Answers
Answer:
[tex]\begin{gathered} 0.44x^{2}-2.67x+3 \\ or \\ \frac{1}{2.25}(x-3)^2-1 \end{gathered}[/tex]Explanation:
From the graph, we will observe that the vertex is at the point:
[tex]\begin{gathered} (h,k)=(3,-1) \\ \text{We will obtain the quadratic equation from the vertex form using the formula:} \\ f(x)=a(x-h)^2+k \\ \text{Inputting the values of ''h'' \& ''k'', we have:} \\ f(x)=a(x-3)^2-1 \\ \text{We have the x-intercept at point:} \\ (x,y)=(1.5,0) \\ f(1.5)=0 \\ \Rightarrow0=a(1.5-3)^2-1 \\ 0=a(-1.5)^2-1 \\ 0=a(2.25)-1 \\ 0=2.25a-1 \\ \text{Add ''1'' to both sides, we have:} \\ 1=2.25a \\ 2.25a=1 \\ \text{Divide both sides by ''2.25'', we have:} \\ a=\frac{1}{2.25}=0.44 \\ \text{We will substitute the value of ''a'' into the vertex equation, we have:} \\ f(x)=\frac{1}{2.25}(x-3)^2-1 \\ \text{Expand the bracket, we have:} \\ f(x)=\frac{1}{2.25}(x-3)(x-3)-1 \\ f(x)=\frac{1}{2.25}[x(x-3)-3(x-3)]-1 \\ f(x)=\frac{1}{2.25}[x^2-3x-3x+9]-1 \\ f(x)=\frac{1}{2.25}[x^2-6x+9]-1 \end{gathered}[/tex]We will obtain the quadratic function as shown below:
[tex]\begin{gathered} \frac{1}{2.25}[x^2-6x+9]-1 \\ \text{Expand the bracket, we have:} \\ 0.44x^2-2.67x+4-1 \\ 0.44x^2-2.67x+3 \\ or \\ \frac{1}{2.25}(x-3)^{2}-1 \\ \end{gathered}[/tex]Related Questions
8) y= V1-5 A) Domain: x 20 Range: y 2-5 B) Domain: x > 0 Range: y'z 5 C) Domain: {All real numbers. } Range: {All real numbers. } D) Domain: x 25 Range: y 20
Answers
Domain:
we know that a root cannot have negative values inside so
[tex]\begin{gathered} \sqrt[]{x}\ge0 \\ x\ge0^2^{} \\ x\ge0 \end{gathered}[/tex]the domain is X >= 0
Range:
we solve the equation for y
[tex]\begin{gathered} y=\sqrt[]{x}-5 \\ y+5=\sqrt[]{x} \\ (y+5)^2=x \end{gathered}[/tex]and we replace the condition that x must be greater than or equal to 0
so
[tex](y+5)^2\ge0[/tex]now solve y
[tex]\begin{gathered} y+5\ge0^2 \\ y+5\ge0 \\ y\ge-5 \end{gathered}[/tex]so the range is Y >= -5
then the right option is A
The lines given by the equations y= 2x and y=-3x areA. neither perpendicularnorparallelB. parallelC. perpendicular
Answers
Consider that the general form of a line can be written as follow:
y = mx + b
where m is the slope and b the y-intercept.
Take into account that if two lines are parallel, then, the slopes of the line are equal. Based on the given equations, you can notice that the slopes are different, m1 = 2 and m2= -3.
Two lines are perpendicular if:
m1 = -1/m2
you can notice, based on the given equations that m1 is not equal to -1/m2, that is, 2 ≠ -1/(-3).
Hence, the lines are neither perpendicular nor parallel
Find the expected value of the winningsfrom a game that has the followingpayout probability distribution:Payout ($) 246810Probability 0.35 0.2 0.1 0.2 0.15Expected Value = [?]
Answers
The formula for the expected value from an event is given as;
[tex]\text{Expected value=}\sum ^{}_{}xPr(x)[/tex]From the table given, we can obtain the expected value of winning as;
[tex]\text{Expected value=}2(0.35)+4(0.2)+6(0.1)+8(0.2)+10(0.15)=5.2[/tex]Therefore, the expected value of winning is $5.2
selected the ordered pair that represent solutions to the system of inequalities. A) (-6,3)B) (-3,3)C) (-5,0)D) (-4,2)E) (0,0)F) (-6,6)G) (-3,-6)H) (-4,0)PLEASE ANSWER FAST
Answers
To detremine the ordered pairs that represent the system of inequalities given, from the choices given, the corredct ordered pairs are:
(x, y) ==> (-6, 3), (-4, 2), (-6, 6), (-4, 0)
Melinda ate 3/5 of the cookies and left the rest for Suzanne. What fraction of the cookies are left for Suzanne?
Answers
The fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.
What is fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. Example - 5/9. Here, (5) is called numerator and (9) is called denominator.
Given is Melinda who ate 3/5 of the cookies and left the rest for Suzanne.
Assume that the fraction of cookies left for Suzanne is represented by [x].
Fraction of cookies ate by Melinda = [y] = 3/5
The sum of the fractions representing the cookies eaten by both Suzanne and Melinda will be equal to 1. Mathematically -
x + y = 1
x + 3/5 = 1
x = 1 - 3/5
x = (5 - 3)/5
x = 2/5
Therefore, the fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.
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Tucker is painting his pool deck over the weekend. The area of the deck is 76 1/2 square meters. He paints 2/3 of the deck before stopping to eat lunch. How many square meters does Tucker have left to paint after lunch?Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
Answers
Tucker is painting his pool deck over the weekend. The area of the deck is 76 1/2 square meters. He paints 2/3 of the deck before stopping to eat lunch. How many square meters does Tucker have left to paint after lunch?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
we have that
total area=76 1/2 m2
Convert to an improper fraction
76 1/2=76+1/2=153/2 m2
1-(2/3)=1/3
Multiply the total area by 1/3
(153/2)*(1/3)=51/2=25.5 m2 ------> 25 1/2 m2
the answer is 25 1/2 m2suppose 84% of students chose to study spanish their junior year,. and that meant that there were 378 such students. How many students chose not to take spanish their junior year?
Answers
Let x be the total of students in their Junior Year.
So, 84% of x =378
84% = 0.84
0.84x=378 (divided by 0.84)
x= 450 students.
The ones that chose not to take spanish will be:
450-378=72
72 students chose not to take spanish in their junior year.
State if the following are perfect square trinomials. Show work that proves your conclusion.
Answers
Solution:
A quadratic expression is said to be a perfect square trinomial if it has repeated factors.
Given the expression below:
[tex]x^2+7x+\frac{49}{4}[/tex]By factorization, we have
[tex]\begin{gathered} (x^2+\frac{7}{2}x)+(\frac{7}{2}x+\frac{49}{4}) \\ factor\text{ out the common term,} \\ x(x+\frac{7}{2})+\frac{7}{2}(x+\frac{7}{2}) \\ This\text{ gives} \\ (x+\frac{7}{2})(x+\frac{7}{2}) \\ \Rightarrow(x+\frac{7}{2})^2 \\ \end{gathered}[/tex]Since the above expression has a repeated factor of
[tex](x+\frac{7}{2})[/tex]We can conclude that the expression is a perfect square trinomial.
Select the y-intercept and another point that lies on the graph of the equation y = 3x − 2.
Answers
The y-intercept of the equation y = 3x − 2 is (0, -2).
y-intercept
In Mathematics, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx + c, where m is slope and c is the y-intercept.
Equation of a line
The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.
Given that lies on the graph of the equation y = 3x − 2.
We know that
In an equation of line
y = mx + c
m = slope of a line
c = y intercept
So therefore in given equation of line the y intercept is (0, -2).
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PLEASE HELP!!!
Solve the following word problem. The air temperature at 9 a.m. is −5.8 degrees Celsius. The air temperature at noon is −1.6 degrees Celsius. What is the change in the temperature during these three hours? Write and solve an equation to show your answer. Then explain what your answer means
Answers
The equation to show the change in temperature between 9 a.m. and noon is given as d = x - y.
What is an equation?An equation contains two mathematical expressions that state that they are equal or equivalent.
We use the equation mark (=) to show that two expressions possess equality.
Air temperature at 9 a.m., y -5.8 degrees Celsius
Air temperature at noon, x = -1.6 degrees Celsius
Change in temperature, d = 4.2 degrees Celsius (-1.6 - -5.8)
The equation to show the change is d = x - y, where d is the change in temperature, x is the final temperature, and y is the initial temperature.
Thus, based on the equation, the temperature increased by 4.2 degrees Celsium from the earlier -5.8 degrees Celsius to result in a final temperature of -1.6 degrees Celsius at noon.
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The rate of growth dPdt of a population of bacteria is proportional to the square root of t with a constant coefficient of 9, where P is the population size and t is the time in days (0≤t≤10). The initial size of the population is 600. Approximate the population after 7 days. Round the answer to the nearest integer.
Answers
To solve this question we are going to need to define an equation with the data that the problem gives us
The first part (rate of growth) shows us a derivate, this is equal to 9 square root of t or:
[tex]\frac{dP(t)}{dt}=9\sqrt{t}[/tex]where P is the population size and t is the time in days
Now we need the population after 7 days, so we need the P(t) formula, which means that we need the integration
First, we send the dt to the other side to have something to integrate
[tex]\int dP(t)=\int9\sqrt{t}dt[/tex]Solving
[tex]\begin{gathered} P(t)=9(\frac{2}{3}t^{\frac{3}{2}})+C \\ \\ P(t)=6t^{\frac{3}{2}}+C \end{gathered}[/tex]We know that P(0)=600 so
[tex]P(0)=600=C[/tex][tex]P(t)=6t^{\frac{3}{2}}+600[/tex]Now we replace the t by 7
[tex]\begin{gathered} P(7)=6(7^{\frac{3}{2})}+600 \\ P(7)=711.121 \end{gathered}[/tex]Answer: 711
Kayla notices that she can buy snacksandcandy in bulk at the grocery store.Write a formula that helps Kayla determinehow much she'll have to pay if she buys thefood in bulk.Let's lett = total pricep = price per kilogramk = number of kilograms of foodEnter the correct answer.
Answers
In this problem the total price (p) will be equal to the price per kilogram (p) times the number of kilograms of food (k) so the equation will be:
[tex]t=p\cdot k[/tex]is n divided by -1 always equal to -1
Answers
if n = a negative number is divided by a negative number the answer is positive.
So if (n) is -4 / -1 = 4
Two negatives = positive for multiplication and division
Answer:
Yes
Step-by-step explanation:
Any number divided by 1 equals itself. This rule tells us simply that if we have a number divided by 1, our answer will equal that number regardless of what that number is.
Hope this helps you
Tell me if I'm wrong
factor x2 − 2xy − 10y2
Answers
factor x2 − 2xy − 10y2 is (x+2y)(x−5y) .
What is meant by polynomial's ?A polynomial is an expression made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.
Therefore,
phrase reordering
x2−10y2−2xy
Rearrange 10y2 and 2xY.
x2−2xy−10y2
Subtract 3 from 3xy.
x2−2(xy)−10y2
Write 2as 2 plus 5 x2+(25)(xy)10y2 instead.
The distributive property should be used.
x2+2(xy)−5(xy)−10y2
Delete any extra parentheses.
x2+2xy−5(xy)−10y2
Delete any extra parentheses.
x2+2xy−5xy−10y2
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅ c=1⋅−10=−10 and whose sum is b=−2
Put the first and last two terms together.
(x2+2xy)
−5xy−10y2
Subtract each group's GCF, or greatest common factor.
x(x+2y)−5y(x+2y)
Remove the polynomial's x+2y largest common factor to factor it.
(x+2y)(x−5y)
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1. It costs $5820 to get new windows for a certain house. Each of the 28 windows costs the same amount.
(a) Determine an estimate for the cost of each window. Justify your reasoning.
(b) What is the cost of each window, rounded to the nearest dollar? Show your work. Leave the remainder undivided.
Answers
Answer:
1) 6000/30=200
2)5820/28=207.9 (1dp)
Step-by-step explanation:
Alan takes a taxi at the rate of $3 per mile. The taxi company charges an additional pickup fee of $5. How many miles, d, did Alan travel if the total fare was $29?
Answers
Answer:
8 miles
Step-by-step explanation:
You want to know the distance Alan traveled for $29 in a taxi that charges a fee of $5 plus $3 per mile.
Mileage chargeThe amount of the $29 that paid for mileage was $29 -5 = $24.
At $3 per mile, that will pay for ...
$24/($3/mile) = 8 miles
Alan traveled 8 miles for a total fare of $29.
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While on vacation in Washington DC the cab ride for the Dulles airport to the hotel is 15 miles. The total cost of the cab ride was $25.50. The cabbie charges $1.50 per mile for the entire trip A. Write an equation to that can be used to determine B. What is the flat rate of the cab ride? C. How much does it cost to travel 7 miles in a cab?
Answers
The total distance from Washington DC to Dulles airport is 15 miles
The total cost of the cab ride is $25. 50
The cabbie charges $1.50 per mile for the entire trip
Let T be the total cost of the entire trip
Let x represents the number of miles traveled
Let y be the flat rate of the cab ride
Total cost = flat rate + charge per trip x number of miles covered
Mathematically,
T = y + 1.5 * x
T = y + 1.5x
Where, 1.5 is the charge per trip.
The equation becomes
T = y + 1.5x
B
To calculate the flat rate of the cab ride?
The total cost = $25.50
Charges per mile = $1.5
Total number of miles = 15
Substitute the above values into the equation
25.50 = y + 1.5 x 15
25.50 = y + 22.5
Make y the subject of the formula
y = 25.50 - 22.5
Y = $3
The flat rate of the cab ride is $3
C
How much does it cos
Prorate the following expenses and find the corresponding monthly expense.Lan pays a semiannual premium of $650 for automobile insurance, a monthly premium of $150 for health insurance, and an annual premium of $350 for life insurance.Question content area bottomThe monthly expense is $ (Round to the nearest cent as needed.)
Answers
Given:
Lan pays,
A semiannual premium of $650 for automobile insurance.
A monthly premium of $150 for health insurance.
An annual premium of $350 for life insurance.
To find:
The monthly expense.
Explanation:
According to the problem,
The amount paid for automobile insurance per year will be,
[tex]650\times2=1300[/tex]The amount paid for health insurance per year will be,
[tex]150\times12=1800[/tex]The amount paid for life insurance per year will be,
[tex]350\times1=350[/tex]The total expenses in a year are,
[tex]1300+1800+350=3450[/tex]So, the monthly expense is,
[tex]\frac{3450}{12}=\text{ \$}287.50[/tex]Therefore, the monthly expense is $287.50.
Final answer:
The monthly expense is $287.50.
photo question graphing linear equations
Answers
We want to select the graph that represents the equation;
[tex]2x-5y=-10[/tex]Let's rewrite this equation as;
[tex]\begin{gathered} -5y=-2x-10 \\ divide\text{ both sides by -5, we obtain;} \\ y=\frac{2}{5}x+2 \end{gathered}[/tex]This equation has a slope of 2/5, an x-intercept of -5. and a y-intercept of 2, lets inspect the graphs to see which one matches it.
Going through the options, we see that the matching graph-the correct graph is Option A.
Arrange the numbers 5^3, 6^2, and 2^7 in order from least to greatest.
Answers
5^3 = 5x5x5 = 125
6^2 = 6x6 = 36
2^7 = 2x2x2x2x2x2x2 = 128
From least to greatest
36 - 125- 128
6^2- 5^3 - 2^7
6. Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. x = 2 when y = 2.Ok = 1, y = 1xk = 4, y = 4x4= 4, y = 2 / 24= 1, y = 1/2
Answers
ANSWER:
k = 4, y = 4/x
STEP-BY-STEP EXPLANATION:
Since they are inverses they have the following form the equation
[tex]y=k\cdot\frac{1}{x}[/tex]now, x = 2 and y = 2, therefore, replacing and solving for k:
[tex]\begin{gathered} 2=k\cdot\frac{1}{2} \\ k=2\cdot2 \\ k=4 \end{gathered}[/tex]We replace and we would have the equation
[tex]\begin{gathered} y=4\cdot\frac{1}{x} \\ y=\frac{4}{x} \end{gathered}[/tex]The entire graph of the function h is shown in the figure below.
Write the domain and range of h as intervals or unions of intervals.
Answers
The domain of the function f is [-5. -2] U [ 1, 2].
The range of the function f is [-4, 3].
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
A graph of the function f.
We can see two curves on the graph.
One curve:
Domain = [1, 2]
Range = [-4, 0]
Another curve:
Domain = [-5, -2]
Range = [-3, 3]
We can combine both the curves domain and the range.
Domain = [-5. -2] U [ 1, 2 ]
Range = [-4, 3]
Thus,
The domain of the function f is [-5. -2] U [ 1, 2].
The range of the function f is [-4, 3].
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The polynomial function f(x) is graphed below. Fill in the form below regarding the features of this graph.
Answers
Answer:
Step-by-step explanation:
degree 6 -- triple root, double root, single root
leading coefficient is negative -- it opens downward
3 distinct roots
3 relative extrema
MATH PROBLEM HELP please make sure it correct
Answers
For the value of c = 0,c=1 then A is not invertible
For given matrix A is invertible if c≠ 0 and c≠ 1
[tex]Given \ $A=\left[\begin{array}{ll}1 & 1 \\ c & c^2\end{array}\right]$ \\A matrix $A$ is invertible if $|A|={det}(A) \neq 0$.\\Now consider $|A|={det}(A)=0$.[/tex]
[tex]$$\begin{aligned}&\Rightarrow\left|\begin{array}{ll}1 & 1 \\c & c^2\end{array}\right|=0 \\&\qquad \quad \text { If } A=\left[\begin{array}{ll}a & b \\c & d\end{array}\right] \text { then }|A|={det}(A)=a d-b c\end{aligned}$$[/tex][tex]$$\begin{aligned}&\Rightarrow c^2-c=0 \\&\Rightarrow c(c-1)=0 \\&\Rightarrow c=0, c=1\end{aligned}$If $c=0$ or $c=1$ then \A \is \\not \ invertible. \\$\therefore$ Given matrix $A$ is invertible iff $c \neq 0$ and $c \neq 1$. \\ie Given marix $A$ is invertible for $c \in \mathbb{R}-\{0,1\}$.[/tex]
What are matrix?Matrix, a collection of numbers arranged in rows and columns forming a rectangular array. The number is called the elements or entries of the matrix. Matrices have wide applications in engineering, physics, economics and statistics, as well as in various areas of mathematics. Matrices also have important applications in computer graphics, where they have been used to represent image rotations and other transformations.
Different types of matrices are
row matrixcolumn matrixzero matrixsquare matrixdiagonal matrix upper triple matrixlower triple matrixsymmetric matrix asymmetric matrix.To learn more about matrix, refer;
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The population of bobcats in northern Arizona since 2008 can be modeled using the function b(t) = –0.32t2 + 2.7t + 253
What does t represent?: the number of years since 2008
What is the domain for this function?:t values greater than or equal to 0
Which range values would not make sense for this function?:negative values
Would the graph be continuous or discrete, and why?:discrete, because number of bobcats cannot be broken into fractional parts (these are the answers to function notation EDGE 2022 algebra1)
Answers
A polynomial function is a function that only employs non-negative integer powers or only positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, etc. For instance, the exponent of the polynomial 2x+5 is 1.
Explain about the polynomial function?A polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.
The variable t in the formula b(t) stands for the number of years following 2008. This function's range of application is. More over 258.7 wouldn't make sense as a range. The function's graph is continuously drawn at all times.
Explanation:
Since 2008, the provided function b(t) displays the bobcat population in Northern Arizona. The number of years following 2008 is therefore represented by the variable t.
The domain of this function is because t stands for the number of years after 2008, which can be either positive or zero.(0,∞)
Provided that the given function is a quadratic function with a negative coefficient, it is a descending parabola. There is no meaning in the range above the vertex's y-coordinate.
Vertex function is (4.2,258.7)
This is polynomial function so the graph of the function always continuous
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how do i find the markup price and retail price
Answers
Price = 72.87
The markup is 30% or 30/100 = 0.3
Let's find the markup of the price:
[tex]72.87\cdot0.3=21.861[/tex]The retail price, or selling price, is the price + markup.
Thus, retail price is:
[tex]72.87+21.861=94.731[/tex]Answers:
Markup = $21.86Retail Price = $94.73Need help asap extra points
Answers
The equation of line is y = 8/5x-26/5.
What is a line equation?
A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
Equation 8x-5y=4 is given.
-5y = 4-8x
y = 8/5x-4/5 and we are aware that the line's equation is y = mx+b
m = 8/5
Nowadays, coordinates are (2,-2)
Y=-2, X=2, and m=8/5
y = mx+c
-2 = 8/5(2)+c
c = -26/5
Consequently, the line's equation is
y = 8/5x-26/5
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A cat with 850 J of energy is stuck in a tree that is 15 meters off the ground. What is the mass of th. cat?
O 56.7 kg
O 12,750 kg
O 5.78 kg
O 147 kg
Answers
Compute the average rate of change of the function. Exercise A:
Answers
ANSWER
(a). Average Rate of Change = - 4
(b). Average Rate of Change =
[tex]12+6h+h^2^{}[/tex]EXPLANATION
(a).
Step 1: Given
[tex]h(x)=5-2x^2\text{ at interval \lbrack-2, 4\rbrack}[/tex]Step 2: Determine the Average Rate of Change
[tex]\text{Average rate of change = }\frac{h(b)\text{ - h(a)}}{b-a}[/tex]1/2 ▾
8-10. Answer each multiple choice question to indicate which reason
corresponds to each missing statement in the 2 column proof (3
points).
Proof Diagram
A
Statements
1.2125 Given
Reasons
2.24 21 a
3.24 25 b.
4.pr
8. Choose the correct reason:
a. Linear Pair Postulate
C
b. Angle Addition Postulate
c. Vertical Angles Postulate
1 Pt
B
O Search the web
Given: 21 25
Prove: pr
*
9. Choose the correct reason:
a. Symmetric Property
b. Reflexive Property
c. Transitive property
1 Pt
hn
A
B
r
E
Answers
1) ∠4 ≅∠1
Vertically opposite angle
2) ∠4 ≅∠5
Alternate angle
Define angles.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
An acute angle is one that is smaller than 90 degrees. Right Angle: An angle with a 90 degree exactness. More than 90 degrees but less than 180 degrees is referred to as an obtuse angle. A straight angle is one that has a 180 degree angle. An angle that is more than 180 degrees but less than 360 degrees is called a reflex angle.
Given Data
∠1 ≅∠5
1) ∠4 ≅∠1
Vertically opposite angle
2) ∠4 ≅∠5
Alternate angle
3) p ║r
When a transversal cuts two lines so that the accompanying angles are congruent, the lines are said to be parallel. When a transversal cuts two lines so that their opposing interior angles coincide, the lines are said to be parallel.
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