1)
d = √{(0 + 8)² + (0 - 1)²}
d =√{64 + 1}
d = √65
For NL N (-8 , 1), L (1 , 8)
d = √{(-8 - 1)² + (1 - 8)²}
d =√{81 + 49}
d = √130
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HURRY PLEASE!!!!!!!!!!!
Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate 1/3 of an ounce per second. Diego starts with his usual 20 ounce milkshake and drinks at the same rate as before, 2/3 an ounce per second.
What does the graph tell you about the situation? Specifically answer the following:
a.) How many solutions are there? (25 pts)
b.) Interpret the solution(s). (25 pts)
c.) Who finishes the milkshake first? (25 pts)
The solution is
a) The number of solutions to the equation is 1
b) Diego finishes the milkshake in 30 seconds and Lin finishes the milkshake in 36 seconds
c) Diego finishes the milkshake first
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the time to finish the milkshake by Lin and Diego be represented as A and B respectively
Now , the equation will be
The amount of milkshake with Lin = 12 ounce
The rate at which Lin finishes her milkshake = 1/3 milkshake per second
The time for Lin to finishes her milkshake A = amount of milkshake with Lin / rate at which Lin finishes her milkshake
Substituting the values in the equation , we get
The time for Lin to finishes her milkshake A = 12/ ( 1/3 )
The time for Lin to finishes her milkshake A = 36 seconds
Now ,
The amount of milkshake with Diego = 20 ounces
The rate at which Diego finishes his milkshake = 2/3
The time for Diego finishes his milkshake B = 20 / ( 2/3 )
The time for Diego finishes his milkshake B = 30 seconds
Hence , Diego finishes his milkshake faster
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