Answer:
(A) true.
(B). False.
Step-by-step explanation:
(A). F(x) = 4xe^-2x.
Let's make the assumption that 2x = b -----------------------(1).
Therefore, taking the differentiation with respect to x, we have;
2x dx = db.
The next thing thing to do is to integrate, taking the upper limit to be infinity and the lower limit to be zero:
∫( b e^-b db).
Changing the Lim. infinity = 2.
= ∫( b e^-b db). ----------------------------(2).
The step (2) above can be solve with Integrations by part;
Lim. 2 ---> infinity [ b e^-b + ∫( 1 e^-b db|
( | = Upper boundary = 2 and the lower boundary = 0).
Lim. 2 ----> infinity [ 2 e^-2 - 0] - lim. 2 --> infinity [ 0 - 1].
Lim 2 ---> infinity [ 2/e^2 + 1].
Let 2/e^2 = j.
The, lim 2 ---> infinity j + 1.
To solve this, there is need to make use of L'hospital rule,
j = Lim 2 ---> infinity [ 1 /e^2] = 0.
Thus, j = 0. And 0 + 1 = 1.
(PROVED TO BE TRUE).
(B). Taking limit from 1 (upper) to 0( lower). Assuming that b = 3 - 4x.
Therefore, -4dx = db.
∫( 8 /(3 - 4x)^3 dx.
Taking the upper boundary = -1 and the lower boundary = 3.
∫ ( - 2db/ b^3.
= 2 ∫ ( - db/ b^3.
= 2 [ b^-3 + 2) / -3 + 1.
= 2 | - 1/ 2 db
= 8/9.
Not true.
find the perimeter of the triangle with the vertices $(0,\ 1),\ (3,\ 6)$ , and $(4,\ 1)$ . if necessary, round your answer to the nearest hundredth.
The perimeter of the triangle having vertices (0,1),(3,6), and (4,1) will be 10.83 units.
Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.
Any polygon's perimeter is equal to the sum of its side lengths. Considering a triangle
The sum of the three sides equals the perimeter.
Units are always a part of the ultimate response. The final solution should be given in centimeters if the triangle's sides are in that unit.
Because the y values between U and V differ, the distance is equal to the x value difference.
Because the x values of V and W differ, the distance equals the difference between their y values.
The hypotenuse of a right triangle, or U to W, equals sqr (sum of squares on the other two sides)
Perimeter = sum of the 3 sides
[tex]= \sqrt{34} + \sqrt{26}+ \sqrt{16}= 5.83 + 5.1 + 4 = 10.83\:units[/tex]
As the value of 34 is 5.83 squared, 26 is 5.1 squared, 16 is about 4 squared.
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The total distances add up to the triangle's perimeter is 10.00
The triangle's perimeter may be calculated by summing the distances between its three vertices. Use the distance formula to calculate the separation between the points:
d = √((x2 - x1)2 + (y2 - y1)2)
The distances between the points are as a result for the triangle with vertices (0,1), (3,6), and (4,1)
Utilizing the distance formula, determine the separation between (0,1) and (3,6):
d = √((x2 - x1) 2 + (y2 - y1) 2) = √((3-0) 2 + (6-1) 2) = √(32 + 52) = √45
Utilizing the distance formula, determine the separation between (3,6) and (4,1):
d = √((x2 - x1) 2 + (y2 - y1) 2) = √((4-3) 2 + (1-6) 2) = √(12 + 52) = √25
Utilizing the distance formula, determine the separation between (4,1) and (0,1):
d = √((x2 - x1) 2 + (y2 - y1)2) = √((0-4) 2 + (1-1) 2) = √(42 + 02) = √16
The triangle's perimeter is calculated by adding the three distances together:
Perimeter = √45 + √25 + √16 = 10.00.
Hence, the perimeter of the triangle is 10.00, rounded to the closest hundredth.
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Thomas starts a canned food collection with 2 cans of food. He challenges his friends to bring 4 cans on the second day, 8 cans on the third day, and 16 cans on the fourth day. Thomas and his friends plan to collect cans for 10 days. Which statement describes why this sequence is a function? Select each correct answer. Responses The graph of the sequence would pass the horizontal line test. The graph of the sequence would pass the horizontal line test. The graph of the sequence would pass the vertical line test. The graph of the sequence would pass the vertical line test. Each amount of cans corresponds to a unique day in this sequence. Each amount of cans corresponds to a unique day in this sequence. Each day corresponds to a unique amount of cans in this sequence.
Furthermore, it is evident that 'every day corresponds to a distinct quantity of cans'. As a result, alternatives B and C are accurate.
What is function?A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output.
Here,
We presume Thomas only invited one buddy to participate.
The pattern for days and cans can be seen as follows:
Thomas has two cans on the first day, i.e. cans.
Thomas has four cans on the second day, i.e. cans.
Thomas has 8 cans on the third day, i.e. cans.
Thomas has 16 cans on the fourth day, i.e. cans.
This trend continues until day ten.
So, on x day, Thomas has cans, and x varies from 1 to 10.
As a result, the relevant function is.
This means that for each day (x), there is a distinct value for the number of cans:
The 'Vertical Line Test,' on the other hand, is a test in which we draw a vertical line through the graph and if it cuts the graph at exactly one place, then the graphed curve is a function.
As shown in the graph below, the vertical line intersects f(x) at precisely one location. As a result, f(x) is a function.
As a result, the sequence graph passes the vertical line test.
Furthermore, it is evident that 'every day corresponds to a distinct quantity of cans'. As a result, alternatives B and C are accurate.
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convert to tons 2,600 pounds
2600 pounds are equal to 1.3 tons.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.
Given,
2,600 pounds to tons
1 US ton = 2000 pound
1 pound = 1/2000 US tons
2,600 pound = 2600/2000 US tons
2600 pound = 1.3 US tons.
Hence, 1.3 US tons are there in 26000 pounds.
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What is the measure of angle d1
What is the tangent ratio of angle C2
100 POINTS!!!
Answer:
[tex]\sf \tan\left(c_2\right)=\dfrac{OD}{OC}=\dfrac{2\sqrt{66}}{19}[/tex]
Step-by-step explanation:
**Please note that if the segment AO = 3.8 cm then the 50° angle on the given rhombus is incorrect. It should be 49.46° (2 d.p.)**
In a rhombus, all four sides are equal in length. Therefore:
CD = AB = 5cmDiagonals bisect each other at 90°. Therefore:
OC = AO = 3.8 cmm∠COD = 90°Therefore, triangle COD is a right triangle.
To find the tangent ratio of angle c₂, first find the length of OD using Pythagoras Theorem:
[tex]\implies OC^2+OD^2=CD^2[/tex]
[tex]\implies 3.8^2+OD^2=5^2[/tex]
[tex]\implies 14.44+OD^2=25[/tex]
[tex]\implies OD^2=10.56[/tex]
[tex]\implies OD^2=\dfrac{1056}{100}[/tex]
[tex]\implies OD^2=\dfrac{1056 \div 4}{100 \div 4}[/tex]
[tex]\implies OD^2=\dfrac{264}{25}[/tex]
[tex]\implies OD^2=\dfrac{4 \cdot 66}{25}[/tex]
[tex]\implies OD=\sqrt{\dfrac{4 \cdot 66}{25}}[/tex]
[tex]\implies OD=\dfrac{\sqrt{4 \cdot 66}}{\sqrt{25}}[/tex]
[tex]\implies OD=\dfrac{2\sqrt{66}}{5}[/tex]
[tex]\boxed{\begin{minipage}{6 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]
Given:
θ = c₂O = ODA = OCSubstitute the values into the tan ratio:
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{OD}{OC}[/tex]
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{3.8}[/tex]
Rewrite 3.8 as 19/5:
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{\frac{19}{5}}[/tex]
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{2\sqrt{66}}{19}[/tex]
What number must be multiplied to the vector <-4,2,-3> so it is normalized
A. [tex]\frac{1}{\sqrt{29} }[/tex]
B. -[tex]-\sqrt{29}[/tex]
C. [tex]-\frac{1}{\sqrt{29} }[/tex]
D. [tex]\sqrt{29}[/tex]
On Saturday, Pam spent 1 hour and 15 minutes working on a puzzle. On Sunday, she spent 48 minutes on the puzzle. How many seconds did Pam work on the puzzle in all?
Using hour and minutes conversion, Pam spent 7380 seconds on the puzzle.
What is the formula for converting hours to minutes?We can convert an hour into minutes by multiplying it by 60 since an hour is made up of 60 minutes. Therefore, if one wants to translate three hours into minutes, they can do it by multiplying three by sixty, which gives them three times sixty or 180 minutes.
On Saturday, Pam spent 1 hour and 15 minutes working on a puzzle.
On Sunday, she spent 48 minutes on the puzzle.
1 hour = 60 minutes
1 minute = 60 second
1 hour = 60 × 60 seconds
1 hour and 15 minutes = 60 × 60 seconds + 15 × 60 seconds
⇒ 3600 + 900 seconds
⇒ 4500 seconds
48 minutes = 48 × 60 = 2880 seconds
Total seconds spent = 4500 + 2800 = 7380 seconds
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PLEASE HELP ASAP WILL GIVE BRAINLIEST
Which linear graph represents a proportional relationship?
If a quantity increases or decreases as per the increase or decrease in other quantity, the two quantities are said to be in a proportional relationship.
And here, the graph representing the proportional relationship is the one with positive slope (2nd graph)
What are the statements and reasons for this problems.
Anything helps! Thank you :)
From the congruency of triangles we can prove,
A: D is the midpoint of AC,
B: Measure of ∠D = ∠E,
C: BD bisect the angle ABC.
What are congruent triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.
Given BD bisect ∠ABC
AB ≅ CB
from the figure, AB = CB
since BD bisects ∠ABC
∠1 = ∠2
and BD = BD (common side)
from SAS property,
ΔABD ≅ ΔCBD
Triangles can be shown to be congruent after which the final dimension can be anticipated without actually measuring the triangle's sides and angles.
from CPCT, AD = CD
since AD = CD so D should be the midpoint of AC.
B: Given B is the midpoint of AC,
AB = CB
and BD ║ AE,
so ∠1 and ∠2 are equal due to corresponding angles between parallel lines,
∠1 = ∠2
BD = AE
ΔABE ≅ ΔCBD
from CPCT, ∠D = ∠E
C: Given ∠A and ∠C are right angles,
∠A = ∠C = 90°
AD = CD
BD = BD (common side and hypotenuse of a right triangle)
from RHS property ΔABD ≅ ΔCBD
from CPCT, ∠ABD = ∠CBD
since both angles are equal so BD is the angle bisector.
Hence all the statements are proved by the congruency of triangles.
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Consider the following equation, known as the Arrhenius Equation Two-point form.
Solve for:
a)
b)
c)
d)
It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1
What is the Arrhenius Equation?
The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction and the temperature (T) of the reaction. The equation was first proposed by Svante Arrhenius in 1889 and it states that the rate constant of a chemical reaction is directly proportional to the exponential of the negative activation energy (Ea) of the reaction, divided by the gas constant (R) and the absolute temperature (T). The equation can be written as:
K = A * e^(-Ea / (R*T))
The Arrhenius Equation Two-point form is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction, the activation energy (Ea) of the reaction, the universal gas constant (R), and the temperature (T) of the reaction.
Given the equation K2/K1 = Ea / R (1/T1 - 1/T2)
a. To solve for K2, we can multiply both sides of the equation by
K1: K2 = K1 * Ea / R (1/T1 - 1/T2)
b. To solve for K1, we can divide both sides of the equation by
Ea / R (1/T1 - 1/T2): K1 = K2 / Ea / R (1/T1 - 1/T2)
c. To solve for Ea, we can multiply both sides of the equation by
R (1/T1 - 1/T2): Ea = K2/K1 * R (1/T1 - 1/T2)
d. To solve for T2, we can use the equation 1/T2= 1/T1 - Ea/R * K1/K2
It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1.
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please need help asap 28, and 29
The length of the mid-segment of the trapezoid for these problems is given as follows:
28. n + 12 = 17.
29. 2n + 11 = 27.
How to obtain the length of the mid-segment of a trapezoid?The length of the mid-segment of a trapezoid is half the sum of the lengths of the bases.
Hence the value of n for item 28 is given as follows:
n + 12 = 1/2(2n - 2 + 4n + 6)
n + 12 = 0.5(6n + 4)
n + 12 = 3n + 2
2n = 10
n = 5.
Hence the length of the mid-segment is of:
n + 12 = 5 + 12 = 17.
The value of n for item 29 is given as follows:
2n + 11 = 1/2(5n - 2 + n + 8)
2n + 11 = 0.5(6n + 6)
2n + 11 = 3n + 3
n = 8.
Hence the length of the mid-segment is of:
2n + 11 = 16 + 11 = 27.
(replacing n = 8 into 2n + 11).
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If a rectangular garden is 45 ft. by 20 ft., how many feet of fence are needed to enclose it?
Answer:
130 feet
Step-by-step explanation:
45 feet is one of the lengths of the rectangular garden and 20 feet is the other.
The perimeter of a rectangle is 2(l+w) and we know that these must be the lengths and widths.
Communitive property of addition states that it doesn't matter the order that we add so we know it's just 20+45 (65) then times 2 which is 130
130 feet is your answer.
Starsky and Hutch shared their profits in the ratio 3:1. If Starsky got £606, how much did hutch get?
Answer:
£202
Step-by-step explanation:
It is import that you read ratios from left to right - the subjects/names and the ratio itself. In this case the "subjects" are Starksy and Hutch. So Starsky = 3, Hutch = 1.
Use cross multiplication:
S(Starksy):H(Hutch)
3 : 1
606. : ?
(606 * 1) divided by 3 = your answer = 202
Reply if you are unfamiliar with the cross multiplication method
Answer:
202
Step-by-step explanation:
Ratios
Starsky : Hutch
3 : 1
Starsky has 606 so divide 606 by 3
606/3 = 202
Multiply each term by 202
Starsky : Hutch
3*202 : 1*202
Starsky : Hutch
606 : 202
find the length of the curve. r(t) = 6t i + 8t3/2 j + 6t2 k, 0 ≤ t ≤ 1
The length of the curve is given by the integral of the magnitude of the velocity vector, which is the derivative of the position vector. Taking the derivative of the position vector, we get the velocity vector as follows:
v(t) = 6i + 24t1/2j + 12tk
The magnitude of this vector is
√(6²+ 24²t + 12²t²)
= √(36 + 576t + 144t²).
To find the length of the curve, we need to integrate this magnitude from t=0 to t=1. This is given by the integral:
L = ∫0² √(36 + 576t + 144t²)dt
This evaluates to L = 18.75. Therefore, the length of the curve is 18.75.
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Write the equation of the line shown.
Answer:
y = -1/2x
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
The slope = rise/run
Let's pick 2 points (0,0) (4, -2), we see that the y decrease by 2 and the x increase by 4, so the slope is
m = -2/4 = -1/2
Y-intercept is located at (0,0)
So, our equation is
y = -1/2x
Please help me step by step pls
there is no question!
please help me with this thank you
Answer:
3rd one is 100.6⁰F I think... not sure
Answer: B
Step-by-step explanation: 100.7 is current. In the past, it was lower so we have to subtract. We know how much we subtract (2.5). In B, if we subtract 2.5 we are taking 2.5 away from his current temp to get yesterday's temp.
While playing basketball, Ava’s heartbeat `is 80` times in `30` seconds. While running, her heartbeat `was 60` times in `20` seconds. Which activity made Ava’s heart beat faster? Basketball, running, or they were the same.
Running made Ava’s heart beat faster.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
While playing basketball, Ava’s heartbeat is 80 times in 30 seconds.
And, While running, her heartbeat was 60 times in 20 seconds.
Clearly, Ava's heartbeat is faster when he was running.
So, Running made Ava’s heart beat faster.
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A deposit of 800 at 3.5% for seven years 
Answer:
Interest = Principal x Rate x Time
($2,840)
Step-by-step explanation:
interest earned on a deposit of $800 at 3.5% interest for 7 years, you can formula: Interest = Principal x Rate x Time
In this case, the interest earned would be:
Interest = $800 x 0.035 x 7 = $2,040
So, after 7 years the deposit would be worth $800 + $2,040 = $2,840.
The highest temperature ever recorded for a person with a fever who survived was 115 degrees. Alternatively, the lowest temperature ever recorded on a patient who survived was 56.7 degrees. If the average temperature is 98.6 degrees, which extreme temperature was furthest from the norm? How much further?
Answer:
the minimum temperature was furthest from the norm. it was 23.5 degrees further
Step-by-step explanation:
difference between the max and median = 115-98.6 = 16.4
difference between the median and minimum = 98.6 - 58.7 = 39.9
the difference between the median and minimum (39.9) is greater than the distance between the maximum and median (16.4). thus, the minimum temperature was furthest from the norm. the difference in differences is 39.9 - 16.4 = 23.5 degrees. this means that the minimum temperature was 23.5 degrees further away from the norm than the maximum was
The image point using the translation (x, y) → (x + 4, y – 1) for the point (3, 3) is:
None of these choices are correct.
(7, 2).
(1, 2).
(7, 4).
Answer:
(7,2)
Step-by-step explanation:
(3,3) 》(x+4, y-1)
3=x
3+4=7
3=y
3-1=2
=(7,2)
Answer:
(7, 2 )
Step-by-step explanation:
the translation rule (x, y ) → (x + 4, y - 1 ) means
add 4 to the original x- coordinate and subtract 1 from the original y- coordinate.
(3, 3 ) → (3 + 4, 3 - 1 ) → (7, 2 )
Joel hit b baseballs at practice and another 15 baseballs at the batting cage. Choose the expression that shows how many baseballs Joel hit in all.
The expression that shows how many baseballs Joel hit in all is y = b + 15.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that Joel hit (b) baseballs at practice and another 15 baseballs at the batting cage.
We can write the expression that shows how many baseballs Joel hit in all is given by -
y = b + 15
Therefore, the expression that shows how many baseballs Joel hit in all is y = b + 15.
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Mike bought some books that cost $6 each. He spent a total of $18. How many books did he buy?
Fill the boxes with appropriate denominator /numerator
Answer:
the first box is 3 and the second box is 25
Step-by-step explanation:
Answer: Box 1: 3 Box 2: 25
Step-by-step explanation:
Box 1:
Since the top is divided by 3, you have to do the same to the bottom
9 / 3 = 3
Box 2:
The bottom is multiplied by 1 ⅔, so you do the same to the bottom
1 ⅔ x 15 = 25
Statins are used to keep cholesterol in check and are a top-selling drug in the
U.S. The equation:
S - 1.5x = 4.9
gives the amount of sales (S) of statin in billions of dollars a years after 1998.
According to this equation, how much will/did people in the U.S. spend on
statins in the year 2010?
Answer: People in the U.S. will spend ??
Billion dollars on statins in 2010.
Answer: 87
Step-by-step explanation:
find the domain of the rational function?
The domain is the set of all real numbers except the x values.
And x : denominator ≠ 0.
What is domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
Let y = f(x) be a rational function.
And to find the domain of the rational function:
We have to find the all achievable values that rational function can have.
That means, we have to find the values where function is defined.
Rational function have numerator and denominator.
To find the domain of the rational function y = f(x):
Set the denominator ≠ 0 and solve for x.
The domain is the set of all real numbers except the x values mentioned in the last step.
Therefore, the complete explanation is given above.
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Use the image below to answer the following question find the value of sine X and cosine y what relationship do the ratios of sine x and cosine y share
The value of sin x is [tex]\frac{5}{13}[/tex] and the value of cos y is [tex]\frac{5}{13}[/tex]. The ratio of sin x and cos y is 1.
What is Pythagorean triplet?The Pythagorean Triples, which comprise the three positive numbers a, b, and c, are the integer solutions to the Pythagorean Theorem.
What is Pythagoras theorem?A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem.
The given triangle has sides 12 and 5.
According to the Pythagorean triplet the length of the third side is 13.
The value of sin x is [tex]\frac{5}{13}[/tex].
The value of cos y is [tex]\frac{5}{13}[/tex].
The ratio of sin x and cos y is:
[tex]\frac{sin x}{cos y} = \frac{\frac{5}{13}}{\frac{5}{13}} = 1[/tex]
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Find the sums of the interior angles and the sum of the measures of the exterior angles of the polygon. Please answer 1, 2, and 3, 30 points!!!!!!!!!!!!!!!!!!!!!!!!
The sum of the internal angles of the polygons are
a) The sum is A = 540°
b) The sum is A = 360°
c) The sum is A = 1800°
What is the sum of the interior angles of a polygon?The sum of the interior angles of a polygon is given by the formula
Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
where n is the number of sides
θ = angle in degrees
Given data ,
Let the sum of the internal angles of a polygon be represented as A
Now , the value of A is
The sum of exterior angle of n polygon is = 360°
Now ,
a)
The number of sides of the polygon = 5 sides
So , Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
Substituting the value of n = 5 in the equation , we get
nθ = 180° ( 5 - 2 )
nθ = 180° x 3
nθ = 540°
b)
The number of sides of the polygon = 4 sides
So , Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
Substituting the value of n = 4 in the equation , we get
nθ = 180° ( 4 - 2 )
nθ = 180° x 2
nθ = 360°
c)
The number of sides of the polygon = 12 sides
So , Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
Substituting the value of n = 12 in the equation , we get
nθ = 180° ( 12 - 2 )
nθ = 180° x 10
nθ = 1800°
Hence , the sum of the internal angles of the polygon is solved
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Which value of x is in the domain of f(x)=√x - 8?
OA. x = 0
OB. x=7
OC. x = -8
OD. x = 10
SUBMIT
Answer: OC. x = -8 is not in the domain of the function f(x) = √x - 8 because the square root of a negative number is not a real number. Therefore, the only value of x that is in the domain of the function is x ≥ 0.
Step-by-step explanation:
A line includes the points (3, 1) and (4, 4). What is its equation in slope-intercept form?
The equation in slope-intercept form is y = 3x - 8.
What is the slope-intercept form?
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point-slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
Here, we have
Given: Line includes the points (3, 1) and (4, 4).
Slope intercept: y = mx + b
We first find the slope, m, using the point-slope
Slope(m) = (y₂ - y₁)/(x₂ - x₁) = (4 - 1)/(4 - 3) = 3
Now, we find the y-intercept, b, Using any points' x and y values in y = mx + b with the found slope.
Put the slope into y = mx + b
y = 3x + b
Now, we took points (3, 1) to get slope intercept form and we get
1 = 3(3) + b
b = -8
Now, we put the value of b in y = mx + b and we get
y = 3x - 8
Hence, the equation in slope-intercept form is y = 3x - 8.
To learn more about the slope-intercept form from the given link
https://brainly.com/question/25826868
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6. Explain what must occur to the parent
function f(x) = x² to transform the
function to g(x) = (x-4)² +2.
Answer:
4 units right, 2 units up
Step-by-step explanation:
For [tex]g(x)=(x-4)^2+2[/tex], the graph of [tex]f(x)=x^2[/tex] would need to move 4 units to the right and 2 units up. Hence, the vertex would be [tex](4,2)[/tex] if we compare the function g(x) with the form [tex]y=a(x-h)^2+k[/tex].