Answers
The length of the unknown side of the triangle using similar triangle ratio concept is; x = 24
How to Solve similar triangles?We want to find the length of the unknown side of the similar triangles.
Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. Thus, we can say that if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the given triangle ADE which is divide into a similar triangle ABC with an unknown side x, we can use the concept of similar triangle ratios to get the unknown value of x as;
6/x = 8/(x + 8)
Cross multiply to get;
6(x + 8) = 8x
6x + 48 = 8x
8x - 6x = 48
2x = 48
x = 48/2
x = 24
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Related Questions
Use the definition of the derivative to find the derivative of the function with respect to the given variable.
Show steps
Answers
The derivative of the given function [g(r) = -2r + 2] is d/dr (rⁿ) = nrⁿ⁻¹.
What is derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's fundamental tool is the derivative. In conclusion, the tangent line's slope, or instantaneous rate of change, at any point on the curve is essentially what the derivative is. When you take a function's derivative, you're left with a different function that gives you the slope of the original function.So, g(r) = -2r + 2:
Differentiate with respect to r as follows:
g(r) = -2r + 2Using Power rule:
d/dr (rⁿ) = nrⁿ⁻¹Therefore, the derivative of the given function is d/dr (rⁿ) = nrⁿ⁻¹.
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the equation of the regression line for the data in the table is y = 4.9 - 198 where x represents the height and y is the predicted walking speed
Answers
The numerical value of 4.9 in the equation of the regression line
[y = (4.9x - 198)] determines "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.
As per the question statement, the equation of the regression line goes as [y = (4.9x - 198)], where "x" represents the height and "y" is the predicted walking speed.
We are required to determine, what the numerical value of 4.9 expresses in the regression line.
To solve this question, first we need to know about the formula to express the point-slope form of a line, which goes as, [(y - y₁) = m(x - x₁)], where (x₁, y₁) is a point through which the line passes, and "m" is the slope of the line, and compare this standard form to our question mentioned equation, to establish the numerical significance of 4.9.
Now, [y = (4.9x - 198)] can be written as [(y - 0) = 4.9(x - 40.41)], and comparing it to the standard point-slope form of a line, we get (m = 4.9), i.e., the slope of our concerned line of regression is 4.9.
Hence, 4.9 in 4.9x signifies "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.
Equation: In mathematics, an equation is a statement that expresses the relation of equality between two or more separate expressions, by connecting them with the "equal to" sign.To learn more about Equations, click on the link below.
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Answer:
For every 1 inch increase in height, walking speed increases by 4.9 m/min.
Step-by-step explanation:
Just took it, hope this helps.
Use synthetic division to divide 2x^4 − 12x^3 + 18x^2 − 13x +20 ; x−4.
Answers
The result of the synthetic division of 2x^4 - 12x³ + 18x² - 13x + 20 by x - 4 is given by:
2x³ - 4x² + 2x - 5.
How does synthetic division works?In synthetic division, the coefficients of a polynomial are each divided by a value.This value is the zero of the divided polynomial, which goes into the far left box.For this problem, the polynomial is given by:
2x^4 - 12x³ + 18x² - 13x + 20.
Hence the coefficients are:
2, -12, 18, -13, 20.
The divisor is:
x - 4.
Hence the left coefficient is:
4.
From the image at the end of the answer, the resulting coefficients are given as follows:
2, -4, 2, -5, with a remainder of 0.
Hence the result is:
2x³ - 4x² + 2x - 5.
For the procedure, we consider that the coefficient 2, the first of the polynomial, is moved down, then multiplied with 4 and added with the next coefficient(-12), and this procedure happens until the last coefficient.
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Help Me Pleaseeeeeee.
Answers
Based on the dimensions of the right triangle, the equation to be used to find the missing lengths is hypotenuse² = Known leg² + Unknown leg².
How to find a missing length on a right angled triangle?To find the missing length of a right-angled triangle, you should use Pythagoras theorem.
This theorem allows you to find the dimensions of missing leg as:
hypotenuse² = Known leg² + Unknown leg²
When you solve for the missing length, the length is:
9² = 6² + Unknown leg²
81 = 36 + Unknown leg²
Unknown leg² = 81 - 36
Unknown leg = √(81 - 36)
Unknown leg = 6.7
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Write an equation (slope-intercept form) of the line
passing through the point (-20, 4)
that is perpendicular to the line
2x + 5y = 10.
y =
Blank 1:
Answers
The equation in the slope-intercept form will be y = (-2/5)x + 4.4.
What do we mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, point is (-20, 4) and line is 2x + 5y = 10, then the equation will be:
m = -2/5y = (-2/5)x + bNow, solve for b as follows while inserting the values of x and y:
y = (-2/5)x + b4 = (-2/5)-20 + b4 = 40/-100 + b4 = -0.4 + b4.4 = bb = 4.4So, equation will be y = (-2/5)x + 4.4
Therefore, the equation in the slope-intercept form will be y = (-2/5)x + 4.4.
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Tammy has 4 more then five times the amount of dimes than nickels in her pocket. She has total of $1.50 in her pocket. Write an equation that could be used to determine the number of nickels(x) she has in her pocket.
Answers
In a case whereby Tammy has 4 more then five times the amount of dimes than nickels in her pocket and have total of $1.50 in her pocket the equation that could be used to determine the number of nickels(x) she has in her pocket is (0.05)(X+3) = 1.50.
How can the number of nickels(x) she has in her pocket been determined?The number of nickels(x) that can be found her pocket be determined by adding the the number of times the amount of dimes is than nickels, which can be expressed as :
let x will be number of dimes
let x+4 will be number of nickels
Therefore the number of nickels(x) that is required will be (0.10)X + (0.05)(X+3) = 1.50
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The rooftop of a 5-story building is 50 feet above the ground.
How long does it take the water balloon dropped from the
rooftop to pass by a third-story window at 24 feet?
Using the model h(t) = h, 16², solve the equation
h(t) = 24. (When you reach the step at which you divide
both sides by -16, leave 16 in the denominator rather than
simplifying the fraction because you'll get a rational
denominator when you later use the quotient property.)
Answers
With the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.
What do we mean by Quotient?In this example, the number divided by (15) is known as the dividend, and the number divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8 and the divisor is 4. The quotient and divisor are always less than their dividend, as you can see.So, h(t) = 24:
= 50Then, calculate as follows:
h(t) = - 1624 = 50 - 1616 = 50 - 2416 = 26 = 26/16t = √26/16t = 1.3secTherefore, with the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.
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Over the last three evenings, Amy received a total of 112 phone calls at the call center. The first evening, she received 7 more calls than the second evening. The third evening, she received 3 times as many calls as the second evening. How many phone calls did she receive each evening?
Answers
Based on the relationship between the number of phone calls that Amy received for the three evenings, the number of phone calls received on each evening was:
First evening - 28 calls Second evening - 21 calls Third evening - 63 calls How to find the number of phone calls received?The first evening saw Amy receiving 7 more calls than the second evening while the third evening saw Amy receiving 3 times as many calls as the second evening.
Assuming the second evening is x, the relationship can be represented by the equation:
First evening calls + Second evening calls + Third evening calls = Total number of calls
(7 + x) + x + 3x = 112
Solving for the number of phone calls on the second evening gives:
(7 + x) + x + 3x = 112
7 + x + x + 3x = 112
7 + 5x = 112
5x = 112 - 7
x = 105 /5
= 21 calls
Number of calls on first evening:
= 21 + 7
= 28 calls
Number of calls on third evening:
= 21 x 3
= 63 calls
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Answer the following.
Answers
To convert 2.21 x 10⁻⁶, place 6 zeros before 2.21 and move the decimal point to the left:
= 0.000021210
To convert 28,000 to scientific notation, write the non-zero digits, placing a decimal after the first non-zero digit: 2.8, then, multiply by 10 elevated to 4 (number of digits after 2):
28,000 = 2.8 x 10
nswer:
Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
Answers
The expression which can be used to represent the total owed for 3 months given the cost per month and a one-time equipment fee is 3(c) + 25
The correct answer option is option C
The expression that represents the total owedPrice of the cable per month = cOne time equipment fee = $25Number of months = 3 monthsThe total owed = Number of months(Price of the cable per month) + One time equipment fee
The total owed = 3(c) + 25
I'm conclusion, the expression for the total owed is represented by 3(c) + 25
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Answer: option c
bc 3<c> is the fee for 25
Find the domain and range of the function represented by the graph.
The graph is a filled-in point at ordered pair negative 4 comma negative 1, a line segment from ordered pair negative 4 comma negative 1 to ordered pair 0 comma 3, a line segment from ordered pair 0 comma 3 to ordered pair 2 comma 3, a line segment from ordered pair 2 comma 3 to ordered pair 3 comma 4, and a filled-in point at ordered pair 3 comma 4.
The domain is
$\le x\le$
.
The range is
$\le y\le$
.
Answers
A person invests 1000 dollars in a bank. The bank pays 6% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 2100 dollars?
Answers
Solution
For this case we have the following information given:
A= 1000
r= 0.06
n = 1
A= 2100
So we can set up the following formula:
[tex]2100=1000(1+\frac{0.06}{1})^t[/tex]We can solve for t on this way:
[tex]\ln (\frac{2100}{1000})=t\cdot\ln (1.06)[/tex]Solving for t we got:
[tex]t=\frac{\ln (2.1)}{\ln (1.06)}=12.73[/tex]Rounded to the nesrest tenth we got:
12.7 years
Find the value of x:
Answers
Answer:
3
because 3 divided by one is 3 so then you would have to divide with nine which we know is 3
Step-by-step explanation:
Have a great day!
For a test whose scores are normally distributed, with mean 470 and standard deviation 52, what is the cutoff score separating the bottom 11% of the test scores from the rest (that is, the score so that 11% of all scores are below this score)?
Answers
We will employ the z score table in this problem.
The shaded part is our area of interest.We will be required to seek the value of the z score at 0.11.
when we ahave a probability of 0.11 or 11%
This corresponds with a z-score of -1.225.
We then substitute into our z-score equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} z=z\text{ score} \\ x=\text{cut off point} \\ \mu=\operatorname{mean} \\ \sigma=\text{standard deviation} \end{gathered}[/tex]Therefore, we have
[tex]\begin{gathered} x=\sigma z+\mu \\ x=52(-1.225)+470 \\ x=406.3 \end{gathered}[/tex]Suppose that the mean cranial capacity for men is 1160 cc (cubic centimeters) and that the standard deviation is 200 cc. Assuming that men's cranial capacities are normally distributed, complete the following statements.
Answers
Solution:
Given;
[tex]\mu=1160,\sigma=200[/tex]The z-score is calculated using;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{760-1160}{200}\text{ at }x=760 \\ \\ z=-2 \\ \\ z=\frac{1560-1160}{200}\text{ at }x=1560 \\ \\ z=2 \end{gathered}[/tex]Thus;
[tex]P(-2ANSWER: 95%(b) The z-score of 99.7 probability is between -3 and 3. Thus;
[tex]\begin{gathered} -3=\frac{x_1-1160}{200} \\ \\ x_1=560 \\ \\ 3=\frac{x_2-1,160}{200} \\ \\ x_2=1760 \end{gathered}[/tex]ANSWER: Approximately 99.7% of men have cranial capacities between 560 cc and 1760 cc
Determine if the sequence below is arithmetic or geometric and determine
the common difference / ratio in simplest form.
64, 16, 4, ...
Answers
The sequence 64, 16, 4,. is geometric
What is an arithmetic sequence?Arithmetic Sequence can simply be defined as a sequence in which the difference between successive or consecutive terms is known as a constant.
The sequence is in the form a, a + d, a + 2d, a + 3d, a + 4d
Where;
a is the first termd is the common difference of the sequenceThe formula for the nth term of an arithmetic sequence is expressed as;
Tn = a + (n – 1)d
What is a geometric sequence?Geometric sequence can simply be defined as a sequence where the ratio of every two consecutive or successive terms is a known constant.
Given the sequence;
64, 16, 4, ...
We can see that the common ratio between the terms is 4 and hence a geometric sequence
Hence, it is a geometric sequence
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Wilbert bought a new dirt bike and is now $229 in debt. How much money does Wilbert have? What does $0 represent in this problem? 6.NS.5
Answers
Answer:
The money that Wilbert has is -$229 because of the debt.
$0 Represents his current, with no debts.
Where is the least common denominator of two fractions to product of the denominator?
Answers
When two or more fractions are provided, the least common denominator is defined as the smallest common multiple of all the common multiples of the denominators.
What is the least common denominator?The smallest number that is a common denominator for a particular set of fractions is referred to as the least common denominator (LCD). For fraction addition and subtraction, as well as comparing two or more fractions, the given fractions must have common denominators.Let's assume we have to add the fractions: (2/9)+(3/4)
We need to determine a common integer that is a multiple of both denominators, which are 9 and 4.
This common multiple will aid in the solution of the problem. As a result, the least frequent multiple for 9 and 4 is 36. As a result, the expression can be written as follows:
(2/9)+(3/4) = (2/9 × 4/4) + (3/4 × 9/9) = (8/36) + (27/36) = 35/36
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A particle moves along the r-axis so that its velocity vat any given time t, for 0 St $ 16, is given byW(0) =e»-1. At time r=0, the particle is at the origin. At what time does the particle's accelerationequal zero for the first time?Round to the nearest thousandth or write as a fraction
Answers
Given: The velocity function of a moving particle as
[tex]V(t)=e^{2sint}-1[/tex]To Determine: The time at which the acceleration equals to zero
Solution
Note that at time t=0, the particle is at origin, so
[tex]\begin{gathered} V(0)=e^{2sin0}-1 \\ V(0)=e^{2\times0}-1 \\ V(0)=e^0-1 \\ V(0)=1-1 \\ V(0)=0 \end{gathered}[/tex]Determine the acceleration function
The acceleration of a particle is the rate of change of velocity or the derivative of the velocity function. Therefore,
[tex]A(t)=\frac{dV(t)}{dt},or,A(t)=V^{\prime}(t)[/tex][tex]\begin{gathered} V(t)=e^{2sint}-1 \\ let:u=2sint:\frac{du}{dt}=2cost \\ V(t)=e^u \\ \frac{dV(t)}{du}=e^u=e^{2sint} \\ A(t)=\frac{dV(t)}{dt}=\frac{dV}{du}\times\frac{du}{dt} \\ A(t)=e^{2sint}\times2cost \\ A(t)=2e^{2sint}cost \end{gathered}[/tex]When the acceleration is equal to zero, then we have
[tex]\begin{gathered} A(t)=0 \\ 2e^{2sint}cost=0 \end{gathered}[/tex]Let us plot the graph of the acceleration function
The time for given interval for which the acceleration is zero are
[tex]t=\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2},\frac{7\pi}{2},\frac{9\pi}{2}[/tex]ence, thre first time the acceleration is zero is π/2 or 1.571
HURRY!!!!!!!1Solve the equation −112 = 8x for x. −14 14 −104 120
Answers
The solution to the equation, −112 = 8x, is: x = -14.
How to Solve an Equation?To find the value of the variable in an equation, means to solve the equation.
To solve any given equation, we are to apply all necessary properties of equality in other to isolate, as much as possible, the variable of the equation to one side of the equation. Th value of the variable is the solution to the equation.
Given the equation:
-112 = 8x
Divide both sides of the equation by 8:
-112/8 = 8x/8 [division property of equality]
-14 = x
x = -14
Check: Plug in x = -14 into the equation:
-112 = 8(-14)
-112 = -112 [true]
Thus, the solution to -112 = 8x is: x = -14.
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Determine the rate of this problem -> A 18-kg bag of cherries for $2.65 =_____per kg
Answers
Answer:
$0.14 per kg
Step-by-step explanation:
A 18-kg bag of cherries for $2.65
for 1 kg
[tex] \frac{2.65}{18} = 0.14 \\ [/tex]
so, the answer is $0.14
#6 and #7 Axioms of Equality
Answers
It is proved that ∠2 and ∠3 are supplementary angles.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.So, according to the given image below:
(A) m∠1 = m∠3 ⇒ Alternate angles.
(B) m∠1 + m∠2 = 180°
Reason:
R is a straight line through which line m asses making two angles m∠1 and m∠2.As we know a straight line has an angle of 180°.And since, line m divides the angle of 180° into two parts ∠1 and ∠2.So w ecam conclude that: m1 + m∠2 = 180°.(C) m∠3 + m∠2 = 180° due to: Linear Pair Axiom.
(D) m∠2 and m∠3 are supplementary because: Since a linear pair of angles always results in a straight line, their sum is always 180°.
Therefore, it is proved that ∠2 and ∠3 are supplementary angles.
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What is the value of 8 in 8.260
Answers
Answer:
Step-by-step explanation:
The value of 8 in 8.260 is 8 units.
determine whether the ordered pair is a solution of the given equation Remeber to use alphabetical order for substitution (-6,-2) a solution of the equation r-s=4 is (-6,-2) a solution of the equation r-s=4?
Answers
To check if an ordered pair is a solution to an equation, substitute the value for each coordinate into the equation.
Since the substitution has to be performed in alphabetical order, then the coordinates are given in the form:
[tex](r,s)[/tex]Substitute r=-6 and s=-2 into the given equation to check if (-6,-2) is a solution:
[tex]\begin{gathered} r-s=4 \\ \Rightarrow(-6)-(-2)=4 \\ \Rightarrow-6+2=4 \\ \Rightarrow-4=4 \end{gathered}[/tex]Since -4 is NOT equal to 4, then the point (-6,-2) is not a solution to the equation r-s=4.
1/4(n-6)=1/4n-3/2
Hint: undo the fraction
Answers
The solution to 1/4(n - 6) = 1/4n - 3/2 is infinite many solutions
How to solve the equation?The equation is given as
1/4(n - 6) = 1/4n - 3/2
Multiply through the fraction equation by 4
So, we have the following equation
4 x 1/4(n - 6) = 4 x 1/4n - 4 x 3/2
Evaluate the products in the equation
So, we have the following equation
n - 6 = n - 6
Evaluate the like terms
0 = 0
The equation cannot be solved further
If the solution to an equation is 0 = 0, then the equation has infinite many solutions
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Answer: infinite many answers
Step-by-step explanation:
The point (-2, 1) is on the graph of which of these functions?
A. y = -x² -1
B. y = -3x -5
C. y = x² + 3
D. Y = 1/2x
Answers
-3(-2)-5=Y
6-5=1
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the function with its inverse.
Answers
The correct pairs of the functions and their inverses are given by the image at the end of the answer.
How to find the inverse function?To find the inverse function, we exchange x and y in the original function, then isolate y.
The first function that we want to find the inverse is:
f(x) = (2x - 1)/(x + 2).
Hence:
x = (2y - 1)/(y + 2)
(y + 2)x = 2y - 1
xy + 2x = 2y - 1
xy - 2y = -1 - 2x
y(x - 2) = -1 - 2x
y = (-1 - 2x)/(x - 2) (which is the inverse function).
The second function which we want to find the inverse is:
y = (x + 2)/(-2x + 1)
Then:
x = (y + 2)/(-2y + 1)
x(-2y + 1) = y + 2
-2yx + x = y + 2
-2yx - y = 2 - x
-y(2x + 1) = 2 - x
y = (x - 2)/(2x + 1) (which is the inverse function).
The third function which we want to find the inverse is:
y = (x - 1)/(2x + 1)
Then:
x = (y - 1)/(2y + 1)
2yx + x = y - 1
2yx - y = -1 - x
y(2x - 1) = -1 - x
y = (-x - 1)/(2x - 1) (which is the inverse function).
The fourth function which we want to find the inverse is:
y = (2x + 1)/(2x - 1)
Then:
x = (2y + 1)(2y - 1)
2yx - x = 2y + 1
2yx - 2y = 1 + x
2y(x - 1) = (1 + x)
y = (x + 1)/(2(x - 1)) (which is the inverse function).
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The normal cruising speed of a certain airplane is about 170 m/sec. What is this speed in miles per hour?
Answers
The speed of airplane in miles per hour (mph) is 380.2968 .
What is speed?
Speed is the time rate at which an object is moving along a path. The SI unit of speed is meter per second ( m/s ). Miles per hour ( mph ) is a British imperial and United States customary unit of speed expressing the number of miles travelled in one hour.
Given that
Speed of a certain airplane = 170 m/s or m[tex]s^{-1}[/tex]
We know that
In 1 meter = 0.0006214 miles
In 1 sec = [tex]\frac{1}{3600}[/tex] hour
but 1 [tex]sec^{-1}[/tex] = 3600 hour
Speed of this airplane in miles per hour = 170 × 0.0006214 × 3600 mph
= 0.105638 × 3600 mph
= 380.2968 mph
Hence, the speed of airplane in miles per hour (mph) is 380.2968 .
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Consider the lines that contain the segments in the figure and the planes that contain the faces of the figure. All angles are right angles. Which plane(s) contain point B and appear to be parallel to plane CDH?
Answers
The plane containing point B and parallel to the plane CDH is plane ABF.
What is defined as the parallel plane?Parallel planes are spatial planes that never intersect. The length about any line segment perpendicular both to planes connecting two parallel planes is indeed the distance between them. There are an infinite number of perpendicular line segments between two parallel planes. Two of the perpendicular segments the above are line segments AB and CD. Any line segment that is perpendicular to both planes also has the shortest distance between them.As, from the diagram we can see that there are two plane passing from point B; plane ABF and ABC.
But plane ABC is intersecting the given plane CDH, while plane ABF is not.
Thus, plane ABF is parallel to the plane CDH.
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Can I get help please ?
Answers
SOLUTION:
Case: Pythagoras Triple
Method:
The Pythagorean triple:
(8, 15, 17) can be formed with factor integers
8----> 4
15---->3.
Final answer:
x=4, y= 3