Answers
Answer:
[tex]\textsf{A.} \quad \dfrac{-3}{2}[/tex]
Step-by-step explanation:
The critical points of a function are the points where the derivative of the function is either zero or undefined.
We can find the derivative of the given function using the product rule.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
Given function:
[tex]f(x)=(2x+1)e^x[/tex]
[tex]\textsf{Let}\; u=2x+1 \implies \dfrac{\text{d}u}{\text{d}x}=2[/tex]
[tex]\textsf{Let}\; v=e^x \implies \dfrac{\text{d}v}{\text{d}x}=e^x[/tex]
Apply the product rule:
[tex]\begin{aligned}f'(x)&=(2x+1)e^x+e^x(2)\\&=(2x+1)e^x+2e^x\\&=e^x(2x+1+2)\\&=e^x(2x+3)\end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\begin{aligned}f'(x)&=0\\e^x(2x+3)&=0\\2x+3&=0\\2x&=-3\\x&=-\dfrac{3}{2}\end{aligned}[/tex]
Therefore, the critical point of the function f(x) is when x = -3/2.
Related Questions
Which of the following functions have the following attributes?
-2 is a zero with multiplicity 2
5 is a zero with multiplicity 1
The graph is tangent to x-axis at x = 1
Answers
The function f(x) = (x+2)²(x-1)(x-5)² has-2 is a zero with multiplicity 2
5 is a zero with multiplicity 1 and the graph is tangent to x-axis at x = 1
For the function f(x) = (x+2)²(x-1)(x-5)²
-2 is a zero with multiplicity 2
This is represented by the factor (x+2)², indicating that -2 is a zero that appears twice in the function.
5 is a zero with multiplicity 1
This is represented by the factor (x-5), indicating that 5 is a zero that appears once in the function.
The graph is tangent to the x-axis at x = 1:
This is represented by the factor (x-1), indicating that the graph touches the x-axis at x = 1.
Therefore, the function f(x) = (x+2)²(x-1)(x-5)² has all the specified attributes.
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good people please help me!!!!!!
2.1show a=2,b=-2,c=-10 and d=-6
2.2 calculate the co-ordinate of turning point B
Answers
The coordinates of the point of intersection of the tangent and the secant are;
T(a, b) = (9/5, -14/5)
C = (0, -1)
What is a tangent to a circle?A tangent is a line or segment that touches a circle only once.
The equation of the line AN is; y - 2 = ((-2 - 2)/(2 - 3)) × (x - 3)
y = 4·x - 12 + 2 = 4·x - 10
y = 4·x - 10
The coordinates of the center of the circle is; ((-5 + 3)/2, (4 + 2)/2) = (-1, 3)
The radius of the circle is; √((3 - (-1))² + (2 - 3)²) = √(17)
The equation of the circle is; (x + 1)² + (y - 3)² = 17
The point C indicates;
(0 + 1)² + (y - 3)² = 17
(y - 3)² = 17 - 1 = 16
y - 3 = √(16) = ±4
y = 4 + 3 = 7, and y = -4 + 3 = -1
The coordinates of the point C is; (0, -1)
The slope of AC = (2 - (-1))/(3 - 0) = 1
AC is perpendicular to BC
The slope of BC = -1
The equation of BC is therefore; y - 4 = -(x - (-5)) = -x - 5
y = -x - 1
The equation of the segment AN is; y - 2 = ((2 - (-2))/(3 - 2))×(x - 3)
y - 2 = 4·(x - 3)
y = 4·x - 12 + 2 = 4·x - 10
-x - 1 = 4·x - 10
x-coordinate of T = 9/5
The y-coordinate of T = -9/5 - 1 = -14/5
Therefore, at the point T, we get; (9/5, -14/5)
a = 9/5, b = -14/5, C = (0, -1)
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Solve (y + 2)² +5=50, where y is a real number.
Round your answer to the nearest hundredth.
Answers
Answer:
y = 4.71 and y = -8.71
Step-by-step explanation:
Step 1: Subtract 5 from both sides:
((y + 2)^2 + 5 = 50) - 5
(y + 2)^2 = 45
Step 2: Take the square root of both sides, subtract 2 from both sides, and round to the nearest hundredth to solve for y.
Remember that taking the square root will give us both a negative and positive answer on the right-hand side of the equation. This is because squaring both a positive and negative number gives us. For example 2^2 = 2 * 2 = 4 but (-2)^2 = -2 * -2 = 4 alsoPositive answer:
√(y + 2)^2 = √45
(y + 2 = √45) - 2
y = √45 - 2
y = 4.708203932
y = 4.71
Thus, one answer for y (rounded to the nearest hundredth) is approximately 4.71.
Negative answer:
√(y + 2)^2 = -√45
(y + 2 = -√45) - 2
y = -√45 - 2
y = -8.708203932
y ≈ - 8.71
Thus, the other answer for y (rounded to the nearest hundredth) approximately. -8.71
Optional Step 3: We can check our work by plugging in 4.71 and -8.71 for y and seeing whether we get 50. Because they're rounded, you won't get exactly 50, but the answer should be close enough for us to trust our approximations:
Plugging in 4.71 for y:
(4.71 + 2)^2 + 5 = 50
(6.71)^2 + 5 = 50
45.0241 + 5 = 50
50.0241 > 50
Our answer is close enough to 50 that we can trust our approximation.
Plugging in -8.71 for y:
(-8.71 + 2)^2 + 5 = 50
(-6.71)^2 + 5 = 50
45.0241 + 5 = 50
50.0241 > 50
Again, our answer is close enough to 50 that we can trust our approximation.
12. A rectangle has a perimeter of 12y² - 2y +18 and has a width of 4y²-y + 6. What is the length of the rectangle?
Answers
Answer:
2y² + 3
Step-by-step explanation:
width of one side is 4y² - y + 6.
two equal sides of rectangle = 2(4y² - y +6) = 8y² - 2y + 12.
perimeter = 2 lengths + 2 widths
12y² - 2y + 18 = 2 lengths + 8y² - 2y + 12
2 lengths = (12y² - 2y + 18) - (8y² - 2y + 12)
= 4y² +6
length = 1/2 (4y² +6)
= 2y² + 3
Samuel was given the diagram below and asked to prove that AC ED. What
would be the reasoning for the third step of the proof?
Given: Quadrilateral ABCD is a rectangle.
Prove: AC & BD
Statements
1. Quadrilateral ABCD is a rectangle
2. AB & CD
3. ZBAD ZCDA
4. AD AD
5. ABAD ACDA
6. AC BD
B
A
Reasons
Given
Opposite sides of a rectangle are equal
Reflexive Property of Equality
SAS Triangle Congruence Theorem
Corresponding parts of congruent
triangles are congruent
C
O
Answers
The reasoning for the third step of the proof is the SAS Triangle Congruence Theorem, which establishes the congruence of the two triangles involved.
In the given proof, we are trying to prove that AC is equal to ED in a rectangle ABCD. The reasoning for the third step of the proof can be explained as follows:
Statement 3: ZBAD = ZCDA
Reason: SAS Triangle Congruence Theorem
Explanation: The SAS (Side-Angle-Side) Triangle Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
In this case, we are considering triangles ZBA and ZDA. We know that AB is congruent to AD (statement 2, "AB & CD") and that the angles ZBA and ZDA are right angles since ABCD is a rectangle (statement 1, "Quadrilateral ABCD is a rectangle").
Therefore, by the SAS Triangle Congruence Theorem, we can conclude that triangle ZBA is congruent to triangle ZDA. And since corresponding parts of congruent triangles are congruent (CPCTC), we can say that angle ZBAD is congruent to angle ZCDA.
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I WILL GIVE THE BRAINIEST
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an
Now let a be the number of students who went on the trip and s9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
Answers
An equation can be written to determine the number of students that went on this trip is: C. [tex]\frac{1259}{s} + 12=\frac{1259}{s+9}[/tex]
How to write an equation to determine the number of students that went on this trip?In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;
Let the variable s represent the number of students who went on the trip.Let the expression s + 9 represent the original number of students who had planned to go on the trip.Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;
[tex]\frac{1259}{s} + 12=\frac{1259}{s+9}[/tex]
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Complete Question:
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.
Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
Question 2 of 9
17 - (9 - 10) = (17- 9) - 10
O A. True
3
B. False
Answers
19
For an ideal gas, it is assumed that no attractive force exists between particles.
This is not true for reall gas. What effect does this attraction have on the
properties of a real gas when compared to those of an ideal gas under
equivalent conditions?
A
The pressure of the real gas is higher.
B
The temperature of the real gas is higher.
C
The pressure of the real gas is lower.
D
The temperature of the real gas is lower.
Answers
Find the following measure for this figure.
Area of the base =
Answers
The area of the base of the cylinder is A = 16π units²
Given data ,
Let the area of the base of the cylinder be A
Now , the radius of the cylinder is r = 4 units
And , the height of the cylinder is h = 6 units
where A = πr²
The base of the cylinder is a circular disk of radius r units
On simplifying , we get
A = π ( 4 )²
A = 16π units²
So , the value of A is 16π units²
Hence , the area of the base is A = 16π units²
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what is the reason behind Russia and ukarine war?
Answers
Answer:
Step-by-step explanation:
Ukraine wants to join the european union.Due to this Russia realize that if ukraine join the european union then if war started between Ukraine and any other country like Russia it means Ukraine and european union both attack on this country.
The 2008 attendance at the Ohio State Fair was at least 16,700 less than the attendance in 2009. If the attendance in 2008 was 809,300, write and solve an inequality to find the 2009 attendance
Answers
The solution to the inequality indicates that the attendance in 2009 must be 826,000 or more.
Let's assume the attendance in 2009 is represented by the variable A. According to the given information, the attendance in 2008 was at least 16,700 less than the attendance in 2009.
Mathematically, we can express this as:
A - 16,700 ≥ 809,300
To find the attendance in 2009, we need to solve this inequality.
First, we add 16,700 to both sides of the inequality:
A - 16,700 + 16,700 ≥ 809,300 + 16,700
Simplifying, we have:
A ≥ 826,000
Therefore, the attendance in 2009 is greater than or equal to 826,000.
In this case, the inequality A ≥ 826,000 indicates that the attendance in 2009 must be equal to or greater than 826,000 for the statement to hold true.
If the attendance in 2009 is less than 826,000, it would not satisfy the given condition that the attendance in 2008 was at least 16,700 less than the attendance in 2009.
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if two distinct numbers are chosen randomly from the set {-2, -6/5, -1/3, 0, 1/2, 5/6, 3}, find the probability that they will be the slopes of two perpendicular lines
Answers
To find the probability that two distinct numbers chosen randomly from the set {-2, -6/5, -1/3, 0, 1/2, 5/6, 3} will be the slopes of two perpendicular lines, we need to determine the total number of possible pairs of distinct numbers and the number of pairs that result in perpendicular slopes.
Total number of possible pairs:
Since we are choosing two distinct numbers from a set of seven, the total number of possible pairs is given by the combination formula:
C(7, 2) = 7! / (2!(7 - 2)!) = 7! / (2! * 5!) = 21
Pairs resulting in perpendicular slopes:
For two lines to be perpendicular, the product of their slopes must be -1. So, we need to count the number of pairs whose product is -1.
The set contains two negative numbers {-2, -6/5} and one positive number {3}. None of these numbers have a reciprocal within the set that gives a product of -1. Therefore, no pairs can be formed from these numbers that result in perpendicular slopes.
Hence, the number of pairs resulting in perpendicular slopes is 0.
Therefore, the probability of randomly choosing two distinct numbers from the set {-2, -6/5, -1/3, 0, 1/2, 5/6, 3} that will be the slopes of two perpendicular lines is 0/21, which simplifies to 0.
Suppose you own 125 shares of a stock that pays a dividend of $0.29 per
share per year. How much will you receive in dividends over 6 years,
assuming the dividends stay the same and you buy no more stock?
OA. $161.25
OB. $217.50
C. $174.00
D. $36.25
PREVIOUS
Answers
Hello !
125 * $0.29 * 6 = $217.50
Each member of a sports club plays at least one of soccer, rugby, or tennis. The following information is known: 43 members play tennis, 11 play tennis and rugby, 7 play tennis and soccer, 6 play soccer and rugby, 84 play rugby or tennis, 68 play soccer or rugby, and 4 play all three sports.
1. Display the information in a Venn diagram.
2. How many members play soccer only?
3. How many members play tennis or soccer, but not rugby?
4. How many members play exactly two sports?
5. How many members play at least one sport?
6. If 60 members play soccer, how many members play tennis?
Answers
1. The number of members who play soccer only is 59.
2. The number of members who play tennis or soccer, but not rugby, is 37.
3. The number of members who play exactly two sports is 20.
4. The number of members who play at least one sport is 195.
5. If 60 members play soccer, then 7 members play tennis.
1. To find the number of members who play soccer only, we need to subtract the members who play soccer and other sports from the total number of soccer players.
Soccer only = Total soccer players - (Soccer and Rugby) - (Soccer and Tennis) + (All three sports)
Soccer only = 68 - 6 - 7 + 4
Soccer only = 59
Therefore, 59 members play soccer only.
2. To find the number of members who play tennis or soccer but not rugby, we need to subtract the members who play all three sports from the total number of tennis and soccer players.
Tennis or Soccer (not rugby) = (Tennis + Soccer) - (All three sports)
Tennis or Soccer (not rugby) = 43 + 68 - 4
Tennis or Soccer (not rugby) = 107
Therefore, 107 members play tennis or soccer but not rugby.
3. To find the number of members who play exactly two sports, we need to add the members who play tennis and soccer (TS), tennis and rugby (TR), and soccer and rugby (RS).
Exactly two sports = TS + TR + RS
Exactly two sports = 7 + 11 + 6
Exactly two sports = 24
Therefore, 24 members play exactly two sports.
4. To find the number of members who play at least one sport, we can add the number of members who play each sport individually (Tennis, Rugby, Soccer) and then subtract the number of members who play none of the sports.
At least one sport = Tennis + Rugby + Soccer - None
At least one sport = 43 + 84 + 68 - 0
At least one sport = 195
Therefore, 195 members play at least one sport.
5. If 60 members play soccer, we can calculate the number of members who play tennis by subtracting the members who play both sports (TS) and the members who play soccer only from the total number of soccer players.
Tennis = Total soccer players - (Soccer only) - (TS)
Tennis = 60 - 59 - 7
Tennis = -6
It is not possible to have a negative number of members playing tennis. Please double-check the provided information or calculations.
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answer from the 4 options.
ASAP
Answers
Answer :
From the figure XY and WZ are opposite sides and XW and YZ are the opposite sides.
Opposite sides of Parallelogram are equal.XY = WZ
3a - 4 = a + 2
3a - a = 2 + 4
2a = 6
a = 6/2
a = 3
Now put the value of a in XY
XY = 3a - 4
XY = 3(3) - 4
XY = 9 - 4
XY = 5Similarly,
XW = YZ
2b = b + 1
2b - b = 1
1b = 1
b = 1
Now put the value of b in YZ
YZ = 2b
YZ = 2 × 1
YZ = 2XY = 5 and YZ = 2Answer :
D. XY = 5 , YZ = 2Step-by-step explanation :
As We Know that Opposite sides of the Parallelogram are equal.
SO,
(i) YZ = XW (opposite sides)
YZ = 2bXW = b + 1→ 2b = b + 1
→ 2b - b = 1
→ b = 1
Since, YZ = 2b
→ YZ = 2 × 1
→ YZ = 2.
Also,
(ii) XY = WZ (opposite sides)
XY = 3a - 4WZ = a + 2→ 3a - 4 = a + 2
→ 3a - a = 2 + 4
→ 2a = 6
→ a = 6/2
→ a = 3 .
Since, XY = 3a - 4
putting the value of a = 3.
=> 3(3) - 4
→ 9 - 4
→ 5
XY = 5.
Therefore, Option D is the required answer.
DATE 02 June 04 June TRANSACTION DESCRIPTION Opening Balance ATM Cash Debit card Payment Clothing Debit card POS Purchase Debit card POS Purchase #Monthly account fee 12 June 17 June 29 June 29 June #Service fees Zorro MTN Molino AMOUNT 100,00 A 1004.00 2840.00 12.50 5.25 CREDIT CHARGES 5154.69 5154 69 5034,69 4030 69 1190.69 B 1172.94 5.25 3.2.1 What is the opening balance? 3.2.2 The opening balance is on the credit side. Explain the implications on the bank statement 3.2.3 If Gloria decides to withdraw money at Capital bank ATM, how is this going to aff her finances? 3.2.4 Calculate the value of B
Answers
The opening balance is 100.00 A. Its placement on the credit side implies funds deposited before the statement period. The specific impact on Gloria's finances and the value of B are not provided.
Based on the provided information, let's address each question:
3.2.1 The opening balance is 100.00 A (currency is not specified). This amount represents the initial balance in the bank account before any transactions occur.
3.2.2 When the opening balance is on the credit side of the bank statement, it indicates that there were funds deposited or credited to the account before the statement period. In this case, the opening balance of 100.00 A suggests that there were funds deposited or credited into the account before the statement period began.
3.2.3 If Gloria decides to withdraw money at Capital Bank ATM, her account balance will decrease by the amount of the withdrawal. The specific amount of the withdrawal is not mentioned in the provided information, so we cannot determine the exact impact on her finances. However, it's important to note that ATM withdrawals may also incur transaction fees, which could further reduce her account balance.
3.2.4 Based on the information given, the value of B is not explicitly provided. It seems to be missing or not specified in the provided data. Without knowing the value of B, it is not possible to calculate it.
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A box contains 19 large marbles and 11 small marbles. Each marble is either green or white. 3 of the large marbles are green, and 4 of
the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is large or green? Express your
answer as a fraction or a decimal number rounded to four decimal places.
Answers
The probability of selecting a large or green marble is 0.7333.
The probability of selecting a large marble is 19/30 (19 large marbles out of 30 total marbles). The probability of selecting a green marble is 3/30 (3 green marbles out of 30 total marbles).
To find the probability of selecting a large or green marble, you need to find the probability of selecting a marble that is either large or green. This is known as the union of two events. The union of two events is found by adding the individual probabilities of each event together.
The probability of selecting a large or green marble is 19/30 + 3/30 = 22/30 = 0.7333.
Therefore, the probability of selecting a large or green marble is 0.7333.
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After a 95% reduction, you purchase a new television on sale for $181. What was the original price of the television? Round your solution to the nearest cent.
Answers
Answer:
The original price of the television was $3620.00.
Answer:
$3620.00
Step-by-step explanation:
5% = 181
1% = 36.2
100% = 3620
help me please so hard
Answers
Gradient is another word for slope.
Slope = rise/run = (y2-y1)/(x2-x1)
So pick 2 points.
Let's do line A first.
(1,1) and (2,4)
slope = (1-4)/(1-2)
= -3/-1 = 3
The slope (aka gradient) of line A = 3.
Line B.
(0,5) and (1,1)
slope = (5-1)/(0-1)
= 4/-1
= -4
The slope (aka gradient) of line B = -4.
is the ordered pair a solution to the equation. y=-7; (-5,6)
Answers
Answer: No
To check if (-5,6) is a solution to the equation y=-7, we need to substitute -5 for x and 6 for y in the equation.
If the equation is true, then the ordered pair is a solution to the equation.
If we put (-5,6) into y=-7, we get 6=-7, which is not true.
So, (-5,6) is not a solution to the equation y=-7.
Which side lengths form a right triangle?
Choose all answers that apply:
A 5,√8,33
B 8, 15, 17
√2, √2,2
Answers
Answer:
B and C
Step-by-step explanation:
Answer: B and C
Step-by-step explanation:
Pythagorean Theorem:
c²=a²+b² >where a and be are the shorter legs and c is the
longer/hypotenuse
Let's plug each into the pythagorean theorem
A) Not a right triangle
33² = 5² + (√8)²
1089 = 25 +8
1089 = 33 >Not equal, The statement is not true, so this is not a
right triangle.
B) Yes, it is a right triangle
17²=8²+15²
289=64+225
289=289 They are equal, true statement, so yes it is a right triangle
C) No, it is not a right triangle
2² = (√2)²+(√2)²
4 = 2+2
4=4 They are equal, true statement, so yes it is a right triangle
expand and simplify (x+2)(x-2)-(x+3)²
Answers
The Simplified form of the expression (x+2)(x-2) - (x+3)² is -13 - 6x.
The expression (x+2)(x-2) - (x+3)², we'll follow the distributive property and simplify each term.
First, let's expand (x+2)(x-2):
(x+2)(x-2) = x(x) + x(-2) + 2(x) + 2(-2)
= x² - 2x + 2x - 4
= x² - 4
Next, let's expand (x+3)²:
(x+3)² = (x+3)(x+3)
= x(x) + x(3) + 3(x) + 3(3)
= x² + 3x + 3x + 9
= x² + 6x + 9
Now, we can substitute these expansions into the original expression:
(x+2)(x-2) - (x+3)² = (x² - 4) - (x² + 6x + 9)
To simplify further, let's distribute the negative sign to every term inside the parentheses:
(x² - 4) - (x² + 6x + 9) = x² - 4 - x² - 6x - 9
Now, we can combine like terms:
(x² - x²) + (-4 - 9) - 6x = -13 - 6x
Therefore, the simplified form of the expression (x+2)(x-2) - (x+3)² is -13 - 6x.
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I thought of a number add 7 multiplied by 3 subtracted 3 divide by 2 then multiplied by 12.the result was 72 what the number I thought of ?
Answers
72/12 = 6
6x2 =12
12 +3 =15
15/3 = 5
5 -7 = -2
The answer is -2
A bag contains 3 gold marbles, 8 silver marbles, and 30 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
Answers
Answer: To calculate the expected value, we need to multiply each possible outcome by its probability and then add up the results.
The probability of selecting a gold marble is 3/41, the probability of selecting a silver marble is 8/41, and the probability of selecting a black marble is 30/41.
The winnings/losses associated with each outcome are $3 for gold, $2 for silver, and -$1 for black.
Step-by-step explanation:
Therefore, the expected value can be calculated as follows:
(3/41) x $3 + (8/41) x $2 + (30/41) x (-$1)
= $0.073
The expected value is $0.073, which means that on average, you can expect to win $0.073 per game if you play this game many times.
Therefore, if you play this game, you can expect to win a small amount of money on average, but it is not a guaranteed win.
References:
Grinstead, C.M. and Snell, J.L. (2006). Introduction to Probability. American Mathematical Society.
"Expected Value," Investopedia, accessed May 14, 2023, https://www.investopedia.com/terms/e/expectedvalue.asp.
pls help will mrak brainleist
Answers
Answer:
x = 18°Step-by-step explanation:
We know that,
sum of three side of triangle is 180°
So,
x + 72° + 90° = 180°
x + 162° = 180°
x = 180° - 162°
x = 18°
[tex]\underline{\rule{190pt}{4pt}}[/tex]
The value of x in the triangle is 18 degrees.
The given triangle is a right angled triangle.
We have to find the value of x.
As the triangle is a right angle one angle is 90 degrees.
And the other angle is 72 degrees.
The missing angle is x which we have to find.
By angle sum property we know that the sum of three angles is 180 degrees in a triangle.
72+90+x=180
Combine the like terms:
162+x=180
Subtract 162 from both sides:
x=180-162
When one hundred sixty two is subtracted from one hundred eighty, we get 18.
x=18 degrees
Hence, 18 degrees is the value of x in the triangle.
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Which side lengths form a right triangle?
Choose all answers that apply:
A 5,√8,33
B 8, 15, 17
√2, √2,2
Answers
Answer:
B and C
Step-by-step explanation:
We can determine which three sides will form a right triangle using the Pythagorean theorem, which is
a^2 + b^2 = c^2, where
a and b are the legs,and c is the hypotenuse and the longest sidesThus, a three side lengths can only form a right triangle if the sum of the squares of the shorter sides equal the square of the longest side (the hypotenuse)We can simply check A, B, and C to see which side lengths form a right triangle:A:
5 and √8 (approximately 2.236) are the shorter sides, so we plug these in for a and b in the Pythagorean theorem; 33 is the longest side, so we plug it in for c:5^2 + (√8)^2 = 33^2
25 + 8 = 1089
33 ≠ 1089
Because 33 is not equal to 1089, these three lengths do not form a right triangle.
B:
8 and 15 are the shorter sides, so we plug these in for a and b in the Pythagorean theorem;17 is the longest side, so we plug it in for c:8^2 + 15^2 = 17^2
64 + 225 = 289
289 = 289
Thus, these three side lengths form a right triangle.
C:
The two √2 (approximately 1.414) are the shorter sides, we plug these in for a and b in the Pythagorean theorem;2 is the longest side, so we plug it in for c:(√2)^2 + (√2)^2 = 2^2
2 + 2 = 4
4 = 4
Thus, these three side lengths also form a right triangle.
What is the result when - 2/3m + 4 is added to 5/6m - 1/2? A. - 1/6m + 7/2 B. 1/6m + 7/2 C. 3/2m - 9/2 D. - 3/2m + 9/2
Answers
The result when (-2/3m + 4) is added to (5/6m - 1/2) is 4 - 1/3m.
Hence, the correct answer is option A: -1/6m + 7/2.
To find the result when (-2/3m + 4) is added to (5/6m - 1/2), we need to combine like terms.
First, let's simplify the expression -2/3m + 4:
This can be rewritten as (4 - 2/3m).
Next, let's simplify the expression 5/6m - 1/2:
This can be rewritten as (5/6m - 3/6m).
Now, let's add the two expressions together:
(4 - 2/3m) + (5/6m - 3/6m)
Combining the constants and the terms with "m," we get:
4 + 5/6m - 2/3m - 3/6m
To simplify further, we need to find a common denominator for the fractions:
4 + 5/6m - (2/3m + 3/6m)
The common denominator for the fractions is 6:
4 + 5/6m - (4/6m + 3/6m)
Now, let's combine the like terms:
4 + 5/6m - 7/6m
Finally, we can simplify the expression:
4 - 2/6m
Simplifying further, we have:
4 - 1/3m.
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if y=- 5x {}^{2} determine the value of..
y if x=0
Answers
Answer:
Step-by-step explanation:
y = -5x^2
if x = 0 , then
y = -5(0)
y = 0
Which of the following ordered pairs represents the point plotted and labeled B?
(3, −1)
(−1, 2)
(3, 1)
(1, 2)
Answers
(3,1)
Ordered pairs are always ordered as (x,y). Point B has an x-value of 3 and a y-value of 1.
An angle with an initial ray pointing in the 3-o'clock direction measures θ radians (where 0≤θ<2π). The circle's radius is 3 units long and the terminal point is located at (−2.69,−1.33)
a. The terminal point is how many radius lengths to the right of the circle's vertical diameter. H=____ radians
B.When we evaluate cos−1(h) using a calculator or computer, the value returned is
____ radians
c.Therefore, θ=
Answers
a) The terminal point is 0.896 radius length.
b) The value returned is -0.896.
We have,
The circle's radius is 3 units long and the terminal point is located at (−2.69,−1.33)
a. Since the circle's radius is 3 units long, we divide the x-coordinate by 3:
x-coordinate of terminal point: -2.69
Number of radius lengths to the right: -2.69 / 3 ≈ -0.896
However, since the angle is measured from the 3-o'clock direction, we consider it to be in the clockwise direction.
Thus, the number of radius lengths to the right is
Number of radius lengths to the right: -(-0.896) = 0.896
Therefore, the terminal point is 0.896 radius length.
b. Using Trigonometry
cos(h) = x-coordinate of terminal point / radius length
cos(h) = -2.69 / 3 ≈ -0.896
c. As, θ = h. From the given information, we have:
θ ≈ -0.896 radians
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