NSWER
y = 11
EXPLANATION
wo lines are parallel if they have the same slope and diffenrent y-intercepts.
In this case, we have to write the equation of a line parallel to the line y = 8, which is a line with a slope of 0 - i.e. it is a horizontal line. Therefore, the equation of the line we have to find must have the same form - y equal to a constant. This constant is the y-coordinate of the point where the line must pass through, (-3, 11).
Hence, the equation of the described line is y = 11.
Calculate the property tax on a condominium located in a city in British Columbia and assessed at $496,300 if the current tax rate is 1.825%
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
property value = $496300
tax rate = 1.825%
Step 02:
percentage:
property tax:
= 1.825 / 100 = 0.01825
property tax = property value * tax rate
$496300 * 0.01825 = 9057.475$
The answer is:
property tax =
The sum of two numbers is 402. The difference between the two numbers is 148. Find the two numbers
After solving the equations we can conclude that the two numbers are 265 and 137.
What exactly are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.such as 3x + 5 = 15 as an example.There are many different types of equations, including linear, quadratic, cubic, and others.So, let the first number be 'x' and the second is 'y'.
Now, the two equations can be formed as:
x + y = 402x - y = 128Merge equations as follows:
x + y - 402 = x - y - 128x - x + y + y = -128 + 4022y = 274y = 137So x will be:
x + y = 402x + 137 = 402x = 402 - 137x = 265Therefore, after solving the equations the two numbers are 265 and 137.
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Find the sum: 4-2(x-3)=24
The first step to find the value of 'x' in this expression is to calculate the product with the parenthesis term:
[tex]\begin{gathered} 4-2(x-3)=24 \\ 4-2x+6=24 \end{gathered}[/tex]Then, we need to isolate in one side of the equation the terms with the variable 'x', and in the other side the terms without the variable 'x'. Then, we can calculate the value of x:
[tex]\begin{gathered} 4-2x+6=24 \\ -2x=24-4-6 \\ -2x=14 \\ x=\frac{14}{-2}=-7 \end{gathered}[/tex]So the value of x in this expression is -7
A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and free concert tickets to every 100th caller. When will the station first give away all three prizes to one caller? When this happens how much money and how many tickets are giving away
On 300 call the station first give away all three prizes to one caller.
What is LCM?The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory. The LCM method is used to determine the least multiple of two or more numbers. Least Common Multiple is referred to as LCM. The LCM of two numbers can be divided by both of them. The LCM of 6 and 8 is 24, for instance. 24 can be divided by both 6 and 8.
Given Data
A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and free concert tickets to every 100th caller.
To find When will the station first give away all three prizes to one caller, we will take LCM
5 15 , 25, 100
5 3, 5 , 20
3 3, 1 , 4
4 1, 1 , 4
LCM = 5² × 3× 4
LCM = 300
On 300 call the station first give away all three prizes to one caller.
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Please help fast I need help
The mapping diagram above does not represent a function since
for each number in Set A (the input) where there are multiple mappings
from Set B (the output).
What is a function?In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set A) to an output variable (Set B).
Based on the mapping diagram shown above, we can reasonably infer and logically deduce that Set A with inputs (-4, 8), (1, 8) and (1, -3) are ordered pairs which does not represent a function because they indicate multiple mappings in Set B (the output).
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Hi hi job hi thank everyone for
We are asked to determine the value of the variation of the angle with respect to "x". To do that we will determine an equation that relates "x" and the angle using the following right triangle:
We can use the function tangent since this is defined as:
[tex]\tan\theta=\frac{opposite}{adjacent}[/tex]Now, we plug in the values:
[tex]\tan\theta=\frac{3000}{x}[/tex]Now, we will determine the angle when "x = 2000". We substitute 2000 in the equation:
[tex]\tan\theta=\frac{3000}{2000}[/tex]Now, we take the inverse function of the tangent:
[tex]\theta=\tan^{-1}(\frac{3000}{2000})[/tex]Solving the operations we get:
[tex]\theta=56.31°[/tex]Therefore, the angle is 56.31 degrees or 0.983 radians.
We are asked to determine the value of the derivative of "x" with respect to "t". Since this is equivalent to the velocity of the plane we have that:
[tex]\frac{dx}{dt}=-200\frac{ft}{s}[/tex]Now, we are asked to determine the derivative of the angle with respect to time. To do that we will determine the derivative with respect to time on both sides of the equation:
[tex]\frac{d}{dt}(\tan\theta)=\frac{d}{dt}(\frac{3000}{x})[/tex]For the derivative on the left side, we know that the derivative of the tangent is the secant squared, therefore, we have:
[tex]\sec^2(\theta)\frac{d\theta}{dt}=\frac{d}{dt}(\frac{3000}{x})[/tex]Now, we determine the derivative on the right side using the following formula:
[tex]\frac{d}{dx}(\frac{a}{x})=-\frac{a}{x^2}[/tex]Applying the rule we get:
[tex]\sec^2\theta\frac{d\theta}{dt}=-\frac{3000}{x^2}\frac{dx}{dt}[/tex]Now, we solve for the derivative of the angle with respect to time:
[tex]\frac{d\theta}{dt}=-\frac{1}{\sec^2\theta}(\frac{3000}{x^2})\frac{dx}{dt}[/tex]Now, we substitute the values:
[tex]\frac{d\theta}{dt}=-\frac{1}{\sec^2(0.983)}(\frac{3000ft}{(2000ft)^2})(-200\frac{ft}{s})[/tex]Solving the operations:
[tex]\frac{d\theta}{dt}=0.047\frac{rad}{s}[/tex]Therefore, the variation of the angle with respect to time is 0.047 rad/s.
This means that the dish is rotating at a speed of 0.047 rad/s.
Answer: We are asked to determine the value of the variation of the angle with respect to "x". To do that we will determine an equation that relates "x" and the angle using the following right triangle:We can use the function tangent since this is defined as:Now, we plug in the values:Now, we will determine the angle when "x = 2000". We substitute 2000 in the equation:Now, we take the inverse function of the tangent:Solving the operations we get:Therefore, the angle is 56.31 degrees or 0.983 radians. We are asked to determine the value of the derivative of "x" with respect to "t". Since this is equivalent to the velocity of the plane we have that:Now, we are asked to determine the derivative of the angle with respect to time. To do that we will determine the derivative with respect to time on both sides of the equation:For the derivative on the left side, we know that the derivative of the tangent is the secant squared, therefore, we have:Now, we determine the derivative on the right side using the following formula:Applying the rule we get:Now, we solve for the derivative of the angle with respect to time:Now, we substitute the values:Solving the operations:Therefore, the variation of the angle with respect to time is 0.047 rad/s.This means that the dish is rotating at a speed of 0.047 rad/s.
Step-by-step explanation:
x² + y² = 64
y = -8
Answer:
x=0
Step-by-step explanation:
if y = -8
the y^2 = -8 times -8 = 64
x^2 + 64 = 64
-64 -64
x^2=0
x=0
Check off the methods of differentiation required, and complete the derivative.
Given:
[tex]f(x)=\sqrt[]{5x^2-2}[/tex]f(X) will be differentiated by chain rule.
[tex]\begin{gathered} f^{\prime}(x)=\frac{1}{2\sqrt[]{5x^2-2}}\lbrack5(2x)\rbrack \\ f^{\prime}(x)=\frac{5x}{\sqrt[]{5x^2-2}} \end{gathered}[/tex]In the diagram the smaller triangle is an image of the larger triangle. a) Name the angle in the image that corresponds to ZT in the preimage. b) List all pairs of corresponding sides.
this is transformations or enlagement of triangle by a certain scale factor.
which simply means it can either be double, or shortened .
solution
a. angle T is the preimange of angle T'
b. line RS and RS'
c. line RT and RT'
line ST and ST'
extra note: this is ∆RST filled over but shortened by x factors to mirror image ∆RST
Explain if there is or is not a universal test point that can be used for testing the shading for a linear inequality
Answer:
no universal test point
Step-by-step explanation:
You want to know if there is or is not a universal test point that can be used for testing the shading for a linear inequality.
Test pointThe purpose of a test point for the graph of an inequality is to determine whether the shaded area includes the test point or not. A single inequality will divide the universal set into two parts: one part that is the solution set, and one part that is not the solution set.
Non-boundary point(s)A point that is well inside the solution set (or not-a-solution set) will tell you which side of the boundary is shaded. Any point that always meets that requirement could be considered a universal test point.
Boundary point(s)The boundary point(s) between these sets may or may not be shaded, but its(their) shading, or lack of it, will not tell you which half of the universal set is the solution set. That is, any point that falls on the boundary of the solution set is not a suitable test point.
The boundary can be anywhere, so there is no single universal test point.
__
Additional comment
A set of three non-collinear points can be considered to be a universal test set. Together, they can tell you which part of the universal set is the solution set. At most, the boundary line can pass through two of them, so the third can tell you which half of the universe it lies in.
Solve 2x + 5y=30 for y
Answer:
[tex]y=-6+\frac{2x}{5}[/tex]
Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model:a√x+b+c=dUse a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation.Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.Part 3. Explain why the first equation has an extraneous solution and the second does not.
we have the equation
[tex]a\sqrt[\square]{x+b}+c=d[/tex]i will assume
a=2
b=5
c=3
d=5
solve for x
substitute the given values
[tex]2\sqrt[\square]{x+5}+3=5[/tex]subtract 3 both sides
[tex]2\sqrt[\square]{x+5}=5-3[/tex][tex]2\sqrt[\square]{x+5}=2[/tex]Divide by 2 both sides
[tex]\sqrt[\square]{x+5}=\frac{2}{2}[/tex][tex]\sqrt[\square]{x+5}=1[/tex]squared both sides
[tex]\begin{gathered} x+5=\pm1 \\ x=-5\pm1 \end{gathered}[/tex]the values of x are
x=-4 and x=-6
Verify each solution
For x=-4
[tex]\begin{gathered} \sqrt[\square]{-4+5}=1 \\ 1=1 \end{gathered}[/tex]x=-4 ------> is a solution
Verify x=-6
[tex]\begin{gathered} \sqrt[\square]{-6+5}=1 \\ \sqrt[\square]{-1}=1 \end{gathered}[/tex]Is not true
therefore
x=-6 --------> is an extraneous solution
Florence wishes to retire at age 65 with $1,200,000 in her retirement account. When she turns 22, she decides to begin depositing money into an account with an APR of 7% compounded monthly. What is the monthly deposit that Florence must make in order to reach her goal? Round your answer to the nearest cent, if necessary.
The monthly deposit that Florence must make in order to reach her goal is $366.74.
What should be the monthly deposit?The series of payments that must be made is known as an annuity. An annuity is a series of payment made over a period of time. The amount that is invested monthly would grow at an exponential rate. This is because both the amount invested and the interest that has been accrued grows at each compounding period.
The formula to determine the monthly deposit is:
Monthly deposit = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 7 / 12 = 0.583%n = number of periods = number of years x number of compounding periods(65 - 22) x 12
43 x 12 = 516
1,200,000 ÷ [((1.00583)^516]}- 1 / 0.00583] = $366.74
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Graph the function h(x) =-3x-1
we have the function
h(x)=-3x-1
this is the equation of a line
To graph a line we need at least two points
so
Find out the intercepts
step 1
Find out the x-intercept (value of x when the value of y=0)
For h(x)=0
substitute
0=-3x-1
3x=-1
x=-1/3
the x-intercept is (-1/3,0)
as the value is a fraction, take another point
For x=2
h(x)=-3(2)-1
h(x)=-7
we have the point (2,-7)
step 2
Find out the y-intercept (value of h(x) when the value of x=0)
For x=0
h(x)=-3(0)-1
h(x)=-1
the y-intercept is (0,-1)
step 3
we have the points
(2,-7)
(0,-1)
To graph, the line, plot the given points and join them
using a graphing tool
Help please thank you
If $44,900 is invested at an interest rate of 7% per year,investment at the end of 5 years is
1)Annual =61712.27
2)Semiannual=62066.34
3)monthly= 62375.51
4)daily = 62287.59
What is compound interest ?Over a specific time period, compound interest builds up on both the principal and interest. A principal is also included when accounting for interest that has accrued on it over time. The cumulative principal value is used to calculate interest for the upcoming period as well.
Given that : If $44,900 is invested at an interest rate of 7% per year .
p =44,000
R = 7%
t =5
(2)Semiannual means compounding is in a year done means two times hence, n = 2
We know
A(t) =p[tex][1 +\frac{r}{n} ]^{nt}[/tex]
A(5) = 44000[tex][1+\frac{0.07}{2} ]^{2(5)}[/tex]
A(5)=62066.34
(1) Annual means. compounding is done 1 time for a year
So, n = 1
A (5) = 44000[tex][1 + 0.07]^{(5)}\\[/tex]
A(5)= 61712.27
(3)Monthly means compounding is done 12 times in a year.
So, n = 12
= 44000[tex][1 + \frac{0.07}{12} ]^{60}\\[/tex]
= 62375.51
(4)For daily put n = 365
A(5) = 44000[tex][1 + \frac{0.07}{5} ]^{5(5)}\\[/tex]
= 44000[tex][1 + \frac{0.07}{5} ]^{25}\\[/tex]
=62287.59
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At the clothing store where you work, T-shirts are on sale, 3 for $10. A customer at the store says that one T-shirt should cost $7 at this rate. What error did the customer make?
The customer divided 10 by 3 instead of dividing 3 by 10.
The customer divided 3 by 10 instead of dividing 10 by 3.
The customer subtracted 3 from 10 instead of dividing 10 by 3.
The customer added 10 and 3 instead of dividing 3 by 10.
The customer subtracted 3 from 10 instead of dividing 3 by 10.
The error that the customer made was that he subtracted 3 from 10 instead of dividing 3 by 10.
It is given in the question that at the clothing store T-shirts are on sale, 3 for $10. A customer at the store says that one T-shirt should cost $7 at this rate.
We have to find the error made by the customer while calculating the rate of a T- shirt.
To find the rate of a shirt we will divide the number of shirts by the total amount.
Hence, the rate of a shirt will be $ 10/3
But the customer subtracted 3 from 10 to get $ 7 as the rate of a T-shirt.
Hence, the customer subtracted 3 from 10 instead of dividing 3 by 10.
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what is the 4th dimension, what would it be like to live in?
Can somebody help me with this I’ve been stuck on this for so long and I don’t know the answer, I need someone to help me please.( the answer I need help with is number 1)
The required numbers are [tex]2\frac{2}{5}[/tex] and [tex]2\frac{5}{8}[/tex] .
In this question , given is [tex]2\frac{2}{5}[/tex] , [tex]2\frac{2}{7}[/tex] , [tex]1\frac{7}{8}[/tex] , [tex]2\frac{1}{10}[/tex] , [tex]2\frac{5}{8}[/tex]
So when we solve it we get; [tex]\frac{12}{5} , \frac{16}{7} , \frac{15}{8} , \frac{21}{10} , \frac{21}{8}[/tex]
We need two numbers whose sum should be greater than 5
first adding the numbers which have the same denominator we get:
[tex]\frac{15}{8} + \frac{21}{8}[/tex]
[tex]\frac{36}{8}[/tex]
which on dividing will give us 4.5 < 5
Lets take numbers [tex]\frac{12}{5} , \frac{16}{7}[/tex]
On taking LCM we get ;
[tex]\frac{84+ 80}{35}[/tex] = [tex]\frac{164}{35}[/tex] = 4.6 < 5
Lets now take [tex]\frac{16}{7} + \frac{15}{8}[/tex] = [tex]\frac{128+ 105 }{56}[/tex] = [tex]\frac{233}{56}[/tex] = 4.16 < 5
Lets take [tex]\frac{12}{5} + \frac{21}{8}[/tex] = [tex]\frac{96+ 105}{40}[/tex] = 5.025 > 5
Thus the required numbers are : [tex]\frac{12}{5} and \frac{21}{8}[/tex].
So in these type of questions we are supposed to take two or the numbers which have been given in the question and then we should add or subtract them as per the question .
Likewise in this question we had to find two numbers and after so many trials we were able to get the two required numbers.
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Marcel and his 8 friends have a snow shoveling business. Last season, they earned a total of $2,240.64. How much
money did each friend make?
$280.08
B$17,925.12
$248.96
D) $20,165.76
int(s)
HIDE HINT
1/1
| How many people were there all together?
if all tree friends worked 20 hours during the week, how much ith each person earn
The amount of money earned by each person will be;
Savannah = $190
Greg = $180
Kevin = $165
How to calculate the amount?From the information, the following can be deduced:
Savannah works $9.50 per hour.
Greg works $9 per hour.
Kevin works $8.25 per hour
Therefore, they all work for 20 hours. The amount for each person will be:
Savannah works $9.50 per hour. = $9.50 × 20 = $190
Greg works $9 per hour. = $9 × 20 = $180
Kevin works $8.25 per hour = $8.25 × 20 = $165
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Savannah works $9.50 per hour.
Greg works $9 per hour.
Kevin works $8.25 per hour
If all tree friends worked 20 hours during the week, how much does each person earn?
I need help with this question please. The graph below is just option A. Also, I have options to choose from.
From geogebra
Answer Letter A
A Shopper has $140 to spend. The shopper wants to buy shirts and hats. Each shirts coats $21, and each hat cost $16. What combination of shirts and hats maximizes the amount of money the shopper can spend
The combination of two shirts and six hats will maximize the amount of money the shopper can spend.
What are Mathematical Inequalities?An inequality results from the comparison of two or more algebraic expressions using the symbols <, > ≤, or ≥. They are mathematical expressions with unequal sides.
Let's assume x is the number of shirts and y is the number of hats brought then,
Total amount spend = 21x + 16y
It is given that the total amount the shopper can spend is $140.
So, 21x + 16y ≤ 140,
As x and y are the number of shirts and the number of hats so x and y will assume positive integral values only, to find out the values of x and y plot the region 21x + 16y ≤ 140 with x ≥ 0, y ≥ 0 as shown in the graph.
From the graph, it is clear that the highest integer value which is close to the boundary of 21x + 16y ≤ 140 is x = 2 and y = 6.
The amount spend when x = 2 and y = 6 is 21(2) + 16(6) = 138
Hence, two shirts and six hats will maximize the amount of money the shopper can spend.
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Tell whether each number is a real number, a rational number, an irrational number, an integer or a whole number. Then order the numbers from these to greatest
26. -11.5, -11, -10, 12.5, 12
The order from smaller to greatest is -11.5, -11, -10, 12, 12.5.
What are whole number?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold math Z.
What are real numbers?The value of a continuous quantity that can represent a distance along a line is a real number. René Descartes first used the word "real" in this meaning in the 17th century when he made a distinction between the real and imaginary roots of polynomials.
Given numbers are -11.5, -11, -10, 12.5, 12
The order from smaller to greatest is -11.5, -11, -10, 12, 12.5.
Real numbers: -11.5, -11, -10, 12, 12.5.
Rational numbers: -115/10, 125/10
Integer numbers: -11.5, -11, -10, 12, 12.5.
Whole numbers: 12, 12.5, 26
Therefore, the order from smaller to greatest is -11.5, -11, -10, 12, 12.5.
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1) Which of the following is the additive inverse of a - b ?
The number that produces zero when multiplied by an is known as the additive inverse of a number, or a, in mathematics. The opposite (number),[1] sign change,[2] and negation are other names for this number. [3] The additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive, when applied to a real number. The additive inverse of zero is zero.
Associated with subtractionSubtraction, which can be seen as adding the opposite, is closely related to additive inverse:
a − b = a + (−b).
On the other hand, additive inverse can be compared as subtracting from zero:
−a = 0 − a.
As a result, the unary minus sign can be used to represent subtraction without using the "0" symbol, even though there shouldn't be a space after the unary "-" in proper typography.
Other featuresNegation has the following algebraic characteristics in addition to the identities mentioned above:
It is an Involution operation when (a) = a.
−(a + b) = (−a) + (−b)
−(a − b) = b − a
a − (−b) = a + b \s(−a) × b = a × (−b) = −(a × b)
(−a) × (−b) = a × b
Particularly, (a)2 = a2.
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Please answer the following in the picture 100 points
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Explain about congruent?
For these items, the word equal is frequently used in place of congruent. If two line segments are the same length, they are said to be congruent. If two angles have the same measure, they are said to be congruent. If two circles have the same diameter, they are congruent.
While equality deals with numbers, congruence deals with shapes (also known as objects). Neither "two shapes are equal" nor "two numbers are congruent" are statements that you make. If one shape can be perfectly superimposed on the other, then two shapes are said to be congruent. While equality deals with numbers, congruence deals with shapes (also known as objects).
Gestures are logical and consistent with what is being spoken. Despite not being the same, both ideas are entirely consistent. We play a game, say things we don't mean, and act contrary to our ideals. The choice is more challenging if the hip appears to be in congruence even with the
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Find the derivative.
g(x) = 8x^5+ x^4- 5x² + 6, find g'(-4)
Answer:
the anwser is 100x69 yes
Hence, the derivative of [tex]g(x)=8x^5+x^4-5x^2+6[/tex] is [tex]g`(-4)=10536[/tex].
What is the derivative?
The derivative is a way to show instantaneous rate of change: that is, the amount by which a function is changing at one given point.
Here given function is
[tex]g(x)=8x^5+x^4-5x^2+6[/tex]
So,
[tex]g`(x)=5(8x^4)+4x^3-2(5x)\\\\g`(x)=40x^4+4x^3-10x\\\\x=-4\\\\g`(-4)=40(-4)^4+4(-4)^3-10(-4)\\\\g`(-4)=40(256)+4(64)+40\\\\g`(-4)=10240+256+40\\\\g`(-4)=10536[/tex]
Hence, the derivative of [tex]g(x)=8x^5+x^4-5x^2+6[/tex] is [tex]g`(-4)=10536[/tex].
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A line's slope is 8, and its y-intercept iS 8. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=8x+8
Step-by-step explanation:
Slope Intercept form: y=mx+b
m=slope
b=y-intercept.
so if you put them together using what we have, you get y=8x+8
What is the simplified base of the function f(x) = (108)*?
3
33/4
633
27
Answer:33/4
Step-by-step explanation: its hard to explain but thats the correct answer 33/4 decimal form is 8.25 and mixed number is 8 1/4
Compare 364,879; 463,000; 436,765 using scientific notation. Which number has the least value?
The comparison of 364, 879; 463, 000; 436, 765 using scientific notation ,number has the least value is 3.64879 x 10⁵ .
As given in the question,
Converting 364, 879 using scientific notation, 364, 879 = 3.64879 x 10⁵
Converting 463, 000 using scientific notation, 463, 000 = 4.63 x 10⁵
Converting 436, 765 using scientific notation, 436, 765 = 4.36765 x 10⁵.
Hence when ordered in ascending terms, using scientific notations, the given numbers can be arranged as follows:
3.64879 x 10⁵ < 4.63 x 10⁵ < 4.36765 x 10⁵.
First term 364, 879 has the least value, since it is the smallest number.
Therefore, comparison of 364, 879; 463, 000; 436, 765 using scientific notation ,number has the least value is 3.64879 x 10⁵.
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In the triangle below , XZ=YZ, find the measure of< YZX
ANSWER:
80°
STEP-BY-STEP EXPLANATION:
Since the sides XZ and YZ are equal, the angle We know that the sum of all the angles is equal to 180 °, therefore:
[tex]\begin{gathered} 180=50+50+\text{YZX} \\ \text{YZX}=180-50-50 \\ \text{YZX = }80\text{\degree} \end{gathered}[/tex]