Answers
Using the bearing and trigonometry in the problem, the distance of the waterfall from the lake is 7.94km
How far away is the waterfall from the lake?To determine the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the distance in a south direction.
To find the distance between the waterfall and the lake, we can use the concept of right triangles and trigonometric functions.
Since the bearing is given as 236°, we can subtract this angle from 180° to find the angle formed by the south direction and the line connecting the lake and the waterfall:
180° - 236° = -56°
Now, we can consider the south direction as the reference direction (0°) and the line connecting the lake and the waterfall as the hypotenuse of a right triangle.
Using the cosine function, we can calculate the length of the side adjacent to the angle (-56°), which represents the distance between the waterfall and the lake:
cos θ = adjacent / hypothenuse
Adjacent = Hypotenuse * cosθ
Let's substitute the values into the formula:
Adjacent = 14.2 km * cos(-56°)
To calculate the cosine of -56°, we can use the fact that the cosine function is an even function:
cos(-56°) = cos(56°)
Adjacent side = 14.2 cos(56)
Adjacent side = 7.94km
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Answer:
The waterfall is approximately 8.91 km away from the lake
Step-by-step explanation:
To find the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the southward direction.
Since the waterfall is 14.2 km south of the lake, the line connecting the waterfall and the lake forms a right triangle with the south direction being the adjacent side, the distance between them being the hypotenuse, and the angle formed between them being the bearing of 236°.
To find the distance between the waterfall and the lake, we can use the cosine function, which relates the adjacent side, hypotenuse, and angle:
cos(236°) = adjacent side / hypotenuse
Let's denote the distance between the waterfall and the lake as "d." The adjacent side represents the southward direction.
cos(236°) = d / 14.2 km
Solving for "d":
d = cos(236°) * 14.2 km
Using a calculator:
d ≈ -8.91 km
Since distance cannot be negative, we take the absolute value:
|d| ≈ 8.91 km
Therefore, the waterfall is approximately 8.91 km away from the lake.
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Related Questions
How many degrees must Figure A be rotated counterclockwise around the origin in order to line up with Figure B?
A. 90
B. 180
C. 270
D. 360
Answers
The number of degrees the Figure A must be rotated counterclockwise around the origin to line up with Figure B is = 270°
Given data ,
Let the number of degrees the Figure A must be rotated counterclockwise around the origin to line up with Figure B be represented as A
Now , the triangle is represented by the figure A with coordinates as
A ( -2 , 3 )
And , the coordinates of the rotated triangle is A' ( 3 , 2 )
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
So , the triangle is rotated 270° counterclockwise rotation
Hence , the rotation is 270° counterclockwise
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Compare the functions shown below:
f(x)
polynomial graph with x intercepts at negative 3, negative 2, 1, 2, y intercept at negative 12
g(x)
trig graph with points at 0, 3 and pi over 2, 0 and pi, negative 3 and 3 pi over 2, 0 and 2 pi, 3
Over the interval x = 0 to x = 2π
h(x) = 2x3 − 2x2 − 3x + 2
Which function has the most x-intercepts? (2 points)
f(x)
g(x)
h(x)
All three functions have the same number of x-intercepts.
Answers
f(x)
Answer:
f(x) has the most x intercepts
PLEASE HELP AS SOON AS POSSIBLE !
The diameter, , of a sphere is 14.6. Calculate the sphere's volume, .
Use the value 3.14 for pi , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
Answers
The volume of the sphere, given that the sphere has a diameter of 14.6 mm is 1628.7 mm³
How do i determine the volume of the sphere?The following data were obtained from the question:
Diameter (D) = 14.6 mmRadius (r) = Diameter (D) / 2 = 14.6 / 2 = 7.3 mmPi (π) = 3.14Volume of sphere =?The volume of a sphere is giving by the following formula
Volume of sphere = 4/3πr³
Inputting the given parameters, we can obtain the volume of the sphere as follow:
Volume of sphere = (4/3) × 3.14 × 7.3³
Volume of sphere = (4/3) × 3.14 × 389.017
Volume of sphere = 1628.7 mm³
Thus, we can conclude from the above calculation that the volume of the sphere is 1628.7 mm³
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Please Help 8x + 1
115⁰
Answers
Both the angles are supplementary angles hence the value of x is 8°.
To solve for the value of x in the given scenario, we can use the fact that the interior angles between two parallel lines are supplementary, meaning they add up to 180 degrees.
Given:
Angle 1: (8x + 1)
Angle 2: 115°
Since these two angles are supplementary, we can set up the equation:
(8x + 1) + 115 = 180
Now we can solve for x by simplifying and isolating the variable:
8x + 1 + 115 = 180
8x + 116 = 180
8x = 180 - 116
8x = 64
To isolate x, we divide both sides of the equation by 8:
8x/8 = 64/8
x = 8
Therefore, the value of x is 8.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The meaure of m∠KJL in the circle is:
m∠KJL = 25°
How to find the angle m∠KJL in the circle?Since ΔJKL is inscribed in circle P with diameter JK and mJL = 130°. Thus, m∠JLK is an inscribed angle.
Since an angle inscribed in a semicircle is a right angle.
Thus, m∠DFE = 90°
Since the measure of inscribed angle is half the measure of its intercepted arc. Thus:
m∠JKL = 1/2 * mJL
m∠JKL = 1/2 * 130
m∠JKL = 65°
Therefore:
m∠KJL = 180 - 90 - 65 = 25° (sum of angles in a triangle)
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Which mathematical statement represents "17 more than a number is 26"?
17>26
On+17-26
17<26
O26+n-17
Answers
The mathematical statement that represents "17 more than a number n is 26" can be written as: n + 17 = 26
Given that a statement we need to convert it into a mathematical statement,
The mathematical statement that represents "17 more than a number n is 26" can be written as:
n + 17 = 26
To solve for n, we can subtract 17 from both sides of the equation:
n + 17 - 17 = 26 - 17
Simplifying the equation gives:
n = 9
Therefore, the number n is 9.
Hence the mathematical statement that represents "17 more than a number n is 26" can be written as: n + 17 = 26
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Lee and Olivia share some money. Lee has 7/11 of the money. If Lee gives Olivia £18 then they have the same amount of money How much money did they share? Lee Olivia
Answers
The total amount of money shared by Lee and Olivia is £132 and Lee and Olivia shared £84 and £48, respectively.
Lee has 7/11 of the total money, which means Lee has (7/11) × x amount of money.
When Lee gives Olivia £18, they have the same amount of money.
So Olivia's share becomes equal to Lee's share.
Therefore, we can set up the following equation:
(7/11) × x - £18 = (1/2)×x
To solve this equation, we can simplify it:
7x/11 - £18 = x/2
Multiplying both sides of the equation by 22 (the least common multiple of 11 and 2) to eliminate the denominators:
14x - 22 × £18 = 11x
14x - 396 = 11x
Subtracting 11x from both sides:
14x - 11x - 396 = 0
3x - 396 = 0
Adding 396 to both sides:
3x = 396
Dividing both sides by 3:
x = 396/3
x = 132
To find Lee and Olivia's individual shares, we can substitute this value back into the initial conditions:
Lee's share = (7/11)× £132 = £84
Olivia's share = £132 - £84 = £48
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Why is ΔABC ~ ΔDEC? Use the drop-down menus to explain your answer. Why is ΔABC ~ ΔDEC? Use the drop-down menus to explain your answer.
Answers
The triangles are similar because they are both right triangles, so they both have an angle that is equals to 90º. They both share a common vertex, <C. So they are similar by the Angle-Angle criterion.
What are similar triangles?Two triangles are defined as similar triangles when they share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.For this problem, they have two equal angle measures, the right angle and < C, hence the third angle also must be equal, and they are similar by the Angle-Angle criterion.
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What is the distance between $500 and $-61.63
Answers
Answer: $561.63
Step-by-step explanation: To find the distance you subtract 500 by -61.63
You get the equation 500--61.63
The two negative signs cancel out to become a positive sign
So the new equation is 500+61.63
So the distance is $561.63
Answer:
$561.63
Step-by-step explanation:
To find out the distance between 500 and -61.63 it will be $500-$-61.63. So 500 - (-61.63) becomes 500 + 61.63 because 2 negatives in a row make a positive. So when you do 500+61.63, you'll get 561.63.
A recipe calls for 3.5 cups of rice. If a cup of rice weighs 158 grams, and a bag of rice weighs 2 pounds, how many bags would be needed to make 80 recipes? (2.2 lbs. = 1 kg, 1kg = 1000 g) (Convert 80 recipes to bags)
Answers
The number of bags of rice that would be needed to make 80 recipes is 48.664 bags.
How many bags would be needed to make 80 recipes?1 recipe = 3.5 Cups of rice
If
1 cup of rice = 158 grams
1 bag of rice = 2 pounds
2.2 lbs. = 1 kg,
1kg = 1000 g
80 recipes = 3.5 cups 80
= 280 cups
1 cup of rice = 158 grams
280 cups = 158 × 280
= 44,240 grams
1kg = 1000 g
44,240 grams = 44.24 kg
2.2 lbs. = 1 kg; x lbs = 44.24
2.2/1 = x/44.24
x = 2.2 × 44.24
x = 97.328 pounds
1 bag of rice = 2 pounds ; x bags = 97.328 pounds
1/2 = x/97.328
97.328 = 2x
x = 48.664 bags
Hence, 48.664 bags of rice is needed for 80 recipes.
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Enter the number that belongs in the green box
Answers
The number in the green box is 31.78° .
Given,
Triangle with sides 11 , 12 , 20.
From Cosine Law.
Let △ABC have sides a, b, c.
Here,
a = 11
b = 20
c = 12
Length of the side opposite vertex A is called a.
Length of the side opposite vertex B is called c.
Length of the side opposite vertex C is called c.
Let θ = ∠C
Then, the Cosine Law says that
c²=a²+b²−2abcosθ.
Substitute the values of a , b , c .
12² = 11² + 20² - 2 × 11× 20 cosθ
θ = 31.78°
Hence the angle can be found out from cosine law.
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a trucker is driving on the highway traveling 65 miles per hour write an equation that shows the relationship between the number of hours of highway travel x and the number of miles traveled 7 answer quickly for 20 points!!
Answers
y = 65x
Pizza General charges 10 dollars per medium pizza and a 5-dollar delivery fee. Fill in the table to show how much you would pay to get each number of pizzas delivered. Make sure to consider both the cost of the pizzas and the delivery fee.NOWWWWW
Answers
Answer:
Step-by-step explanation:
$15 for one pizza it's simple
What is n^2-11n+10
Please explain step by step and detailed to get the answer
Answers
The value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).
To find the value of the expression [tex]n^2 - 11n + 10[/tex], we can follow these steps:
Start with the given expression: [tex]n^2 - 11n + 10.[/tex]
Look for any like terms that can be combined. In this case, there are no like terms.
Since there are no like terms, we can simplify further by factoring the expression. We need to find two numbers that multiply to give 10 (the constant term) and add up to -11 (the coefficient of the middle term, which is -11n).
The numbers that satisfy these conditions are -1 and -10, because
(-1) × (-10) = 10 and (-1) + (-10) = -11.
Now we can rewrite the expression using these numbers:
[tex]n^2 - 11n + 10 = (n - 1)(n - 10).[/tex]
So the factored form of the expression is (n - 1)(n - 10).
Therefore, the value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).
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Circle the error in the problem and rewrite what the correct step should be
Answers
The error in the problem is given by the equation in step(3). and the value is given by g ( x ) = 2x² + 4x - 4
Given data ,
Let the equation be represented as g ( x )
Now , the value of g ( x ) is
g ( x ) = 2 ( x + 1 )² - 6
On simplifying the equation , we get
From the distributive law of multiplication , we get
g ( x ) = 2 ( x + 1 ) ( x + 1 ) - 6
g ( x ) = 2 ( x² + 2x + 1 ) - 6
On further simplification , we get
g ( x ) = 2x² + 4x + 2 - 6
g ( x ) = 2x² + 4x - 4
Therefore, the value of g ( x ) is g ( x ) = 2x² + 4x - 4
Hence , the equation is g ( x ) = 2x² + 4x - 4
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Find the missing side length.
1) 10 / ?
2) 24 / 15
( look at photo )
Answers
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The area of the slice of pizza is 25.1 inches squared.
How to find the area of the slice of pizza?The circular pizza has a diameter of 16 inches. Each slice of pizza have a angle of 45 degrees.
Therefore, the area of the slice of pizza can be calculated as follows:
area of the slice of pizza = ∅ / 360 × πr²
where
r = radius∅ = central angleTherefore,
r = 16 /2
r = 8 inches
area of the slice of pizza = 45 / 360 × 3.14 × 8²
area of the slice of pizza = 45 / 360 × 3.14 × 64
area of the slice of pizza = 9043.2 / 360
area of the slice of pizza = 25.12 inches²
area of the slice of pizza = 25.1 inches²
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solve x^2+1/2x+_=2+_
Answers
The complete equation is x² + 1/2x -2 = 2 + 2
The given equation can be rewritten as:
x² + (1/2)x + () = 2 + ()
Since the equation involves two missing values, let's consider them one by one.
Solve for the first missing value indicated by (_):
To find the missing value indicated by (_), we equate the quadratic equation to 2:
x² + (1/2)x + (_) = 2
Comparing this with the standard form of a quadratic equation,
ax² + bx + c = 0, we have:
a = 1, b = 1/2, c = (_ - 2)
Using the quadratic formula, x = (-b ± √(b²- 4ac)) / (2a), we can substitute the values:
x = (-(1/2) ± √((1/2)² - 4(1)(_-2))) / (2(1))
x = (-1/2 ± √(1/4 + 8(1)(_-2))) / 2
x = (-1/2 ± √(1/4 + 8(_ - 2))) / 2
Therefore, the first missing value is represented by (_ - 2).
Solve for the second missing value indicated by (_):
To find the missing value indicated by (_), we equate the constant term to 2:
(_) = 2
This indicates that the second missing value is equal to 2.
Putting it all together, the solution to the equation x² + (1/2)x + _ = 2 + _ is:
x = (-1/2 ± √(1/4 + 8(_ - 2))) / 2
with (_ - 2) representing the first missing value, and the second missing value is 2.
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30 points !! :) Thank you in advance
Answers
The solutions of the quadratic equation are: x = 1
The x-intercept is x = 1
What is the Solution to the quadratic equations?The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The y-intercept is the point at which the graph crosses the y-axis and in this case it is: y = 1
The x-intercepts are where the graph touches the x-axis and in this case, it is x = 1
The zeros of the quadratic equation are the x-intercepts and since the curve does not cross, then we can say that the zeros are x = 1 and x = 1 which signifies double root and as such the solution is x = 1
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please help with this question
Answers
The statistics that always corresponds to the 75th percentile in a distribution include the following: B. Third Quartile.
What is an interquartile range?In Mathematics and Statistics, IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) of a data set is the difference between third quartile (Q₃) and the first quartile (Q₁):
IQR = Q₃ - Q₁ = 75th percentile - 25th percentile.
In this context, we can reasonably infer and logically deduce that the 75th percentile in a distribution is always equal to the third quartile.
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Help me pls….. I’m confused on this!!!!!
Answers
A truck is being filled with cube-shaped packages that have side lengths of foot, the volume of the part of the truck that is being filled is 34,808 cubic feet.
To discover the finest range of applications that may in shape in the truck, we want to calculate the volume of the truck and divide it by using the quantity of every cube-formed bundle.
The quantity of the truck is given with the aid of the method:
Volume = Length x Width x Height
Volume = 8 ft x 61 ft x 71 ft
Volume = 34,808 cubic toes
The volume of every cube-shaped bundle is given with the aid of the method:
Volume = Side [tex]Length^3[/tex]
Volume = 1 [tex]ft^3[/tex]
Number of packages = Volume of truck / Volume of each package
Number of packages = 34,808 ft^3 / 1 ft^3
Number of packages = 34,808
Thus, the greatest number of packages that can fit in the truck is 34,808.
Volume of the part of the truck being filled = Number of packages x Volume of each package
Volume of the part of the truck being filled = 34,808 x 1 ft^3
Volume of the part of the truck being filled = 34,808 ft^3
Thus, the volume of the part of the truck that is being filled is 34,808 cubic feet.
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Find the value of x to
the nearest whole
number.
Answers
Answer: i'm kind of just guessing, but i think x = 13
Step-by-step explanation:
please don't ask me how i don't know
Name an equation parallel to: y = -2/3 x + 10
Answers
Answer: The answer is...
y = -2/3 x + 1
Step-by-step explanation:
The others would have crossed paths with y = -2/3 x + 10
6.56*10^-7 by 4.86*10^-7
Answers
6.56 × [tex]10^{-7}[/tex] by 4.86×[tex]10^{-7}[/tex] is 3.18816 × [tex]10^{-13}[/tex] is factorize.
To find the product of 6.56 × [tex]10^{-7}[/tex] by 4.86×[tex]10^{-7}[/tex]. The conventions of scientific notation can be applied. To get 31.8816, we must first multiply the coefficients, which are 6.56 and 4.86. The exponents, which are -7 and -7, are then added to provide -14.
The product of 6.56 × [tex]10^{-7}[/tex] by 4.86 × [tex]10^{-7}[/tex] is 3.18816 × [tex]10^{-13}[/tex] This, according to the conventions of scientific notation, can be calculated by multiplying the coefficients and adding the exponents.
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write an explicit formula for an the nth term of the sequence 6, 12, 18
Answers
Answer:
[tex]a_{n}[/tex] = 6n
Step-by-step explanation:
there is a common difference between consecutive terms, that is
12 - 6 = 18 - 12 = 6
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 6 and d = 6 , then
[tex]a_{n}[/tex] = 6 + 6(n - 1) = 6 + 6n - 6 = 6n
Which three lengths could be the lengths of the sides of a triangle?
Answers
Any three lengths that satisfy the triangle inequality theorem can form the sides of a triangle. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In order for three lengths to form a triangle, they must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider three lengths: a, b, and c.
To determine if they can form a triangle, we need to check the following conditions:
a + b > c
a + c > b
b + c > a
If all three conditions are true, then the lengths a, b, and c can form a triangle.
For example, let's consider the lengths 3, 4, and 5.
3 + 4 > 5 (True)
3 + 5 > 4 (True)
4 + 5 > 3 (True)
Since all three conditions are true, the lengths 3, 4, and 5 can form a triangle.
Therefore, any three lengths that satisfy the triangle inequality theorem can be the lengths of the sides of a triangle.
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1
2
3
4
5
I
Statement
+
ZHKI ZGKH
HJ I GI
H
m2GKH+mZHKI = 180°
m2GKH + m2GKH = 180°
m2GKH = 90°
Reason
Given
Angles forming a linear pair sum to 180°
Definition of congruence
Answers
Answer:
3. Substitution because it said angle HKI = angle GKH, so we substitutioned that angle for the other one. I'm not sure about 4. If you provide us with the answer choices for that one, then I could help
Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. The hotel served 540 gallons of orange juice last year. This year, the hotel served 5% less orange juice than it did the previous year. How much was served this year
Answers
The amount of juice served this year is given as follows:
513 gallons.
How to obtain the amount of juice?The amount of juice served this year is obtained applying the proportions in the context of the problem.
The amount last year was given as follows:
540 gallons.
The percentage of this year's amount relative to last year's amount is given as follows:
95%, due to the decay of 5%, 100 - 5 = 95%.
Hence the amount of juice served this year is given as follows:
0.95 x 540 = 513 gallons.
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the value stock in 1940 is $1.25. it’s value grows by 7% each year after 1940. write an equation representing the value of the stock V(t), in dollars, t years after 1940
Answers
This equation represents the value of the stock, V(t), in dollars, t years after 1940, taking into account the 7% annual Growth rate V(t) = $1.25 * (1 + 0.07)^t.
The value of the stock, V(t), in dollars, t years after 1940, we can use an exponential growth equation since the stock's value grows by 7% each year after 1940.
formulate the equation step by step:
1. We know that the initial value of the stock in 1940 is $1.25. This initial value serves as the starting point for our equation.
2.We are given that the value of the stock grows by 7% each year. This means that for every year that passes, the stock's value increases by 7% of its previous value.
3. In mathematical terms, if V(0) represents the initial value in 1940 ($1.25), then the value of the stock after t years can be represented as:
V(t) = V(0) * (1 + r)^t,
where r is the growth rate expressed as a decimal (in this case, 7% = 0.07).
4. Plugging in the given values, our equation becomes:
V(t) = $1.25 * (1 + 0.07)^t.
This equation represents the value of the stock, V(t), in dollars, t years after 1940, taking into account the 7% annual growth rate.
For example, if we wanted to find the value of the stock 10 years after 1940, we would substitute t = 10 into the equation:
V(10) = $1.25 * (1 + 0.07)^10.
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What is the value of x
Enter your answer in the box
Answers
Answer:
x = 8 units
Step-by-step explanation:
Because this is a right triangle, we can find x using the Pythagorean theorem, which is given by:
a^2 + b^2 = c^2, where
a and b are the shorter sides called legs,and c is the longest side called the hypotenuse (always opposite the right angle).In the triangle, the 6 unit side and the x unit sides are the legs while the 10 unit side is the hypotenuse.
Thus, we can solve for x by plugging in 6 for a and 10 for c in the theorem and solving for a (aka x, simply a in the theorem):
a^2 + 6^2 = 10^2
a^2 + 36 = 100
a^2 = 64
a = 8
x = 8
Thus, x is 8 units.