The total interest paid by him to the bank would be: Rs. 28,500. Ram should have waited for 3 years, to start his business without borrowing extra loan, until the age of 19.
What is an interest?
Let the sum deposited by Ram at the age of 16 be x.
After compounding for n years, the balance becomes x(1.1)^n.
As per the given condition, we have:
x*[tex](1.1)^{n}[/tex] = 121x
[tex](1.1)^{n}[/tex] = 121
n = 2
So, after two years, Ram's balance became 121 times the initial principal.
After this, he deposited 1/4 of the existing balance, i.e. 1/4 * 121x = 30.25x
After one year of this deposit, the balance becomes 30.25x * 1.2 = 36.3x
So, Ram's total balance at the age of 19 becomes 121x + 36.3x = 157.3x
This is given to be Rs. 359 less than thrice of the initial principal, i.e.
157.3x = 3x - 359
Solving this equation, we get:
x = Rs. 480
So, the sum deposited by Ram at the age of 16 was Rs. 480.
Now, he borrowed Rs. 1,10,000 at 15% p.a. compounded annually.
The interest for the first year would be (15/100) * 1,10,000 = Rs. 16,500
After paying this interest, the remaining balance becomes:
1,10,000 + 16,500 = Rs. 1,26,500
Now, he cleared his debt by paying equal installments in the next 2 years and 1 year.
Let the equal installment be x.
So, the balance after the first year becomes:
1.15x + (1.15)²x + (1.15)³x - x = 1,26,500
Solving this equation, we get:
x = Rs. 45,000
So, Ram paid a total of Rs. 1,35,000 to clear his debt.
The total interest paid by him to the bank would be:
16,500 + 0.15 * 45,000 + 0.15 * 45,000 + 0.15 * 45,000 = Rs. 28,500
To start his business without borrowing extra loan, Ram should have waited for 3 years, until the age of 19, when his balance was Rs. 157.3x = Rs. 75,264. With an interest rate of 20% p.a. simple interest, the balance would become:
75,264 + 0.2 * 75,264 = Rs. 90,316.8
This amount would be sufficient for him to start his business without borrowing extra loan.
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I need help ASAP PLEASEEEEEEEEE!!!
Answer:
14 units.
Step-by-step explanation:
2(4y - 3) + 2(3y - 1) = 62 Distribute the 2's.
8y - 6 + 6y -2 = 62 Combine like terms
14y -8 = 62 Add 8 to both sides
14y = 70 Divide both sides by 14
y = 5
Now find side QR:
3y - 1
3(5) - 1
15 - 1
14
Helping in the name of Jesus.
Find the measure of the arc or central angle indicated.Assume that lines which appear to be diameters are actual diameters
Answer: What do you mean where is the arc?
Step-by-step explanation:
giving brainlist(for the right answer) ! ⚠
Solve this non linear Second Order Differential Equations,
(but don't use Ai) I know if it's from there
The general solution to the differential equation is M = (1/2)n² + Bn, where B is an arbitrary constant.
Describe Differentiation?In calculus, differentiation is a process of finding the rate at which a function changes with respect to its input variable. It is the process of finding the derivative of a function, which represents the slope of the tangent line to the graph of the function at a given point.
The derivative of a function f(x) at a point x=a is denoted as f'(a) and is defined as the limit of the difference quotient as the interval between a and a+h approaches zero, where h is a small nonzero number.
The process of differentiation involves applying differentiation rules or formulas, which are a set of rules that make it easier to find the derivative of various functions. Some of the common rules include the power rule, product rule, quotient rule, and chain rule.
To solve the given differential equation:
[tex]\frac{d^{2}M }{dn^{2} } + 2n\frac{dM}{dn} =n[/tex]
We can assume a solution of the form:
[tex]M= An^{p}[/tex]
where A and p are constants to be determined.
Taking the first derivative of M with respect to n, we get:
[tex]\frac{dM}{dn} = Apn^{p-1}[/tex]
Taking the second derivative of M with respect to n, we get:
[tex]\frac{d^{2}M }{dn^{2} }= A(p)(p-1)n^{p-2}[/tex]
Substituting these expressions into the original differential equation, we get:
[tex]A(p)(p-1)n^{p-2} + 2Apn^{p-1}= n[/tex]
Simplifying, we get:
[tex]A(p)(p-1)n^{p-2} + 2Apn^{p}=n^{p+1}[/tex]
Since this equation must hold for all values of n, we can equate the coefficients of each power of n to get two equations:
A(p)(p-1) = 0
2Ap = 1
From the first equation, we get:
p = 0 or p = 1
If p = 0, then M = A, a constant. Substituting into the differential equation, we get:
0 = n
This is not true for all values of n, so p cannot be 0.
If p = 1, then M = An. Substituting into the differential equation, we get:
2An + 2nA = n
Simplifying, we get:
A = 1/2
Therefore, the solution to the differential equation is:
M = (1/2)n² + Bn
where B is a constant of integration.
Thus, the general solution to the differential equation is:
M = (1/2)n² + Bn
where B is an arbitrary constant.
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I need an answer to this,
Answer:
use what u learn from the teacher
Help with question please
A graph of the image of ABC under a dilation whose center is P and scale factor is 2 is shown in the image below.
What is dilation?In Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape.
In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 2 centered at P.
Based on the image (see attachment), we can logically deduce that each vertex is 2 times as far from center P as the original vertex and each segment is 2 times as long as the original:
Side length A'C' = 8.2 × 2 = 16.4
Side length A'B' = 5.0 × 2 = 10.0
Side length B'C' = 5.8 × 2 = 11.6
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significant figure of 9,876 ,540,000
Answer:
The number you provided is **9,876 ,540,000**. The significant figures of this number are **10**¹.
The trailing zeros in this number are not significant, so they do not count toward the total number of significant figures
rosa has a limit to the time she may play video games each day she plays for 9 mins on monday which is 30% of the time she can play how many more minutes can rosa play on monday?
According to the calculations we can conclude that Rosa can play 21 more minutes on Monday.
If 9 minutes represents 30% of the time Rosa can play video games, we can use proportional reasoning to find the total time she can play. Let x be the total time she can play in minutes.
9 / x = 30 / 100
We might cross-multiply and simplify to find x's value:
9 * 100 = 30 * x
900 = 30x
x = 900 / 30
x = 30
So Rosa can play a total of 30 minutes each day.
To find how many more minutes she can play on Monday, we subtract the time she has already played from the total time:
30 - 9 = 21
Therefore, Rosa can play 21 more minutes on Monday.
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Can anyone helppppppp look at picture
The graph of the original triangle and the after the dilation are shown below:
Triangle dilation graph 8.
What is dilation?Dilation refers to the process of expanding or stretching an object or a space in one or more directions. In mathematics, dilation is a geometric transformation that changes the size of an object or a figure by either enlarging or reducing its dimensions, while preserving its shape and orientation.
In the context of image processing and computer vision, dilation is an operation that is commonly used to enhance and extract features from images. It involves convolving an image with a small structuring element or kernel, which slides over the image and replaces each pixel with the maximum value within the kernel.
For a dilation with a scale factor of 0.5 and centered at the origin, each coordinate of the triangle will be multiplied by 0.5. Thus:
J(8,0) will become J'(4,0)
L(-2,0) will become L'(-1,0)
K(4,4) will become K'(2,2)
The graph of the original triangle and the image after the dilation are shown below:
Triangle dilation graph 6
For a dilation with a scale factor of 2 and centered at the point (8,3), each coordinate of the triangle will be multiplied by 2 and then translated by the vector (8,3). Thus:
A (9,8) will become A'(26,14)
C (0,2) will become C'(8,7)
G (3,3) will become G'(14,9)
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What happens to the surface area of a rectangular prism if you double one dimension? Let's create several examples and see if a pattern emerges.
Let's take a look at Karen's post.
My rectangular prism has sides of 8 units, 6 units, and 5 units. To find the total surface area of the prism, I have to find the area of each face of the prism. There are two faces that have an area of 8(5) = 40 units2, two that have an area of 6(5) = 30 units2, and two that have an area of 8(6) = 48 units2. Adding all the areas I get the surface area is 236 units2.
If the smallest side is doubled the dimensions would be 8 units, 6 units, and 10 units. There are two faces that have an area of 8(10) = 80 units2, two that have an area of 6(10) = 60 units2, and two that have an area of 8(6) = 48 units2. Adding all the areas I get the surface area is 376 units2.
The surface area increased by 140 units2 or a factor of about 1.6.
Now it's your turn.
Come up with a set of dimensions for a rectangular prism, and calculate its surface area.
Double one of the dimensions of your prism. List the new set of dimensions, and find the new surface area.
Describe how doubling one of the dimensions affects the surface area.
Look at your classmates' posts. Add a response to one of the posts stating any patterns you noticed in the calculations of all your classmates, and the effect of doubling on dimension on the surface area.
Use the discussion rubric to see how you will be graded.
Answer:
All you need to do now is plug the numbers in and use the right units.
Step-by-step explanation:
Karen and Wayne need to buy a refrigerator because theirs just broke. Unfortunately, their savings account is depleted, and they will need to borrow money in order to buy a new one. Sears offers them an installment loan at 14% (add-on rate). If the refrigerator at Sears costs $1,598 plus 5% sales tax, and Karen and Wayne plan to pay for the refrigerator for 3 years, what is the monthly payment? (Round your answer to the nearest cent.)
Karen and Wayne will need to make monthly payments of $66.39 for 3 years to pay off the loan for their new refrigerator for a given sales tax.
The add-on interest loan formula can be used to determine the monthly payment:
(Loan amount + Interest) / the number of payments equals a payment.
We must first determine the refrigerator's total cost, including sales tax:
Final price is $1,598 plus 5% of $1,598.
$1,677.90 is the total price.
Secondly, we must determine the loan's interest rate:
Interest is calculated as Loan Amount * Addition Rate. Ages in years
Interest equals $702.25 when $1,677.90 multiplied by 0.14 by three.
When interest is included, the total loan amount is:
Loan amount = Purchase price plus interest
Total of the loan: $1,677.90 plus $702.25
Amount borrowed: $2,380.15
In the end, we can figure out the monthly payment:
Payment: ($2,380.15) divided by (3 years * 12 months/year) =
monthly payment of $66.39
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Jane and Rob go to the local cafe to have breakfast. A single chocolate muffin has 290 calories, and a blueberry muffin has 270 calories. Both muffins can be bought at the local cafe. The fruit platter has 190 calories and the french toast has 350 calories. A glass of orange juice is 40 calories and milk is 102 calories. The hashbrowns and eggs have twice the calories of the fruit platter. Jane has half a blueberry muffin with a whole fruit platter and a third of a glass of milk for breakfast. Rob has hash browns and eggs with a half glass of orange juice.
What was the smaller amount of total calories consumed, between Jane and Rob? Round to the nearest whole calorie. Do not include units in your answer. For example, if the answer is 19 calories, put 19.
The smaller amount of total calories consumed is 359 calories.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a broad area of study that includes a wide range of topics, such as equations, inequalities, functions, polynomials, matrices, and more.
Algebraic expressions are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations, on the other hand, are mathematical statements that assert the equality of two algebraic expressions. Inequalities are mathematical statements that assert the relationship between two algebraic expressions using the symbols "<", ">", "<=", or ">=".
Functions in algebra are mappings from one set of numbers to another set of numbers that obey certain rules. These rules may involve properties such as continuity, differentiability, and invertibility.
Jane consumes:
Half a blueberry muffin: 0.5 * 270 = 135 calories
Whole fruit platter: 190 calories
A third of a glass of milk: (1/3) * 102 = 34 calories
So her total calorie intake is: 135 + 190 + 34 = 359 calories (rounded to the nearest whole calorie).
Rob consumes:
Hashbrowns and eggs: 2 * 190 = 380 calories
Half a glass of orange juice: 0.5 * 40 = 20 calories
So his total calorie intake is: 380 + 20 = 400 calories.
Therefore, the smaller amount of total calories consumed is 359 calories.
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When 18 liters of oil were poured out, the oil level went down by 90 %. How much oil was in the tank at first?
Find the missing side lengths. Leave your answers and radicals in the simplest form.
Answer:
x = 6;
y = 3√3
Step-by-step explanation:
Use trigonometry:
[tex] \ \cos(60°) = \frac{3}{x} [/tex]
Use the property of proportion to find x:
[tex]x = \frac{3}{ \cos(60°) } = \frac{3}{0.5} = 6[/tex]
Use the Pythagorean theorem to find y:
[tex] {y}^{2} = {x}^{2} - {3}^{2} [/tex]
[tex] {y}^{2} = {6}^{2} - {3}^{2} = 36 - 9 = 27[/tex]
[tex]y > 0[/tex]
[tex]y = \sqrt{27} = \sqrt{9 \times 3} = 3 \sqrt{3} [/tex]
Which of the following statements is NOT true? (graph in the picture)
The slope of the line of best fit is 4,744.
The y-intercept of the line of best fit is 9,994.
The slope of the line of best fit means that the value of the house increased
$4,744 each year.
The y-intercept of the line of best fit means that it cost $9,994 to build the house.
The statement that is NOT true is: "The y-intercept of the line of best fit means that it cost $9,994 to build the house."
Hi! Based on the given information and without a visual of the graph, I will provide a general answer using the terms provided. Please note that an accurate response may require additional information or context.
The slope of the line of best fit indicates the rate of change in the value of the house over time, and a positive slope signifies that the value has increased. However, the y-intercept of the line of best fit does not necessarily mean that it cost $9,994 to build the house.
The y-intercept represents the estimated value of the house when the independent variable (usually time) is zero, but it does not account for factors like construction costs, inflation, or changes in the real estate market.
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A computer science teacher wants to show how many lines of code each of her students wrote for a specific assignment. She thought about using a box plot, but in the end she used a line plot. What is the most likely explanation for her choice?
Answer:
Step-by-step explanation:
She chose a line plot because it is an easier way to display the amount of students and how many lines of code they each wrote. That way on a line plot, it displays the number of students, and the frequency amount of times the same number of lines of code were written.
Several friends each want to buy a ticket to a football game that costs $75.99. To earn money, they worked extra hours at their job where they each earn $9.10 per hour. The table shows the number of hours each person worked each day. Who earned enough money to buy a ticket? What inequality can you write to represent this situation?
Total earnings < Ticket cost, this inequality represents this situation.
What is inequality ?
The inequality, A declaration of relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Equations and questions can both be used to formulate and answer inequality problems.
How to solve inequalities statements?Write two values being compared in the problem in step one. Decide the first value is greater or less than the second value in step two.In step third Insert inequalities symbol between the first and second values if the first value is greater than the second.
We calculate who earned enough money to buy a ticket,than need to calculate the total amount earned by each friend.
For the total amount earned by each friend by multiplying the number of hours worked by hourly rate,
In Friend 1; 5 hours x $9.10 per hour = $45.50
In Friend 2; 4 hours x $9.10 per hour = $36.40
In Friend 3; 7 hours x $9.10 per hour = $63.70
In Friend 4; 3 hours x $9.10 per hour = $27.30
In Friend 5; 6 hours x $9.10 per hour = $54.60
If each friend earned enough money to buy a ticket, than need to compare their total earnings to the cost of a ticket =$75.99. That is, Total earnings ≥ Ticket cost
Now ,substitute their total earnings for each friend,
In,Friend 1; $45.50 ≥ $75.99 that is Not enough money
In Friend 2; $36.40 ≥ $75.99 that is Not enough money
In Friend 3; $63.70 ≥ $75.99 that is Not enough money
In Friend 4; $27.30 ≥ $75.99 that is Not enough money
In Friend 5; $54.60 ≥ $75.99 that is Not enough money
Nobody of friends earned enough money to buy a ticket,
therefore ,Total earnings < Ticket cost.
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Cam anyone answer these 4 questions?
Answer:
The first one is correct
Step-by-step explanation:
ITs all good
In 2019, the average high school GPA for incoming University of Maryland freshman was 4.32 with a standard deviation of 0.285. Suppose UMD freshman are randomly assigned into groups of 25.
What is the standard deviation of the sampling distribution of all samples like this:
Give the formula with values that you entered in your calculator as a way of showing your work:
The standard deviation of the sampling distribution of all samples is 0.057.
What is the standard deviation?
The standard deviation is a measurement of how much a group of values vary or are dispersed. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Here, we have
Given: In 2019, the average high school GPA for incoming University of Maryland freshmen was 4.32 with a standard deviation of 0.285. Suppose UMD freshmen are randomly assigned into groups of 25.
We have to find the standard deviation of the sampling distribution of all samples.
Let x = High-school GPA scores of students in 2019.
E(x) = 4.32, S.D(x) = 0.285, n = 25
Suppose we consider the sampling distribution of the sample mean of all these samples, then we have
E(x) = 4.32
S.D(x) = 0.285/√25
= 0.057
Hence, the standard deviation of the sampling distribution of all samples is 0.057.
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Prove the following: in a group [tex]G[/tex],[tex](a^{m})^{n}=a^{mn}[/tex], for all [tex]a\in G[/tex] and [tex]m,n\in \mathbb{Z}[/tex]?
we have shown that [tex]$(a^m)^n = a^{mn}$[/tex] for all [tex]$a \in G$[/tex] and [tex]$m, n \in \mathbb{Z}$[/tex].
How to prove the given Problem?To prove that in a group G, [tex]$(a^m)^n = a^{mn}$[/tex] for all [tex]$a \in G$[/tex] and [tex]$m, n \in \mathbb{Z}$[/tex], we need to show that both sides of the equation are equal.
We start by simplifying the left-hand side:
[tex]$(a^m)^n = a^{mn}$[/tex]
This is because raising a to the power of m and then to the power of n is the same as raising a to the power of mn. This property is known as the associative property of exponents.
Next, we need to show that the right-hand side of the equation is also equal to [tex]$a^{mn}$[/tex]:
[tex]$a^{mn} = a^{nm}$[/tex]
This is because multiplication is commutative in [tex]$\mathbb{Z}$[/tex], which means that [tex]$mn = nm$[/tex]
Therefore, we have shown that [tex]$(a^m)^n = a^{mn}$[/tex] for all [tex]$a \in G$[/tex] and [tex]$m, n \in \mathbb{Z}$[/tex].
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64. A polyhedron has 4 vertices and 4 faces. How
many edges does the polyhedron have?
(F) 4
(G) 5
(H) 6
(J) 8
(K) 16
Answer:
(H)
Step-by-step explanation:
Recall that [tex]V-E+F=2[/tex].
Setting [tex]V=F=4[/tex] yields [tex]E=6[\tex].
Luna's pet miniature pig, Fiona, weighed 50 pounds at her one-year check-up. Based on her
weight at an earlier check-up, the vet had predicted Fiona would weigh 6% more than that.
What weight had the vet predicted for Fiona?
Need help factoring each expressions
Answer:
a. factors of 3x²-7x-6 =(x-3) and (3x+2)
b factors of 4x²-49=(2x-7) and (2x+7)
a boat is tied to a dock using 2 ropes. what is the length of rope A?
Solve the systems by substitution.
-y=x
-16=9x-7y
Answer: The solution to the system of equations by substitution is (x, y) = (-1, 1).
Step-by-step explanation:
Find the x-coordinate where the graph of the function f of x equals e raised to the power of negative 1 times x squared has a slope of 0.
There is no x-coordinate where the graph of the function [tex]f(x) = e^{-x^{2}}[/tex] has a slope of 0. However, the best answer would be (A) 0.
If the prisms below are similar, what is the ratio of the height of the smaller prism to the height of the larger prism? V = 15 cm3 V = 405 cm3
The ratio of the height of the smaller prism to the height of the larger prism is 1:sqrt(27).
what is prism?
A prism is a geometric solid that has two parallel and congruent polygonal bases, and the sides connecting the bases are parallelograms. These parallelograms are typically rectangles, but they can also be squares or rhombuses. A prism can be named based on the shape of its base, such as a rectangular prism, triangular prism, hexagonal prism, etc.
Since the prisms are similar, their corresponding sides are proportional. In particular, the ratio of the heights of the prisms is the same as the ratio of their volumes.
Let the height of the smaller prism be h1 and the height of the larger prism be h2. Let the volume of the smaller prism be V1 = 15 cm^3 and the volume of the larger prism be V2 = 405 cm^3. Then:
V1/V2 = (h1^2 * 5) / (h2^2 * 5)
V1/V2 = h1^2 / h2^2
sqrt(V1/V2) = h1 / h2
Substituting the given values, we get:
sqrt(15/405) = h1 / h2
sqrt(1/27) = h1 / h2
1/sqrt(27) = h1 / h2
Therefore, the ratio of the height of the smaller prism to the height of the larger prism is 1:sqrt(27), or approximately 1:5.2.
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What will be the new position of the given point (-4,-3) after rotating 180° about the origin?
Answer:
(4,3)
Step-by-step explanation:
The rule (x,y) → (-x, -y)
Helping in the name of Jesus.
eight x equals two thirds
Answer:
x = [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
8x = [tex]\frac{2}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
24x = 2 ( divide both sides by 24 )
x = [tex]\frac{2}{24}[/tex] = [tex]\frac{1}{12}[/tex]
2x22222222222222222222222222222222222222
Answer:
=4.44444444×10UP38
Step-by-step explanation:
that is your answer:)
HELP I NEED THIS ANSWERED PORFAVOR
Answer:
3) x = 19
4) x = 4
Step-by-step explanation:
3) Co interior angles are supplementary.
6x - 30 + 96 = 180
Combine like terms,
6x + 66 = 180
Subtract 66 from both sides,
6x = 180 - 66
6x = 114
Divide both sides by 6,
x = 114 ÷ 6
[tex]\boxed{\bf x = 19}[/tex]
4) When two lines are intersected by a transversal, alternate exterior angles are equal.
7x + 5 = 33
Subtract 5 from both sides,
7x = 33- 5
7x = 28
Divide both sides by 7,
x = 28 ÷ 7
[tex]\boxed{\bf x = 4}[/tex]
The angles and their converse are:
a) ∠9 ≅ ∠22
Parallel lines: q and r.
Converse: if two lines are parallel, then their corresponding angles are congruent.
b) m∠8 + m∠13 = 180
Parallel lines: p and q.
Converse: if two lines are parallel, then their supplementary angles sum up to 180°
c) ∠1 ≅ ∠17
Parallel lines: p and r.
Converse: if two lines are parallel, then their corresponding angles are congruent.
d) ∠16 ≅ ∠20
Parallel lines: q and r.
Converse: if two lines are parallel, then their alternate angles are congruent.
e) m∠2 + m∠22 = 180
Parallel lines: p and r.
Converse: if two lines are parallel, then their supplementary angles sum up to 180°
f) ∠10 ≅ ∠13
No lines are parallel.
Converse: if two angles in a quadrilateral are adjacent then they are said to be congruent.
g) ∠5 ≅ ∠15
Parallel lines: p and q.
Converse: if two lines are parallel, then their opposite angles are congruent.
h) m∠2 + m∠16 = 180
Parallel lines: p and q.
Converse: if two lines are parallel, then their supplementary angles sum up to 180°
How to find the missing angles?a) ∠9 ≅ ∠22
The parallel lines for this to be true are lines q and r.
Converse is if two lines are parallel, then their corresponding angles are congruent.
b) m∠8 + m∠13 = 180
The parallel lines for this to be true are lines p and q.
Converse is if two lines are parallel, then their supplementary angles sum up to 180°
c) ∠1 ≅ ∠17
The parallel lines for this to be true are lines p and r.
Converse is if two lines are parallel, then their corresponding angles are congruent.
d) ∠16 ≅ ∠20
The parallel lines for this to be true are lines q and r.
Converse is if two lines are parallel, then their alternate angles are congruent.
e) m∠2 + m∠22 = 180
The parallel lines for this to be true are lines p and r.
Converse is if two lines are parallel, then their supplementary angles sum up to 180°
f) ∠10 ≅ ∠13
No lines are parallel.
Converse is if two angles in a quadrilateral are adjacent then they are said to be congruent.
g) ∠5 ≅ ∠15
The parallel lines for this to be true are lines p and q.
Converse is if two lines are parallel, then their opposite angles are congruent.
h) m∠2 + m∠16 = 180
The parallel lines for this to be true are lines p and q.
Converse is if two lines are parallel, then their supplementary angles sum up to 180°
3) The co interior angles are supplementary.
Thus:
6x - 30 + 96 = 180
6x + 66 = 180
Subtract 66 from both sides,
6x = 180 - 66
6x = 114
Divide both sides by 6,
x = 24
4) When two lines are intersected by a transversal, the alternate exterior angles are equal.
7x + 5 = 33
Subtract 5 from both sides,
7x = 33- 5
7x = 28
Divide both sides by 7,
x = 4
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