Analyze the following rational function: f(x) = (5+2x^2)/(2-X-X^2)
a. What are the x intercept(s)? b. What are the equations of x asymptote(s)? c. What is the y-intercept, as an ordered pair?
d. What is the equation of the y asymptote?
Answers
The following rational function: f(x) = (5+2x^2)/(2-X-X^2). Hence Your answers are a. There are no x-intercepts.
b. The x asymptotes are x = -2 and x = 1. c. The y-intercept is (0, 5/2). d. The y asymptote is y = 0.
a. To find the x-intercepts, we set f(x) = 0 and solve for x:
(5+2x^2)/(2-X-X^2) = 0
5+2x^2 = 0
2x^2 = -5
x^2 = -5/2
Since there is no real number solution for x^2 = -5/2, there are no x-intercepts.
b. To find the equations of the x-asymptotes, we look at the behavior of the function as x approaches positive and negative infinity. Since the degree of the numerator and denominator are the same (both 2), we can use the ratio of the leading coefficients to find the horizontal asymptote:
y = 2x^2/-x^2 = -2
Therefore, the equation of the x-asymptote is y = -2.
c. To find the y-intercept, we set x = 0:
f(0) = (5+2(0)^2)/(2-0-0^2) = 5/2
Therefore, the y-intercept is (0, 5/2) as an ordered pair.
d. To find the equation of the y-asymptote, we look at the behavior of the function as x approaches the vertical asymptotes. The vertical asymptotes occur when the denominator equals zero:
2 - x - x^2 = 0
\Using the quadratic formula, we find that the roots are x = (-1 ± sqrt(3))/2. These are the values where the function is undefined, so they are the vertical asymptotes. Therefore, the equation of the y-asymptote are x = (-1 + sqrt(3))/2 and x = (-1 - sqrt(3))/2.
To analyze the rational function f(x) = (5 + 2x^2) / (2 - x - x^2).
a. To find the x-intercept(s), set f(x) equal to 0 and solve for x.
0 = (5 + 2x^2) / (2 - x - x^2)
0 = 5 + 2x^2 (since the numerator must equal 0)
2x^2 = -5
x^2 = -5/2
Since we cannot have a square root of a negative number, there are no x-intercepts.
b. To find the equation of the x asymptote(s), find the vertical asymptotes by setting the denominator equal to 0.
2 - x - x^2 = 0
x^2 + x - 2 = 0
(x + 2)(x - 1) = 0
So there are two vertical asymptotes: x = -2 and x = 1.
c. To find the y-intercept as an ordered pair, set x equal to 0 and solve for f(0).
f(0) = (5 + 2(0)^2) / (2 - 0 - (0)^2)
f(0) = 5 / 2
The y-intercept as an ordered pair is (0, 5/2).
d. To find the equation of the y asymptote, compare the degrees of the numerator and the denominator. Since the degree of the denominator is higher (2) than the degree of the numerator (1), the horizontal asymptote is y = 0.
Your answer:
a. There are no x-intercepts.
b. The x asymptotes are x = -2 and x = 1.
c. The y-intercept is (0, 5/2).
d. The y asymptote is y = 0.
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Related Questions
This table shows the amount a store in
Indiana charges customers on selected purchases.
Price of Item
$40.00
$65.00
$125.00
$210.00
Price
Including
Sales Tax
$42.80
$69.55
$133.75
$224.70
Use the table to determine the Indiana
Answers
explanation:
Before Tax Price:40
Sales Tax Rate: 6.5%
After Tax Price: $42.80
Which of the following graphs represents a function? If you don’t know then please don’t write “i don’t know” or “I can’t help with that” Just for points.
Answers
Answer:
B. x
Step-by-step explanation:
The answer would be graph x. A function must be that one x value should only have one y value. graph w doesn't work since when you plug in 0, you get two y's. same thing with z. Y doesn't work since at x value of 3, it curves back so x value 2 has 2 y's. X is the only one that each x value has only one y.
Answer:
X
Step-by-step explanation:
For a relationship to be a function, every input has exactly one output, so for every x value there is only one value.
If you look at answer's w and z for x=1 there is two y values, therefore they are not functions, letter Y is tricky. Even though every x value has only one y value, If you were to extend the graph x=0 would have more than one y values.
That leaves X. If you extend the graph of X every x value will only have one y value so it is a function
A borrower received a 30-year ARM mortgage loan for $200,000. Rate caps are 3/2/6. The start rate is 3. 50% and the loan adjusts every 12 months for the life of the mortgage. The index used for this mortgage is MTA (for this exercise, 3. 00% at the start of the loan, 4. 45% at the end of the first year, and 4. 50% at the end of the second year). The margin on the loan is 3. 00%, which remains the same for the duration of the loan
Answers
A 30-year ARM mortgage loan means that the borrower will have a fixed interest rate for the first 30 years of the loan. After that, the interest rate will adjust annually based on the index and margin.
In this case, the start rate is 3.50%. This means that for the first year, the borrower will pay interest at a rate of 3.50%. At the end of the first year, the interest rate will adjust based on the index and margin.
The index used for this mortgage is MTA, which was 3.00% at the start of the loan. At the end of the first year, the MTA was 4.45%, and at the end of the second year, it was 4.50%.
To calculate the new interest rate at the end of each year, we need to add the margin to the current index rate. The margin is 3.00% and remains the same for the duration of the loan.
Let's calculate the new interest rate at the end of the first year:
New Interest Rate = Current Index Rate + Margin
New Interest Rate = 4.45% + 3.00%
New Interest Rate = 7.45%
However, the rate caps limit how much the interest rate can increase or decrease. In this case, the rate caps are 3/2/6, which means that the interest rate can increase by a maximum of 3 percentage points after the first adjustment, 2 percentage points for subsequent adjustments, and 6 percentage points over the life of the loan.
Since the new interest rate calculated above (7.45%) exceeds the rate cap of 3 percentage points for the first adjustment, the interest rate will be capped at the maximum allowed increase. Therefore, the new interest rate at the end of the first year will be 6.50%.
For subsequent adjustments, the interest rate can increase by a maximum of 2 percentage points. Let's calculate the new interest rate at the end of the second year:
New Interest Rate = Current Index Rate + Margin
New Interest Rate = 4.50% + 3.00%
New Interest Rate = 7.50%
Since the new interest rate calculated above (7.50%) exceeds the rate cap of 2 percentage points, the interest rate will be capped at the maximum allowed increase. Therefore, the new interest rate at the end of the second year will be 6.50%.
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Which number is greater . 60 or 7.5
Answers
Answer:
60 is greater than 7.5.
step by step
Daniel has 7 photo books. Each book has 5 pages with 1 photo on each page. He gets 2 more pages with 1 photo on each page.
How many total photos does Daniel have? Enter the answer in the box
Answers
Hope this helps
Last year you mowed grass and shoveled snow for 12 houses. You earned $225 for each lawn you mowed
and $200 for each house you shoveled for a total of $2600. How many lawns did you mow? How many
driveways did you shovel?
Answers
1800 lawns were mowed. 800 driveways were shoveled.
What is equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Given Data
Let mowed grass be x
Let shoveled snow be y
Last year you mowed grass and shoveled snow for 12 houses
x + y = 12
y = 12 -x
You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.
225x + 200y = 2600
Equating value of y
225x + 200(12-x) = 2600
225x + 2400 - 200x = 2600
225x - 200x = 2600 - 2400
25x = 200
x = 8
For value of y,
y= 12 -x
y = 12 - 8
y = 4
Lawn mowed = 225(8)
Lawn mowed = 1800
Shoveled snow = 200(4)
Shoveled snow = 800
1800 lawns were mowed. 800 driveways were shoveled.
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How would you prove that QRST is a rectangle?
Answers
-the longer sides are parallel and the shorter sides are parallel
One-way anova is a procedure for comparing the means of several populations. it is the generalization of what procedure for comparing the means of two populations?
Answers
One-way ANOVA is a statistical procedure that is used for comparing the means of several populations. Also, it is the generalization of pooled t-procedure for comparing the means of two populations.
What is a mean?A mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
What is an ANOVA?ANOVA is an abbreviation for analysis of variance which was developed by the notable statistician Ronald Fisher. The analysis of variance (ANOVA) is a collection of statistical models with their respective estimation procedures that are used for the analysis of the difference between the group of means found in a sample.
This ultimately implies that, the analysis of variance (ANOVA) helps to ensure we have a balanced data by splitting the observed variability of a data set into random and systematic factors.
In Statistics, the analysis of variance (ANOVA) procedure is typically used as a statistical tool to determine whether or not the means of two or more populations are equal, especially through the use of the following:
Null hypothesisF-test.Pooled t-procedureIn this context, we can infer and logically deduce that a one-way ANOVA is a statistical procedure that is used for comparing the means of several populations. Also, it is the generalization of pooled t-procedure for comparing the means of two populations.
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Complete Question:
One-way ANOVA is a procedure for comparing the means of several populations. It is the generalization of what procedure for comparing the means of two populations?
A. nonpooled t-procedure
B. paired t-test
C. pooled t-procedure
D. None of the above
The sum of three consecutive even numbers is 108. Write and evaluate an expression in terms of x to determine the smallest of the three numbers. Include parentheses in your expression.
Answers
Answer:
\(34\)
Step-by-step explanation:
Let the first number be \(x\)
The next number be \(2\) more than the previous as it is an even number
The second number is \(x+2\)
and the last number is \(x+4\)
The sum of the numbers is \(108\), so the expression will be
\(x+(x+2)+(x+4)=108\)
\(\Rightarrow 3x+6=108\)
\(\Rightarrow x=\dfrac{108-6}{3}\)
\(\Rightarrow x=34\)
The smallest of the three numbers is \(34\).
Finding the standard deviation round answer two decimal places when necessary
Answers
Answer:
\(\begin{equation*} SD=1.55 \end{equation*}\)Step-by-step explanation:
The standard deviation of a data set is represented by the following equation:
\(\begin{gathered} SD=\sqrt{\frac{\sum_^\lvert{x_i-\bar{x}}\rvert^2}{n}} \\ where, \\ x_i=\text{ represent each number in the data set} \\ \bar{x}=\text{ mean} \\ n=\text{ number of elements in the data set} \end{gathered}\)Therefore, for the given sample:
\(\begin{gathered} 6,10,6,6,7 \\ \text{ mean=}\frac{6+10+6+6+7}{5} \\ \text{ mean=7} \end{gathered}\)For each data point, find the square of its distance to the mean.
\(\begin{gathered} \sum_^\lvert x_i-\bar{x}\lvert{}^2=(6-7)^2+(10-7)^2+(6-7)^2+(6-7)^2+(7-7)^2 \\ \sum_^\lvert x_i-\bar{x}\lvert{}^2=12 \end{gathered}\)Now, solving for the standard deviation:
\(\begin{gathered} SD=\sqrt{\frac{12}{5}} \\ SD=1.55 \end{gathered}\)These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=
Answers
The area of the larger figure that is similar to the smaller one is: 28.2 m².
How to Find the Area of Similar Figures?Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:
Area of figure A / Area of figure B = a²/b².
Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:
Perimeter of smaller figure = 20 m
Area of smaller figure = 19.6 m²
Perimeter of larger figure = 34m
Area of larger figure = x
Therefore:
20/34 = a/b
Simplify:
10/17 = a/b.
Find the area (x) of the larger figure using the formula given above:
10²/12² = 19.6/x
100/144 = 19.6/x
100x = 2,822.4
x = 2,822.4/100
x ≈ 28.2 m²
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Can I get all the right answers only
Answers
Answer:
yes, you can get all right answers.
Answer:
yes i believe that you can get all the answers right
Step-by-step explanation:
Can someone help me with these problems having trouble and show work please !!
Answers
Answer:
(2x-5)(2x-5), 81 meters
Step-by-step explanation:
All of the sides of a square are equal, so to find the area we need to multiply 2x-5 by 2x-5: (2x-5)(2x-5)
Using this equation we can plug in 7 for x:
(2(7)-5)(2(7)-5) =
(14-5)(14-5) =
9*9 = 81
Select the correct answer.
Which number is an irrational number?
A. \sqrt(100)
B. 1/8
C. -2.2675
D. \root(3)(6)
Answers
The number which is an irrational number is the: D. ∛6.
Which number is an irrational number?An irrational number is a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.
√100 = 10 which is a rational number since it can be expressed as the fraction 10/1.
1/8 = 0.125 which is a rational number since it can be expressed as the fraction 1/8.
-2.2675 is a rational number since it can be expressed as a decimal which terminates after a finite number of digits.
∛6 ≈ 1.8171 which is an irrational number since it cannot be expressed as a fraction and has a non-repeating decimal representation.
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A motor car drives at an average speed of 106 km/h for 2 hours 45 minutes. At which constant speed must the car drive to travel the same distance in 2 hours 35 minutes?
Answers
Answer:
Average speed = 106km/h = 106km/ 60 minFor Time = 2 hours 45 minutes = 2× 60 +45 minutes = 165 minutes
\(distance \: = \: speed \times time \\ \: \: \: \: = \frac{106}{60} \times 165 \\ = \frac{17490}{60 } \\ = 291.5km\)
New time = 2 hours 35 minutes = 2×60+35 minutes = 155 minutes .Distance = 291.5 km\(av.speed = \frac{distance}{time} \\ = \frac{291.5}{155} \\ = \frac{1.88km}{min} \\ \\ = 1.88km \times 60h \\ = \frac{112.8km}{h} \)
Answer :- 122.8km/hAnswer:
speed required = 113 km/h
Step-by-step explanation:
The question tells us that a car travels at an average speed of 106 km/h for 2 hours and 45 minutes. It then asks us to calculate the constant speed the vehicle would need to drive at to travel the same distance in 2 hours and 35 minutes.
To solve this, we must first find the distance travelled by the car in 2 hours and 45 minutes. But before that, let's convert 2 hours and 45 minutes into hours:
2 hours 45 minutes = \(\mathrm{2 +\frac{45 }{60} }\)
= 2.75 h
Now, let's calculate the distance:
distance = speed × time
= 106 × 2.75
= 291.5 km
Now that we know the distance travelled by the car, we can easily calculate the speed it would need to cover it in 2 hours and 35 minutes (2.58 h):
speed = distance ÷ time
= 291.5 ÷ 2.58
= 112.98 km/h
\(\approx\) 113 km/h
Therefore, the car must drive at a constant speed of approximately 113 km/h to travel the same distance in 2 hours 35 minutes.
What is the difference between the greatest and least amounts of rain?
Answers
Answer:
1 inch
Step-by-step explanation:
hshuehevdjdbevejdj
WILL GIVE BRAINLY!!!
Find the value of x. Round to the
nearest tenth.
9
4
O
X= | ?
Answers
tan x = 4/9
x = tan^-1 (4/9)
x = 23.9624....
x = 24.0
Answer:
66.03 so 70
Step-by-step explanation:
since hypotunees has no value it cancels.
aso it leaves with an adjacent and oppisite
using trig function you will get
tan(x)=(9/4)
inverse tan to get x on its own
(x)=tan^-1(9/4)
put that on the calculater and you will get the angle
therefore
(x)=66.04 round it the nearest ten which is
70
please help me!! i need mathematicians on this post right now!!
Cam, Yusef, and Spencer have resolved to drink more water each day. The recommended amount of water per day is 64 ounces.
1. At breakfast, Yusef drinks 16 ounces of water. What percentage of the daily amount of water does Yusef drink at breakfast? Show your work and/or explain your reasoning.
2. Spencer decides to drink more than the recommended amount. By dinner time, he has already drunk 64 ounces of water, which is 80% of his goal for the day. How many total ounces of water does Spencer plan to drink? Show your work and/or explain your reasoning.
Answers
Answer:
1) 25%
2) 80 ounces
Step-by-step explanation:
1) 16 oz/64 oz = 1/4 or 25%
2) 64 oz/0.80 = 80 ounces
Answer:
1. 25%
2. 80 ounces
Step-by-step explanation:
1. 16 oz \64 oz=1\4 or 25%
2. 64 oz\0.80=80 ounces
a rate
12. A class of 60 is 30% girls. How many girls are there in the class?
b. 180
d. 18
a. 24
c. 240
Answers
Answer:
18
Step-by-step explanation:
30% of 60 is 18
Answer:
24 is the answer
Step-by-step explanation:
you can see in
Find the sum of 6x+7 and 8x^2 +5x-1
Please hurry I need this asap
Answers
Answer:
11x+8x^(2)+6
Step-by-step explanation:
Answer:
8x² + 11x + 6
Step-by-step explanation:
Expression addition:Combine like terms. Like terms have same variable with same exponent.
5x and 6x are like terms. Add the coefficient of the like terms.
(-1) & 7 are constants and add (-1) & 7.
8x² + 5x - 1 + 6x + 7 = 8x² + 5x + 6x - 1 + 7
= 8x² + 11x + 6
Find the value of x for 3(x - 10) = 5x +2. Once you have solved for x, then determine the value of 4x+2.
Answers
Distribute
3x - 30 = 5x + 2
-3x on both sides
-30 = 2x + 2
-2 on both sides
-32 = 2x
/2 on both sides
x = -16
4x + 2
4(-16) + 2
-64 + 2
-62
Answer: -62
Find two monomials whose product equals -20a^4b², and whose sum is a monomial with a coefficient of 1.
Answers
Answer:
-4a²b
5a²b
Step-by-step explanation:
A monomial is a polynomial that has one term only but can have multiple variables.
Given monomial:
\(-20a^4b^2\)
The coefficient of the given monomial is -20.
Therefore, we need to find two numbers that multiply to -20 and sum to 1.
Factors of -20:
-1 and 20-2 and 10-4 and 5-5 and 4-10 and 2-20 and 1Therefore, the two numbers that multiply to -20 and sum to 1 are:
-4 and 5Rewrite -20 as the product of -4 and 5:
\(\implies -4 \cdot 5 \cdot a^4b^2\)
Rewrite the exponents as sums of equal numbers:
\(\implies -4 \cdot 5 \cdot a^{2+2} \cdot b^{1+1}\)
\(\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c\)
\(\implies -4 \cdot 5 \cdot a^2 \cdot a^2\cdot b^{1}\cdot b^{1}\)
Rearrange as the product of two monomials with the same variables:
\(\implies -4a^2 b^{1}\cdot 5 a^2 b^{1}\)
\(\implies -4a^2 b\cdot 5 a^2 b\)
Therefore, the two monomials whose product equals -20a⁴b², and whose sum is a monomial with a coefficient of 1 are:
-4a²b5a²bCheck the sum of the two found monomials:
\(\begin{aligned}\implies -4a^2b+5a^2b&=(-4+5)a^2b\\&=(1)a^2b\\&=a^2b\end{aligned}\)
Thus proving that the sum of the monomials has a coefficient of 1.
Drawling not to scale find the value of x and y.
Answers
Answer:
y=43
x=90
Step-by-step explanation:
angles a and c are equal, so to find y you just add 47+47=86 and divide 86/2=43
x is a right angle because it splits the triangle in half
A quadratic function is shown on the graph.
an upward opening parabola beginning with closed circle at negative 2 comma 4, which decreases to a vertex at 0 comma 0 and then increases to an open circle at 3 comma 9
What is the range of the function?
{x | −2 ≤ x < 3}
{x | −2 < x ≤ 3}
{y | 0 ≤ y < 9}
{y | 0 < y ≤ 9}
Answers
The range of the quadratic function is {y |0 ≤ y < 9}
What is the range of a function?The range of a function is the set of output values of the graph. This in other words mean the range of a function is the set of y values of the graph.
How to determine the range of the function?From the question, we have the following parameters:
The parabola opens upwardVertex = (0, 0)Closed circle point = (-2, 4)Open circle point = (3, 9)Write out the vertex
So, we have
Vertex = (0, 0)
Remove the x value
y = 0
From the question, we have
The parabola opens upward
This means that the vertex is a minimum
So, the range is
y ≥ 0
Rewrite as
0 ≤ y
Recall that:
Closed circle point = (-2, 4)
Open circle point = (3, 9)
Remove the x values
Closed circle point = 4
Open circle point = 9
Remove the smaller y value
Open circle point = 9
This means that the highest value of y is at open circle point = 9
This is represented as
y < 9
So, we have
0 ≤ y and y < 9
Combine both
0 ≤ y < 9
Rewrite properly as
{y |0 ≤ y < 9}
Hence, the range of the quadratic function is {y |0 ≤ y < 9}
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{y |0 ≤ y < 9}
The person above need the shine, im just making it simple
If f(x) = 3x-2, find f^-1(x)
Answers
Answer:
i think po -1x
Step-by-step explanation:
pero hindi ako cguro sa answer ko
Answer:
Step-by-step explanation:
f(x) = 3x - 2
f^-1(x)= ?
let y = f(x)
y = 3x - 2
Interchanging the roles of x and y we get
x = 3y - 2
x + 2 = 3y
y = (x+2)/3
f^-1(x) = (x+2)/3
Write the quotient as a mixed number.
35 ÷ 4 = 8 R3
Answers
Answer:
8 3/4 (8.75)
Step-by-step explanation:
I divided 35 by 4 on a calculator to get 8.75
I know that 8.75 is the same as 8 3/4
So, say you're dividing 35 jellybeans with 3 of your friends (you're the fourth person, because you need some jellybeans too!)
Each would get 8 jellybeans. But there are 3 left over.
Split each jellybean into 4 parts.
Each of you would get 3/4 of one of the jellybeans. (three tiny parts of the total four tiny pieces)
Hope I helped :)
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What is the perimeter of a quadrilateral with vertices at (1,5), (6,5),
(1,11), and (6,11)? Enter the answer in the box.
Answers
Answer:
Step-by-step explanation:
What is the perimeter of a quadrilateral with vertices at (1,5), (6,5),
(1,11), and (6,11)? Enter the answer in the box.
Answer:
22 is the answer I just took the test
Please help i will give brainly!
Answers
Answer:
Step-by-step explanation:
7.056
7 is units place = 7 *1
0 is tenth place = 0 *(1/10)
5 is hundredth place = 5 *(1/100)
6 is thousandth place = 6 * (1/1000)
\(7.056 = 7*1+ 0*\frac{1}{10}+5*\frac{1}{100}+6*\frac{1}{1000}\)
Seven and fifty six thousandths
18.3
Eighteen and one third
\(18.3 = 1*10 + 8*1 + 3*\frac{1}{10}\)
918.0201
Nine hundred eighteen and two hundred one ten thousandths
\(918.0201=9*100 + 1*10 + 8*1 +0 +2*\frac{1}{100}+0+1*\frac{1}{10000}\)
The total area of a square is 25 square meters? What is the length of the side?
Answers
Answer:
u would do 25 divided by 4
Step-by-step explanation:
hope i helped
I got the first part but i dont onow how to get the other ones
Answers
The value of x for this problem is given as follows:
x = 5.
Hence the angle measures are given as follows:
m < CAB = 32º.m < FDE = 32º.How to obtain the value of x?
We have that angles A and D are congruent for this problem, meaning that they have the same measure.
Hence the value of x is obtained as follows:
7x - 3 = 5x + 7
2x = 10
x = 5.
Hence the angle measures are given as follows:
m < CAB = 7(5) - 3 = 35 - 3 = 32º.m < FDE = 5(5) + 7 = 32º.More can be learned about angle measures at https://brainly.com/question/25716982
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