using the converse of the same-side interior angles postulate what equation shows that g∥h
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Answer: [tex]\angle 2+\angle 4=180^{\circ}[/tex] or [tex]\angle 1+\angle 3=180^{\circ}[/tex]
Related Questions
Find the equation of the line passing through points (6,0) and (-1,14)
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Answer:
y = -2x + 12
Step-by-step explanation:
Hope this helps!!
From the diagram below, given the side lengths marked, and if we know that < C is congruent to < F, we can say that ___
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SAS Similarity Theorem: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
AC is proportional to DE while BC is proportional to FE, but F is not the included angle between those sides, therefore, those triangles are not similar by SAS.
The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Since we have information only about one of the angles, ASA also doesn't apply.
For two triangles to be congruent, all of their measures must be congruent, which is not the case of our triangles.
The answer is option d. The two cannot be proven to be similar.
Martha's video game rental plan costs $18 per month. Which tableshows the sum of the amounts that Martha will pay for her video gamerental plan over the next 5 months?
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Let's complete a table with the amounts of cost per month:
Month Sum od cost
1 18
2 2 * 18 = 36
3 3 * 18 = 54
4 4 * 18 = 72
5 5 * 18 = 90
So, please select the table that is correct
Given the equation y = 6sin(2x - 10) + 3
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We have the equation:
[tex]y=6\sin(2x-10)+3[/tex]We have to find the amplitude, the period, the horizontal shift and the midline.
The amplitude can be calculated as half the difference between the maximum and minimum value of the function.
The maximum value will happen when the sine is equal to 1 and the minimum when the sine is equal to -1.
We can then calculate the amplitude A as:
[tex]\begin{gathered} A=\frac{y_{max}-y_{min}}{2} \\ A=\frac{6(1)+3-(6(-1)+3)}{2} \\ A=\frac{6+3-(-6+3)}{2} \\ A=\frac{9-(-3)}{2} \\ A=\frac{12}{2} \\ A=6 \end{gathered}[/tex]Now we have to calculate the period.
The period will be equal to the horizontal distance at which the function starts repeating itself (or complete a period).
As we have a sine function we know that:
[tex]\sin(u)=\sin(u+2n\pi)\text{ }n\in Z[/tex]That means that it will repeat itself for any multiple of 2π.
We can calculate the period as:
[tex]\begin{gathered} y(x+2\pi)=y(x+T) \\ 6(2x-10+2\pi)+3=6(2(x+T)-10)+3 \\ 2x-10+2\pi=2(x+T)-10 \\ 2x+2\pi=2x+2T \\ 2\pi=2T \\ T=\pi \end{gathered}[/tex]The period is π.
The horizontal shift will be given by the constant value inside the argument of the sine function. We can ignore the other terms and factors and use only the sine function in this case.
For example, for sin(2x) = 0, this value corresponds to x = 0.
In the case of sin(2x-10) = 0 this corresponds to an x that is 5.
That is because the function has a frequency that is twice as the frequency of the hpure sine function.
If the function wasn't periodice we would see it translated by 10 to the right.
We can calculate the midline as the average of the function.
This average value will be given by the average value of the sine function, which is 0, so we can calculate the midline as:
[tex]y_{avg}=6(0)+3=3[/tex]Answer:
The amplitude is 6.
The period is π.
The horizontal shift is 10 units to the right.
The midline is y = 3.
i inserted a picture of the question can you please state whether the answer is A,B, C or D check all that apply
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Solution:
In the given figures, angles of the triangle ABC are corresponding equal to triangle DEF and the sides are proportional to each other.
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{1}{2}[/tex]Thus, the triangle ABC is similar to triangle DEF.
Therefore, the relationship between both triangles is the proportional side lengths.
Both triangles are not of the same size as their sides are not equal.
Both triangles are also not congruent as they do not satisfy any five conditions of congruence.
Hence, the correct option is A.
Find all X values where the tangent line to the graph of the function…
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Consider the function,
[tex]f(x)=6\sin x+\frac{9}{8}[/tex]The first derivative gives the slope (m) of the tangent of the curve,
[tex]\begin{gathered} m=f^{\prime}(x) \\ m=\frac{d}{dx}(6\sin x+\frac{9}{8}) \\ m=6\cos x+0 \\ m=6\cos x \end{gathered}[/tex]The equation of the line is given as,
[tex]y-3\sqrt[]{3}x=\frac{7}{3}[/tex]This can be written as,
[tex]y=3\sqrt[]{3}x+\frac{7}{3}[/tex]Comparing with the slope-intercept form of the equation of a line, it can be concluded that the given line has a slope,
[tex]m^{\prime}=3\sqrt[]{3}[/tex]Given that the tangent to the curve is parallel to this line, so their slopes must also be equal,
[tex]\begin{gathered} m=m^{\prime} \\ 6\cos x=3\sqrt[]{3} \\ \cos x=\frac{\sqrt[]{3}}{2} \\ \cos x=\cos (\frac{\pi}{6}) \end{gathered}[/tex]Consider the formula,
[tex]\cos A=\cos B\Rightarrow A=2k\pi\pm B[/tex]Applying the formula,
[tex]x=2k\pi\pm\frac{\pi}{6}[/tex]Thus, the required values of 'x' are,
[tex]x=2k\pi\pm\frac{\pi}{6}[/tex]Therefore, options 1st and 2nd are the correct choices.
Grade 12 math can you please explain each step, what are you doing, why and the final result that contributes to the sketch.
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ANSWER and EXPLANATION
We want to sketch the graph of the given function:
[tex]y=\frac{2x^2-7x+5}{2x-1}[/tex]First, we have to check for the asymptotes of the function.
To find the vertical asymptote, we have to equate the denominator to 0 and solve for x:
[tex]\begin{gathered} 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}[/tex]That is the vertical asymptote.
To find the horizontal asymptote, we have to check the degrees of the numerator and denominator. Since the degree of the numerator is greater than the denominator's, there is no horizontal asymptote.
To find the slant asymptote, divide the numerator by the denominator and identify the quotient:
This implies that the slant asymptote is:
[tex]y=x-3[/tex]The asymptotes will provide the boundaries for the graph of the function as follows:
Now, we have to find some coordinate points that satisfy the function.
Let us solve for y for values of x = -2, -1, 0, 1, 2, 3:
[tex]\begin{gathered} \Rightarrow x=-2 \\ y=\frac{2(-2)^2-7(-2)+5}{2(-2)-1}=-5.4 \\ \Rightarrow x=-1 \\ y=\frac{2(-1)^2-7(-1)+5}{2(-1)-1}=-4.67 \\ \Rightarrow x=0 \\ y=\frac{2(0)^2-7(0)+5}{2(0)-1}=-5 \\ \Rightarrow x=1 \\ y=\frac{2(1)^2-7(1)+5}{2(1)-1}=0 \\ \Rightarrow x=2 \\ y=\frac{2(2)^2-7(2)+5}{2(2)-1}=-0.33 \\ \Rightarrow x=3 \\ y=\frac{2(3)^2-7(3)+5}{2(3)-1}=0.4 \end{gathered}[/tex]We also have to identify the x and y intercepts of the function.
For the x-intercept, solve for x when y = 0:
[tex]\begin{gathered} 0=\frac{2x^2-7x+5}{2x-1} \\ \Rightarrow2x^2-7x+5=0 \\ 2x^2-2x-5x+5=0 \\ 2x(x-1)-5(x-1)=0 \\ (2x-5)(x-1)=0 \\ x=\frac{5}{2};x=1 \end{gathered}[/tex]For the y-intercept, solve for y when x = 0:
[tex]\begin{gathered} y=\frac{2(0)^2-7(0)+5}{2(0)-1} \\ y=\frac{5}{-1} \\ y=-5 \end{gathered}[/tex]Let us draw the table of values:
Now, we can use the calculated points, the intercepts, and the asymptotes to sketch the graph of the function:
That is the sketch of the function.
f(x) = - 3x + 4; g(x) = f(x) + 1
Graph it and then describe the graph
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The graph of function f(x) and g(x) is parallel lines separated by 1 unit.
In this question we have been given two functions f(x) = - 3x + 4 and g(x) = f(x) + 1
We need to graph these functions and then describe the graph.
The graph of given functions is as shown below.
The graph of function f(x) is a straight line with slope -3 and y-intercept 4.
The function g(x) is nothing but but function f(x) translated upward by 1 unit.
The graph of function g(x) is also a straight line with slope -3 and y-intercept 5.
Therefore, the graph of function f(x) and g(x) is parallel lines separated by 1 unit.
Learn more about graph of function here:
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Melanie has pears and papayas in a ratio of 13:25. How many pears does she have ifshe has 2500 papayas?On the double number line below, fill in the given values, then use multiplication ordivision to find the missing value.
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Given that the ratio of pears to papayas is 13:25,
[tex]\frac{\text{ Pears}}{\text{ Papayas}}=\frac{13}{25}[/tex]It means that Melanie has 13 pears, then the number of papayas must be 25.
It is asked to determine the number of pears corresponding to 2500 papayas.
First plot the values in the blank boxes on the double number line as below,
Let 'x' be the number of pears corresponding to 2500 papayas.
Now, cross multiply the terms,
[tex]25\cdot x=13\cdot2500[/tex]Divide both sides by 25,
[tex]\begin{gathered} 25\cdot x\cdot\frac{1}{25}=13\cdot2500\cdot\frac{1}{25} \\ x=13\cdot100 \\ x=1300 \end{gathered}[/tex]Thus, there should be 1300 pears corresponding to 2500 papayas.
40% of what number is 26? Please show work!
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65
1) To find that, we need to write an equation:
[tex]x(0.4)=26[/tex]Note that we rewrote that 40% as 0.4.
2) Now, let's solve it
[tex]\begin{gathered} x0.4=26 \\ \frac{0.4x}{0.4}=\frac{26}{0.4} \\ x=65 \end{gathered}[/tex]3) So the 26 is 40% of 65
how do you simplify this complex fraction in the lowest terms
[tex]\frac{77x^9/15y^5}{7x^7/10y^4}[/tex]
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Answer:
[tex]\frac{22x^{2}}{3y}[/tex]
Step-by-step explanation:
[tex]\frac{(77x^{9})(10y^{4}) }{(7x^{7})(15y^{5}) }[/tex]
[tex]\frac{(11x^{2})(2)}{3y}[/tex]
Been looking for help for 2 hrs hopefully you can help
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Given:
[tex]\begin{gathered} \mu=19.9 \\ \sigma=33.1 \\ n=40 \end{gathered}[/tex]To Determine:
[tex]P(X>8.9)[/tex]Solution
[tex]\begin{gathered} P(X>z) \\ z=\frac{x-\mu}{\sigma}=\frac{8.9-19.9}{33.1}=\frac{-11}{33.1}=-0.3323 \end{gathered}[/tex][tex]P(X>8.9)=1-P(X<8.9)=1-0.36982=0.63018[/tex]Hence, P(x>8.9) = 0.6302 (nearest 4 d. p)
which of the following is true?Blaine and Cruz made an error in picking their first steps.Cruz made and error in picking his first step All three made an error because the right side equals -1.All three chose a valid first step toward solving the equation.
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Given data:
The given expression is 4/7 (7-n)=-1.
Aaron starts with multiplying 7/4 on both sides, Blaine starts with distributive property by multiplying 4/7 with 7 and -u, Cruz starts by dividiing 4/7 on both sides.
Thus, all of them are correct, correct option is last one.
Answer: d
Step-by-step explanation: yw
ILL GIVE BRAINLY AND 15 POINTS
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Using functions, it is found that:
a. The costs for two years are as follows:
Option A: $4,600.Option B: $1,720.b. The pros and cons are as follows:
Option A: pro is the lower fixed fees, con is the higher hourly fee.Option B: pro is the lower hourly fee, con is the higher fixed fees.Option A functionThe cost of $2,600 for the first year is obtained as follows:
$500 set up fee.$2,000 of the 100 hours at $20 per hour.$100 of the hosting fee.For the second year, only the hourly cost will be paid, hence $2,000 will be added and the total cost is of:
$2,600 + $2,000 = $4,600.
The pros of Option A are the lower initial fees, hence for a lower number of hour, the cost is smaller, while the con is the high hourly price, meaning that for a high number of hours, option B is better.
Option B functionThe cost of $2,600 for the first year is obtained as follows:
$1,000 set up fee.$30 a month of hosting fee.For the second year, only the hosting fee is paid, meaning that $360 is added to the cost, thus:
$1,360 + $360 = $1,720.
The pros and cons are basically opposite of option A, higher basic fees with lower hourly/monthly fees, meaning that it is better over longer periods.
More can be learned about functions at https://brainly.com/question/24808124
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what is the value of x in the solutions to the system of equations below3x-8y=112y+x=13
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Given system of equations
3x - 8y = 11 ______________________1
2y + x = 13 ______________________ 2
Use the substution method
How to use the substitution method
1. pick one of the equation
2. make one of the variable subject of relation
3. substitute
From equation (1)
2y + x = 13
x = 13 - 2y
substitute x from equation 1 to 2.
3(13 - 2y) - 8y = 11
39 - 6y - 8y = 11
39 - 11 = 6y + 8y
28 = 14y
y = 28/14
y = 2
Next, substitute y in equation 2 to find x.
x = 13 - 2y
x = 13 - 2(2)
x = 13 - 4
x = 9
Final answer x = 9
How do I write down the size of Angles and marked by letters?
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we can assume the lines are parallels so both triangles will have equal angles, so:
s=55° and p=x
now if we add 110 and x, we have a line this means
110+x=180
x=180-100
x=80
so p=x=80
and finally, the angles inside a triangle must add 180° so
55+p+t=180
55+80+t=180
135+t=180
t=180-135=45
So the answer is:
p=80°
s=55°
t=45°
What is the value of x? 20/72=x/360
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The value of x = 100
Using this picture, describe what we are doing with the factored form of p(x) shown in the image in order to create a sketch of the function.
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Given:
[tex]p(x)=(x-1)(x+1)(x-4)^2[/tex]Sol:
[tex]\begin{gathered} p(x)=(x-1)(x+1)(x-4)^2 \\ \\ p(0)=(0-1)(0+1)(0-4)^2 \\ \\ p(0)=-16 \end{gathered}[/tex]X-intercept is at p(x) = 0 then,
[tex]\begin{gathered} p(x)=0 \\ \\ p(x)=(x-1)(x+1)(x-4)^2 \\ \\ 0=(x-1)(x+1)(x-4)^2 \\ \\ x=-1,1,4 \end{gathered}[/tex]At y- intercept the value of x is zero and at x = 0 function value is:
[tex]\begin{gathered} y=-16 \\ \\ \text{ The point is:} \\ (0,-16) \end{gathered}[/tex]At x-intercept y value is zero and x-intercept is -1,1,4 is:
[tex]\begin{gathered} \text{ At }x=-1 \\ \\ the\text{ value of }y=0 \\ \\ (-1,0) \\ \\ At\text{ }x=1 \\ \\ \text{ The value of }y=0 \\ \\ (1,0) \\ \\ \text{ At }x=4 \\ \\ \text{ The value of }y=0 \\ \\ (4,0) \end{gathered}[/tex]So all point is (-1,0) ,(1,0) and (4,0)
six reduced by the product of 5 and h
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Find the distance between the points (5,5) and (-3,7). Round your answer to the nearest tenth, if necessary.8.2 units11.8 units3.2 units12.2 units
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The formula for the distance between two points in the plane is:
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]So:
[tex]\begin{gathered} (x_1,y_1)=(5,5) \\ (x_2,y_2)=(-3,7) \\ d=\sqrt[]{(5-(-3))^2+(5-7)^2} \\ d=\sqrt[]{(8)^2+(-2)^2} \\ d=\sqrt[]{64+4} \\ d=\sqrt[]{68} \\ d=8.2462\ldots\approx8.2 \end{gathered}[/tex]So, the distance is approximately 8.2 units.
1. ¿Qué expresiones a continuación se pueden usar para encontrar el área del prisma rectangular de abajo? ¡ELIJA TODOS LOS QUE SE APLIQUEN! Nota: Puede probarlos todos para asegurarse de que sean iguales. * 15 (5x2x3) + (2x3x3) (5x2) + (5x2) + (5x2) + (5x2) 5x2x2 2 (5x2) + 2 (5x2) + 2 (2x2)
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We need to find the area of the prism given in the following image:
You need to add the surfaces of ALL rectangles in the image (recall that the area of a rectangle is : Base x Height)
So for this prism we have:
FOUR rectangles that measure 5 x 2
and also TWO small squares of area 2 x 2
So we need to select all the formulas they give you that read like the addition of the two above:
(5x2) + (5x2) + (5x2) + (5x2) + (2x2) + (2x2)
It can also be written as:
2 (5x2) + 2 (5x2) + 2 (2x2)
8) Use the graph to determine the independent variable. Money Saved 240 210 180 A Number of Weeks 150 120 Amount of Money ($) B) The Amount of Money 90 © Money Saved 60 30 0 1 2 6 7 8 3 4 5 Number of Weeks
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Generally equations are in the form:
y = mx + b
Where
x is the independent variable, you can choose any value for x
y is the dependent variable. The value of y depends on x.
In the graph, the x-axis is number of weeks and y-axis is amount.
Amount depends on the number of weeks, which is the independent variable, here in this graph.
Could you tell me the process of solving the problem?
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Given:
[tex]Ln8=\frac{2\pi m\xi}{\sqrt{1-\xi^2}}[/tex]m=250
Required:
Find the value of
[tex]\xi[/tex]Explanation:
The value of ln8 is:
[tex]ln8=2.079[/tex][tex]\begin{gathered} 2.079=\frac{2\times3.14\times\xi}{\sqrt{1-\xi^2}} \\ 2.079(\sqrt{1-\xi^2})=6.28\xi^ \end{gathered}[/tex]Take the square on both sides.
[tex]\begin{gathered} 4.322(1-\xi^2)=39.44\xi^2 \\ \frac{1-\xi^2}{\xi^2}=\frac{39.4384}{4.322} \\ \frac{1}{\xi^2}-1=9.125 \\ \frac{1}{\xi^2}=9.125+1 \\ \frac{1}{\xi^2}=10.125 \end{gathered}[/tex]An electronic store discounted a tablet computer by 30%. The discounted price of the computer was $486.50. Determine the original price of the tablet
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The discounted price of the computer was $486.50.
An electronic store discounted a tablet computer by 30%.
So, the original price was
[tex]\begin{gathered} C=486.50+(486.50\times30percent) \\ =486.50+(486.50\times\frac{30}{100}) \\ =486.50+145.95 \\ =632.45 \end{gathered}[/tex]So, the original price of the tablet computer was $632.45.
An album received the following ratings on a 1-to-10 scale from10 music critics. What is the mean of the ratings?9.6, 9.8, 7.2, 6.4, 10.0, 8.9, 5.0, 9.8, 9.4, 6.8
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Given:
The ratings are
[tex]9.6,9.8,7.2,6.4,10.0,8.9,5.0,9.8,9.4,6.8[/tex][tex]\begin{gathered} \text{Mean}=\frac{9.6+9.8+7.2+6.4+10.0+8.9+5.0+9.8+9.4+6.8}{10} \\ \text{Mean}=\frac{82.9}{10} \\ \text{Mean}=8.29 \end{gathered}[/tex]what is the driving distance between the police station and Art Museum
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First, locate the coordinate points (x,y) of each place, by looking at the graph:
Police station = (0,-4)
Art museum = (6,1)
Apply the distance formula:
[tex]D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Replacing:
[tex]D=\sqrt[]{(6-0)^2+(1-(-4))^2}=\sqrt[]{6^2+5^2}=\sqrt[]{36+25}=\sqrt[]{61}=7.81[/tex]the cone has a height of 19 mm and the radius of 15 mm what is its volume use pie and round your answer to the nearest hundredth
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Answer
Volume = 4,478.57 mm³
Explanation
The volume of a cone is given as
Volume = ⅓ (πr²h)
where
π = pi = 3.142
r = radius of the cone = 15 mm
h = height of the cone = 19 mm
Volume = ?
Volume = ⅓ (πr²h)
Volume = ⅓ (3.142 × 15² × 19) = 4,478.57 mm³
Hope this Helps!!!
In the diagram below of AGJK, H is a point onGJ, HJ = JK, m2 = 28, and mZGJK = 76.What is mZGKH?2870H
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Problem
Solution
For the triangle GKJ we can find the angle K on this way:
28 +70 + Now we know that HJ= JK so then the triangle HJK is an isosceles triangle so then < JHK = < HKJ and we can do this:
70+ 2x = 180
2x= 110
x= 55
And then we can find the angle < GKH with the following equation:
28+70 + (55+y) = 180
y= 180-55 -28-70= 27
Find the values of the variables in the parallelogram. The diagram is not drawn to scale. (Image is attached below)thank you in advance :)
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For this problem, we are given a parallelogram with a diagonal drawn, inside it there are markings for a few angles. We need to determine the unknown angles.
Opposite sides of a parallelogram are parallel, this means we can treat the diagonal as a transversal line that crosses two parallel lines. Since this is the case, the angles 33º and xº are alternate interior angles and have the same length:
[tex]x=33º[/tex]The opposite angles in a parallelogram are congruent, therefore:
[tex]z=109º[/tex]The sum of internal angles is 360º, therefore we have:
[tex]\begin{gathered} 2\cdot109+2\cdot(x+y)=360\\ \\ 218+66+2y=360\\ \\ 284+2y=360\\ \\ 2y=360-284\\ \\ 2y=76\\ \\ y=38 \end{gathered}[/tex]The value of x is 33º, the value of y is 38º and the value of z is 109º.
Paulina bought a used car as she was entering college and planned to trade it in when she graduated four years later. She had learned in her high school financial algebra class that the average used car depreciated at an annual rate of 15%. If she had paid $13,900 for her car, how much can she expect to get when it is time for her to trade it in for a new car?
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1st year
depreciable value: $13900
annual depreciation: $13900*15% = $2085
2nd year
depreciable value: $13900 - $2085 = $11815
annual depreciation: $11815*15% = $1772.25
3rd year
depreciable value: $11815 - $1772.25 = $10042.75
annual depreciation: $10042.75*15% = $1506.41
4th year
depreciable value: $10042.75 - $1506.41 = $8536.34
annual depreciation: $8536.34*15% = $1280.45
Final value: $8536.34 - $1280.45 = $7255.89