The remainder when 101⁴⁸⁰⁰⁰⁰⁰⁰²³ is divided by 35 is 12.
Now, let's look at how we can use the Chinese Remainder Theorem to compute 101⁴⁸⁰⁰⁰⁰⁰⁰²³ mod 35. First, we need to express 35 as a product of prime powers:
=> 35 = 5 x 7.
Then, we can consider the congruences 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ a (mod 5) and 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ b (mod 7), where a and b are the remainders we want to find.
Since 101 is not divisible by 5, we have 101⁴ ≡ 1 (mod 5). Therefore,
=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ (101⁴)¹²⁰⁰⁰⁰⁰⁰⁰⁵ ≡ 1 (mod 5).
This means that a = 1.
Since 7 is a prime number, φ(7) = 6, so we have 101⁶ ≡ 1 (mod 7). Therefore,
=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ (101⁶)⁸⁰⁰⁰⁰⁰⁰⁰³ ≡ 1 (mod 7).
This means that b = 1.
Now, we need to find a number that is equivalent to 1 modulo 5 and 1 modulo 7. This number is
=> 1 x 7 x 1 + 5 x 1 x 1 = 12.
Therefore,
=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ 12 (mod 35).
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In a group consisting of 21 people from small towns and 28 people
from cities, 15 of the small-town residents and 21 of the city
residents exercise regularly. What is the probability that a person
selected at random from this group exercises regularly, given that the
person comes from a small town?
Enter your answer as a fraction, a decimal value accurate to two
places, or a percent accurate to the nearest whole number.
Answer:
31%
Step-by-step explanation:
21 s - 15 exercise
28 c - 21 exericse
15/49 = 31%
Answer:
85Step-by-step explanation:
21 + 28 = 49
49 + 15 = 64
64 + 21 = 85
Have a Nice Day : ) if Incorrect sorry.
Travis had a box of 61 french fries. He gave 14 french fries to each of f friends. Which expressions shows how many french fries he had left after giving some to his friends? A. 61 + f × 14 B. 61 - f × 14 C. (61 + f) × 14 D. (61 - f) × 14
Answer: B
Step-by-step explanation: 61 - (f x 14) would give us the number of french fries he had left over
What kind of function is an exponential function?
An exponential function is a function in which the variable (usually represented by "x") is the exponent, rather than the base.
The most common form of an exponential function is f(x) = b^x, where b is a positive constant known as the base of the function.
Exponential functions can take many different forms, but they all have one thing in common: the variable is in the exponent. In most cases, the base of the function is a positive constant, and the exponent is the input variable. Exponential functions can also be used to model a wide variety of real-world phenomena, such as population growth, compound interest, and decay of radioactive materials.
The graph of an exponential function is always a smooth curve that increases or decreases at an increasing rate. The slope of the curve increases as x increases, which means that the rate of change of the function also increases as x increases.
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Eliana puts $20.50 in her savings account every week for 25 weeks leading up to Christmas. How much money does she have to spend on Christmas presents?
Answer: $512.50
Step-by-step explanation:
Eliana saved for 25 weeks and put $20.50 in her savings account every week. We will use multiplication to help us solve.
$20.50 * 25 weeks = $512.50
Ans$w3r:
The answer is $512.50
Step By Step Explanation:
25 weeks x $20.50 = $512.50
Why is a line of longitude called a meridian Class 6?
A line of longitude is called a meridian because it connects the North and South poles and forms a circle around the Earth, like the sun's meridian path during the day.
A line of longitude is an imaginary line that circles the Earth and runs in a north-south direction. It is measured in degrees and divides the Earth into two equal halves, the Eastern Hemisphere and the Western Hemisphere. This line is called a meridian because it is derived from the Latin word meridies which means mid-day or noon. The sun's path across the sky during the day follows a meridian from the North Pole to the South Pole, and this is what inspired the term "meridian" to describe the line of longitude.
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I Bet you can't answer
"5(2x+4)-3(-6-x)"
answer this with full formula
also expand simplify them
Answer:
13x+38
Step-by-step explanation:
PLEASE HELP 100 POINTS
A line has a slope of 5/3 and passes through the point (4,6). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = [tex]\frac{5}{3}[/tex] , then
y = [tex]\frac{5}{3}[/tex] x + c ← is the partial equation
to find c substitute (4, 6 ) into the partial equation
6 = [tex]\frac{5}{3}[/tex] (4 ) + c = [tex]\frac{20}{3}[/tex] + c ( subtract [tex]\frac{20}{3}[/tex] from both sides )
[tex]\frac{18}{3}[/tex] - [tex]\frac{20}{3}[/tex] = c , so
c = - [tex]\frac{2}{3}[/tex]
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex] ← equation of line
A recipe uses 4 cups of milk to make 24 servings. If the same amount of milk is used for each serving, how many servings can be made from two gallons?.
The servings can be made from two gallons is 192 serving
From the question, we know that 4 cups of milk equals to 24 servings.
4 cups = 24 serving
To solve total serving which can be made from two gallons of milk, we have to convert unit from gallon into cup, so it can be multiplied with the amount of serving
1 gallon equals to 4 quarts .....(1)
1 quart equals to 2 pints ..........(2)
From info no. 1 and 2, we can know that
1 gallon = 4 x 2 = 8 pints ..........(3)
Next, 1 pint equals to 2 cups ...........(4)
Since 1 gallon equals to 8 pints from information no. 3, we combine information no. 3 and information no. 4 to convert gallon to cup.
1 gallon = 8 x 2
= 16 cups ....................(5)
For 2 gallon, we just simply multiply info no 5
2 gallon = 16 x 2 cups
= 32 cups .................(6)
In the case of 4 cups can make 24 serving, Total number of serving can be calculated with info no. 6
Number of serving = 32 / 4 x 24 = 8 x 24 = 192 serving
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5x^3 + 8x^2 +2x^1 + 7 if x = 10
Answer:
5,827
Step-by-step explanation:
substitute x = 10 into the expression
5(10)³ + 8(10)² + 2(10) + 7
= 5(1000) + 8(100) + 20 + 7
= 5000 + 800 + 27
= 5,827
Sean deposits $275 each month into his savings. He started with $1000 in the account.
The slope of the line will be
In 10 months the savings will be at
The graph of this line will
y = savings and x = months
Type the equation WITH NO SPACES
(positive or negative)
dollars (type the number)
(increase or decrease)
4
The slope of the line will be,In 10 months the savings will be at,The graph of this line will positive slop.
What is positive slop?Sean deposits $275 each month into his savings. He started with $1000 in the account.
The slope of the line will be In 10 months the savings will be at ,The graph of this line will y = savings and x = months
When two variables have a positive slope, it implies that they are positively correlated; that is, when x rises, y rises as well, and when x falls, y falls as well. A line on a line graph that has a positive slope rises as the line advances from left to right.Positive slopes are founded on the idea that when x rises, y rises as well, making the ratio of y/x positive. Negative slopes are founded on the idea that when x rises, y falls. This results in a negative change in y and a positive change in x, which yields a negative result.The slope of the line will be,In 10 months the savings will be at,The graph of this line will positive slop.
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A playground slide is 14. 5 feet long with an 8. 5-foot tall ladder. A playground slide is 14. 5 feet long and has an 8. 5 foot tall ladder. The angle formed by the ladder with the ground is 90 degrees. The angle formed by the slide with the ground is x. What is the measure of the angle that the slide makes with the ground, x, to the nearest degree?.
The angle made by the slide of length 14.5 ft with the ground is 36°
The length of the slide = 14.5ft
The length of the ladder = 8.5 ft
The angle made by the ladder and ground = 90°
The angle formed by the slide can be found using the Pythagoras theorm,
sinθ = O / H
where θ is the angle made by the slide
O is the side opposite to the angle of the slide
H is the side that is hypotenuse with the slide
Let us rearrange the above equation in order to get the angle of the slide,
θ = sin⁻¹ (O/H)
Let us substitute the known values in the above equation, we get
θ = sin⁻¹ (8.5 / 14.5)
= sin⁻¹ (0.586)
≈ 36°
Thus, the angle of the slide is 36°
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A cubical box of cardboard has an edge 4.8 m long. how many closed cuboidal boxes of dimension 24 cm×12cm×10cm can be made out of it
Answer
38,400
Step by Step Explanation
Firstly we have to get the volume of the cube box in cm³ which is 480³ = 110,592,000
Secondly we have to get the volume of the cuboid in cm³ too which is 24×12×10 = 2,880
And lastly, 110,592,000/2,880 = 38,400
The number of closed cuboidal boxes is 38400.
Side of the Cubical Box, a = 4.8 m
Using the formula,
Volume of a cube: V = a³
V1 = a³
V1 = (4.8)³
V1 = 110.59 m³
Dimension of Cuboidal Boxes,
Length, l = 24 cm
Breadth, b = 12 cm
Height, h = 10 cm
Using the formula,
Volume of cuboid : V = l × b × h
V2 = l × b × h
V2 = 24 × 12 × 10
V2 = 2880 cm³ or 0.0028m³
Number of closed cuboidal boxes,
[tex]=\frac{Volume of cube}{Volume of cuboid}[/tex]
[tex]= \frac{110.59}{0.0028}[/tex]
[tex]= 38400[/tex]
Hence, there are 38400 closed cuboidal boxes.
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Determine the domain of the graph
You need to look at the graph and identify where the x-axis is located.
In this graph Domain is {-2,2,4,6}
How to determine the domain of a graph?To determine the domain of a graph, you need to look at the graph and identify where the x-axis is located.
The domain of a graph is the set of all possible x-values for which the graph is defined.
In other words, it is the set of all x-values that the graph will plot.
For example, if the x-axis of the graph is between 0 and 10, then the domain of the graph is the set of all numbers between 0 and 10, including 0 and 10.
The domain of a sine wave graph is all real numbers. This is because the sine wave graph is periodic and repeats itself over and over again.
In this graph domain is {-2,2,4,6}
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Let’s begin with a 30°-60°-90° triangle. A 30°-60°-90° triangle with a hypotenuse of 2 units is shown.
If another right triangle contains a 30° or a 60° angle but is a different size, what can you say about the side lengths of that triangle in terms of the given triangle? Explain your answer.
The side lengths of the new right triangle can be determined by the ratio of the given triangle.
What is triangle?A triangle is a three-sided polygon with three straight sides that are connected at three corners. It is one of the most basic shapes in geometry and is found in many areas of mathematics. Triangles can be classified according to their angles, sides, and size. They can be equilateral, isosceles, or scalene, depending on the size of their angles and sides. Triangles are used in a variety of fields, including architecture, engineering, construction, art, and design.
The side opposite the 30° angle will always be half the length of the hypotenuse, while the side opposite the 60° angle will always be equal to the square root of three times the length of the side opposite the 30° angle. This means that if the hypotenuse of the given triangle is 2, then the side opposite the 30° angle will be 1 and the side opposite the 60° angle will be √3.
Therefore, for any other right triangle containing a 30° or a 60° angle, the side length can be found by multiplying the side length of the given triangle by the same ratio. For example, if the hypotenuse of the new triangle is 6, then the side opposite the 30° angle will be 3 and the side opposite the 60° angle will be 3√3.
In conclusion, for any right triangle containing a 30° or a 60° angle, the side lengths can be determined by multiplying the side lengths of the given triangle by the same ratio.
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The cost of 1 cap and 1 wallet is
£28.
The cost of 2 caps and 1 wallet is
£45.
a) How much does 1 cap cost?
b) How much does 1 wallet cost?
Answer:
cap: 17, wallet: 11
Step-by-step explanation:
45 - 28 = 17
45 - (17 x 2) =
45 - 34 = 11
could also do:
28 - 17 = 11
Hope this helps have a good day
1. Which ordered pairs are solutions of the
inequality 5y - 3x ≤ 7?
A. (0,0)
B. (3,5)
D. (1, 2.5)
(C.) (-2,-5)
E. (5,-3)
Graph
The ordered pairs (0,0), (- 2, - 5), (5, - 3) are solutions of the inequality 5y - 3x ≤ 7.
What is inequality?A linear inequality is one that would result in a linear equation if we were to substitute the equals relation for the inequality. When solving the inequality, the direction of an inequality is reversed when we multiply or divide both sides by a negative value.The collection of all solutions makes up the solution set for an inequality.
Here,
Now, in order to determine which ordered pairs are a solution, we need to substitute the coordinate points into the left side of the inequality and check against right side for the validity.
A. (0,0)
5(0) - 3(0) = 0 ≤ 7
So, (0,0) is a solution.
B. (3, 5)
5(5) - 3(3)= 25 - 9 = 16 ≥ 7
So, (3, 5) is not a solution.
C. (1,2.5)
5(2.5) - 3(1)= 12.5 - 3 = 9.5 ≥ 7
So, (1,2.5) is not a solution.
D. (- 2, - 5)
5(-5) - 3(-2) = - 25 + 6 = - 19 ≤ 7
So, (- 2, - 5) is a solution.
E. (5, - 3)
5(-3) - 3(5) = - 15 - 15 = -30 ≤ 7
So, (5, - 3) is a solution.
Hence, the ordered pairs (0,0), (- 2, - 5), (5, - 3) are solutions of the inequality 5y - 3x ≤ 7.
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10) Find the value of the term in the arithmetic sequence. (an = a₁ + (n − 1)d)
-
16, 7, -2, -11, -20,... (10th term)
a10= - 74
a10 = -56
a10 = -65
a10= - 83
The value of the term in the arithmetic sequence is -65. Option C
How to determine the term of the arithmetic sequenceThe general formula for the nth term of an arithmetic sequence is expressed as;
an = a₁ + (n − 1)d
Given the sequence;
16, 7, -2, -11, -20,...
The common difference is determined as = second term - first term
= 7 - 16
= -9
The first term, a = 16The common difference, d = -9Now, substitute the values, we get;
a10 = 16 + (10-1)-9
expand the bracket, we get;
a10 = -6 + 9(-9)
multiply the values, we have;
a10 = 16 -81
Subtract the terms
a10 = -65
Thus, the value is -65
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A parabola is modeled with the equation x2 – 6x + 4y – 19 = 0. Which is the domain and range of the parabola?
D: (–∞, ∞); R: [7, ∞)
D: (–∞, ∞); R: (–∞, 7]
D: (–∞, 7]; R: (–∞, ∞)
D: [7, ∞); R: (–∞, ∞)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
The polynomial x² - 6x + 4y - 19 = 0 has domain and range along D: (–∞, ∞); R: (–∞, 7], the foci is at (3, 6), it's directrix and axis of symmetry are y = 8 and x = 3 respectively
What is a PolynomialA polynomial is an equation made up of constants, such as integers and algebraic operations, and variables (sometimes referred to as coefficients) (such as addition, subtraction, multiplication, and division). The quantity of terms it contains determines what it is. Quadratic equations, cubic equations, and quartic equations are typical examples of polynomials.
In the given problem, the polynomial is
x² - 6x + 4y - 19 = 0
4y = -x² + 6x + 19
The domain of this function is;
domain = (-∞, ∞)
The range of the function is all possible values along the y - axis
range = (-∞, 7]
The focus is along (3, 6)
The directrix of the polynomial is y = 8
The axis of symmetry is x = 3
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Is 0 and 3 a function?
Answer:
Yes it is!
Step-by-step explanation:
Hope it helps!
Answer: If I'm correct it's 3
Step-by-step explanation:
0 + 3 = 3
What is this for math 1
Yes, it showed you the fomula
Answer: 64x^6y^3
A hotel has four elevators. One of them
is a freight elevator. When pressing the
button, one of the elevators randomly
services your floor. If you use the
elevators seven times, what is the
probability that you use the freight
elevator exactly four times?
O 57.68%
O 5.768%
O 68%
O 5.6%
On solving the provided question, we can say that probability, P( use the freight elevator exactly four times) = 4/7 *100 = 57.1428571429 %
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
the favorable out come is 4 times
total outcomes = 7 times
Probability, P( use the freight elevator exactly four times) = 4/7 *100 = 57.1428571429 %
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Solve for x.
2(x−3 1/2)=10 3/4
Enter your answer as a mixed number in simplest form in the box.
Answer:
x = 71/8
Step-by-step explanation:
Solve for x:
2 (x - (3 + 1/2)) = 10 + 3/4
Put 3 + 1/2 over the common denominator 2. 3 + 1/2 = (2×3)/2 + 1/2:
2 (x - (7/2)) = 10 + 3/4
2×3 = 6:
2 (x - (1/2 6 + 1/2)) = 10 + 3/4
6/2 + 1/2 = (6 + 1)/2:
2 (x - (7/2)) = 10 + 3/4
6 + 1 = 7:
2 (x - 1/2 7) = 10 + 3/4
Put each term in x - 7/2 over the common denominator 2: x - 7/2 = (2 x)/2 - 7/2:
2 ((2 x)/2 - 7/2) = 10 + 3/4
(2 x)/2 - 7/2 = (2 x - 7)/2:
2 (1/2 (2 x - 7)) = 10 + 3/4
(2 (2 x - 7))/2 = 2/2×(2 x - 7) = 2 x - 7:
(2 x - 7) = 10 + 3/4
Put 10 + 3/4 over the common denominator 4. 10 + 3/4 = (4×10)/4 + 3/4:
2 x - 7 = ((4×10)/4 + 3/4)
4×10 = 40:
2 x - 7 = 40/4 + 3/4
40/4 + 3/4 = (40 + 3)/4:
2 x - 7 = ((40 + 3)/4)
40 + 3 = 43:
2 x - 7 = 43/4
Add 7 to both sides:
2 x + (7 - 7) = 43/4 + 7
7 - 7 = 0:
2 x = 43/4 + 7
Put 43/4 + 7 over the common denominator 4. 43/4 + 7 = 43/4 + (4×7)/4:
2 x = (43/4 + (4×7)/4)
4×7 = 28:
2 x = 43/4 + 28/4
43/4 + 28/4 = (43 + 28)/4:
2 x = ((43 + 28)/4)
43 + 28 = 71:
2 x = 71/4
Divide both sides by 2:
x = (71/2)/4
4×2 = 8:
Answer: x = 71/8
A man deposited ghc 1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.
Calculate the
a.simple interest for the 4 years
b.amount at the end of the 4 types
a. The simple interest for 4 years would be $960.
b. The amount at the end of the 4 years would be $2160.$
A man deposited $1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.
a. For calculating simple interest for the 4 years
We have been given data as:
Principal (P) = $1200
Rate of Interest (R) = 20%
Time (T) = 4 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
The simple interest for 4 years would be:
⇒ 1200 x 20% x 4 = 960
b. For calculating the amount at the end of the 4 years
The amount at the end of the 4 years would be:
1200 + 960 = 2160
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A.
In which graph is y a direct variation of .x?
ABCD
Previous
B.
C.
D.
The option D is correct. The line is going through the origin.
What is graph?A graph is a mathematical structure used to model relationships between objects. It is composed of a set of vertices (also called nodes) and a set of edges, which connect the vertices. The vertices represent the objects and the edges represent the relationships between them. Graphs can be used to model a wide variety of real-world systems, such as networks of roads, social networks, and biological networks. There are many different types of graphs, including undirected graphs, directed graphs, weighted graphs, and bipartite graphs. Graphs are used in a variety of fields such as computer science, mathematics, engineering and operations research. They are used for solving complex problems such as routing, scheduling, clustering and many more. Graph algorithms are also used in machine learning and data mining.To learn more about graph refer :
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Identify the center of dilation. plss
So on solving the provided question we cans say that rom the graphs Area 0f triangle = 1/2 AB = 1/2 . 250 . 200 = 25000sq units
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle.
Here,
Given :
from the graph we can say that -
B = 250
A = 200
Area 0f triangle = 1/2 AB = 1/2 . 250 . 200
Area = 25000sq units
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What is midpoint formula Class 9?
In class 9, the midpoint formula is a mathematical formula used to find the midpoint of a line segment given the coordinates of its two endpoints. The midpoint formula is:
(x, y) = ( (x1 + x2) / 2, (y1 + y2) / 2)
Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and (x, y) are the coordinates of the midpoint.
For example, if the coordinates of the two endpoints of a line segment are (3, 4) and (7, 10), you can use the midpoint formula to find the coordinates of the midpoint:
(x, y) = ( (3 + 7) / 2, (4 + 10) / 2)
(x, y) = (5, 7)
So the midpoint of the line segment with endpoints (3, 4) and (7, 10) is (5, 7)
The midpoint formula is used in class 9 to find the midpoint of a line segment in coordinate geometry. It's a simple way to find the point which is exactly in the middle of two given points. It can be used to find the center of a circle if we know the coordinates of two points on the circumference.
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help plssssssssssssssssssssss
Answer:
28
Step-by-step explanation:
a² + b² = c² where c is the hypotenuse (8)
a² + 6² = 8²
a² + 36 = 64
a² = 64 - 36
a² = 28
take square root of both sides
a = square root 28
I need the sender to 2x4 x x3
Answer: two times four times three ( or if you meant 3x) then three x
Step-by-step explanation:
According to the Polygon Interior Angles Sum Theorem, the sum of the interior angle measures of an n-sided convex polygon is (n−2)·180°. Write an equation setting this expression equal to the given angle measure. Then solve for n.
The equation will be represented as angle = (n - 2) × 180.
The value of n is 2.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Since the sum of the interior angle measures of an n-sided convex polygon is (n−2)·180°.
An equation setting this expression equal to the given angle measure will be:
angle = (n - 2) × 180
Angle = 180n - 360
The value of n will be:
180n - 360 = 0
180n = 360
Divide
n = 360/180
n = 2.
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Which graph shows a linear equation?
The correct option is A.
The linear equation y = 2x + 1 is shown in Graph A.
The equation of a straight line's shape with slope and y-intercept is as follows:
y = mx + b
where
y is equal to a point's y-coordinate on a line.
m is the line's slope.
The point on the line whose y-coordinate is y has the x-coordinate of x.
B is the line's y-intercept, or b.
As opposed to y = mx + b, y = 2x + 1
As we can see, the
m = 2 slope
b = 1 as the y-intercept
The graph that crosses the y-axis at the point where y = 1 is only option A, as shown by the intercept value.
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Note the correct question would be as bellow,
Which graph shows the linear equation y = 2x + 1