Answers
The value of the sides are;
h = 2√3
c = 4√2
How to determine the valueTo determine the value, we need to note that the trigonometric identities are represented with the fraction;
sin θ = opposite /hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the diagram shown, we have that;
Using the sine identity
sin 60 = 3/h
Now, cross multiply the values, we have;
h = 3/sin 60
find the sine value
h = 3/√3/2
divide the values
h = 6√3/3 = 2√3
For the second triangle.
sin 45 = 4/c
cross multiply
c = 4/1/√2
c = 4√2
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Answer:
[tex]h = \boxed{2\sqrt{3}}\\\\c = \boxed{4\sqrt{2}}[/tex]
Step-by-step explanation:
We can use the law of sines to determine the sides indicated
Law Of Sines
The ratio of the sides of a triangle to the sine of the angle opposite to that side is the same for all sides
In the triangle on the leftwe have side of length 3 opposite 60° and side of length h opposite 90°
So
[tex]\dfrac{h}{\sin 90} = \dfrac{3}{\sin 60}\\[/tex]
sin 90 = 1
[tex]\sin 60 = \dfrac{\sqrt{3}}{2}[/tex]
Therefore we get
[tex]\dfrac{h}{1} = \dfrac{3}{\dfrac{\sqrt{3}}{2}}\\\\h = 3 \times \dfrac{2}{\sqrt{3}}\\\\h = \dfrac{6}{\sqrt{3}}\\\\[/tex]
Rationalizing the denominator by multiplying by √3 we get
[tex]h = \dfrac{6\sqrt{3}}{3} = \boxed{2\sqrt{3}}[/tex]
(Answer)
-----------------------------------------------------------------------------------------
For the triangle on the right we have
[tex]\dfrac{c}{\sin 90} = \dfrac{4}{\sin 45}\\\\\sin 90 = 1\\\sin 45 = \dfrac{1}{\sqrt{2}}\\\\c = \dfrac{4}{\dfrac{1}{\sqrt{2}}}\\\\c = 4 \times \sqrt{2}\\\\c = \boxed{4\sqrt{2}}[/tex]
(Answer)
-----------------------------------------------------------------------------------------
In the both above computations we are using the fact that dividing by a fraction involves flipping the denominator fraction and multiplying
Related Questions
Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's? Let m represent the monthly cost.
Answers
Solving a linear equation we can see that the answer is 40 months.
How many months is it until your cost is the same as Plan A's?We know that company A only charges $70 per month, so the cost in dollars after x months is given by the linear equation:
A(x) = 70*x
For company B you need to pay $50 per month plus the $500 phone, so here the cost is:
B(x) =500 + 50*x
We want to find for what value of x we have B(x) = A(x), then we needto solve:
70x = 500 + 50x
70x - 50x = 500
20x = 500
x = 500/20
x = 40
After 40 months the cost will be the same one than in company A.
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assume that you want to construct a 95% ci for the mean of a normal distribution with population variance 30. the sample average is 10 and the sample size is 20. what is the lower limit of the ci? approximate your answer using only one decimal.
Answers
By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.
To construct a 95% CI for the population mean of a normal distribution, we can use the formula:
CI = sample mean ± z* (standard error)
Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:
standard error = population standard deviation / √sample size
In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:
standard error = 5.48 / √20 = 1.226
Now, we can use the formula for the CI:
CI = 10 ± 1.96 x 1.22
Simplifying this expression gives us:
CI = (7.59, 12.41)
This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.
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Arabella drive 17. 8 miles a day,yaya drives 1. 6 times as far for each day how far does yaya drive in three weeks
Answers
Arabella drive 17. 8 miles a day, Yaya drives 1. 6 times as far for each day. Therefore, 598.08 miles Yaya drive in three weeks.
Miles:
The mile, sometimes the international mile or the regulation mile, to distinguish it from other miles, is an imperial unit of the United Kingdom and a customary unit of distance in the United States; both are based on the old imperial unit of length, 5,280 imperial feet or 1,760 meters. The statute mile was standardized by an international agreement between the Commonwealth of Nations and the United States in 1959, when it was officially redefined as 1,609,344 meters in terms of SI units.
According to the Question:
We know that:
In a week there are 07 days
Therefore,
In 03 weeks there are = 7×3
= 21 days
Given that :
Arabella drive 17.8 miles daily
and Yaya drives 1.6 times far from 17.8 miles daily.
Therefore,
Yaya drives = 17.8 × 1.6 miles
= 28.48 miles
Now,
for three weeks = 28.48 × 21
= 598.08 miles.
Therefore, 598.08 miles Yaya drive in three weeks.
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Trapezoid EFGH ~ trapezoid MNOP. Find the indicated value.
z
Answers
Answer:
x=2.4
y=2.5
z=3.3
Step-by-step explanation:
6/5=1.2
1.2 = scale factor
x=2x1.2=2.4
y=3/1.2=2.5
z=4/1.2=3.3
Find f(2) if f(x) = (x + 1)2.If f(x) is a function and f(1) = 5, then which of the following could not be true?
Answers
The function that could not be true is , f(-1) = 4.option b, f(3) = 30 is not correct.
How to find the function?To find f(2), we simply substitute 2 for x in the function f(x):
[tex]f(2) = (2 + 1)^2 = 9[/tex]
Therefore,
[tex]f(2) = 9.[/tex]
Now, to determine which of the following statements could not be true if f(x) is a function and f(1) = 5, we need to check whether they violate any properties of functions. Here are the statements:
f(1) = 5
means that y = 5x
so when y = 1
x = 5
Therefore, option b, f(3) = 30 is not correct.
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Complete question:
Find f(2) if f(x) = (x + 1)2.
If f(x) is a function and f(1) = 5, then which of the following could not be true?
f(10) = 50
f(3) = 30
f(2) = 10
f(7) = 35
how can you make two pairs of adjacent and vertical angles but explained in a simple way.
Answers
Answer:
there
Step-by-step explanation:
find the missing term in the following patterns.
1. 12,25 , 37, 50,__ ,__ ,__
Answers
Find the missing dimension of the triangle.
1.5 in
Area = 2 in²
pls help I'll mark brainlisest
Answers
Answer:
Fraction form:
[tex]\text{h} = \dfrac{4}{1.5} \ \text{in}[/tex]
Decimal form:
[tex]2.667 \ \text{in}[/tex]
Step-by-step explanation:
I've attached the work below
The formula use is usually use to find the area of a triangle but allowed us to work backward after inputting given values
Hope it helps, Let me know if you have any more questions/concerns.
What are the coordinates of point s after a dilation with the center at the origin and a scale factor of 12?
Answers
The new coordinates of point s after the dilation are (12x, 12y)
A dilation is a type of transformation that changes the size of an object. It can be thought of as a resizing or stretching of the object. In this case, we are dilating a point with a center at the origin (0,0) and a scale factor of 12.
The center of dilation is the point around which the dilation occurs. In this case, the center of dilation is the origin. This means that the point will be resized relative to the origin.
The scale factor is a number that determines the amount by which the object is resized. In this case, the scale factor is 12. This means that the point will be enlarged 12 times its original size.
To find the new coordinates of the point after the dilation, we multiply the original coordinates by the scale factor. Let the original coordinates of the point be (x, y). Then, the new coordinates of the point after the dilation are:
New x-coordinate = 12 × x
New y-coordinate = 12 × y
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13. security y has the following returns over five years: 3%, 6%, 0%, 6%, and 3%. what is the arithmetic mean (average) return and the standard deviation (sample) for security y?
Answers
The arithmetic mean return is 3.6%, and the standard deviation is 2.14%.
To find the arithmetic mean, we add up the five returns and divide by the number of returns (in this case, 5):
(3% + 6% + 0% + 6% + 3%) / 5 = 3.6%
To find the standard deviation, we first need to find the variance. We can do this by taking each return, subtracting the mean return (3.6%), squaring the result, summing these values, and dividing by the number of returns minus 1 (4 in this case):
((3% - 3.6%)^2 + (6% - 3.6%)^2 + (0% - 3.6%)^2 + (6% - 3.6%)^2 + (3% - 3.6%)^2) / 4 = 0.046
The standard deviation is the square root of the variance:
√0.046 = 0.214 or 2.14%
Therefore, the arithmetic mean return for security y is 3.6%, and the standard deviation (sample) is 2.14%.
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Pls help keep it simple
Answers
Opioids are a class of drugs that include both prescription painkillers, such as oxycodone, hydrocodone, and fentanyl, and illegal drugs, such as heroin.
What are opioids?Opioids are highly addictive and can lead to physical dependence and addiction with prolonged use. They can also cause a range of negative side effects, including drowsiness, confusion, constipation, nausea, and respiratory depression, which can be life-threatening in high doses.
Opioid addiction has become a major public health crisis in many countries, including the United States, where it has been linked to a dramatic increase in overdose deaths.
The numbers that match the phrases are;
1 - j
2 - c
3 - b
4 - a
5 - i
6 - d
7 - e
8 - f
9 - j
10 - h
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g the sequence is decreasing and bounded below by 0. explain in clear english (briefly) why this means it must have a limit.
Answers
Since the sequence is always decreasing and cannot go below the lower bound, it becomes increasingly closer to the lower bound, and thus converges to a limit.
A sequence is said to be decreasing if each term is smaller than the previous one, and bounded below if there exists a lower bound such that no term in the sequence is smaller than this bound. In this case, the sequence is decreasing and bounded below by 0.
When a sequence is both decreasing and bounded below, it must have a limit because the terms cannot continue to decrease indefinitely, as they cannot go below the lower bound (in this case, 0). This means that as we progress through the terms of the sequence, the difference between consecutive terms will decrease and eventually approach a constant value.
The limit of a sequence is a value that the terms of the sequence approach as they get closer and closer to the end. In this situation, the limit is the smallest possible value that the sequence can approach, without going below the lower bound.
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your chronometer is set for greenwich mean time (gmt or universal time, ut). high noon at your present location is 9 pm ut. what is your longitude?
Answers
Your longitude in DMS is 135 degree. So the option D is correct.
This is because there are 12 hours left in the local time ( i.e. 12 hours noontime or mid-day).
As UT (or GMT) time is 9 p.m., there are 9 hours between GMT time and local time.
9 hours = 9 × 60 minutes = 540 minutes
Now, we know that:
Every four minutes, the Earth turns one degree.
Thus, 1-degree longitude difference = 4 minutes
Or, 4 minutes of time difference = 1 degree of longitude
Or, 1 minute of time difference = 1/4 degree of longitude
Or, 540 minutes of time difference = (1/4) × 540 degrees of longitude
540 minutes of time difference = 135 degrees of longitude
Also, we can infer that the current location is in the Western hemisphere because we know that it is 9 hours behind GMT (or UT) time.
Hence, the longitude of the current location = 135⁰
So the option 4 is correct.
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The complete question is:
Your chronometer is set for Greenwich Mean Time (GMT or Universal Tim, UT). High noon at your present location is 9 pm UT. What is your longitude in DMS (not decimal degrees)?
1. 30° 18'W
2. 30° 16'W
3. 30° 17'W
4. none of the above
Evaluate (2. 7)3 - (1. 6)3 - (1. 1)3 using a suitable identity. Please answer. Have to submit it tomorrow!!
Answers
Evaluating the (2.7)³ - (1.6)³ - (1.1)³ using the suitable identity is given by the term 26.19.
The sum of cubes (of two integers) formula is what is known as the a3 + b3 formula. Without computing the two cubes, the total may be calculated using the a cube + b cube formula. The binomials of cubes are factorised using it as well.
Let a = 2.7, b = 1.6, c = 1.1
We see that,
a + b + c = 2.7 + 1.6 + 1.1 = 5.4
Now as we know that,
If a+b+c = 5.4
then using the identity:
a³ - b³ - c³ = ( a+ b+ c ) (a² + b² + c² - ab - bc - ca) + 3 abc
so,
a³ - b³ - c³ = 5.4(2.7² + 1.6² + 1.1² - 4.32 - 1.76 - 2.97) + 14.256
= 5.4(7.29 + 2.56 + 1.41 - 4.32 - 1.76 - 2.97) + 14.256
a³ - b³ - c³ = 26.19
Therefore, (2.7)³ - (1.6)³ - (1.1)³ is 26.19
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The difference between numbers tell you how far apart they are on the number line 8 and -16 our units apart because 8 -6 = 14
Answers
The answer of the given question based on the number line is the difference between 8 and -16 is not 14, it is 24. and 8 and -16 are 24 units apart on the number line.
What is the use of number line?A number line is a visual representation of the real number system, where numbers are placed in order from left to right, with zero in the center. The number line is an important mathematical tool used in a variety of ways, including:
Understanding and comparing numbers: By plotting numbers on a number line, we can visually see the relative size and position of numbers in relation to each other.
Performing arithmetic operations: The number line can be used to add, subtract, multiply, and divide numbers.
Graphing functions: The number line can be used as the horizontal axis of a graph to plot functions and other mathematical relationships.
Actually, the difference between 8 and -16 is not 14, it is 24.
To find the difference between two numbers on a number line, you need to subtract the smaller number from the larger number. In this case, 8 is larger than -16, so we subtract -16 from 8:
8 - (-16) = 8 + 16 = 24
Therefore, 8 and -16 are 24 units apart on the number line.
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8) Calculate the total distance the plane traveled in miles. (Hint - Notice the 5 triangles. Solve for the hypotenuse of each triangle) Show ALL of your work neatly below.
Answers
Answer:
Step-by-step explanation:
2 cards are selected from a standard deck of 52 cards. (don't know about playing cards? click here.) the first card is not placed back in the deck before the second card is drawn. match the probabilities to their corresponding situations. question 4 options: 3 p(spade and ace of hearts) 4 p(2 aces) p(2 of the same card) 2 p(red card and four of spades) 1 p(heart and club) 1. 13/204 2. 1/102 3. 1/204 4. 1/221 5. 0
Answers
Hence, the correct match of probabilities with their corresponding situations is given by option 4.
To match the probabilities with their corresponding situations, we can utilize the formulas given below:
[tex]P(A ∩ B) = P(A) x P(B|A)P[/tex](2 aces) =[tex](4/52) x (3/51) = 1/221[/tex]
P(heart and club) =[tex](13/52) x (13/51) = 169/2652[/tex]P(spade and ace of hearts) = 0P(2 of the same card) = (1/52) + (3/51) + (2/50) + (1/49) + (4/48) + (3/47) + (2/46) + (1/45) = 20/663P(red card and four of spades) = (16/52) x (1/51) = 4/663
Therefore, the probabilities with their corresponding situations are:3: P(spade and ace of hearts) = 0 (Not possible as Ace of hearts is not spade)
4: P(2 aces) = 1/2211: P(heart and club) = 169/26521: P(heart and club) = 169/26522: P(red card and four of spades) = 4/663
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x + 16[tex]\leq[/tex]19
Answers
Answer:
[tex]X\leq 3[/tex]
Step-by-step explanation:
[tex]X +16\leq 19[/tex]
[tex]X\leq 3[/tex]
Help please it’s urgent
Answers
The 0.05(x+4)+0.10(x) = $1.25 equation could be used to determine the number of dimes, x, in his pocket.
What is equation ?An equation is a mathematical expression containing an equal sign that states the equality of two expressions. It is essentially a statement of balance, showing that two expressions are equal in value. Equations are used to solve a wide variety of problems in mathematics, science, and engineering. For example, the equation x+2=4 expresses the fact that when 2 is added to any number x, the result is 4.
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You have a trust that when mature will be $250,000 that you will receive when you are 50 years old. You are 25 years old now. If the trust is growing at 8% per year what is the value of the trust now?
Answers
The present value of the trust which grows at the rate of interest 8% for 25 years is equal to $ 36504.477
The future value of the trust is equal to $250,000
Interest rate is equal to 8% per year
To calculate present value of the trust use the formula,
Present Value = Future Value / (1 + r)^n
r is the annual interest rate
n is the number of years.
Let us consider PV represents the present value of the trust.
Present age = 25 years
Maturity age of the trust = 50 years
Number of years used amount to mature is equal to,
= 50 - 25
= 25 years
Substitute the values into the present value formula we have,
PV = 250,000 / (1 + 0.08)^25
Simplify it we get,
⇒ PV = 250,000 / 6.848475
⇒ PV = 36504.477
Therefore, the present value of the trust mature for 25 years is equal to approximately $36504.477.
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Domain function of f(x)=2 square root -x^2+10x
Answers
The domain of a function f(x) = 2√(-x² + 10x) in interval notation is given by (-∞, 0] ∪ [10, ∞).
Function f(x) = 2√(-x² + 10x).
Domain of a function is the set of all possible input values of x for which the function is defined.
Values of x for which the expression inside the square root is non-negative.
As the square root of a negative number is not a real number.
Take out the common factor -x we have,
-x² + 10x ≥ 0
⇒ -x(x - 10) ≥ 0
⇒ -x ≥ 0 or ( x - 10 ) ≥ 0
The inequality is satisfied when x ≤ 0 or x ≥ 10.
This implies,
The domain of the function f(x) = 2√(-x² + 10x) is the set of all real numbers such that x ≤ 0 or x ≥ 10.
In interval notation form,
The domain is represented as,
(-∞, 0] ∪ [10, ∞).
Therefore, the domain of the given function is equal to (-∞, 0] ∪ [10, ∞).
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The above question is incomplete , the complete question is:
What is the domain of a function f(x) = 2√-x²+ 10x
counting problem the eight people from four husband-and-wife couples are arranged in a row. each wife is somewhere to the left of her husband. how many such arrangements are there?
Answers
8 persons can be arranged in a row in 384 different ways, with each wife positioned to the left of her husband.
8! = 40,320 ways to arrange the 8 people in a row, without any restrictions. To take into account the restriction that each wife must be somewhere to the left of her husband, we can first arrange the 4 couples in a row. There are 4! = 24 ways to do this. For each of these arrangements, we can then arrange the couples in the row. There are 2 ways to arrange each couple, so the total number of arrangements is 24 x 2⁴ = 384. Therefore, there are 384 ways to arrange the 8 people in a row, with each wife somewhere to the left of her husband.
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IM GIVING OUT THE FIRST PERSON BRANLIEST WHO ANSWERS RIGHT FIRST: a floor that is 8 feet x 10 feet is covered by tiles that are 6 inch squares. How many fewer tiles would it take to cover the floor if the tiles were 12 inch squares? AND NO IT IS NOT 80!!
Answers
Therefore , the solution of the given problem of surface area comes out to be 240 tiles will cover the floor.
What is a surface area ,exactly?Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.
Here,
Let's first determine how many 6 inch squares are required to span the floor:
=> 80 square feet is the size of the floor (8 feet by 10 feet).
We require the following because each 6-inch square spans an area of => (1/2) ft x (1/2) ft = 1/4 square feet:
=> 80 square feet 1/4 square foot = 320 tiles in a row of 6 inch tiles.
Since a 12 inch square encompasses a space that is 1 foot by 1 foot, we require:
=> 80 square feet / 12 inch square tile,
which equals 80 tiles.
Using 12 inch squares rather than 6 inch squares allows us to save the following amount of tiles:
=> Number of 6 inch tiles - Number of 12 inch tiles = 320 - 80 = 240 tiles
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A solid shape is made from centimetre cubes. Here are the plan, front elevation and side elevation of the shape. How many cubes are added? (see below)
Answers
Answer:
Step-by-step explanation:
To make this Cuboid you need to workout how many cubes are missing from this cuboid.
To get the cubes numbers you have to get the volume of this cuboid which is 3x4x3=36
So there is 36 cubes in this cuboid.
And then workout how many cubes are missing from this plan, front and side elevation.
Front Elevation 3x3=9
Side Elevation 4x3=12 then deduct 3 blocks from the left. Then deduct 4 blocks from right top corner which is 4 blocks.
3+4=7 missing blocks, then do this 12-7=5 Side has 5 added blocks fron the front.
Front 9 blocks Side 5 blocks. 9+5=14
So 36-14=22 ANSWER is 22 BLOCKS has been added.
pls help math scientific notation (view photo)
Answers
Just ignore this answer, its incorrect
*edited*
solve for x 144/25=x/5
Answers
Answer:
Step-by-step explanation:
144/25=x/5
times both sides by 5
144/5=x
simplify
x=144/5 or 28.8
Answer: x= 144/5
Step-by-step explanation:
Cross-Multiply
144/25 = 25x
Swap the sides so you can solve
720 =25x
Divide both sides
25x=720
x=144/5
function “p” is in the form y = ax 2+c. if the values of “a” and “c” are both less than 0. which graph could represent “p”?
Answers
Since the value of a is less than 0, the graph of the parabola would be opening downwards. Because of this we can rule out option C. In a quadratic equation, c represents the y-intercept, and, in this case c is negative, meaning the y-intercept is less than 0. Only option B has a downward-opening curve and a y-intercept less than 0, so it is the answer.
Answer: p= 2+c
Step-by-step explanation:
In the figure below, find the exact value of z. (Do not approximate your answer.)
Answers
Answer:
z=8
Step-by-step explanation:
Considering the triangle on the RHS,
Let the Unknown side be "x"
from pythagora's theorem,
x ^ 2 = 4 ^ 2 - 2 ^ 2 x = √(4 ^ 2 - 2 ^ 2)
x = √(16 - 4)
x = √12
cos alpha = 2/4 , alpha = arccos(2/4)
alpha = 60°
< ABC + theta + alpha = 180°
theta = 180 - alpha - <ABC
theta = 180 - 60 - 90
theta = 30°
Now Considering the triangle on the LHS,
tan 30 = (√12)/y
y = (√12)/(tan 30°)
y = 6
z = y + 2
z = 8
please please help!!! And if you don't know the answer, please stop saying "I don't know" or "this is too hard". if you don't know, then don't answer the question please!
Answers
P (-1, -2/5) is the point of segment of line .
What is the name of a line segment?
When both end points of a line segment are vertices of a polygon or polyhedron, the line segment is either a diagonal or an edge (of that polygon or polyhedron) if the vertices are close to one another.
A line segment is known as a chord when both of its end points are on a curve (such as a circle) (of that curve).
A = (-3,2)
B = (7,-10)
1: 4
P (x,y) partition A (x₁ , y₁) B (x₂ , y₂) into ratio
= (4 * -3 + 1 * 7) / (1 + 4)
= -5/5
= -1
y = (by₁ + ay₂) / (a+b)
= (4 * 2 + 1 * -10) / (1 + 4)
= -2/5
P (-1, -2/5)
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which angle is complemantry to 4
Answers
Answer: 6
Step-by-step explanation:
angles 4, 5, and 6 add up to 180
angle 5 is opposite of angle 3 which means they have the same measure, so angle 5 = 90
that means angles 4 and 6 add up to 90 so they are complimentary