The equation of the line is will be y = -2x + 4.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Calculate the slope of the line,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -2 - 0) / ( 2 - 1) = -2
The y-intercept will be calculated as,
y = mx + c
0 = -2 x 2 + c
c = 4
The equation of the line will be,
y = mx + c
y = -2x + 4
Therefore, the equation of the line will be y = -2x + 4.
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What is the image point of (2,0)(2,0) after the transformation D_{\frac{1}{2}}\circ R_{270^{\circ}}D
2
1
∘R
270
∘
The image of point (2,0) after the transformation involving the dilation and the rotation is given as follows:
(0, -1).
What are the transformations applied to the point?The first transformation applied to the point is a dilation, which multiplies the coordinates of the point by the scale factor.
The point has these following coordinates:
(2,0).
The scale factor of the dilation is:
k = 1/2 = 0.5.
Then each coordinate of the point is multiplied by 0.5, hence:
2 x 0.5 = 1.0 x 0.5 = 0.Hence the coordinates are:
(1,0).
The rule for a rotation of 270º clockwise around the origin is:
(x,y) -> (y,-x).
Then:
x = 1, -x = -1.y = 0.Thus the coordinates of the image are given as follows:
(0, -1).
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A rotating light is located 17 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
When the the light's angle is 20° from perpendicular to the wall, and the light is rotating at an angular speed of one rotation in 2 seconds the rate the light projected onto the wall is moving is approximately 60.48 feet/s
What is angular speed?Angular speed, ω, is the angle, θ, in radians rotated by a rotating object per second. The unit of angular speed is radians per second, rad/s.
Mathematically;
[tex]\omega = \dfrac{\Delta \theta}{\Delta t}[/tex]
Where;
Δt = The time the object rotates through an angle of Δθ
The distance of the light from the wall, x = 17 feet
Time it takes the light to complete one rotation = 2 seconds
Angle the light makes with the perpendicular wall = 20°
[tex]tan(\theta) = \dfrac{y}{x}[/tex]
The distance the light has moved along the wall, y = x × tan(θ)
Therefore;
The y = 17 × tan(θ)
The angular velocity of the light, ω = θ/t
Therefore, θ = ω × t = ω·t
Which gives; y = 17 × tan(ω·t)
[tex]\omega = \dfrac{2\cdot \pi}{2}\ rad/s = \pi \ rad/s[/tex]
Therefore; x = 17 × tan(·t)
[tex]\dfrac{dy}{dt} = \dfrac{d}{dt} \left(17\times tan(\omega\cdot t)\right) = 17\cdot \omega\cdot sec^2(\omega \cdot t)[/tex]
ω = π rad/s (constant)
ω·t = θ
Therefore;
[tex]\dfrac{dy}{dt}= 17\cdot \omega\cdot sec^2(\theta)[/tex]
Rate the light is moving along the wall, dy/dt when θ = 20°, is therefore;
[tex]\dfrac{dy}{dt}= 17\times \pi\cdot sec^2(20^{\circ}) \approx 60.48[/tex]
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9.8 x 100 =
0.040 x 1,000 =
61 divide 10 =
8.909 x 100 =
Answer:
9.8 * 100 = 980
0.040 * 1000 = 40
61 / 10 = 6.1
8.909 * 100 = 890.9
Step-by-step explanation:
Eve and Patty swam fewer laps than Maureen. Patty swam more laps than Eve, and Maureen swam fewer laps than Raymond. Who swam the most laps?
Answer:
Raymond
Step-by-step explanation:
1 ) Eve and Patty swam fewer laps than Maureen so...
Eve and Patty < Maureen
2 ) Patty swam more laps than Eve...
Patty > Eve
3 ) Maureen swam fewer laps than Raymond...
Maureen < Raymond
4 ) We can eliminate Eve and Patty since they swam fewer laps than Maureen. The ones who are left are...
Maureen and Raymond
5 ) We know that Maureen swam fewer laps than Raymond so we can eliminate Maureen.
Raymond
6 ) This mean that the one who swam the most laps is...
Raymond
Hope this helps! :)
Version 1 for Game Design Determine the center and radius of the circle with equation x² + y² + 4x − 6y + 12 = 0
Answer:
Step-by-step explanation:
Equation of circle is, (x-h)^2+ (y-k)^2=r .......(eqn1)
where, (h,k) is the center and r is the radius.
therefore, from the question by rearranging the equation,
x² + y² + 4x − 6y + 12=0
viz, (x² +4x+4) + (y²-6y+9)-1=0
(x+2)^2 + (y-3)^2=1
therefore from eqn1, (-2,3) is the center and radius is 1
Which of the following are less than -0.625
Answer: The answer is A
Step-by-step explanation:
-5/8 is literally equal to -0.625 meaning this asnwer is equal not less
-0.5 is Greater than -0.625 because -0.6 is much larger
-8/5 is -1.6 which is Less than -0.625
Approximately 72% of persons living in Cape Town who are aged 70 to 84 live in elderly care facilities. If four persons are randomly selected from this population, what is the probability that exactly two of the four live in elderly care facilities?
Select one:
The probability that exactly two of the four live in elderly care facilities is; 0.244
How to solve Binomial Probability Distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The general formula of binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
where;
Px = the probability of exactly x events occurring.
x = the number of expected successful outcomes.
p is probability of success
n is sample size
We are given;
p = 72% = 0.72
n = 4
Thus;
P(X = 2) = 4C2 * (0.72)^(2) * (1 - 0.72)^(4 - 2)
P(X = 2) = 0.244
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How many times greater is 5.96 × 10^4 then 2.98 × 10^3?
A. 20
B. 500
C. 50
D. 200
The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ , the correct option is (a) .
In the question ,
it is given that
the number is 5.96 × 10⁴ ,
we have to find that how many times greater is 5.96 × 10⁴ then 2.98 × 10³ .
to find that the number is how many times greater ,
we divide 5.96 × 10⁴ by 2.98 × 10³ .
So , on dividing the numbers we get
= ( 5.96 × 10⁴ ) / ( 2.98 × 10³ )
= 5.96/2.98 × 10⁴⁻³
= 2 × 10¹
= 20 times
Therefore , The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ .
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Can anyone please help me I would really appreciate it a lot
Using the geometric mean theorem,
[tex]\frac{y}{14.4}=\frac{14.4}{19.2} \\ \\ y=10.8[/tex]
Using Pythagoras on triangle [tex]ABD[/tex],
[tex]x=\sqrt{14.4^2+10.8^2}=18[/tex]
Triangles [tex]ABD[/tex] and [ted]CBD[/tex] are similar because corresponding angles are congruent and pairs of corresponding sides have proportional lengths.
To determine this, use the complementary angles.
A cell phone plan costs $100 to start. Then there is a $25 charge each month. What is the total cost (start-up fee and monthly charge) to use the cell phone plan for 1 month? 6 months? Be sure to show your work. What is the total cost for months? Enter your first and last name below and then click start. If this is your second attempt, be sure to put a "2" after your name so I know it is your second attempt. Graph the cost of the cell phone plan over a period of two years, using months as the units of time. Be sure to label your axes and scale them by labeling each gridline with a number.
The $100 start-up fee and $25 monthly rental gives;
The cost of using the phone for 1 month = $125
The cost of using the phone for 6 months = $250
The cons of using the phone for n months = $(100 + 25·n)
Please find attached the graph of the cellphone plan over a period of two years (24 months)
What is a graph of a function?A graph is a visual representation of the variation of one variable of a function with respect to other variables of the function.
The start-up fee of the cell phone plan = $100
The amount charged each month = $25
First part;
The total cost for the start-up fee and monthly rental for 1 month = $100 + $25
The total cost for 1 month = $125
The total cost for 6 months = $100 + 6 × $25 = $250
The total cost for n months = 100 + n × 25 = $(100 + 25·n)
Please find the graph of the total cost to the number of months created with MS Excel
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marie bought 1/2 gallon of milk which she finished after 6 days if she drank the same amounteach day how many gallons a day did she drink
She drinks 1/12 gallons of milk each day
How to determine how many gallons a day did she drink?From the question, we have the following parameters that can be used in our computation:
Size of milk = 1/2 gallons
Number of days = 6 days
These parameters can be represented as
(x, y) = (6, 1/2)
The number of gallons a day she drinks can then be represented as the slope/unit rate and the unit rate is then calculated as
unit rate = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (6, 1/2)
Substitute the known values in the above equation
So, we have the following equation
Slope = (1/2 - 0)/(6 - 0)
Evaluate the quotient
Slope = 1/12
Hence, the number of gallons she drinks a day is 1/12
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The animals at a safari park include camels,
kangaroos and meerkats.
There are 12 more kangaroos than there are
camels.
There are 3 times as many meerkats as there
are camels.
There are the same number of kangaroos as
there are meerkats.
How many camels are there at the safari park?
Number of camels are there at the safari park are 6 unit.
The animals at a safari park include camels, kangaroos and meerkats.
Let kangaroos are represented as K and Camels are represented as C and Meerkats are represented as M.
There are 12 more kangaroos than there are camels which means
K = C + 12.
There are 3 times as many meerkats as there are camels which means
M = 3C.
There are the same number of kangaroos as there are meerkats which means
K = M
If K = M
therefore,
3C = C + 12
2C = 12 ,
C = 6 unit.
So, K = 6 + 12 = 18
Or M = 18
Therefore number of camels, kangaroos and meerkats at the safari park are 6 , 18 and 18 respectively.
Number of camels are there at the safari park are 6 unit.
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A straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form. 8 in. 5 in. 5 in.
The length of the straw fitted in the box is 10.67 inches.
What is cuboid?A cuboid is a solid three-dimensional object which has six faces that are rectangular with eight vertices, and twelve edges.
Given that, a straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner,
Diagonal of a cuboid = √ l² + w² + h²
Therefore, diagonal of the box = √ 5² + 5² + 8² = 10.67 in
Hence, The length of the straw fitted in the box is 10.67 inches.
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No one bothers to help, plsssssssssss!!!!!!!!!!!!!!!!!!!!!!!
slope-related question image pasted below!!!
Answer:
I'm not sure if its right but I got
6/9
Step-by-step explanation:
What I did was:
I took the 2 points:
(-4,4) and (5,-2)
Then did rise over run
Which left me with 6/9
What is the value of x?
The required value of x is 3 in the given equilateral triangle.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The triangle given in the figure is an equilateral triangle.
We know that all sides are equal in the equilateral triangle.
As per the given figure,
side AB = side AC
6x - 3 = 3x + 6
6x - 3x = 6 + 3
Apply the arithmetic operation,
3x = 9
x = 9/3
x = 3
Therefore, the required value of x is 3 in the given equilateral triangle.
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Find the value of x .. assume that segments that appear to be tangent are tangent .
We got x = 16.54 by using Pythagorean theorem .
What is the Pythagorean theorem in plain English?
According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90° .
18² = 7.1² + x²
324 = 50.41 + x²
x² = 324 - 50.41
= 273.59
x = √ 273.59
x = 16.54
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3. Plumbers deal with measurements in inches and common fractions of an inch, while surveyors use feet and decimal
fractions of a foot. Often one trade needs to interpret the measurements of the other.
(a) A drain has a run of 52 ft at a grade of 1/8 in./in. The high end of the drain has an elevation of 126.30 ft. What is the elevation at the low end?
(b) The elevation at one end of a lot is 84.12 ft, and the elevation at the other end is 94.67 ft. Express the difference in elevation in feet and inches and rounded to the nearest 1/8 in
The elevation at the lower end of a drain is 119.8 feet. For the second drain difference in feet will be 10.55 feet and in inches will be 126.6 inch.
What is elevation?The height above or below a fixed reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. A vertical surface is depicted in an elevation when viewed from a point perpendicular to the viewer's picture plane. You are looking at the front elevation, for instance, if you are standing directly in front of a building and viewing its front. The height between a point and a horizontal surface is known as HEIGHT. The height of a point above (or below) sea level is known as its ELEVATION.
Here,
a. The length of drain= 52 feet
the gradual decrease=0.125 ft
elevation at high end=126.30 feet
elevation at low end,
=126.3-(52*0.125)
=126.3-6.5
=119.8 feet
b. The elevation at one end=94.67 feet
The elevation at other end=84.12 feet
The difference in elevation,
=94.67-84.12
=10.55 feet
=10.55*12
=126.6 inches
The elevation of a drain's lower end is 119.8 feet. The second drain will differ by 10.55 feet in feet and 126.6 inches in inches.
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water faucet leaked 3/5 liters of water over the course of 2/5 hours. How many liters would it have leaked in 1 hour please tell me the answer
Answer:
1.5 liters
Step-by-step explanation:
10 = 6/5 W
Solve the missing variable, W
[tex]\framebox{w=$\dfrac{25}{3}$}[/tex]
Flip the equation:
[tex]\frac{6}{5} w=10[/tex]
Multiply both sides by [tex]\frac{5}{6}[/tex]:
[tex](\frac{5}{6} )\times(\frac{6}{5} w)=(\frac{5}{6} )\times(10)[/tex]
[tex]w=\frac{25}{3}[/tex]
Subtract.
Your answer should be a polynomial in standard form.
(6a³ + 7a²) - (5a³ + 9a² + a) =
Step-by-step explanation:
=6a^3+7a^2-5a^3-9a^2-a
=a^3-2a^2-a this is the final answer.
In a photo contest, two judges are giving scores to each photo. Each judge gives a score for impact (worth 40%), composition (worth 30%), lighting (worth 20%), and color balance (worth 10%). Lester entered a photo in the contest and received the following scores: Impact: 8 and 9 Composition: 7 and 7 Lighting: 8 and 7 Color balance: 5 and 7 Enter a number in each box to create an expression that represents Lester's final score.
Lester's final score from the two Judges is 7.6
How to calculate Lester's final scoreThe scores of the judges are in percentage and this will be converted to decimal by dividing by 100
impact (worth 40%) = 0.4
composition (worth 30%) = 0.3
lighting (worth 20%) = 0.2
color balance (worth 10%) = 0.1
Average score from the Judges will be used to multiply the percentages
Impact: 8 and 9
= 8.5 * 0.4 = 3.4
Composition: 7 and 7
= 7 * 0.3 = 2.1
Lighting: 8 and 7
= 7.5 * 0.2 = 1.5
Color balance: 5 and 7
= 6 * 0.1 = 0.6
sum of the scores gives Lester's final score as 7.6
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Which one is triangle a and b
In both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.
What is Obtuse triangle?
When one of the interior angles of a triangle is more than 90 degrees, the triangle is said to have obtuse angles. The sum of the other two angles in an obtuse triangle is less than 90° if one angle in the triangle is greater than 90°.Degrees with obtuse angles include 110°, 135°, 150°, 179°, 91°, and more. Therefore, all angles that fall between 90° and 180° are obtuse angles.Triangle B = Obtuse triangle
Triangle C = Obtuse triangle
in both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.
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126=2×3×3×k
Solve for k
[tex]{ \huge{ \boxed{ \red{ \sf{x = 7}}}}}[/tex]
Step-by-step explanation:-
[tex]{ \sf{126 = 2 \times 3 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 6 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 18 \times k}}[/tex]
[tex]{ \sf{126 = 18k}}[/tex]
Divide both the sides by 18 in order to find the value of k. Then,
[tex]{ \sf{ \frac{126}{18} = \frac{18}{18} k}}[/tex]
[tex]{ \boxed{ \boxed{ \purple{ \sf{x = 7}}}}}[/tex]
.
Radioactive Strontium The half-life of strontium-90 is 28 years. How long will it take a 50- mg sample to decay to a mass of 32 mg?
The time taken is obtained as 3 years.
What is the time taken?We know that radioactivity has to do with the fact that a substances does disintegrate gradually over a period of time.
Let us recall the formula;
N/No = (1/2)^t/t1/2
N = The mass of radioactive atoms at time t
No = The mass of radioactive atoms initially present
t = time taken
t/12 = half life of the radioactive nucleus
Then;
32/50 = (1/2)^t/28
0.64 = (1/2)^t/28
log 0.64 = t/28 log0.5
t/28 = log(0.64/0.5)
t = 28 * log(0.64/0.5)
t = 3 years
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Mia is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 15 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 18^{\circ}
∘
, and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^{\circ}
∘
. If her eyes are 1.75 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.
Considering the angle of elevations, the distance from point AA to point BB which is the height of the antenna is 5.34 meters
How to find the distance between the pointsinformation given in the question
Mia stands at a horizontal distance of 15 meters from the building
The angle of elevation from her eyes to the roof ((point AA)) is 18
the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^
her eyes are 1.75 meters from the ground
The direction of movements describes a right angle triangle of
opposite = height of antenna + height of the building
adjacent = 15 meters
The distance from point AA to point BB and the height of the antenna is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The the height of the antenna is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
using 53 gives the height of the antenna + height of the building, while using 18 gives height of the building only
tan 53 = opposite / 15
opposite = 15 * tan 53 = 19.906 meters
opposite = 15 * tan 18 = 14.266 meters
Height of the antenna
= 19.606 - 14.266
= 5.34 meters
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Graph the line with slope 1 passing through the point (-2 , -5)
Graph the line.
The equation of the line is y = x -3. The graph of the line is attached below.
What is a line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
Given that the slope of the line is 1.
Assume that the equation of the line is y = mx +c, where m is the slope of the line and c is y-intercepts.
Putting m = 1 in y = mx +c:
y = 1 × x +c
y = x +c
Since the line passes through the point (-2, -5), thus the point satisfies the given equation of line.
Putting x = -2 and y = -5 in y = x +c
-5 = -2 + c
c = -3
The equation of line is y = x - 3.
The points on the line are
(-2, -5), (0, -3), (3, 0).
Plot the points and join them:
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Carl is making accessories for the soccer team. He uses 773.85 inches of fabric on headbands for 29 players and 4 coaches. He also uses 279.56 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.
No. of players = 29
No. of coaches = 4
Total fabric used for headbands = 773.85 inches
Total no. of people for headbands = 29 + 4
= 33
Fabric used for headband for 1 person = 773.85/33
= 23.45 inches
Total fabric used for wristbands = 279.56 inches
Total no. of people for wristbands = 29
Fabric used for headband for 1 person = 279.56/29
= 9.64 inches
Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.
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PLEASE HELP!!
F(n)=3n-4
find term 3
The third term of F(n)=3n-4 is 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
F(n)=3n-4
F of n equal to three times of n minus four.
We need to find the third term.
To find third term we need to plug 3 in place of n.
F(3)=3(3)-4
Three times three minus four
F(3)=9-4
Nine minus four gives 5
F(3)=5
Hence, the third term of F(n)=3n-4 is 5.
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35. Rosa plants rows of flowers with exactly the same number
in each row. Each row has more than one flower. She has
28 flowers. What is the largest number of rows she can make?
A 4
B
7
12
D 14
Answer: 10 rows of rose plants
Step-by-step explanation:
The number of rose plants in first, second third,..., and last row are respectively.
23,21,19,....,5.
number of rose plants: n
The sequence 23,21,19,....,5 is an A.P. with first term a(=23), common difference d(=−2) and n
=a+(n−1)d
⟹5=23+(n−1)×−2
⟹5=23−2n+2⟹20=2n⟹n=10
Triangle PQR is isosceles, Q being the right angle. If the hypotenuse is 38.47cm, find: i. Lengths of sides PQ and QR. ii. The size of angle QPR
The size of angle QPR is 45° and the length of sides PQ and QR are both 27.20cm
What are Isosceles triangle?An isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal angle,
since ∆PQR is a right angle isosceles triangle then, if angle Q is 90^°, QPR = PRQ=x( angles of an isosceles triangle).
Therefore 90+x+x= 180°
2x= 90
x= 45°
To find line PQ and QR, we use trigonometry ratio
cos 45°= adj/hyp
I/√2= QR/38.47
QR= 38.47/√2
= 27.20cm
QR= PQ= 27.20
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