The largest angle of the triangle is ∠C = 66°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
Now , the measure of ∠A = measure of ∠B = x
And , the measure of ∠C = measure of ∠A + 9°
Substituting the values in the equation , we get
x + x + ( x + 9 ) = 180
On simplifying the equation , we get
3x + 9 = 180
Subtracting 9 on both sides of the equation , we get
3x = 171
Divide by 3 on both sides of the equation , we get
x = 57°
So , the measure of ∠A = 57°
Now , the measure of ∠C = 57 + 9 = 66°
Hence , the measure of ∠C of triangle is 66°
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210 people are asked how many siblings they have?
# of Siblings Frequency Relative Frequency Cumulative Frequency
43
43
41
0
1
2
3
4
43
Submit Question
0.2048
0.2048
0.2048
0.1905
43
86
127
210
a. Complete the table (Use 4 decimal places when applicable)
b. What percent of the people have exactly one sibling?
Hint: Frequency Tables
The frequency table is completed and the percent of the people who have exactly one sibling is 20.48%.
What is Relative Frequency and Cumulative Frequency?Relative frequency is found by dividing the frequency with the total number of values.
Cumulative frequency is calculated by adding the previous frequencies together.
(a) From the table,
Total number of people = 210
So, Total frequency = 210
Frequency of number of siblings as 4 = 210 - (43 + 43 + 41 + 43) = 40
Relative frequency = Frequency / Total frequency
Relative frequency of number of siblings as 2 = 0.1952
Cumulative frequency of number of siblings as 3 = 127 + 43 = 170
(b) Percent of people having exactly 1 sibling = (43 / 210) × 100
= 20.48%
Hence the percent of people having exactly 1 sibling is 20.48%.
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Solve the equation
below. Show all of your
work.
20= m÷-5
Answer:
The solution to the equation 20 = m ÷ -5 is m = -100
To see this, we can multiply both sides of the equation by -5 to isolate the variable m:
20 × -5 = m ÷ -5 × -5
Expanding the right side of the equation:
20 × -5 = m × 1
Combining like terms:
-100 = m
And the solution is:
m = -100
Verification:
To verify the solution, we can plug in the value of m back into the original equation and see if it is true:
20 = -100 ÷ -5
Expanding -100 ÷ -5:
20 = 20
Since 20 = 20 is a true statement, we have verified that the solution m = -100 is correct.
Find the area of the trapezoid.
14 mm
15 mm
36 mm
1. 270 mm²
2. 375 mm²
3. 750 mm²
5. 3780 mm²
Answer: no one cares
Step-by-step explanation:
because it's to hard[tex]\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \left \{ {{y=2} \atop {x=2}} \right. x_{123} \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx \left \{ {{y=2} \atop {x=2}} \right. \sqrt{x} \sqrt{x} \sqrt{x} \alpha \pi x^{2} x^{2} x^{2} \\ \\ \neq \pi \pi 5069967.94389438.494898 that's the answer[/tex]Which equation represents a nonlinear function?
Answer:
A nonlinear function is a function in which the rate of change of the output (y) is not proportional to the rate of change of the input (x). In other words, a nonlinear function is a function where the graph of the function is not a straight line.
Here are a few examples of equations that represent nonlinear functions:
y = x^2: This is the equation for a parabolic function, which is a classic example of a nonlinear function.
y = sin(x): This is the equation for the sine function, which is periodic and nonlinear.
y = |x|: This is the equation for the absolute value function, which is nonlinear and has a "kink" at x = 0.
y = log(x): This is the equation for the natural logarithmic function, which is also nonlinear.
These are just a few examples of nonlinear functions. There are many other types of nonlinear functions, including polynomial, exponential, and trigonometric functions.
When sales representatives for a pharmaceutical company drive to out-of-town meetings that require an overnight stay, they receive $140 for lodging plus $0.60 per mile driven. How many miles did Joe drive if his company reimbursed him $290 for an overnight trip?
Question content area bottom
Part 1
The equation is enter your response here. Joe drove enter your response here miles.
(Type an equation using x as the variable.)
solve for equation and miles Joe drove
Joe was given $329 for an overnight trip because he drove a distance of 220 miles
How to solve Word Problems ?
Five Easy Steps to Solving Word Problems (WASSP)
Write (or draw) what you know.Ask the question.Set up a math problem that could answer the question.Solve the math problem to get an answer.Put the answer in a sentence to see if the answer makes sense!Given Data
Amount rep receive = $175
Added amount per mile driven = $0.70
Reimbursed/Total = $329
The Mathematical relation for this scenario is
Total amount = Amount Receive+ 0.7*Distance driven
let the distance driven be x
Substituting our given data into the relation we have
329= 175+ 0.7*x
329-175 = 0.7x
154 = 0.7x
divide both sides by 0.7
x = 154/0.7
x = 220miles
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guysss solve this
there are "6" eggs layed on the table
I break "2" of them
I cooked "2" of them
I ate "2" of them
how many eggs did they left?
Answer:
Step-by-step explanation:
4.
first, you broke the 2 eggs, and then cooked the eggs. after cooking them, you ate the two eggs that you cracked and cooked.
The ratio of domestic cars to imported cars in the lot at Al’s Auto Shop is 3 : 2. There are 42 domestic cars in the shop. How many cars are there altogether?
There are 70 cars altogether in the lot.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of domestic cars to imported cars = 3 : 2,
Domestic cars = 42
Since, the number of domestic cars in the shop is 42,
Therefore,
3x = 42
x = 14
Therefore, the number of total cars = 14×5 = 70
Hence, there are 70 cars altogether in the lot.
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Find the value of x
Answer:8
Step-by-step explanation:
Because Angle GJH is 90 degrees, Angle HJZ is also 90 degrees. (Because all right angles are 90 degrees)
Now, find Angle WJZ
90 - 18 = 72 degrees
By the Vertical Angles Theorem, Angle GJL is congruent to Angle ZJW
Now solve for x
72 = 9x
x = 8
Put the equation y=x^2-8x+12 into the form y= (x-h)^2+k
Answer:
y = ( x - 4 )² - 4
Step-by-step explanation:
a² ± 2ab + b² = ( a ± b )²
~~~~~~~~~~~~
y = x² - 8x + 12
y = ( x² - 2(4)(x) + 4² ) - 4² + 12 = ( x - 4 )² - 4
y = ( x - 4 )² - 4
Calvin will plant lily bulbs and iris bulbs in his front garden. He will plant a total of flower bulbs and as many iris bulbs as lily bulbs. The graph below shows the number of lily bulbs (x) and the number of iris bulbs (y) Calvin will plant. Bulbs to Be Planted Which statement describes the point of intersection on the graph?
A. Calvin will plant lily bulbs.
B. Calvin will plant iris bulbs.
C. Calvin will plant lily bulbs and iris bulbs.
D. Calvin will plant lily bulbs and iris bulbs. Lily Bulbs
The statement that describes the point of intersection on the graph is Calvin will plant lily bulbs and iris bulbs. Option C
What is point of intersection of a graph?The point of intersection on the graph represents the values of x and y where both conditions are satisfied.
In this case, the point of intersection represents the number of lily bulbs (x) and the number of iris bulbs (y) that Calvin will plant such that the number of iris bulbs is equal to the number of lily bulbs.
So, the correct statement that describes the point of intersection on the graph is "Calvin will plant lily bulbs and iris bulbs".
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1. Fill in the missing Statement/Reason for the following proof:
Given: LN bisects ZMLO and LM = LO
Prove: ALMN = ALON
M
STATEMENT
1.
2.
3.
4. LN = LN
5.
ALMN a ALON
REASON
N
1.
2.
3. def of Angle Bisector
4.
5.
| I
The completed proof that demonstrates that: ΔLMN ≅ ΔLON is:
LN Bisects ∠MLO; and LM ≅ LO [Given]∠MNL ≈ ∠ONL = 90° [Definition of Angle Bisector]LN ≅ LN [Definition of Reflexive Property]; ThusΔLMN ≅ ΔLON [AAS Postulate]What is the Angle-Angle-Side Postulate (AAS)?The Angle-Angle-Side Postulate (AAS) is a rule used in geometry to prove that two triangles are congruent. It states that if two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the two triangles are congruent.
The reflexive property of equality in algebra asserts that a number is always equal to itself. Equality has a reflexive attribute. If x positive integer, then x = x.
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Why we use Permutation to find the number of ways of something can be arranged when order matters. While use Combination when order does not matter.
The permutation formula is used when the order matters as it does not remove the combinations with the same elements and different order from the equation.
For the combination formula, the term x! is removed, as it removes all the combinations with the same elements but different order.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
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A rancher raises milking cows and goats which he feeds with two types of mixes, type x and type y. Each bag of type x costs P400 and contains 100 units of calcium and 400 units of protein; each bag of type y costs P600 and contains 200 units of calcium and 200 units of protein. The livestock need a minimum of 6,000 units of calcium and 12,000 units of protein per day. What combination of mixes should the rancher buy to minimize daily feed cost?
The combination should be 20 of Brand A and 20 of Brand B.
What is Linear Programming?When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
Given:
Each bag of type x costs P400 and contains 100 units of calcium and 400 units of protein.
Each bag of type y costs P600 and contains 200 units of calcium and 200 units of protein.
So, Max Z = 400x + 600 y
Constraints:
100x + 200 y ≤ 6000
or, 400x + 200y ≤ 12000
Solving the Equation:
300x = 6000
x= 20
and, y= 20
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(8)
Amelia wanted to redeem a voucher. She had only 3/5of the total number
of points needed. After she earned another 50 points, she still needed 3/10
of the total number of points. How many points were needed to
redeem the voucher?
Answer:
The number of points needed to redeem the voucher is 92.5
Step-by-step explanation:
Let x be the total number of points needed to redeem the voucher.
Amelia has [tex]\frac{3}{5}[/tex] × x points,before she earns the another 50 points,
After she earns another 50 points,
Now
she has [tex]\frac{3}{5}[/tex] × x + 50 points.
she still needs [tex]\frac{3}{10}[/tex] × x points to redeem the voucher.
Now
From above we get a equation,
[tex]\frac{3}{5}[/tex] × x + 50 = [tex]\frac{9}{10}[/tex] × x
Solving the equation we can get x,
[tex]\frac{3}{5}[/tex] × x = [tex]\frac{9}{10}[/tex] × x - 50
if we multiply both sides by 5/3, we get,
x = (9/10 × x - 50) × 5/3
After expanding the right side,
x = (9/10 × x - 50) × 5/3
x = (9x/10 - 250/3)
Now,
Subtracting 9x/10 from both sides,
0 = 250/3 - 9x/10
If we add 9x/10 to both sides,
9x/10 = 250/3
Again,
If we multiply both sides by 10/9,
x = 250/3× 10/9
x = 250 × 10 / (3 × 9)
x = 250 × 10 / 27
x = 250 × 10 / 27
x = 250 × 10 / 27
x = 250 × 10 / 27
= 250 × .37
x = 92.5
The number of points needed to redeem the voucher is 92.5
The sum of two numbers is 42. The smaller number is 16 less than the larger number. What are the numbers?
Larger number:
Smaller number:
Answer:
Larger number: 29
Smaller number: 13
Step-by-step explanation:
29 + 13 = 42
29 - 16 = 13
Answer:
Larger number: 29
Smaller number: 13
Step-by-step explanation:
x = larger number
y = smaller number
x+y=42
29-13 = 16
29+13=42
Find the equation for the line through the point (7/5,1/12) that is perpendicular to the line 3x-4y=7. You may leave your answer in the point-slope form if you wish. If you use slope-intercept form, all fractions must be combined and reduced wherever possible.
The equation of the line is (y - 1/12) = -4/3(x - 7/5).
What is the slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.
Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be depicted by
tan θ = Δy/Δx
So, the slope of a line is tan.
The given equation of a line is:
3x-4y=7
-4y = -3x + 7
y = 3/4 x - 7/4
The slope of the line is 3/4.
The slope of the line perpendicular to the given line is - 1/m = - 4/3
The point-slope of a line is y - y₁ = m(x - x₁).
The given point is (7/5,1/12)
The equation of the line is
(y - 1/12) = -4/3(x - 7/5)
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ill give brainliest to whoever can answer
Robert uses f(x) = 1000(1.06)^x to calculate the interest he earns each year for his savings account. What is the yearly interest rate as a percent?
A, B, C and D are four towns.
B is 40 kilometres due East of A.
C is 40 kilometres due North of A.
D is 65 kilometres due South of A.
a) Work out the bearing of B from C.
135
b) Calculate the bearing of D from B.
Answer
+
G
a) The bearing of B from C is; 45° South-East.
b) The bearing of D from B is; 58.39° South Of West
How to calculate the bearing?a) Distance Between B and C is;
BC = √( 40² + 40²)
= 40√2
= 56.57 km
Angle of B from C = Tan⁻¹( 40/40) = 45°
Bearing of B From C = 45° South Of East
Or 90 - 45° = 45°
45° East of South
Thus, that is the bearing of B from C
b) Distance Between B and D is;
BD = √(40² + 65²)
= 76.32 km
Angle of D from B = Tan⁻¹( 65/40)
= 58.39 °
Bearing of D From B = 58.39° South Of West
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Carlos had $400. He decided to spent 40% of it on clothes, and 50% of the remaining money on video games. How much money did Carlos spend? How much does Carlos have left?
Answer:
Step-by-step explanation:
We can start by finding how much money Carlos spent on clothes. To do this, we simply multiply the original amount of $400 by 40%:
Clothes = $400 * 40% = $400 * 0.40 = $160
Next, we find how much money Carlos has left after spending on clothes. To do this, we subtract the amount spent on clothes from the original amount:
Remaining Money = $400 - $160 = $240
Finally, we find how much money Carlos spent on video games. To do this, we multiply the remaining money by 50%:
Video Games = $240 * 50% = $240 * 0.50 = $120
So, in total, Carlos spent $160 on clothes and $120 on video games, for a total of $160 + $120 = $280.
And Carlos has $400 - $280 = $120 left.
After spending 40% of the $400 on clothes, Carlos has $400 x (100 - 40) / 100 = $240 left.
Next, he spent 50% of the remaining $240 on video games, which is $240 x 50 / 100 = $120.
Therefore, Carlos spent a total of $400 - $240 = $160.
Finally, Carlos has $240 - $120 = $120 left.
0.5(1.2)^x percentage
Answer:
20%
Step-by-step explanation:
1 + r = 1.2 = 1 + 0.2 = 1 + 20%
r = 20%
The percent growth is 20%.
Solve for x, please!! I really need help!!
Answer:
x = 13
Step-by-step explanation:
You want to find x when one half of the diagonal of a parallelogram is 80 and the other half is 6x+2.
DiagonalsThe diagonals of a parallelogram bisect each other, so point Y is the midpoint of each. That means ...
VY = YX
80 = 6x +2 . . . . . substitute the given values
78 = 6x . . . . . . . subtract 2
13 = x . . . . . . . . divide by 6
The value of x is 13.
F(-10)=64 and f(15)=54
What is the slope
Equation and x intercept
The equation of the straight line is 2x+5y=340.
The x-intercept point of that line is (170,0).
What is the equation of a straight line?A straight line has different forms like point-slope form, standard form, slope-intercept form, and others. A specific form is used according to the given data for convenience.
As f(-10)=64 and f(15)=54, two points can be wriiten as (x₁,y₁)=(-10,64) and (x₂,y₂)=(15,54).
Now, use the two-point form of the equation of a line.
(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)
(y-64)/(x-(-10))=(54-64)/(15-(-10))
(y-64)/(x-10)=-10/25
25(y-64)=-10(x-10)
5(y-64)=-2(x-10)
5y-320=-2x+20
2x+5y=340
Therefore, the required equation of the line is 2x+5y=340.
To find the x-intercept, substitute y=0 into the equation of the line.
2x+5×0=340
2x=340
x=170
Therefore, the x-intercept point is (170,0).
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four times the sum of the three consecutive even intergers is 240 more than six times the smallest integer.
Answer:
Step-by-step explanation:
Let's call the smallest of the three consecutive even integers "x". Since they are consecutive and even, we know that the next two integers must be "x + 2" and "x + 4".
Now we can set up the equation for the problem:
4 * (x + (x + 2) + (x + 4)) = 240 + 6x
Expanding the parentheses on the left side:
4 * (3x + 6) = 240 + 6x
Simplifying the left side:
12x + 24 = 240 + 6x
Subtracting 6x from both sides:
6x + 24 = 240
Subtracting 24 from both sides:
6x = 216
Dividing both sides by 6:
x = 36
So the smallest of the three consecutive even integers is 36, and the others are 38 and 40.
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Landon sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
28 visitors purchased no costume.
319 visitors purchased exactly one costume.
34 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase exactly one costume as a fraction in simplest form.
Answer:
319/381
Step-by-step explanation:
You want the probability that a customer will buy exactly one costume, given that the numbers buying 0, 1, or >1 costumes were 28, 319, and 34, respectively.
Exactly oneThe probability is the ratio of customers buying one to total customers:
P(n=1) = 319/(28 +319 +34) = 319/381
This fraction cannot be reduced, so ...
The probability the next person will purchase exactly one costume is 319/381.
<95141404393>
Solve 4 x + 16 = y for x if y = 35
Answer:
Below
Step-by-step explanation:
So you have this:
4x + 16 = 35 subtract 16 from both sides of the equation
4x = 19 Divide by 4
x = 19/4
Answer:
The value of x is
[tex]x = 4.75[/tex]
Step-by-step explanation:
Greetings!!!
Given expression [tex]4x + 16 = y[/tex]Thus, the value of y is given as 35, substitute known value of y in expression and solve for x.
[tex]4x + 16 = 35[/tex]
Move the constant to the right
[tex]4x = 35 - 16 \\ 4x = 19[/tex]
Divide both sides of the expression by 4
[tex] \frac{4x}{4} = \frac{19}{4} [/tex]
solve
[tex]x = \frac{19}{4} [/tex]
or
[tex]x = 4 \frac{3}{4} [/tex]
or
[tex]x = 4.75[/tex]
Hope it helps!!!
HelpThe ratio of the perimeters of two similar quadrilaterals is 2:4. What is the ratio of their areas? PLLLLLLLLLLSSSSSSss
a.1:2
b. 4.8
c. 2:4
d. 4:16
e. 5:3
The ratio of the areas of the quadrilaterals is 1:2. Option A
What is the ratio of the perimeter?Let's assume that the two similar quadrilaterals have side lengths of x and 2x, respectively. The ratio of their perimeters is then 2x + 2x + 2x + 2x = 8x : 2 * (2x + 2x + 2x + 2x) = 4 * 8x = 32x. The ratio of the perimeters is 2:4, so we can write the equation:
8x/32x = 2/4
Solving for x, we find that x = 4.
So the ratio of the areas of the two similar quadrilaterals is (x^2)/(2x)^2 = (4^2)/(2 * 4^2) = 16/32 = 1/2.
Therefore, the ratio of the areas of the two similar quadrilaterals is 1:2.
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In this picture B,D, and F are
midpoints. AC=50, CE=60, and
BD=35
B
AE=[? ]
The measure of the side AE would be 70 units.
What is the triangle midpoint theorem?We know that the triangle midpoint theorem says that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
In the given triangle B, D, F are the midpoints of the triangle.
AC=50, CE=60,
BD=35
Then, in the given triangle if BD is connecting the midpoints of AC and CE then it must be parallel to AE and equal to FE ( half of AE).
⇒ BD ≅ FE= 1/2 AE
AE = 70 units
Then, the length of line segment AE = 70 units
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Solve for x, each figure is a trapezoid
By calculating , The value of x we get is 5 as a final resultant.
What is trapezoid ?
A trapezoid is a quadrilateral with two parallel sides, called the "bases," and two non-parallel sides, called the "legs." The parallel sides can have different lengths, and the trapezoid can be either right-angled or oblique. In other words, a trapezoid is a geometric shape that has two parallel sides, two non-parallel sides and four angles.
Since a Trapezoid has 360 Degrees total and since the sides are equal we can say that
180=110+17x-15
70=17x-15
85=17x
x=5
Therefore, By calculating , The value of x we get is 5 as a final resultant.
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BRAINLIEST if correct, 5th grade geometry
Answer:
EF, GH
Step-by-step explanation:
both go on forever from one point
Answer:
A and B
Step-by-step explanation:
Because they go infinitly in one direction and end in another.
find the unknown terms in the sequence: 1 3/4, 1 9/16, 1 3/8, 1 3/16, A, B, C, 7/16, 1/4
The 5th , 6th and 7th term of the arithmetic sequence is 1 , 13/16 and 10/16 respectively
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the first term of the AP be a₁ = 1 3/4
Let the second term of the AP be a₂ = 1 9/16
So , the common difference of AP d = a₂ - a₁
On simplifying the equation , we get
The common difference d = 1 9/16 - 1 3/4 = ( 25/16 - 7/4 )
The common difference d = - ( 3/16 )
And , the nth term of the AP is a + (n - 1) d
So , the 5th term of the AP = ( 1 3/4 ) + ( 4 ) ( -3/16 )
On simplifying the equation , we get
The 5th term of the AP = ( 7/4 ) + ( -3/4 )
The 5th term of the AP = 4/4 = 1
Therefore , the value of A = 1
And , the 6th term of the AP = ( 1 3/4 ) + ( 5 ) ( -3/16 )
On simplifying the equation , we get
The 6th term of the AP = ( 7/4 ) + ( -15/16 )
The 6th term of the AP = 13/16
Therefore , the value of B = 13/16
And , the 7th term of the AP = ( 1 3/4 ) + ( 6 ) ( -3/16 )
On simplifying the equation , we get
The 7th term of the AP = ( 7/4 ) + ( -18/16 )
The 7th term of the AP = 10/16
Therefore , the value of C = 10/16
Hence , the arithmetic progression is solved
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