Answers
Domain - the set of possible x-coordinates of a function.
Range - the set of possible y-coordinates of a function.
Question 32
Domain is:
x ∈ (- 6, 6), both ends exclusive as open circles.Range is:
y ∈ (-6, 2], the -6 is excluded as open circle, the 2 is included as part of the graph.This is a function as it passes the vertical line test.
Question 33Domain is:
x ∈ (- 5, 6], one end is open circle and the other is closed circle.Range is:
y ∈ (-1, 5], the -6 is excluded as open circle, the 2 is included as part of the graph.This is a function as it passes the vertical line test.
Answer:
32.a) Domain: (-6, 6)
32.b) Range: (-6, 2]
32.c) Function: Yes
33.a) Domain: (-6, 6]
33.b) Range: (-1, 5]
33.c) Function: Yes
Step-by-step explanation:
Definitions
An open circle indicates the value is not included in the interval.A closed circle indicates the value is included in the interval.An arrow shows that the function continues indefinitely in that direction.Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 32From inspection of the graph, the endpoints of the continuous curve are:
(-6, 0) and (6, -6)As the endpoints are open circles, the x-values are excluded from the domain. Therefore, the domain in interval notation is:
Domain: (-6, 6)The smallest y-value is y = -6 and the greatest y-value is y = 2.
y = -6 is excluded from the range since it is the y-value of the open circle endpoint, whereas y = 2 is included in the range. Therefore, the range in interval notation is:
Range: (-6, 2]The graph is a function as is each input (x-value) is related to exactly one output (y-value).
Question 33From inspection of the graph, the endpoints of the continuous line are:
(-6, -1) and (6, 5)As the graph is a straight line, the x and y values of the endpoints are the x and y values of the domain and range.
As the (-6, -1) endpoint is an open circle, the values are excluded from the domain and range.
As the (6, 5) endpoint is a closed circle, the values are included in the domain and range.
Therefore, the domain and range in interval notation are:
Domain: (-6, 6]Range: (-1, 5]The graph is a function as is each input (x-value) is related to exactly one output (y-value).
Related Questions
PLEASE HELP
Two swimming pools are being drained so that they can be repaired. The two equations below describe the depth of the two pools, d, as a function of time in hours, t.
d=5 - 1/4t. d=7 - 1/3t
Ted wants to know when the two pools will reach the same depth. He solves the system by equating the two equations for d and then solving for t. The solution he finds is t = 24, so he concludes that after 24 hours the pools will be the same depth. Is Ted’s conclusion reasonable? Why or why not?
A. Yes, Ted’s conclusion is reasonable. Setting the two equations equal and solving for t will solve for the time when the two pools are at the same depth.
B. Yes, Ted’s conclusion is reasonable. Substituting into both equations yields the same value for d, which is the depth of the pools.
C. No, Ted’s conclusion is not reasonable. Ted failed to take into account the limits on the domain and range of the two functions.
D. No, Ted’s conclusion is not reasonable. Ted made a math error when he was finding a common denominator when solving for t.
Answers
Yes, Ted’s conclusion is reasonable.
Setting the two equations equal and solving for t will solve for the time when the two pools are at the same depth.
Option A is the correct answer.
What is an equation?An equation is a mathematical statement made up of two expressions connected by an equal sign.
We have,
d = 5 - (1/4)t ____(1)
d = 7 - (1/3)t ____(2)
Now,
The time at which the depth d is the same.
Make (1) and (2) equal.
5 - (1/4)t = 7 - (1/3)t
(1/3)t - (1/4)t = 7 - 5
(4t - 3t)/12 = 2
t = 2 x 12
t = 24
Thus,
Yes, Ted’s conclusion is reasonable.
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Andrew buys 8 bottles of cranberry juice at the corner store for a total cost of $5.68. If each bottle costs the same amount, how much is 6 bottles of juice?
Answers
Slope/$ per bottle: .71cents
.71 x 6 = 4.26
Answer: $4.26
A tank has an intake valve and a release valve. The rate of follow through each valve is inversely proportional to the area of its cross-section. The cross-section area of the input can be described by the equation, f(x)= x^2+2x+1; The cross-section area of the release can be described by the equation, f(x)= x^2+4x+3. If the proportion constant is equal for the input and output, find x such that the volume of material in the tank remains constant.
Answers
Answer:
x = - 1------------------------------
The volume will remain constant if both input and output cross - sections are equal:
x² + 2x + 1 = x²+ 4x + 34x - 2x = 1 - 32x = - 2x = - 1use the theorem in sec. 77, involving a single residue, to evaluate the integral of f (z) around the positively oriented circle |z|
Answers
The integral of f (z) around the positively oriented circle |z|
[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3
What is integral?In mathematics, an integral lends numerical values to functions to represent notions like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
With the exception of the point where z = z, where f(z) is analytic within and on C, let C be the smooth, simple closed curve except at z =z , then ,
[tex]\int\limits^_ {} \,[/tex] f(z) dz = 2πi [ res f(z)] z = [tex]z_{1}[/tex]
here f(z) is singular at z = -1,
res [tex]f(z)_{z = -1}[/tex] = [tex]\lim_{z\to \-1} z+1 f(z)_[/tex]
[tex]\lim_{z\to \-1}[/tex] [tex]z^{3}[/tex](1-3z)/(1+2[tex]z^{4}[/tex])
when z = -1 then f(z) = -4/3
Therefore [tex]\int\limits^_ {} \,[/tex]f(z) dz = 2πi (-4/3)
[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3.
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Good afternoon! I have a survey for you guys to take. I would appreciate it if you do, because I use it for my schoolwork.
Knowing that the Bacon Cheeseburger meal is about 1000 calories and that you are supposed to consume between 2000 and 3000 calories per day, would you still eat Jack in the Box? Thank you beforehand!
1. I would eat there often
2. I would eat there sometimes
3. I would eat there rarely
4. I would not eat there ever
Answers
Answer:
Step-by-step explanation:
2, i would eat there sometimes!
Answer:
3. I would eat there rarely.
Step-by-step explanation:
Please give brainliest!!!
Hong had 8/9
of a spool of yarn. He used 2/5
of his yarn for a project. What fraction of the spool was used for the project?
Answers
Answer: 16/45 of the spool
Step-by-step explanation:
2/5 of 8/9
2/5 * 8/9 = 16/45 (multiply numerators, and multiply denominators)
Cannot be further simplified.
Answer:
18/45
Step-by-step explanation:
Multiply both denominators to get a common denominator, in this case, it would be 45.
(8/9)*5=40/45
(2/5)*9=18/45
Find the measure of angle 2
a 50°
b 90°
c 140°
d 40°
Answers
Could someone help me answer this multiple-answer question? I'm stuck
Answers
Answer:
x = 2
<1 = 28
Step-by-step explanation:
The two angles equal each other.
4x + 20 = 5x + 18 Subtract 4x from both sides
20 = x + 18 Subtract 18 from both sides
2 = x
4x + 20
4(2) + 20
8 + 20
28
A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 3(1.09)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 5.98 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 2 to m = 8, and what does it represent? (4 points)
Answers
The solution is
A) The domain to plot the growth function is Domain = [ 0 , 8 ]
B) The y-intercept of the graph of the function f ( a ) is f ( 0 ) = 3 cm
C) The average rate of change of the function f ( a ) from m = 2 to m = 8 is given by T = 0.4022 cm per month
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is given by
f ( a ) = 3 ( 1.09 )ᵃ
A)
To find the domain of the function f ( a )
The length of the fish was approximately 5.98 cm
So , substituting the value of f ( a ) as 5.98 cm , we get the value of m,
And , f ( a ) = 5.98 cm
So , 5.98 = 3 ( 1.09 )ᵃ
Solving for a , we get
Divide by 3 on both sides of the equation , we get
1.9933 = ( 1.09 )ᵃ
a = 8
So , the value of a is 8
So , the domain of the function is [ 0 , 8 ]
B)
The y-intercept of the graph is given by substituting the value of a = 0,
So , f ( a ) = 3 ( 1.09 )ᵃ
when a = 0 , we get
f ( 0 ) = 3 ( 1.09 )⁰
f ( 0 ) = 3 cm
Therefore, the value of f ( 0 ) = 3 cm
C)
The average rate of change from m =2 to m = 8 is given by the equation ,
when m = 2 ,
f ( a ) = 3 ( 1.09 )ᵃ
f ( 2 ) = 3 ( 1.09 )²
f ( 2 ) = 3 x 1.1881²
f ( 2 ) = 3.5643
And , when a = 8
f ( a ) = 3 ( 1.09 )ᵃ
f ( 8 ) = 3 ( 1.09 )⁸
f ( 8 ) = 3 x 1.99256
f ( 8 ) = 5.97768
So , the average rate of change is the slope of the graph
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope = f ( 8 ) - f ( 2 ) / ( 8 - 2 )
Slope = ( 5.97768 - 3.5643 ) / 6
Slope = 2.4133879 / 6
Slope = 0.40223 cm per month
Therefore ,
The average rate of change of the function f ( a ) from a = 2 to a = 8 is given by T = 0.4022 cm per month
Hence ,
A) The domain to plot the growth function is Domain = [ 0 , 8 ]
B) The y-intercept of the graph of the function f ( m ) is f ( 0 ) = 3 cm
C) The average rate of change of the function f ( m ) from m = 2 to m = 8 is given by T = 0.4022 cm per month
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what is 2/50 as a percentage’s
Answers
Answer:
4%
Step-by-step explanation:
2/50= 4/100
4/100= 0.04 or 4%
what is the slope of a line that is parallel to the line shown on the graph?
PLEASE HURRY!
Answers
Answer:
-3
Step-by-step explanation:
A (0,2)
B (2,-4)
slope = (-4-2)/(2-0)
-6/2
-3
a parallel line has the same slope
find the length and the slope of each side of the triangle below. then, find the coordinates of the midpoint of each side. when the slope is undefined, write undefined in the response box.
Answers
The triangle has three side x,y and √(x²+y²), the slope of x is zero, the slope of y is undefined, the slope of √(x²+y²) is tanα. The coordinate of the midpoint of x is x/2,0 and y is 0, y/2
how to determine the length and slope of the side of a triangle?suppose the triangle is right-angled and the sum of other two angles are also 90 degrees. we know that the side opposite to the right angle is called hypotenuse. let the other two side is denoted by x and y. Now, x is the base of triangle, and the rest of the side is y. The angle between hypotenuse and base is denoted by α . As per Pythagorean theorem, hypotenuse = √(x²+y²).
slope can be calculated by tanα or using the formula (y₂-y₁)/(x₂-x₁)
according to trigonometric ratio, tanα = opposite side/base = x/y
tanα is the slope of hypotenuse.
the side length x is along the horizontal axis, so its y coordinate is zero and slope is also zero.
the side length y is along the vertical axis whose x coordinate is zero that means slope is undefined.
When does a slope is defined?As per the formula (y₂-y₁)/(x₂-x₁) used to calculate slope, whenever x coordinate is zero the result is written as undefined.
hence, the triangle is right-angled, and the biggest side has a slope only.
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100 POINTS WILL GIVE BRAINLIEST What is the target percent change for Growth Domestic Product?
A. 2-3% growth per period
B. 1-5% growth per period
C. 3-6% growth per period
Answers
Answer:A
Step-by-step explanation:
third-degree, with zeros of -3,-2, and 1, and y-intercept of -8
Answers
The polynomial y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8 is the cubic equation whose zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and intercept is - 8.
How to derive a cubic equation associated with a given set of zeros and a intercept
Herein we must derive a cubic equation such that the zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and its intercept is - 8. Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients.
If we know that (x₁, y₁) = (- 3, 0), (x₂, y₂) = (- 2, 0), (x₃, y₃) = (1, 0) and (x₄, y₄) = (0, - 8), then we solve the following system of linear equations to determine all real coeffcients by numerical methods:
- 27 · a + 9 · b - 3 · c + d = 0
- 8 · a + 4 · b - 2 · c + d = 0
a + b + c + d = 0
d = - 8
(a, b, c, d) = (4 / 3, 16 / 3, 4 / 3, - 8)
The cubic equation is y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8.
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let d be a positive integer. show that among any group of d 1 (not necessarily consecutive) integers there are two with exactly the same remainder when they are divided by d.
Answers
Among any group of d+1 integers there are two with exactly the same remainder when divided by d.
What are Positive Integers?Positive integers are those bigger than 0 that don't contain any fractional portions. On the number line, these figures are located to the right of 0.
Is 0 a Positive Integer?Since it is neither positive nor negative, 0 is not a positive integer. Positive integers are defined as numbers greater than 0 in mathematics.
The possible remainders after dividing an integer by d are 0, 1, 2,..., d-1.
The number of remainders that can be obtained is d, or |0, 1, 2,..., d-1|=d0,1,2,...,d-1=d.
According to the Pigeonhole Theory:
objects are the number of integers in d+1.
"holes" = "remainders" + "d"
[d+1/d]=2
According to the Pigeonhole Principle, there are always two d+1 integers in every group that have precisely the same residual after being divided by d.
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There are always two d+1 numbers in any group that have the exact same residual after division.
Examples of integers and what they are:An integer, pronounced "IN-tuh-jer," is an entire number which can be positive, minus, even zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, among 3,043. 1.43, 1 3/4, 3.14, and other values which aren't integers seem to be some examples.
Briefing:The potential remainders after dividing an integer by d are 0, 1, 2,..., d-1.
The possible number of remainders is d, or I{0,1,2,.......d-1}I = d
By the Pigeonhole Principle:
Objects = umber of integers = d+1
Holes = number of remainders = d
[tex]\frac{d+1}{d} = 2[/tex]
According to the Pigeonhole Principle, there are always two d+1 numbers in every group that have precisely the same residual after being divided by d.
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Samson opened a bank account with 2.25% simple interest. The total amount of interest Samson will earn after 30 years is $812.50. How much did Samson deposit when he opened the account? Round if necessary.
Answers
Answer: The equation for simple interest is:
Future interest = Principal*(interest rate*number of years). Remember to write the interest rate of 1.25% as 0.0125 (rather than directly as 1.25)
812.50 = x(0.0125*20)
812.5 = x(0.25)
x = $3250
This means that Samson deposited $3250 when he opened the account.
Step-by-step explanation:
5 Bob is 5 years younger than twice Mark's age. Bob is 31. How old is Mark?
Answers
Answer:
57 years old
Step-by-step explanation:
Bob=31
Mark= 31 x 2 - 5
31 x 2= 62
62- 5 = 57
Mark is 57 years old
Answer:
Mark is 18
Step-by-step explanation:
A Consumer with a 10 years loan, will have to make 125 payments.
A. True
B. False
Answers
Answer:
False
Step-by-step explanation:
Assuming monthly payments
12 payments per year X 10 years = 120 payments
What is the value of x in |6|=x
Answers
Answer and Step-by-step explanation: I used demos and got (6,0) as my answer.
The developer of the city park shown plans to put a decorative fence around the park. The budget allows for at least 399 feet of fencing but no more than 798 feet to be used.
Answers
The possible lengths of the side x + 30 are given as follows:
199.5 - x ≤ x + 30 ≤ 399 - x.
How to obtain the perimeter of a rectangle?The perimeter of a rectangle of base b and height h is given by the equation presented as follows:
P = 2(b + h).
The dimensions in the triangle in this problem are given as follows:
x.x + 30.The budget allows for at least 399 feet of fencing, hence:
2(x + x + 30) ≥ 399
x + x + 30 ≥ 199.5.
x + 30 ≥ 199.5 - x.
The budget allows for no more than 798 feet to be used, hence:
2(x + x + 30) ≤ 798
x + x + 30 ≤ 399
x + 30 ≤ 399 - x.
Then the range of values that can be assumed by the side with dimensions x + 30 is given as follows:
199.5 - x ≤ x + 30 ≤ 399 - x.
Missing InformationThe park has a rectangular format, with dimensions x and x + 30.
It asks for the possible lengths of the side with dimensions x + 30.
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Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place. Please hurry!!!
Answers
The area of the given figure is 68.6
Calculating the area of a figureFrom the question, we are to determine the area of the given figure.
Area of the given figure = Area of the semicircle + Area of the rectangle + Area of the semicircle
Area of a semicircle = 1/2πr²
Where r is the radius
Area of a rectangle = Length × Width
From the given diagram,
The diameter of the semicircle is 4
Thus,
Radius, r = 4/2 =
r = 2
Length of the rectangle is 14
and the width of the rectangle is 4
Therefore,
Area of the figure = 1/2π(2)² + 14 × 4 + 1/2π(2)²
Area of the figure = 1/2π×4 + 14 × 4 + 1/2π×4
Area of the figure = 2π + 56+ 2π
Area of the figure = 4π + 56
Area of the figure = 68.566
Area of the figure ≈ 68.6
Hence, the area is 68.6
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3(6x-4y)-5. Help i do not know how to do this it’s very confusing I need help
Answers
Answer:
3(6x-4y) -5 18x-12y-5MAY BE IT'S HELP UHHH=^._.^
Answer:
The answer to the expression 3(6x-4y)-5 is 18x - 12y - 5. This is the result of following the order of operations and performing the necessary operations in the correct sequence.
Step-by-step explanation:
To solve this problem, you need to follow the order of operations, which is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is often abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
According to the order of operations, the first step in solving this problem is to evaluate anything inside parentheses. In this case, there are no parentheses, so we can move on to the next step, which is to evaluate any exponents. Again, there are no exponents in this expression, so we can move on to the next step, which is to perform any multiplication or division.
In this case, there is a multiplication operation: 3 * (6x - 4y). So we need to evaluate this first. To do that, we need to multiply 3 by each of the terms inside the parentheses: 3 * 6x and 3 * -4y. This gives us 18x - 12y.
Now that we have performed all of the multiplication and division operations, we can move on to the final step, which is to perform any remaining addition or subtraction operations. In this case, there is only one subtraction operation: 18x - 12y - 5. So we need to subtract 5 from 18x - 12y to get our final answer: 18x - 12y - 5 = 18x - 12y - 5.
Therefore, the result of evaluating the expression 3(6x-4y)-5 is 18x - 12y - 5. I hope this helps! Let me know if you have any other questions.
and are right triangles. Find h. Use a proportion and show work.
Answers
In a triangle, The value of ''h'' will be;
⇒ h = 2.7 m
What is mean by proportion?
A proportion is a fraction of a total amount, in which two ratios are set equal to each other.
Given that;
The triangle is right triangle.
The values are,
AB = 6 m
BD = 12 m
BC = 0.9 m
DE = h m
Now,
Since, The triangle is right triangle.
Hence, By using definition of proportional we get;
⇒ AB / BC = AD / ED
Substitute all the values, we get;
⇒ 6/0.9 = (6 + 12) / h
⇒ 6 / 0.9 = 18 / h
⇒ h = 18 × 0.9 / 6
⇒ h = 2.7 m
Thus, The value of h = 2.7 m
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jonah and haley made brownies to bring as a class treat. some were plain and some had sprinkls the class ate 3/4 of one pan and 1/6 of another pan of plain brownies they ate 5/6 of one pan and 1/10 of another pan of brownies with sprinkles. if the brownies were the same sie dud the class eat more plain brownies or more brownies with sprinkles
Answers
Answer:
5/6
Step-by-step explanation:
he class ate 3/41 = <<3/41=3/4>>3/4 of one pan of plain brownies
They also ate 1/61 = <<1/61=1/6>>1/6 of another pan of plain brownies
The total amount of plain brownies they ate is 3/4 + 1/6 = <<3/4+1/6=5/6>>5/6
The class ate 5/61 = <<5/61=5/6>>5/6 of one pan of brownies with sprinkles
They also ate 1/101 = <<1/101=1/10>>1/10 of another pan of brownies with sprinkles
The total amount of brownies with sprinkles they ate is 5/6 + 1/10 = 5/6 + 1/10 = 41/60
The class ate more plain brownies because 5/6 > 41/60. Answer: {5/6}.
Tommy does 28J of work to push the pencil over 4m. How much force did he use?
Answers
Answer:
Given that,
Tommy does 28 joules of work for pushing up the pencil.And, the distance is 4 meter.We know that
Work = Force × distance
So, the force = work ÷ distance
= 28 ÷ 4
= 7 newtonsTherefore we can conclude that the force that he used is 7 newtons.
If
f(x) = 2x² – 5
and
g(x) = 5x + 7
Find
g(f(x)) = 10x² + [? ]
Answers
Answer:
The missing term in the output of the function [tex]g(f(x))[/tex] is -18.
[tex]g(f(x))=10x^2-18[/tex]
Step-by-step explanation:
Function CompositionIn mathematics, function composition is a term that encompasses a relationship between two functions wherein the output of one function is used as the input for another function. This relationship combines two functions to form a single function, known as a composite function. For future reference, function composition may also be denoted by a small circle, see below:
[tex](g\circ f)(x)=g(f(x))[/tex]
In the given problem, we must evaluate the composite function [tex]g(f(x))[/tex] / [tex](g\circ f)(x)[/tex] to identify the unknown term.
With composite functions, we begin evaluating from the inside. To evaluate [tex]g(f(x))[/tex], we must substitute the output of the function [tex]f(x)[/tex] (given as the expression [tex]2x^2-5[/tex]) as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex]:
[tex]g(f(x))=g(2x^2-5)[/tex]
Now, using [tex]f(x)[/tex] as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex] (given as the expression [tex]5x+7[/tex]), we can substitute [tex]2x^2-5[/tex] into the output for the function [tex]g(x)[/tex]:
[tex]g(f(x))= 5(2x^2-5)+7[/tex]
From here, we can go ahead and distribute the 5:
[tex]g(f(x))=10x^2-25+7[/tex]
Combine like terms:
[tex]g(f(x))=10x^2-18[/tex]
With the composite function evaluated, we can identify our missing term as [tex]-18[/tex].
What is the range of the data set below? * Data Set 13 44 54 2 25 17 7
Answers
Answer: 52
Step-by-step explanation:
To find the range of a data set, we subtract the smallest value from the largest value.
54 - 2 = 52
Order these number from least to greatest. 33 1/3%, 0.3125, 17/48
Answers
(not sure if you meant to put 33 1/3% or just 33 1/3)
Explain why it has no real solution
Answers
Answer:
Step-by-step explanation:
[tex]\sqrt{2x+1} = -4 -1[/tex]
[tex]\sqrt{2x-1} = -5[/tex]
the number under a square root is always 0 or a positive number, so it can’t be equal to a negative number
In triangle DEF, line DE is congruent with line FD and the measurement of angle F is 55. Find the measurement of angle E. (isosceles triangle)
Answers
Step-by-step explanation:
because it is an isoceles triangle (both legs are equally long), E and F are the side angles in the baseline.
and because both leg sides are equally long, also both side angles must be equally large
therefore,
angle E = angle F = 55°.