Answer:
[tex]\dfrac{3(6)-1}{2(6)+1}[/tex]
Step-by-step explanation:
For ...
r(x) = 3x -1 s(x) = 2x +1The expression (r/s)(6) is ...
[tex]\left(\dfrac{r}{s}\right)(6) = \left.\dfrac{3x-1}{2x+1}\right|_{x=6}=\boxed{\dfrac{3(6)-1}{2(6)+1}}[/tex]
Answer:
A
Step-by-step explanation:
Which movie had the audience with the younger median ?
A. Movie A
B. Movie B
C. Both
D. Cannot be determined
How can we tell? Look at the vertical lines inside the box. This is where the median is located. For movie A, the inner vertical line is somewhere between 30 and 40 (perhaps 35 or so). So this is the median for movie A. Meanwhile, the median for movie B is somewhere between 40 and 50. I'd say maybe 46 or 47 as its a bit higher than the halfway point.
-----------
Extra info:
The left edge of the box is the first quartile (Q1).The right edge of the box is the third quartile (Q3).The tip of the left whisker is the min value, assuming there are no outliers to the left.The tip of the right whisker is the max value, assuming there are no outliers to the right.can someone please answer this question as a simplified fraction.
Answer:
33/2
Step-by-step explanation:
6 * 11/4 = 66/4 = 33/2
Please answer this correct answer now fast
Answer:
WX = 8 mm
Step-by-step explanation:
To be able to solve for WX, we need to first find the size of angle [tex]\angle z[/tex].
We use the law of sines in the blue triangle to do such:
[tex]\frac{sin(z)}{11} =\frac{sin(133)}{20} \\sin(z)=\frac{11\,sin(133)}{20} \\sin(z)=0.4022[/tex]
Now we can use this value in the larger right angle triangle where WX is the opposite side to angle [tex]\angle z[/tex], and the 20 mm side is the hypotenuse:
[tex]sin(z)=\frac{opposite}{hypotenuse} \\sin(z)=\frac{WX}{20}\\0.4022=\frac{WX}{20}\\WX=20\,(0.4022)\\WX=8.044\,\,mm[/tex]
which rounded to the nearest integer gives
WX = 8 mm
Solve the equation using the distributive property and properties of equality. One-half (x + 6) = 18 What is the value of x? 6 7 and one-half 14 and one-half 30
Answer:
The value of x is 30.
We have to find the value of x in the given equation.
Using distributive property
We have,
[tex]1/2(x+6)=18\\a.(b+c)=a.b+a.c\\1/2(x+3)=18\\1/2x=15\\x=3[/tex]
other are also solve by this methode;)
The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.
To solve the equation using the distributive property and properties of equality. One-half (x + 6) = 18 and value of x to be determined.
The equation is the well-organized link of the variables of two expressions that contain equal between them.
distributive properties are used to evaluate the math problem easily by distributing numbers to the numbers present in parenthesis. eg, if we apply the distributive property of multiplication to solve the expression
a( b + c ) = a.b + a.c
[tex]1/2(x+6) = 18[/tex]
Using distributive property a( b + c ) = a.b + a.c
[tex]1/2.x+1/2*6 = 18\\1/2x+3=18\\1/2x=18-3\\1/2x=15\\x=2*15\\x=30\\[/tex]
Thus, The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.
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please answers quick ,whats an inequality?
Answer:
Step-by-step explanation:
inequality is a equation with |x|
a inequality equation is like this..
|x|>7
halla la medida del lado de un cuadrado cuya diagonal es de 14 cm
Answer:
7√2 cm
Step-by-step explanation:
Aquí, estamos interesados en encontrar la longitud del lado de un cuadrado que tiene una longitud diagonal de 14 cm.
Una diagonal es una línea que se extiende desde un borde del cuadrado hasta el otro borde del cuadrado internamente.
Ahora, una diagonal de un cuadrado junto con dos lados de un cuadrado forman un triángulo rectángulo isósceles, siendo la diagonal la hipotenusa de este triángulo rectángulo.
Sabemos que los lados de un cuadrado tienen la misma longitud y, por lo tanto, llamemos a este lado desconocido x cm.
Matemáticamente, según el teorema de Pitágoras, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los otros dos lados.
Por lo tanto, tenemos;
14 ^ 2 = x ^ 2 + x ^ 2
196 = 2x ^ 2
dividir ambos lados por 2
98 = x ^ 2 x = √98
x = √ (49 * 2)
x = 7√2 cm
Por lo tanto, la longitud del lado del cuadrado es de 7√2 cm
Type the correct answer in each box. Use the graph to complete the given statements. Enter the letters A, B, C, or D in the boxes. (graph below) The function with the lowest output values as x approaches infinity is ____ . The function with the greatest output values as x approaches infinity is ____ .
As x approaches infinity,
The function with the lowest output is graph A
The function with the greatest output is graph B
===========================================================
Explanation:
As the graphs head to the right, they go up forever. However, the growth rate (how fast they go upward) varies. The red straight line (line A) goes up the slowest. The growth rate is the same throughout the entire function. The rate is the slope of the line. In contrast, the purple curve B goes up the fastest as it has the steepest increase among the four graphs. The graph steadily gets steeper as you move to the right.
The exponential graph will grow the fastest compared to a linear one or parabolic one. Graphs B and C are exponential, where graph B has a steeper curve compared to graph C.
Answer: The function with the lowest output values as x approaches infinity is Graph A.
The function with the greatest output values as x approaches infinity is Graph B.
Step-by-step explanation: I can’t give you a step-by-step explanation, but this is right!
simultaneous equations 2x + y = 21 x - y = 6
Step-by-step explanation:
this is substitution method
Answer:
2x + y = 21
+
x - y = 6
_________
3x = 27
x = 27 ÷ 3
x= 9
x - y = 6
9 - y = 6
9 - 6 = y
3 = y
Therefore, x= 9 and y = 3
Find the length, x,of the third side of the triangle.
====================================================
Explanation:
This is a visual example of the pythagorean theorem. We add the areas of the two squares to get
13+29.25 = 42.25
Then we apply the square root to this to get the value of x, which is the hypotenuse of the right triangle
x = sqrt(42.25) = 6.5
---------
Side note: if you're curious about finding the other lengths of the triangle, apply the square root to those areas. The blue area 29.25 will lead to a side length of approximately sqrt(29.25) = 5.4083269; the red square will follow the same idea.
Answer:
Step-by-step explanation:
area of a square=a²
A=29.25
a=side=√29.25 first square
second square =a=√13
find x(c)
right triangle: a²+b²=c²
(√29.25 )²+(√13)²=c²
29.25+13=c²
c=√(29.25+13)=6.5 unit
A blueprint for a house has a scale factor n = 10. A wall in the blueprint is 7 in. What is the length of the actual wall?
840 ft.
5.83 in.
70 ft.
5.83 ft.
Answer:
5.83 ft
Step-by-step explanation:
Given that
Scale factor, n = 10
Wall in blueprint = 7 in
To find:
Length of actual wall = ?
Solution:
Whenever a blueprint is created for any house or building, it is made smaller by a scale factor.
Here this factor is 10 times.
That means, the blueprint size is 10 times smaller than that of its actual size.
Or we can say that actual wall of building is 10 times the wall of blueprint.
So, wall of building = 10 [tex]\times[/tex] 7 = 70 inches
Now, we know that 12 inches = 1 ft
1 inch = [tex]\frac{1}{12}\ ft[/tex]
70 inches = [tex]\frac{1}{12}\times 70\ ft = 5.83\ ft[/tex]
so, the answer is Wall of building is 5.83 ft.
What is the translation from quadrilateral EFGH to
quadrilateral E'F’G’H
Answer:
The translation from quadrilateral EFGH to quadrilateral E'F'G'H' is [tex]T_{(2, -4)}[/tex], which is two units to the right (x direction) and 4 units down (negative y direction)
Step-by-step explanation:
The coordinates of quadrilateral EFGH are;
Point E has coordinates (-1, 1)
Point F has coordinates (0, 4)
Point G has coordinates (3, 1)
Point H has coordinates (3, 0)
The coordinates of the translation are;
Point E' has coordinates (0, -3)
Point F' has coordinates (1, 0)
Point G' has coordinates (4, -3)
Point H' has coordinates (4, -4)
The change in the y-coordinate values (y values) are;
From point E to point E', we have;
(-3 - 1) = -4 which is four units down
The change in the x-coordinate values (x values) are;
From point E to point E', we have;
(0 - (-1)) = 2 which is two units to the right
The total change in translation is [tex]T_{(2, -4)}[/tex].
hey loves!!! PLz help me
Answer:
Hey there!
We must use what we are given, so even though it looks like there might be four isosceles triangles, we are only given CA=CE, so that only allows us to conclude mathematically that there is only 1 isosceles triangle.
Hope this helps :)
Given: AB = BC, AC is ∠ bisector of ∠BAD Prove: BC ∥ AD
Answer:
<BAC ≅ BCA by rule Base angle theorem
Step-by-step explanation:
What we know:
BAC = DAC
BC = BA
ΔBCA is an isosceles so ∠BCA = ∠DCA and ∠BAC
and we found that out by base angle theorem since
Base angle Theorem = Two base angles of a icosceles triangle are equal.
And since ΔBCA is an isoceles then ∠A and ∠C will be equal. And so we can prove BC is a parallel to AD
The proof that BC ∥ AD from the given statements is that;
BC ∥ AD because of the definition of alternate angles
We are given;
AB = BC
AC is ∠ bisector of ∠BAD
Since AC is the angle bisector of ∠BAD, it means that;
∠BAC = ∠DAC (definition of a bisected angle)
Now, since AB = BC, it means that ΔBCA is an isosceles triangle.
Thus; ∠BCA = ∠BAC (base angle theorem)
Now, since ∠BCA = ∠BAC, and ∠BAC = ∠DAC, we can say that;
∠BCA = ∠DAC
This means ∠BCA and ∠DAC are alternate angles. Thus, we can say that AC is the transversal line carrying the two equal angles.
Thus, we can say that BC is parallel to AD as they are the parallel lines cut by the transversal line AC.
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Two factory plants are making TV panels. Yesterday, Plant A produced 5000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 450 defective panels
Answer:
10,000 panels
Step-by-step explanation:
A TV panel is being produced by two factory plants
Plant A produced 5000 fewer panels than plant B
Let a represent the number of panels produced by plant A and b represent the number of panels produced by plant B
a= b-5000............equation 1
5% of the panels from plant A were defective
= 5/100
= 0.05
2% of the panels from plant B were defective
= 2/100
= 0.02
The total defective panels of both plants is 450
0.05a + 0.02b= 450..............equation 2
Substitute b-5000 for a in equation 2
0.05(b-5000) + 0.02b= 450
0.05b - 250 + 0.02b= 450
Collect the like terms
0.05b+0.02b= 450+250
0.07b= 700
Divide both side by the coefficient of b which is 0.07
0.07 b/0.07= 700/0.07
b= 10,000
Hence plant B produced 10,000 panels
need help a s a p HURRYYYYY
Step-by-step explanation:
v= 4/3πr³
4/3×314/100×8×8×8
•
= 2,143.573
Part 2: describe the shape of your cross section of a slice of banana at 45° angle to a space draw picture of the sheep. Part 3: describe the shape of a cross sections if you slice banana and half with a cut perpendicular to its base draw a picture of the shape (hint remember to think of a banana a cylinder)
Answer:
Part 2:
The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points
The drawing of the angle cross section of a cylinder representing the banana is attached
Part 3:
When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle
The drawing of the perpendicular cross section of a cylinder representing the banana is
Step-by-step explanation:
What is the solution to this equation?
5x= 35
A. x = 7
B. X= 175
C. x = 30
D. x= 9
Answer:
7Option A is the correct option
Step-by-step explanation:
[tex]5x = 35[/tex]
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{35}{5} [/tex]
Calculate
[tex]x = 7[/tex]
Hope this helps...
Best regards!!
Answer:
Option A
Step-by-step explanation:
5x = 35
5x/5 = 35/5
x = 7
Find the area of equilateral triangle with side a.
Answer:
[tex]\frac{\sqrt{3} }{4} a^2[/tex]
Step-by-step explanation:
To find the area of an equilateral triangle, we can apply a formula.
[tex]A=\frac{\sqrt{3} }{4} s^2[/tex]
[tex]A= area\\s=side \: length[/tex]
The side length is given a.
Plug a in the formula as the side length.
[tex]A=\frac{\sqrt{3} }{4} a^2[/tex]
Answer:
3 square root over 4 a square
Step-by-step explanation:
A group of hikers buy 8 bags of trail mix. Each bag contains 3 1/2 cups of trail mix. The trail mix is shared between evenly between 12 hikers. How many cups of trail mix do each hiker receive?
Answer:
The hikers each receive 2 1/3 cups of trail mix.
1. Multiply 8 by 3 1/4 to get how much cups of trail mix they have in total which will come out as 28.
2. Then divide the 28 cups by the 12 hikers, and you will get 2 1/3 as your answer.
What is P(A|B)?
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
What is P(A|B)? 
A.Not enough information
B.0.50 
C.0.10 
D.0.20
Answer:
50
Step-by-step explanation:
The value of P(A|B) = 0.50 which is correct option(B)
What is independent events?
Independent events is defined as an event that is not affected by other events.
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
P(A|B) = P(A∩B)/P(B)
P(A|B) = P(A).P(B)/P(B)
P(A|B) = P(A)
Substitute the value of P(A) = 0.50,
P(A|B) = 0.50
Hence, the value of P(A|B) = 0.50
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Which expression is equivalent to -80
Answer:
what expressions?
Step-by-step explanation:
Given trapezoid PQRS, find the length of midsegment TU.
Answer:
Option (4)
Step-by-step explanation:
In the given picture,
Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.
Segment TU joins the midpoints of the sides PS and RQ.
Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."
Therefore, m(TU) = [tex]\frac{1}{2}(m\text{PQ}+m\text{SR})[/tex]
7x - 26 = [tex]\frac{1}{2}[(3x+23)+(9x-3)][/tex]
7x - 26 = 6x + 10
7x - 6x = 26 + 10
x = 36
m(TU) = 7x - 26
= 7(36) - 26
= 252 - 26
= 226
Therefore, Option (4) will be the answer.
The amount of calories you consume after eating x pieces of candy is represented by the function y=150x. Find the domain of the function and determine whether it is discrete or continuous.
Answer:
The function is:
y = 150*x
where y is the number of calories consumed, and x is the number of pieces of candy consumed.
Now, the domain of a function is the possible values of x that you can input in the function.
For this particular case you can have:
x = 0 (no pieces candy)
x = 1 (one piece of candy)
x = 2 (two pieces of candy)
Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.
So we only use x = whole numbers.
Then the domain of the function is equal to all the natural numbers plus the zero, or:
D = {x ∈ N ∪ {0}}
"x belongs to the union between the set of the natural numbers and the zero"
The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0
The domain of a function is the input values of the function for which it exists.
Given the expression that relates the number of calories you consume after eating x pieces of candy as shown:
y = 150x
The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0
The function is also discrete because the number of candies can be counted. Note that the domain of all discrete functions is countable.
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James bought 12 cookies and ate 3 of them. He ate ____% of the cookies. (Make sure to enter the answer using numbers only. Do not enter special characters such as the percent symbol.)
Answer:
25Step-by-step explanation:
Total cookies = 12
Ate = 3 cookies
Now,
Percentage of the cookies that James are:
[tex] \frac{3}{12} \times 100 \: percent[/tex]
Calculate:
[tex] = 25 \: percent[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
answer is 25
Step-by-step explanation:
Help with alll❤️ Please
Plz
Answer:
A, B, A
Step-by-step explanation:
(3)
Given
- 2x² + 10x + 12 ← factor out - 2 from each term
= - 2(x² - 5x - 6) ← factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)
The factors are - 6 and + 1, since
- 6 × 1 = - 6 and - 6 + 1 = - 5, thus
x² - 5x - 6 = (x - 6)(x + 1) and
- 2x² + 10x + 12 = - 2(x - 6)(x + 1) → A
(4)
[tex]x^{4}[/tex] - 81 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b), thus
[tex]x^{4}[/tex] - 81
= (x² )² - 9²
=(x² - 9)(x² + 9) ← note that x² - 9 is also a difference of squares
= (x - 3)(x + 3)(x² + 9) ← in factored form
x² - 3 is not a factor → B
(5)
Given
5[tex]x^{4}[/tex] - 320 ← factor out 5 from each term
= 5([tex]x^{4}[/tex] - 64) ← difference of squares
= 5(x² - 8)(x² + 8) → A
9. Read the following word problem, then create a linear equation to model the problem. Provide work to show how your linear equation models the problem, such as a brief description, a picture, or a table. Finally, use the linear equation you created to solve the problem.
$2400 is divided between two accounts. One account pays 2% interest, while the other account pays 3.5% interest. At the end of one interest period, the interest earned is $81. How much was invested in each account?
Answer:
$200 at 2%.
$2200 at 3.5%.
Step-by-step explanation:
Let the two amounts be x and y.
x earns 2% interest, and y earns 3.5% interest.
Since the total is $2400, then
x + y = 2400
Now we can solve for y and express the second amount in terms of x.
y = 2400 - y
The two amounts are x and 2400 - x.
In one interest period, the amount of interest earned is the amount of money in the account multiplied by the interest.
2% = 0.02; 3.5% = 0.035
The x amount earns 0.02x interest.
The y amount earns 0.035y interest.
The total interest earned is the sum of the interest amounts of the two accounts.
0.02x + 0.035y
We now replace y with 2400 - x, and we set the sum of the interest amounts equal to the total interest earned, $81.
0.02x + 0.035(2400 - x) = 81
The equation above is the linear equation.
Now we solve it. Distribute on the left side.
0.02x + 84 - 0.035x = 81
Combine like terms on the left side.
-0.015x + 84 = 81
Subtract 84 from both sides.
-0.015x = -3
Divide both side by -0.015.
x = 200
$200 was deposited in the account earning 2%.
y = 2400 - x
y = 2400 - 200
y = 2200
$2200 was deposited in the account earning 3.5%.
What is the length of AC?
Please help me ASAP!!!
Answer:
a
Step-by-step explanation:
For water to be a liquid, its temperature must be within 50 Kelvin of 323 Kelvin. Which equation can be used to determine the minimum and maximum temperatures between which water is a liquid? |323 – 50| = x |323 + 50| = x |x – 323| = 50 |x + 323| = 50
Answer:
Mark as BRAINLIEST plz
|x-323|<50: answer
Step-by-step explanation :
For water to be a liquid, the temperature must be within 50 Kelvin of 323 K.
So, the range of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323.
The equation that can be used to determine the maximum temperature at which water is a liquid can be given by : x < 323 + 50
The equation that can be used to determine the minimum temperature at which water is a liquid can be given by : x > 323 - 50
So the resultant equation can be written as :
|x-323|<50
The solution of inequality equation is | x - 323 | < 50
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the temperature of the water be = x Kelvin
Now , the equation will be
For water to be in the liquid state, the temperature must be within 50 kelvin (K) of 323 K
So , the value of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323
Substituting the values in the inequality equation , we get
For maximum temperature ,
x should be 50 more than 323 and
For minimum temperature ,
x should be 50 less than 323
So ,
The inequality relation is
x > 50 + 323 be equation (1)
x < 323 - 50 be equation (2)
So , the modulus function is expressed as
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
Therefore , the value is | x - 323 | < 50
Hence , The solution of inequality equation is | x - 323 | < 50
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Isiah determined that 5a2 is the GCF of the polynomial
a3 – 25a2b5 – 35b4. Is he correct? Explain.
Answer:
No
Step-by-step explanation:
He's not correct because 5a² isn't a factor of a³ or 35b⁴; in order for something to be the GCF of a polynomial, all of the terms must be evenly divisible by it.
Answer:
a^3 – 25a^2b^5 – 35b^4
He is incorrect since the coefficient of the a^3 term is 1, the GCF cannot contain a coefficient of 5. Also, there is no a in all terms, so a^2 is also not a common factor.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)
Answer: I hope it helps :)
x=6 , y=6√3x =23√3 , y=23u =12 , v= 6a =18√2 , b =18x = 13 , y= 13Step-by-step explanation:
1.
[tex]Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}[/tex]
2.
[tex]Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23[/tex]
3.
[tex]Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6[/tex]
4.
[tex]Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}[/tex]
5.
[tex]Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y[/tex]