The ball reaches a maximum height of 96 feet and it spent 0 seconds in the air
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the maximum height the ball reaches?The quadratic equation is given as
h(t) = -16t^2 + 96
Differentiate the equation of the function
So, we have
h'(t) = -32t
Set the differentiated function to 0
So, we have
-32t = 0
Divide both sides by -32
So, we have
t = 0
Substitute t = 0 in the equation h(t) = -16t^2 + 96
So, we have
h(0) = -16(0)^2 + 96
Evaluate
h(0) = 96
This means that the maximum height of the ball is 96 feet
How to determine the time spent in the air?Recall that the quadratic equation is given as
h(t) = -16t^2 + 96
Next, we differentiate the equation of the function
So, we have
h'(t) = -32t
Set the differentiated function to 0
So, we have
-32t = 0
Divide both sides by -32
So, we have
t = 0
Hence, the ball spent a total of 0 seconds in the air
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Gregoria borrowed $2,450, to be paid back at 3.5% annual simple interest. She repays $3,221.75. How many years was the loan period?
The loan that was borrowed by Georgina was for a period of 9 years.
How to calculate the value?From the information, Gregoria borrowed $2,450, to be paid back at 3.5% annual simple interest. She repays $3,221.75. The Interest will be:
= $3,221.75 - $2,450
= $771.75
Therefore, the time taken for the loan will be expressed as:
Interest = PRT/100
where P = Principal
R = Rate
T = Time.
Interest = PRT/100
771.75 = (2450 × 3.5 × T) /100
Cross multiply
8575T = 77175
Time = 77175 / 8575
Time = 9
The time is 9 years.
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Last year, Elsa invested her money in two purchases. She purchased a certificate of deposit for $7000 that paid 3% interest per year and purchased $9000 in corporate bonds paying 11% interest per year.
Answer the questions below. Do not do any rounding.
Elsa used her money to make two purchases last year. The Total interest earned by the end of the year is 1200.
Given that,
Elsa used her money to make two purchases last year. She spent $7,000 on a certificate of deposit paying 3% interest annually and $9,000 on corporate bonds paying 11% interest annually.
We have to find the Total interest earned by the end of the year.
We know,
Total interest=adding the interest annually payment
Total interest=0.03×7000+0.11×9000
Total interest=1200
Therefore, The Total interest earned by the end of the year is 1200.
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Write brackets in this statement to make each statement correct
Answer:
a. 4 x (5 + 3) = 32
b. 3 + 4 x (5 + 6) = 47
c. (2 + 7) x (5 + 3) =72
Step-by-step explanation:
During a search and rescue process after an earthquake, a team rescued 15 people in 5 hours. At this rate, what is the total number of people that the team can rescue in another 2 hours?
Based on the rate that the team is rescuing people per hour, the total number of people that the team can rescue in another two hours is 6 people.
How to find the number of people?First, find the rate at which people are being rescued by the search and rescue team per hour.
The rate of people rescued is:
= Number of people rescued / Number of hours
= 15 / 5
= 3 people per hour
The number of people rescued in 2 hours is:
= Number of hours x People rescued per hour
= 2 x 3
= 6 people
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Tom says, "If you square a number the answer is always bigger". Show Tom is in correct using two different example.
answer
Answer:
Tom is correct.
Step-by-step explanation:
Squaring is equivalent to multiplying a number by itself, ie:
2 squared = 2x2 = 4
6 squared = 6x6 = 36
1*2 + 2*3 + 3*4 + . . . + n(n + 1) = [ (n)(n + 1)(n + 2) ] / 3 whenever n is a positive integer. What is the next term in the sequence for the equation on the left?
P(k + 1) follows, and it is likewise true.
As a result, after demonstrating that P(k) is true for any chosen value of k, we also demonstrated that P(k + 1) is true. According to the induction hypothesis, P(n) is true for all n ∈ Z+
What is mathematical induction ?To demonstrate that the mathematical proposition P(n) holds for all natural integers n = 1, 2, 3, 4,..., one uses the mathematical induction technique. It is frequently referred to as the induction principle in mathematics. We establish that P(1) holds in order to demonstrate a result P(n) using the mathematical induction technique. If P(1) is valid, we can assume that P(k) holds for some natural number k and use this assumption to demonstrate that P(k+1) is valid. The assertion P(n) applies to all natural numbers if and only if P(k+1) holds true.
Let
P(n): 1×2 + 2×3+3×4+........+n(n+1)=[tex]\frac{n(n+1)(n+2)}{3}[/tex]
Putting n =1 we get
P(1):1×2 =2
and
[tex]\frac{1(1+1)(1+2)}{3}=\frac{1(2)(3)}{3} =2[/tex]
Therefore P(1) is true.
Let P(K) is true
So,
P(k): 1×2 + 2×3+3×4+........+k(k+1)=[tex]\frac{k(k+1)(k+2)}{3}[/tex]
Now we have to show that P(k +1 )is also true.
P(k+1): 1×2 + 2×3+3×4+........+k(k+1)+(k+1)(k+2)=[tex]\frac{k(k+1)(k+2)}{3}+ (k+1)(k+2)[/tex]
= (k+1)(k+2)[[tex]\frac{k}{3}+1[/tex]]
=[tex]\frac{(k+1)(k+2)(k+3)}{3}[/tex]
P(k + 1) follows, and it is likewise true.
As a result, after demonstrating that P(k) is true for any chosen value of k, we also demonstrated that P(k + 1) is true. According to the induction hypothesis, P(n) is true for all n ∈ Z+.
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Find the distance between (5, 10) and (8, 10)?
Answer:
3 units
Step-by-step explanation:
3/11 x 4/9 answered in a fraction form
Answer:
4/33
Hopes this helps!
Have a good day :)
The cosine function for a specific angle in a triangle is defined by the ratio of the triangle's
A. adjacent side and hypotenuse.
B. adjacent side and opposite angle.
C. opposite side and hypotenuse.
D. opposite side and adjacent side.
The cosine function for a specific angle in a triangle is defined by the ratio of the triangle's adjacent side and hypotenuse.
This is further explained below.
What is the cosine function?Generally, trigonometric functions are a set of real functions that link the ratios of the lengths of two sides of a right-angled triangle to an angle in the triangle.
They find widespread use in all fields of study that are in some way connected to geometry, including geodesy, solid mechanics, celestial mechanics, navigation, and a great many more.
In conclusion, The ratio of a triangle's adjacent side to its hypotenuse is used to determine the cosine function for a certain angle in the triangle.
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Find the slope of the line that passes through the pair of points.
(5, −1)
and
(−1, −7)
Answer:
The slope is 1.Step-by-step explanation:
Slope:
[tex]\Rightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
y2=(-7)
y1=(-1)
x2=(-1)
x1=5
[tex]\sf{\dfrac{-7-\left(-1\right)}{-1-5}}[/tex]
Solve.
[tex]\sf{\dfrac{-7-\left(-1\right)}{-1-5}=\dfrac{-6}{-6}=\boxed{\sf{1}}}[/tex]
Therefore, the slope is 1, which is our answer.
I hope this helps, let me know if you have any questions.
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 8 times t squared plus 56 times t end quantity over the quantity t squared plus 3 times t plus 2 end quantity comma where the time, t, is hours after injection.
Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points)
Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
(a). The domain of the function C(t) based on the context of the problem is t≥0
(b). The greatest concentration of the medication that a patient will have in their body is 7mg/L
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
(a). C(t) = (-8t² +50t)/(t² + 3t +2 )
The domain of the function :
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is: t≥0
(b).From the graph, the maximum y-value is 7.
Hence, the greatest concentration of the medication is 7mg/L
(a). The domain of the function C(t) based on the context of the problem is t≥0
(b). The greatest concentration of the medication that a patient will have in their body is 7mg/L
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An elliptical-shaped path surrounds a garden, modeled by quantity x minus 22 end quantity squared over 225 plus quantity y minus 26 end quantity squared over 324 equals 1 comma where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent?
The ellipse has 2 axis, the minor and the major axis,
The major axis is denoted in blue color and the minor axis in purple color. By comparing our equation with the general equation of the ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]where the lenght of the major axis is given by
[tex]\text{lenght major axis=2b}[/tex]Fron the given equation, we can note that
[tex]b=\sqrt[]{324}=18[/tex]Therefore, the lenght of the major axis is 36 feet. Therefore, the maximum distance between any two persons is 36 feet corresponding to the major axis, which is option 3 from top to bottom
11:28 AM Wed Jun 15roseacademies.owschools.comASSIGNMENTSCOURSESAssignment - 18. Solving Two-order InequalitiesAttempt 1 of 3SECTION 2 OF 2Solve the inequalities by graphing. Identify the graph that shows the following equations.y> Iy<-xOOOOS2C
The Solution:
GIven:
[tex]\begin{gathered} y>x \\ \\ y<-x \end{gathered}[/tex]We are asked to graph the given inequalities.
Below is the graph of the inequalities:
Thus, the correct answer is [option 1]
ANSWER THE FOLLOWING:
According to the given function,
Domain = [tex]\left(-\infty, -4\right) \cup \left(-4, 2\right) \cup \left(2, \infty\right)[/tex]
Vertical Asymptote = 4
Horizontal Asymptote = 0
X - intercept = No x - intercepts
Y - intercept = 1/4
Domain:
The the domain of a function referred as the set of inputs accepted by the function
Given,
The function is,
[tex]f(x)=\frac{x-2}{x^2+2x-8}[/tex]
Here we need to find the domain, vertical asymptote, horizontal asymptote, x - intercept, and y-intercept.
To find the domain and intercepts, we have to plot the graph for the given function.
So, the graph of the function is attached below. It can be drawn using the graphing calculator.
As per the graph,
Domain = [tex]\left(-\infty, -4\right) \cup \left(-4, 2\right) \cup \left(2, \infty\right)[/tex]
And the values of
x - intercept = No x-intercepts
y - intercept = 1/4
Now, the vertical asymptote is calculated as,
The line x=L is a vertical asymptote of the function f(x), if the limit of the function (one-sided) at this point is infinite.
In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.
So, find the points where the denominator equals 0 and check them.
x = -4
Then,
[tex]\lim_{x \to -4^+} \frac{1}{x + 4}=\infty[/tex]
Since the limit is infinite, then x=−4 is a vertical asymptote.
And the horizontal asymptote is,
Line y=L is a horizontal asymptote of the function y=f(x), if either '
[tex]\lim_{x \to \infty} f{\left(x \right)}=L[/tex] or [tex]\lim_{x \to -\infty} f{\left(x \right)}=L[/tex] and L is finite.
When we calculate the limits:
[tex]\lim_{x \to \infty}\left(\frac{x - 2}{x^{2} + 2 x - 8}\right)=0\\\\\lim_{x \to -\infty}\left(\frac{x - 2}{x^{2} + 2 x - 8}\right)=0[/tex]
Thus, the horizontal asymptote is y=0.
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Calculate the work done when a load of 50N is lifted through a distance of 6m.
The amount of work done when a load of 50 newton is lifted through a distance of 6m is 300 joules.
What is the amount of work done in lifting the load?Work done is simply the energy transfer that takes place when an object is either pushed or pulled over a distance by an external force.
It is expressed as;
Work done = force × distance
Given the data in the question;
Force applied = 50N = 50kgm/s²Distance covered = 6mWork done = ?To determine the work done, plug the given values into the above formula and solve W.
Work done = force × distance
Work done = 50kgm/s² × 6m
Work done = 50kgm²/s² × 6
Work done = 300kgm²/s²
Work done = 300J
Therefore, 300 joules is the work done in lifting the load.
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1. Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bucket of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.
Answer: Do you know the answer to this yet??
Step-by-step explanation:
The equation is 4x + 2y = 45 and The y-intercept is the point (0,22.5) and The x-intercept is the point (11.25, 0)
Given,
Kevin took $45 with him to spend on snack
and, The price for each bucket of popcorn was $4.
To plot the graph
Now, According to the question:
Sketch the graph that represents the situation and label the intercepts
Let,
x ------> the number of bags of popcorn
y -----> the number of drinks.
we know that
The price for each bag of popcorn was $4
The price of each drink was half the price of a bag of popcorn
So, The price of each drink was (1/2)$4 = $2
The total bags of popcorn multiplied by $4 plus the number of drinks multiplied by $2 must be equal $45
The equation that represent this situation is :
4x + 2y = 45 -----(1)
Now, Find the y - intercept form:
The y-intercept is the value of y when the value of x is equal to zero
For, x = 0 put the value of x in equation(1)
4(0) + 2y = 45
2y = 45
y = 22.5
The y-intercept is the point (0,22.5)
That means -----> The number of drinks that Kevin can buy when the number of bags of popcorn is equal to zero
For, y = 0 put the value of x in equation(1)
4x + 2(0) = 45
4x = 45
x = 11.25
The x-intercept is the point (11.25, 0)
That means -----> The number of drinks that Kevin can buy when the number of bags of popcorn is equal to zero
Hence, The equation is 4x + 2y = 45 and The y-intercept is the point (0,22.5) and The x-intercept is the point (11.25, 0)
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Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut butter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn’t think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
4. Suppose one U.S. dollar is equal to 5.8 Egyptian pounds. About
how many Egyptian pounds would you receive for $48.50?
Round to the greatest place value to make it easier to
compute mentally.
5.8
48.50=
X
Multiply.
So, $48.50 is equal to about 9520 Egyptian pounds.
48.50 U.S. dollars = 281 Egyptian pounds
What is a dollar?
The United States dollar (symbol: $; code: USD; often abbreviated US$ or U.S. Dollar to differentiate it from other dollar-denominated currencies; known colloquially as the dollar, U.S. dollar, American dollar, or buck) is the official currency of the United States and numerous other nations. The Coinage Act of 1792 established the United States dollar on equal footing with the Spanish silver dollar, split it into 100 cents, and permitted the minting of coins denominated in dollars and cents. Federal Reserve Notes, generally known as greenbacks owing to their predominately green hue, are the currency of the United States.
Given, 1 U.S. dollar = 5.8 Egyptian pounds
so, 48.50 U.S. dollars = 5.8 x 48.50 = 281.30 Egyptian pounds
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Seven times the sum of a number and 9
is 5
Seven times the sum of a number and 9 is 5 then the number is -58/7 .
A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
We have been given that
Seven times the sum of a number and 9 is 5
Let the number is n.
let's write "the sum of a number and 9"
n + 9 .
Then, "seven times" the sum can be written as:
7 (n + 9)
This "is 5" or "is equal to 5" and can be written as:
7 (n + 9) = 5
To solve, first expand the term in parenthesis on the left side of the equation by multiplying each term in the parenthesis by
(7×n) + (7×9) = 5
7n + 63 = 5
Next, subtract 63 from each side of the equation to isolate the n term while keeping the equation balanced:
7n + 63 - 63 = 5 - 63
7n = -58
Now, divide each side of the equation by 7 to solve for n while keeping the equation balanced:
7n / 7 = -58 / 7
n = -58/7
The number is −58/7.
Hence , the number is -58/7 when a number is seven times its sum and 9 is 5.
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Mark wants to hang for rectangular pictures in a row on a wall so that the horizontal space between each picture is always the same each picture has a length of 8 inches,the wall has a length of 74 inches.if he wants to have 12 inches of horizontal wall space before the first picture and after the fourth picture how much space should he leave between pictures.help with this please
18 inches space should he leave between pictures of the wall with length 74 inches
What is Addition?Addition: Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum.
Mark wants to hang for rectangular pictures in a row on a wall so that the horizontal space between each picture is always the same
Length of each picture is =8 inches
Length of the wall=74 inches
The horizontal wall space before the first picture and after the fourth picture = 12 inches
we are asked to find the space between pictures
12+12+8+8+8+8+x=74
x+56=74
x=18
the distance between the picture is 18 inches
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There are 3 consecutive integers that add up to 33. What are the integers?
Answer:
-33, -12, -11, -10Step-by-step explanation:
The three consecutive integers whose sum is -33 are -12, -11 and -10
Brainlist maybe :)?
How many halves are there in:
1. 51/2
Answer:
0.25.2
Step-by-step explanation:
1.51/2
So,halves
0.25.2
7. Use the quadratic formula to solve for x. a = 2, b = 4 and c = -3
Answer:
[tex]x=\dfrac{-2 + \sqrt{10}}{2}, \quad x=\dfrac{-2 -\sqrt{10}}{2}[/tex]
Step-by-step explanation:
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Given:
a = 2b = 4c = -3Substitute the given values into the formula and solve for x:
[tex]\implies x=\dfrac{-4 \pm \sqrt{4^2-4(2)(-3)}}{2(2)}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{16-8(-3)}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{16+24}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{40}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{4\cdot 10}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm \sqrt{4}\sqrt{10}}{4}[/tex]
[tex]\implies x=\dfrac{-4 \pm 2\sqrt{10}}{4}[/tex]
[tex]\implies x=\dfrac{-2 \pm \sqrt{10}}{2}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{-2 + \sqrt{10}}{2}, \quad x=\dfrac{-2 -\sqrt{10}}{2}[/tex]
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5. CONSTRUCT ARGUMENTS Isabel wrote the expression 6 + 3 x 5 - 6+8+2 and asked Tamara to evaluate it. When Tamara evaluated it, she got a value of 19. Isabel told Tamara that her value was incorrect and said that the value should have been 38.
Who is correct? Justify your argument.
Answer:
none is correct
Step-by-step explanation:
6+3×5-6+8+2
6+15-6+8+2
6+9+10
=25
If f(x) = x^5 + 4x - 5, then what is the remainder when f(x) is divided by
x - 3?
If f(x) = x^5 + 4x - 5, is divided by x - 3 the remainder is 220.
What is a remainder ?
In mathematics, the term "remnant" refers to the amount that is "left over" after performing a calculation. In mathematics, the integer that is left over after dividing two integers to produce an integer quotient is known as the residual (integer division). In algebra of polynomials, the "remainder" is the polynomial that is left over after dividing one polynomial by another. The operation that yields such a remainder when a dividend and a divisor are both present is the modulo operation.
How are functions divided?
Simply multiply or divide the numbers at each point where it makes sense to multiply or divide a function. If the functions are specified by formulas, you can simply multiply or divide the formulas (inserting numbers before or after is irrelevant).
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Write the equation of the line in slope-intercept form. The coefficients in the equation are b=4 and m=-5
Answer:
y = -5x + 4
Step-by-step explanation:
Slope-intercept form of the equation is:
y = mx + b
In the question, we are given m = -5 and b = 4.
Fill in the numbers for m and b.
The m tells you how steep the line is (the slope) And b tells you where the line crosses the y-axis (y-intercept).
Out of 350 applicants for a job, 163 are male and 56 are male and have a graduate degree. Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they are male? Express your answer as a fraction or a decimal rounded to four decimal places.
Probability of a randomly chosen male applicant that has a graduate degree is 28/175.
Total number of applicants for a job= 350
Number of male applicants having a graduate degree = 56
We have to calculate the probability of a randomly chosen applicant that has a graduate degree, given that they are male.
We know ,
Probability = ( Total Number of favorable outcomes) / (Total Outcomes)
probability of a randomly chosen applicant that has a graduate degree, given that they are male = (Number of male applicants having a graduate degree)/ (Total number of applicants for a job) = 56/350 = 28/175
So, the probability of a randomly chosen applicant that has a graduate degree, that has a graduate degree, given that they are male is 28/175.
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For what values of x is the inequality (x-4)² > 0 true?
The values of x must be greater than 4 for the inequality (x-4)² > 0 to be true.
What values make an inequality true?A value that makes an inequality true is the solution to the inequality. There may be more than one way to solve an inequality.The solution set is the collection of all inequality solutions.Given inequality is (x - 4)² >0.
To solve the inequality, take square root on both sides
So, (x - 4) > 0
Adding 4 on both sides,
x > 4
The values of x must be greater than 4 for the inequality to be true.
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Write down equation of lines l and m
ATTACHED IS THE SOLUTION
I’m really confused on this.. help!!
Answers:
x = 108
y = 111/5 = 22.2
========================================================
Explanation:
The angles 72 and x form a 180 degree straight line.
72+x = 180
x = 180-72
x = 108
Angles x and 5y-3 are congruent corresponding angles assuming the lines pointing to the northwest are parallel
5y - 3 = x
5y - 3 = 108
5y = 108+3
5y = 111
y = 111/5
y = 22.2
Answer:
x = 108°
y = 22.2°
Step-by-step explanation:
Angles on a straight line sum to 180°.
[tex]\implies 72^{\circ} + x = 180^{\circ}[/tex]
[tex]\implies 72^{\circ} + x - 72^{\circ} = 180^{\circ} - 72^{\circ}[/tex]
[tex]\implies x = 108^{\circ}[/tex]
Corresponding Angles Theorem
When a straight line intersects two parallel straight lines, the angles in the same relative position are congruent.
Assuming the two lines that appear parallel in the given diagram are parallel:
[tex]\implies (5y - 3)^{\circ} = x^{\circ}[/tex]
[tex]\implies 5y - 3 = 108[/tex]
[tex]\implies 5y - 3 + 3 = 108 + 3[/tex]
[tex]\implies 5y = 111[/tex]
[tex]\implies 5y \div 5 = 111 \div 5[/tex]
[tex]\implies y = 22.2^{\circ}[/tex]