[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=-3 \end{cases}\implies y=a(x-3)^2 - 3\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=-1 \end{cases} \\\\\\ -1=a(2-3)^2 -3\implies 2=a(-1)^2\implies 2=a~\hfill \boxed{y=2(x-3)^2 -3}[/tex]
Given that f(x)= 2x+8 g(x)= 5x-2/4 and h(x)= 2x+6/x
find
a) g[f(0)]
b) f(-5)
c) f[h(3)]
d) h°f(x)
e) h⁻¹(x)
The values of the functions g[f(0)]b) f(-5), f[h(3)], h°f(x) and h⁻¹(x) are 9.5, -2, 16, (4x+22)/x and 6/(x-2) respectively
How to find the g[f(0)] of the function?
A function is a relationship between inputs where each input is related to exactly one output
Given: f(x)= 2x+8, g(x)= 5x-2/4 and h(x)= 2x+6/x
(a) g[f(0)]
Substitute x = 0 into f(x)= 2x+8 to get f(0)
f(0) = 2(0)+8 =8
g[f(0)] = g(8)
Substitute x = 8 into g(x)= 5x-2/4 to get g[f(0)]
g[f(0)] = g(8)
g[f(0)] = 5x-2/4
g[f(0)] = 5(8)-2/4 = 9.5
b) f(-5)
Substitute x = -5 into f(x)= 2x+8 to get f(-5)
f(x)= 2x+8
f(-5)= 2(-5)+8 = -2
c) f[h(3)]
h(x)= 2x+6/x
h(3) = 2(3)+6/3 = 4
f[h(3)] = f[4]
f[4] = 2(4)+8 = 16
f[h(3)] = 16
d) h°f(x)
h°f(x) = h(2x+8)
Since h(x)= 2x+6/x
h°f(x) = 2(2x+8) +6/x
h°f(x) = 4x+16+6/x = (4x+22)/x
e) h⁻¹(x)
h(x)= 2x+6/x
Let y = 2x+6/x
x = 6/(y-2)
x = h⁻¹(y)
h⁻¹(x) = 6/(x-2)
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Can the following represent a function? Explain
(2,5) (3,5)(4,5)(5,5)
Answer:
Yes
Step-by-step explanation:
If you graphed that, it would be a horizontal line. Which is a function. If it is a vertical line, then it is not.
[tex]2\frac{5}{7}g+3\frac{3}{5} g[/tex]
The solution of the fraction is 6 11/35.
What is fractions?A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of components of a particular size as it is represented in common English. A common, vulgar, or simple fraction is one that has a non-zero denominator shown below (or after) the line that separates the numerator from the denominator. Compound fractions, complicated fractions, and mixed numeral fractions are examples of uncommon fractions that use numerators and denominators.The numerator and denominator of positive common fractions are both natural integers. The denominator shows how many of the numerator's equal parts make up a unit or whole, and the numerator reflects the number of equal parts. Since there can never be zero components in a whole, the denominator cannot be zero.Covert mixed numbers to improper fractions:
[tex]2\frac{5}{7}g=\frac{19}{7}g[/tex]
[tex]3\frac{3}{5}g=\frac{18}{5}g[/tex]
factor out common term g:
=[tex]g(\frac{19}{7} +\frac{18}{5})\\g(\frac{221}{35})[/tex]
Convert improper fractions to mixed numbers:
[tex]=\frac{221}{35}g \\\\=6\frac{11}{35} g[/tex]
Hence, The solution of the fraction is 6 11/35.
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Explain the steps you would use to solve this equation. Find the solution.
8^2z=4096
which of the following two pairs of sets have the same cardinality? question 9 options: natural numbers and irrational numbers integers and natural numbers real numbers and rational numbers irrational numbers and rational numbers
Natural numbers and irrational numbers are two pairs of sets that have the same cardinality.
It is sufficient to demonstrate the existence of a bijection between the set of real numbers R and the set of irrational numbers RQ in order to demonstrate that both have the same cardinality:
For each positive integer n, map n to 2n to produce a countable number of holes in R. Be aware that these countable holes are located at all irrational locations (2n-1), as well. R should be mapped to itself. R should be mapped to itself. Feel free to use your preferred irrational number in the above in place of [tex]\pi[/tex].
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The average ticket price for several NFL teams is listed below.
Seahawks =$84.60
Packers= 89.37
Jets= $105.66
Cowboys= 110.20
Lions = $79.16
how much more would it cost a family of 5 to get the jets game ($105.66) than a Lions game ($79.19?
It would cost a family of 5 $132.35 more to get the jets game than a Lions game
How to determine how much more it would cost a family of 5 to get the jets game than a Lions game?
Given that:
The average ticket price for Jets game = $105.66
The average ticket price for Lions game = $79.19
Jets game for a family of 5 will be:
Jet game cost = 5× $105.66 = $528.3
Lions game for a family of 5 will be:
Lions game cost = 5× $79.19 = $395.95
Difference = $528.3 - $395.95 = $132.35
Therefore, it would cost a family of 5 $132.35 more to get the jets game
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A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 7 freshmen, 9 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
There are 3457440 ways combination in which this dance committee can be formed.
What is permutation and combination?
A set of items can be divided into subsets in two different ways: combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are arranged in a particular order in a permutation.
2 freshmen out of 7 freshmen can be chosen in ⁷C₂ ways.
3 sophomores out of 9 sophomores can be chosen in ⁹C₃ ways.
4 juniors out of 7 juniors can be chosen in ⁷C₄ ways.
5 seniors out of 8 seniors can be chosen in ⁸C₅ ways.
⁷C₂ × ⁹C₃ × ⁷C₄ × ⁸C₅ ways, the dance committee of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors can be chosen.
= 7!/(7-2)!2! × 9!/(9-3)!3! × 7!/(7-4)!4! × 8!/(8-5)!5!
= 7!/5!2! × 9!/6!3! × 7!/3!4! × 8!/3!5!
= 21×84×35×56.
= 3457440 ways.
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The total cost of fencing a square park at rupees 20 per meter are rupees
2880. Find the side of the square park.
The side of square park, whose fencing costed Rs 2880 is 36m.
What is a square?
A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about a square's characteristics, mathematics, and design.
We know perimeter of a square of side 'a' is 4a
Therefore, the cost of fencing a square park at Rs 20/meter would be equal to
= Rs(20*4a)
= Rs 80a
Given, the cost of fencing = Rs 2880
Thus, 80a = 2880
⇒ a = 2880/80
⇒ a = 36
Thus, the side of square park, whose fencing costed Rs 2880 is 36m
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How many days of milking will it take to get enough milk to make all this cheese?
Answer:
depending on how much cheese you are trying to produce is the amount of milk you need
I just need this Answer which is the thing I’m struggling on
The expressions that are equivalent to [tex]\frac{10}{9} + \frac{2}{9}m - \frac{4}{9}n[/tex] are [tex]\frac{2}{9}(5 + m -2n)[/tex] and [tex]-\frac{2}{9}( 2n -m -5)[/tex].
What is an Algebraic fraction?Algebraic fractions are fractions using a variable in the numerator or denominator, such as . Because division by 0 is impossible, variables in the denominator have certain restrictions. The denominator can never equal 0.
[tex]\frac{10}{9} + \frac{2}{9}m - \frac{4}{9}n[/tex] in this algebraic fraction 2/9 is common to all so factoring that out we have
2/9 x 5 + 2/9 x m - 2/9 x 2n so we factor out 2/9
2/9( 5 + m -2n)
This can also be written by multiplying 2/9( 5 + m -2n) by -1 so that it 5becomes
- 2/9(2n -5 - m)
In conclusion the expressions 2/9( 5 + m -2n) and - 2/9(2n -5 - m) are equivalent to [tex]\frac{10}{9} + \frac{2}{9}m - \frac{4}{9}n[/tex]
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In need of help!! Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
The equation is accurate. A line's slope and y-intercept are expressed in the form y is mx + c, where m is the slope and c is the y-intercept.
What does a line's slope-intercept form look like?A line's slope and y-intercept are expressed in the form y = mx + c, where m is the slope and c is the y-intercept.
y = (3/2)x + 1 is the given equation for the line.
Add x = 0 to the above equation, y = (3/2)(0) + 1 y = 1, to determine the line's y-intercept.
Take note that the line's graph's y-intercept is also 1.
The line's graph includes points (2,4).
Put the coordinates of the location into the above equation to see if it matches the coordinates of (2,4) or not:
4 = (3/2)(2) + 1
4 =4
The equation is accurate.
Consequently, it can be claimed that the following equation reflects the graph.
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Brett bought a house five years ago for $150,000. At that time he borrowed $140,000 from his bank. The house is now worth $162,000. The current value of his mortgage must be no higher than ________ for him to request termination of his PMI policy.
$126,360.
Once his equity has increased to 22% of the current market value, he can request that PMI be cancelled. He may request termination of PMI when his mortgage balance reaches $126,360 {$162,000 × (1 − 0.22)}.
The current value of his mortgage must be no higher than $126,360 for him to request termination of his PMI policy.
What is mortgage value?
The appraised value of the property used to determine the mortgage value is determined by a reputable firm. It might not match the purchase-sale value. The mortgage value, which serves as the Bank's guarantee, is the benchmark used in the mortgage application and arrangement process.
Given:
Brett bought a house five years ago for $150,000.
At that time he borrowed $140,000 from his bank.
The house is now worth $162,000.
Once his equity has increased to 22% of the current market value he can request that PMI be canceled.
He may request termination of request when his mortgage balance reaches
162,000(1 - 0.22) = 162,000(0.78) = 126,360.
Hence, the current value of his mortgage must be no higher than $126,360 for him to request termination of his PMI policy.
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1. Which line has a slope of 1, and which has a slope of 2?
2. Use a ruler to help you graph a line whose slope is 1/3. Albee this line a
Answer:
I can't answer unit I know what lines you're talking about, can you insert an image or graph of the questions?
Step-by-step explanation:
Deshaun wants to attend a college that will cost $25,600 for the first year. His uncle gave him a special gift of $2500 to use toward the cost. Deshaun plans to attend the college in 7 years. How much must Deshaun save each month to have enough for the first-year cost?
Deshaun must save the amount of $275 each month to have enough for the first-year cost.
As per the given question, we have
The first-year cost of college = $25,600
The gift cost = $2500
The amount left to pay will be:
⇒ first-year cost - gift cost
⇒25,600 - 2,500 = 23100
The months left till college = 7 × 12 = 84
So, he would have to save per month :
⇒ 23,100/84
Apply the division operation, and we get
⇒ 275
Thus, he must save the amount of $275 each month to have enough for the first-year cost.
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If g (x) = 4x + 6 and f(g(x))
12x + 8 than f(x)
Answer:
Given g(x)=4x+6
f(x)=12x+8
f(g(x))=f(4x+6)
=12(4x+6)+8 (substitute g(x) in f(x) )
=48x+72+8
= 48x+80
A book claims that more hockey players are born in January through March than in October through December. The following data show the number of players selected in a draft of new players for a hockey
league according to their birth month. Is there evidence to suggest that hockey players' birthdates are not uniformly distributed throughout the year? Use the level of significance a = 0.05.
Click the icon to view the table.
Click the icon to view the chi-square table of critical values.
What are the null hypothesis and alternative hypotheses?
OA. H₂: The distribution of hockey players' birth months is uniformly distributed.
H,: More hockey players are born in the first half of the year than the second half.
OB. H: The distribution of hockey players' birth months is uniformly distributed.
H,: More hockey players are born in January-March than October-December.
OC. H: The distribution of hockey players' birth months is not uniformly distributed
H,: The distribution of hockey players' birth months is uniformly distributed.
D. H.: The distribution of hockey players' birth months is uniformly distributed.
H,: The distribution of hockey players' birth months is not uniformly distributed.
Compute the expected counts for each birth month. The total number of hockey players is 188.
Expected Count
Birth Month
January-March
April-June
July-September
October-December
Observed Count
66
59
34
29
(Round to two decimal places as needed.)
The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.
The required details for null hypothesis in given paragraph
The null hypothesis and alternative hypothesis in this case would be:
H₀: The distribution of hockey players' birth months is uniformly distributed.
H₁: The distribution of hockey players' birth months is not uniformly distributed.
The expected counts for each birth month can be calculated as follows:
Expected Count = (Total Number of Players) * (Proportion of Total Players for Each Birth Month)
Since there are 4 birth months and the distribution is assumed to be uniform, the proportion of total players for each birth month is 1/4 = 0.25. Therefore, the expected count for each birth month is:
Expected Count = 188 * 0.25 = 47
To test the null hypothesis, we can then calculate the chi-square statistic using the following formula:
χ² = ∑((O - E)² / E)
where O is the observed count, E is the expected count, and the sum is taken over all birth months.
Plugging in the observed and expected counts, we get:
χ² = ((66 - 47)² / 47) + ((59 - 47)² / 47) + ((34 - 47)² / 47) + ((29 - 47)² / 47)
= 3.87 + 2.04 + 3.87 + 5.57
= 15.35
In this case, df = 3.
Looking up the critical value in the chi-square table with df = 3 and a = 0.05, we find that the critical value is 7.815. Since the chi-square statistic (15.35) is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to suggest that the distribution of hockey players' birth months is not uniformly distributed.
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Given x=a+b. Use the Pythagorean Theorem to find the value of x.
[tex]a=\sqrt{5^2-4^2}=3 \\ \\ b=\sqrt{5^2-4^2}=3 \\ \\ \therefore x=3+3=\boxed{6}[/tex]
Look at photo for problem
Just need chart filled out
3. y=-(x+2)²+1
Following values can be filled in the table:
(0,-3), (-1,0), (1,-8), (-2,1), (2,-15)
It can be solved using the concept of graph plotting and function.
What is graph?
When a set of points are connected together to form a strcture then the structure is known as graph. The set of ponts is known as ordered pair.
Consider the eqution.
[tex]y=-(x+2)^2+1[/tex]
Substitute the simplest value x = 0 and find the value of y.
[tex]y=-(0+2)^2+1\\=-3\\[/tex]
Now, substitute x = -1 and find the value of y.
[tex]y=-(-1+2)^2+1\\=0\\[/tex]
Now, substitute x = 1 and find the value of y.
[tex]y=-(1+2)^2+1\\=-8\\[/tex]
Now, substitute x = -2 and find the value of y.
[tex]y=-(-2+2)^2+1\\=1\\[/tex]
Now, substitute x = 2 and find the value of y.
[tex]y=-(2+2)^2+1\\=-15\\[/tex]
Hence, following values can be filled in the table:
(0,-3), (-1,0), (1,-8), (-2,1), (2,-15)
It can be solved using the concept of graph plotting.
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given f(x) =-2x-5 find (-1)
Answer:
f(-1) = -3
Step-by-step explanation:
f(x) =-2x-5
f(-1) = -2(-1)-5 ==> plug in -1 for x
f(-1) = 2-5
f(-1) = -3
What’s the answer anything helps
Answer: 135
Step-by-step explanation:
Since the expression gives you that n = 5, you'll plug 5 into every "n" within the original equation.
6n^2 -15 = 6(5)^2-15
You'll then square 5
= 6(5*5)-15
= 6(25)-15
= 150-15
= 135
Norah Johns has foreign source income of $30,000 during the current year.As the foreign jurisdiction withholds 25% of such income,she only receives $22,500 What is the non business and business income of Norah Johns?
The answer is in simplest form is 672.
What is simplest form?The simplest form is the smallest possible equivalent of the fraction of the number. Steps for finding to the simplest form: Search for the common factors in to the numerator and the denominator. Check whether one of the numbers in the fraction is a prime for number.
As per the given question the number are
910
238
We have to find 910-238
So,
910-238
We have to calculate sum or difference
And we got 672.
Thus, the answer is 672 or 6.72×10^2 ( in alternate form).
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Find the probability P(E or F) if E and F are mutually exclusive, P(E)= 0.30, and P(F) = 0.47. The probability P(E or F) is (Simplify your answer.)
Given that P(E)= 0.30 and P(F)= 0.47, the probability of P(E or F) if E and F are mutually exclusive will be 0.77.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Here,
P(E)=0.30
P(F)=0.47
P(E∩F)=0 as they are mutually exclusive
P(E∪F)=P(E)+P(F)-P(E∩F)
=0.30+0.47
P(E∪F)=0.77
The probability of P(E or F) if E and F are mutually exclusive will be 0.77 given that P(E)= 0.30, and P(F) = 0.47.
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To copy an angle using only a compass and a straightedge begin by marking the angle. Then draw a ray from the vertex which will be one of the legs of the new angle. What is the next step in the construction
Next step is to Mark off your new arc with this new width by positioning the compass point on the reference line where the previous arc crossed it.
Steps to be followed while measuring an exact angle using compass and straight edge are:
If a reference line is not given, draw one using a straightedge.Add a dot as the reference line's starting point.Position the compass's point at the vertex of the ABC angle (vertex at pointSwing the arc so that the pencil crosses BOTH rays (sides) of the angle. Holding the compass point at the starting point (dot) on the reference line, swing an arc that will cross the reference line and rise above the reference line without adjusting the compass's size. Return to the supplied angle ABC and determine the span (width) of the arc between the points at which it crosses one side of the angle and the other. Mark off your new arc with this new width by positioning the compass point on the reference line where the previous arc crossed it. Join this new intersection point to the reference line's starting point. Mark the duplicate.
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whats 0.00132 in scientific notation
Answer:
1.32x10^-3
Step-by-step explanation:
hope it helps
Find how long it takes a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set on 80 mph.
The time taken by the person to cover 260 miles will be 3 hours and 15 minutes.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Given that a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set at 80 mph.
The amount of time taken by the person to cover the distance of 260 miles with a speed of 80mph is,
Speed = Distance / Time
Time = Distance / Speed
Time = 260 / 80
Time = 3.25 or 3 hours 15 minutes
Therefore, the time taken by the person to cover 260 miles will be 3 hours and 15 minutes.
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you owe $31000 on student loans at an interest rate of 3.35% compounded monthly. You want to pay off the loan in 8 years. What will your monthly payments be? How much interest do you pay?
You owe $31000 on student loans at an interest rate of 3.35% compounded monthly.
The total interest paid would be $556.16.The monthly payment would be $318.54.What is interest?Generally, To calculate the monthly payment amount, you can use the following formula:
monthly payment = (interest rate / 12) x (loan balance / (1 - (1 + (interest rate / 12)) ^ (-term in months)))
Plugging in the values given in the question, the monthly payment would be:
monthly payment = (3.35% / 12) x ($31000 / (1 - (1 + (3.35% / 12)) ^ (-8 years x 12 months/year)))
= (0.00335) x ($31000 / (1 - (1 + 0.00335) ^ (-96)))
= $318.54
So the monthly payment would be $318.54.
To calculate the total interest paid over the course of the loan, you can use the following formula:
total interest = (monthly payment x term in months) - loan balance
Plugging in the values given in the question, the total interest paid would be:
total interest = ($318.54 x 96 months) - $31000
= $30,443.84 - $31,000
= $-556.16
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Amanda is the manager of Gladrags. She just got a new shipment of jeans and is pricing them for the store to make money. Her invoice for the jeans
states that the jeans cost her store $20 per pair. Amanda marks the jeans up to sell for $55 per pair. Find the percent of change.
O 175% increase
O 175% decrease
O 17.5% increase
O 17.5% decrease
To find the percent of change, we need to calculate the difference between the original price and the new price, and then divide this difference by the original price and multiply by 100%.
The difference between the original price of $20 and the new price of $55 is $55 - $20 = $35.
The percent of change is: ($35/$20) * 100% = 1.75 * 100% = 175%
Since the new price is higher than the original price, this is an increase. Therefore, the percent of change is a 175% increase. The correct answer is therefore
O 175% increase.
Given values for x and y to be -3 and 1, evaluate the following ordered triples
-5x - 4y + 2z = -5
-4x + 2y3z = 38
2x + 3y + 4z = -35
The system of linear equation have an ordered triple of (x, y, z) are (-3, 1, -8)
Evaluating Linear EquationTo evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
In the question given, we have a system of linear equations where the value of x and y are given.
-5x - 4y + 2z = -5 ...eq(i)
-4x + 2y + 3z = 38 ...eq(ii)
2z + 3y + 4z = -35 ...eq(ii)
Since we have the value two variables (x, y) which are (-3, 1), we can substitute it in any of the equation to find the value of z.
Taking eq(i)
-5x - 4y + 2z = -5
-5(-3) - 4(1) + 2z = -5
15 - 4 + 2z = -5
11 + 2z = -5
2z = -5 - 11
2z = - 16
z = -8
The ordered triple are (-3, 1, -8)
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Write each sequence as a function. {1,3,5,7,9,…}
can someone help me with this thank you
Answer:
25.
Step-by-step explanation:
1. if according to the condition 'm∠2 is three times m∠1', then it is possible to write: 3m∠1=m∠2, then
2. if according to the condition m∠WXZ=m∠1+m∠2, then it is possible to write it as:
m∠WXZ=m∠1+3m∠1; ⇔m∠WXZ=4*m∠1;
3. if according to the condition m∠WXZ=100, then
100°=4*m∠1, then
m∠1=100°:4=25°.