a) Using theorems pertaining to transverals and parallel lines, prove that m∠1 + m∠2 = 180o
b) Find the value of x.
For the given set of parallel lines l and m, the value of x is equal to 4.
Explanation:According to the question,
l ║ m
As per the theorem pertaining to transversal and parallel lines,
∠1 and ∠2 are supplementary if and only if they are interior angles.
m∠1 + m∠2 = 180° _____(1)
Here, ∠1 = 20x + 5
∠2 = 24x - 1
Substitute the value ∠1 and ∠2 in (1), we get
20x + 5 +24x - 1 = 180°
44x + 4 = 180°
44x = 176
x = 4
Hence, for the given set of parallel lines l and m, the value of x = 4.
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Let f(x)=4x^2+5.
The g(x) is f(x) translated up 4 units.
What is the equation of g(x)
Please help!!
If a 6-sided die is rolled 5 times and rolling a 2 is considered to be a success, what are the chances of rolling exactly three successes?
show work
A.) 0.32% B.) 16.67% C.) 32.15% D.) 33.33% E) none of these
The probability of rolling exactly three 2s in five rolls of a six-sided die is 32.15%, calculated using the binomial probability formula. The correct answer from the provided options is C) 32.15%.
Explanation:The student is asking about the probability of achieving a specific number of successes in a series of independent events, which is a problem that can be solved using the binomial probability formula. In this case, a success is defined as rolling a 2 on a six-sided die. The probability of rolling a 2 (success) on a single roll is \(\frac{1}{6}\), and the probability of not rolling a 2 (failure) is \(\frac{5}{6}\).
Therefore, the probability of rolling exactly three 2s in five rolls can be calculated by the formula:
\(P(X=k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}\)
where \(n\) is the number of trials, \(k\) is the number of desired successes, and \(p\) is the probability of a single success.
Substituting the values:
\(P(X=3) = \binom{5}{3} \cdot \left(\frac{1}{6}\right)^3 \cdot \left(\frac{5}{6}\right)^{5-3}\)
\(P(X=3) = 10 \cdot \left(\frac{1}{6}\right)^3 \cdot \left(\frac{5}{6}\right)^2\)
\(P(X=3) = 10 \cdot \frac{1}{216} \cdot \frac{25}{36}\)
\(P(X=3) = \frac{250}{7776}\)
\(P(X=3) \approx 0.03215 \text{ or } 3.215\%\)
So the correct answer from the provided options is C) 32.15%.
The chances of rolling exactly three successes when rolling a 6-sided die 5 times, where rolling a 2 is considered a success, is approximately 2.143%.
Explanation:To find the chances of rolling exactly three successes, we need to use the concept of binomial probability. In this case, the probability of rolling a 2 (success) is 1/6, and the probability of not rolling a 2 (failure) is 5/6. We can use the formula for binomial probability: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success in one trial.
For this problem, n=5 (since the die is rolled 5 times), k=3 (we want exactly three successes), and p=1/6 (probability of rolling a 2). Plugging these values into the formula:
P(X=3) = (5 choose 3) * (1/6)^3 * (5/6)^(5-3)
Simplifying, we get:
P(X=3) = 10 * (1/6)^3 * (5/6)^2 = 10 * (1/216) * (25/36) = 250/11664 ≈ 0.02143 ≈ 2.143%
Intr-un top de hartie sunt 26 de coli de matematica 15 coli de dictando si 30 de coli de hartie alba. care este probabilteata ca extragand la intamplare o coala ea sa fie de matematica?
What is the simplified form of i13?
A. -i
B. 1
C. -1
D. i
The simplified form of i^13 is -i.
The simplified form of i^13 is -i.
To find the simplified form, remember that i^4 = 1, so i^13 = i^(4*3+1) = i^(4*3) * i = (i^4)^3 * i = 1^3 * i = i.
Therefore, the simplified form of i^13 is -i.
Suppose that it takes Jenny 2 hours to wax a car if she works alone and it takes Carol 4 hours to wax the same car if she works alone. How long will it take them to wax the car, in hours, if they work together?
Calvin and Alvin together take approximately 1.875 hours, or 1 hour and 52.5 minutes, to wax a car.
To find out how long it takes Calvin and Alvin to wax a car together, we can use the formula for working together:
[tex]\[\frac{1}{T} = \frac{1}{T_1} + \frac{1}{T_2}\][/tex]
Where:
-[tex]\( T \)[/tex] is the time taken when working together,
- [tex]\( T_1 \)[/tex] is the time taken by Calvin alone, and
- [tex]\( T_2 \)[/tex] is the time taken by Alvin alone.
Given:
- Calvin takes 3 hours to wax a car alone, so [tex]\( T_1 = 3 \)[/tex] hours,
- Alvin takes 5 hours to wax a car alone, so [tex]\( T_2 = 5 \)[/tex] hours.
Substitute the values into the formula:
[tex]\[\frac{1}{T} = \frac{1}{3} + \frac{1}{5}\][/tex]
To solve for T, first find a common denominator:
[tex]\[\frac{1}{T} = \frac{5}{15} + \frac{3}{15} = \frac{8}{15}\][/tex]
Now, invert both sides of the equation to isolate T:
[tex]\[T = \frac{15}{8} \text{ hours} \approx 1.875 \text{ hours}\][/tex]
So, it takes Calvin and Alvin approximately 1.875 hours, or 1 hour and 52.5 minutes, to wax a car together.
The Correct Question is :
Suppose that it takes Calvin 3 hours to wax a car if he works alone and it takes Alvin 5 hours to wax a car if he works alone.
How long does it take them to wax a car if they work together? Write an equation and solve for the unknown.
Show your work.
Jack unfolded a cardboard box. The figure of the unfolded box is shown below:
Which expression can be used to calculate the area of cardboard, in square inches, that was used to make the box?
A.8 x 6 x 6
B.6 x 4 x 4
C.4 x 6 x 6
D.6 x 8 x 8
Answer:
8*6*6
Step-by-step explanation:
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You have less than 120 minutes to spend in the gym and in the pool. You want to spend less than 45 minutes in the gym and more than 30 minutes in the pool. Which system represents the situation?
The situation can be represented as three inequalities: g + p < 120, g < 45, p > 30, where g is the time spent in the gym and p is the time spent in the pool.
Explanation:The situation you described can be represented as a system of inequalities. Let's denote gym time as g and pool time as p. Then, the system of inequalities would be the following:
g + p < 120 (you want to spend less than 120 minutes in the gym and in the pool total)g < 45 (you want to spend less than 45 minutes in the gym)p > 30 (you want to spend more than 30 minutes in the poolThese inequalities represent the constraints on how you can divide your time between the gym and the pool. Any solution to this system would be a pair of numbers (g, p) that satisfy all three inequalities, meaning it's a valid way for you to divide your time.
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The correct system of inequalities is Option 1: x + y < 120 (representing the total time constraint), x < 45 (reflecting the condition of spending less time in the gym), and y > 30 (representing the condition of spending more time in the pool). This corresponds to Option 1 in the given systems of inequalities.
Explanation:The correct system of inequalities that represents your time allocation between the gym and the pool is Option 1. Let's define x as the time you spend in the gym and y as the time you spend in the pool. According to the given conditions and constraints, the total time, which is the sum of x and y, should be less than 120 minutes (x + y < 120). Furthermore, you want to spend less than 45 minutes in the gym (x < 45) and more than 30 minutes in the pool (y > 30). These three inequalities jointly form a system that accurately represents your situation at the gym and pool.
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The complete question is given below:
You have less than 120 minutes to spend in the gym and in the pool. You want to spend less than 45 minutes in the gym and more than 30 minutes in the pool. Which system represents the situation?
Option 1:
x + y < 120
x < 45
y > 30
Option 2:
x + y = 120
x = 45
y = 30
Option 3:
x + y <= 120
x < 45
y > 30
Option 4:
x + y < 120
x <= 45
y >= 30
robert leaves his home to go to his office . he drives 6km due north and then 4 km due east. approximatel what is the shortest distance from roberts home to his office , in kms?
To find the shortest distance from Robert's home to his office, we use the Pythagorean theorem with the distances traveled north and east to calculate the length of the hypotenuse, which is approximately 7.2 kilometers.
Robert leaves his home and drives 6 km due north and then 4 km due east. To determine the shortest distance from Robert's home to his office, we can use the Pythagorean theorem. This scenario forms a right-angled triangle where the two sides are the north-bound and east-bound legs of his journey, and the hypotenuse is the shortest distance.
Step 1: Label the lengths of the two sides adjacent to the right angle as 'a' and 'b', where 'a' is the 6 km north-bound leg and 'b' is the 4 km east-bound leg.
Step 2: Apply the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides:
c² = a² + b²
Step 3: Substitute the known values into the theorem:
c² = 6² + 4²
Step 4: Calculate the squares of the sides and sum them:
c² = 36 + 16
Step 5: Sum the squares gives us:
c² = 52
Step 6: Take the square root of both sides to find 'c':
c = √52
Step 7: Calculate the square root which approximately equals:
c = 7.2 km
Therefore, the shortest distance from Robert's home to his office is approximately 7.2 kilometers.
If and , find .
A.
B.
C.
D.
Which system of equations can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x?
A). Y=-4x^5+12x^4-6x and y=5x^3-2x
B). Y=4x^5-12x^4+5x^3+4x and y=0
C). Y=4x^5-12x^4+6x and y= -5x^3+2x
D). Y=4x^5-12x^4+6x and y=5x^3-2x
Answer:
D). Y'= [tex]4x^{5}-12x^{4}+6x[/tex] and y'= [tex]5x^{3}-2x[/tex]
Step-by-step explanation:
We are given the equation [tex]4x^{5}-12x^{4}+6x=5x^{3}-2x[/tex].
On simplifying this equation, we get [tex]4x^{5}-12x^{4}-5x^{3}+8x=0[/tex]
i.e. Let, Y'= [tex]4x^{5}-12x^{4}+6x[/tex] and y'= [tex]5x^{3}-2x[/tex]
Now, according to the options,
A) Y = [tex]-4x^{5}+12x^{4}-6x[/tex] = -Y' , that means the graph will be inverse of the required graph.
B) As the coefficient of 'x' in our given equation and the equation of option B are different, both will have different graphs.
C) As y = [tex]-5x^{3}+2x[/tex] = -y', this means that the graph will be inverse of the required graph.
Hence, all above options are discarded and so option D is correct.
A right triangle has legs that are 18 centimeters and 27 centimeters long. What is the length of the hypotenuse?
Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.
Answer:
the length of the hypotenuse = 32.45 centimeters
Step-by-step explanation:
A right triangle has legs that are 18 centimeters and 27 centimeters long
In a right angle triangle , to find hypotenuse we use Pythagorean theorem
[tex]c^2= a^2+b^2[/tex]
where a and b are the length of two legs
Given a= 18 and b = 27
Lets find out C , plug in all the value in the formula
[tex]c^2= 18^2+27^2[/tex]
[tex]c^2=324 +729= 1053[/tex]
c^2 = 1053
now take square root on both sides
c= 32.45
So the length of the hypotenuse = 32.45 centimeters
Solve the system of equations using the substitution method.
{4x+5y=7
{y=3x+9
Enter your answers in the boxes.
x=
y=
The value of x is 2 and value of y is 3 in the system of equation.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of equations are 4x+5y=7
y=3x+9
We have to find the value of x and y by substitution method in system of equation
Substitute the value of y in first equation
4x+5(3x+9)=7
4x+15x+45=7
Add the like terms
19x+45=7
Subtract 45 on both sides
19x=7-45
19x=-38
Divide both sides by 19
x=-2
Now plug in x value
y=3(-2)+9
y=3
Hence, the value of x is 2 and value of y is 3 in the system of equation.
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Find the exact values of the remaining trigonometric functions of θ satisfying the given conditions. (if an answer is undefined, enter undefined.) csc θ = 14, cot θ < 0
Given that csc θ = 14 and cot θ < 0, we find that sin θ = 1/14 and cos θ must be negative. We use the identity sin² θ + cos² θ = 1 to solve for the exact value of cos θ, selecting the negative solution. The remaining trigonometric functions are then found using these values.
Explanation:Given that the cosecant of theta (csc θ) is 14 and cotangent of theta (cot θ) is less than zero, we can find the other trigonometric values. We begin by recalling that cosecant is the reciprocal of the sine function, so sin θ = 1/14. Subsequently, we are told cot θ < 0, which means either the cosine or the sine (or both) must be negative.
Since cot θ is negative and we know sin θ is positive (since csc θ is positive), then we can conclude that cos θ must be negative. However, the exact value of cos θ is not readily identifiable from these properties alone.
To find the trigonometric value of cos θ, we can utilize the identity sin² θ + cos² θ = 1. Substituting our known sin θ value, we solve for cos θ. This gives us two possible solutions for cos θ, either positive or negative. As previously deduced, we select the negative solution for cos θ. The remaining trigonometric functions can then be found given these values:
tan θ = sin θ / cos θ,sec θ = 1 / cos θ, andcot θ = 1 / tan θ, or alternatively, cos θ / sin θ.Learn more about Trigonometry here:https://brainly.com/question/11016599
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can someone explain how to do this question and how to solve problems like this?
An amusement park charges an admission fee of 50 dollars for each person. let c be the cost (in dollars) of admission for p people. write an equation relating c to p . then use this equation to find the cost of admission for 17 people.
The equation relating the cost of admission (c) to the number of people (p) is c = 50 * p. For 17 people, the total cost is c = 50 * 17, which equals $850.
To write an equation relating c to p, we set c, the cost of admission for p people, equal to the admission fee per person multiplied by the number of people. Given that the admission fee per person is $50, the equation is:
c = 50 * p
Using this equation to find the cost of admission for 17 people:
c = 50 * 17
c = $850
Therefore, the cost of admission for 17 people is $850.
You must use the substitution method. 3x+2y=11
y=5x-1
Write 3 16/25 as a percent. PLEASE HELP WILL GIVE MEDAL.
First step to solve this is to convert this mixed fraction into improper fraction. To convert this, you need to multiply the denominator to the whole number then add the numerator. The result would be the numerator of the improper fraction. The denominator is the same:
(25 x 3) + 16 = 91
Therefore, the improper fraction is 91/25. To change this to percentage, you need to divide the numerator with the denominator and multiply by 100.
91/25 = 3.64 x 100 = 364%
Which point slope equation represents a line that passes through (3, -2) with a slope of - 4/5
• y - 3 = -4/5 (x + 2)
• y - 2 = 4/5 (x - 3)
• y + 2 = -4/5 (x - 3)
• y + 3 = 4/5 (x + 2)
Part 1.] Which of the following is the inverse of the given function?
[tex]y= 3 x^{5}-4[/tex]
A.] [tex]y= \sqrt[5]{ \frac{x+3}{4}} [/tex]
B.] [tex]y= \sqrt[5]{ \frac{x-4}{3}} [/tex]
C.] [tex]y= \sqrt[3]{ \frac{x+4}{5}} [/tex]
D.] [tex]y= \sqrt[5]{ \frac{x+4}{3}} [/tex]
Part 2.] What is the inverse of the function [tex]y=3 e^{-4+1} [/tex]?
A.] [tex]y= \frac{1-log(x-3)}{4} [/tex]
B.] [tex]y= \frac{1-log( \frac{x}{3})}{4} [/tex]
C.] [tex]y= \frac{1-ln(x-3)}{4} [/tex]
D.] [tex]y= \frac{1-ln( \frac{x}{3})}{4} [/tex]
What is the number of possible outcomes if two quarters are tossed and the total numbers of heads and tails are counted?
A) 2
B) 3
C) 4
D) 6
Answer:
B
Step-by-step explanation:
TT two tails/no heads
TH one tail/one head
HT
HH two heads/no tails
The number of possible outcomes if two quarters are tossed and the total numbers of heads and tails are counted is 8.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Since there are number of possibility as;
TT two tails/no heads
TH one tail/one head
HTand HH two heads/no tails
Each quarter will come up heads or tails which is 2 possibilities.
Thus for three tosses the number of outcomes is 2 x 2 x 2 = 8.
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(05.07) A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 1.5 centimeters and side length of triangle labeled 3 centimeters.
6.75 cm2
11.25 cm2
20.25 cm2
81.75 cm2
Answer:
11.25 cm2 would be your answer.
Angela used multiplication to simplify the expression by distributing the
1
2
through the parentheses.
Angela's expression:
1
2
(6X + 2)
Simplified expression: 3x + 2
Which statement is true of Angela’s work?
She correctly distributed the mc001-1.jpg through the parentheses.
Division, rather than multiplication, is the operation to use when distributing.
Angela needed to multiply mc001-2.jpg by each of the terms inside the parentheses.
Her product when multiplying mc001-3.jpg is incorrect.
Answer:
Angela needed to multiply [tex]\frac{1}{2}[/tex] by each of the terms inside the parentheses.
Her product when multiplying [tex]\frac{1}{2} X 2[/tex] is incorrect.
Step-by-step explanation:
For simplifying the expression [tex]\frac{1}{2}(3x+2)[/tex], we need to multiply [tex]\frac{1}{2}[/tex] by each of the terms inside the parentheses.
So,
Upon multiplying [tex]\frac{1}{2}[/tex] by 6X we get 3X.
Upon multiplying [tex]\frac{1}{2}[/tex] by 2 we get 1.
Thus the final simplified expression must be 3x+1
So we can say,
Angela needed to multiply [tex]\frac{1}{2}[/tex] by each of the terms inside the parentheses.
Her product when multiplying [tex]\frac{1}{2} X 2[/tex] is incorrect.
Angela attempted to use the distributive property to simplify the expression 1/2 (6X + 2), but while she correctly simplified 1/2 * 6X to 3X, she incorrectly simplified 1/2 * 2 as 2, instead of 1. Therefore, her method was correct, but the computation was incorrect.
Explanation:In mathematics, the Distributive Property is used to simplify expressions like the one Angela has used - 1/2 (6X + 2). In order to distribute correctly, Angela should perform the operation of multiplication for each term inside the parentheses by the 1/2 outside the parentheses. Therefore, it should look like this: (1/2 * 6X) + (1/2 * 2). This will simplify to 3X + 1. The issue with Angela's work was that, while she correctly simplified 1/2 * 6X to 3X, she incorrectly simplified 1/2 * 2 as 2, instead of the correct 1 value. Therefore, the correct statement about Angela's work is "Her product when multiplying is incorrect".
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A restaurant owner spends 892 for 65 pounds of produce. Which equation could you use to find the price per pound
In the triangle below, what is the length of the side opposite the 60 angle?
Answer with explanation:
In the given right triangle
[tex]\sin 60^{\circ}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\ \frac{\sqrt{3}}{2}=\frac{\text{Perpendicular}}{2\sqrt{3}}\\\\ \text{Perpendicular}}=2\sqrt{3} \times\frac{\sqrt{3}}{2}\\\\\text{Perpendicular}}=\sqrt{3} \times\sqrt{3} \\\\\text{Perpendicular}}=3[/tex]
→Side opposite to 60° angle = 3 units
Option C : 3 Units
Which of these choices is considered an environmental cost?
A. Net profit
B. Processing expenses
C. Resource depletion
D. Product price
By definition we have to:
Natural resources are all the material goods and services provided by nature without alteration by human beings; and that they are valuable for human societies because they contribute directly to their well-being and development (raw materials, minerals, food) or indirectly (essential ecological services for the continuity of life on the planet).
Therefore, the depletion of natural resources is considered an environmental cost because without these resources, life on planet Earth is difficult as we know it today.
Answer:
C. Resource depletion
Please please help asap!
What is the volume of this oblique cone?
Some steps to rewrite the expression x3 − x + 2x2 − 2 as a product of three factors are shown below:
Step 1: x3 − x + 2x2 − 2
Step 2: x3 + 2x2 − x − 2
Step 3: x2(x + 2) − 1(x + 2)
Which of the following best shows the next two steps to rewrite the expression? Step 4: (x2 + 1)(x + 2); Step 5: (x + 1)(x + 1)(x + 2)
Step 4: (x2 − 1)(x + 2); Step 5: (x − 1)(x + 1)(x + 2)
Step 4: (x2 − 1)(x + 2); Step 5: (x + 1)(x + 1)(x + 2)
Step 4: (x2 + 1)(x + 2); Step 5: (x − 1)(x + 1)(x + 1)
Darryl deposits $1,500 into a savings account that has a simple interest rate of 2.7%. Lori deposits $1,400 into a savings account that has a simple interest rate of 3.8%. If no other transactions are made, who will have more money in their account after 10 years? How much more?
Answer:
Lori will make $27.00 more.
Step-by-step explanation:
The formula to calculate simple interest is
A = P(1+rt)
P = Principal amount
r = rate of interest ( in decimal )
t = time
First we calculate Darryl's deposit, so put the values in the formula
A = 1,500(1 + 0.027×10)
A = 1,500 ( 1+0.27 )
A = 1,500 × 1.27
A = $1905
Now we will calculate Lori's deposit
A = 1,400 ( 1 + 0.038 × 10 )
A = 1,400 ( 1 + 0.38 )
A = 1,400 × 1.38
A = $1,932
Lori will make money after 10 years = $1,932
Darryl will make money after 10 years = $1905
so Lori will make more than Darryl, the difference will be = 1,932 - 1,905 = $27
After 10 years Lori will have make $27.00 more in their account.
Answer:
$27
Step-by-step explanation:
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The midpoint of a segment is (6,−6) and one endpoint is (13,−1). Find the coordinates of the other endpoint.
Answer: The other endpoint of the segment is (-1, -11).
Step-by-step explanation: Given that the midpoint of a line segment is (6, -6) and one endpoint is (13, -1).
We are to find the co-ordinates of the other endpoint.
Let (a, b) be the co-ordinates of the other end-point.
Then, according to the given information, we have
[tex]\left(\dfrac{a+13}{2},\dfrac{b+(-1)}{2}\right)=(6,-6)\\\\\\\Rightarrow \left(\dfrac{a+13}{2},\dfrac{b-1}{2}\right)=(6,-6).[/tex]
Equating the x and y co-ordinates on both sides of the above, we get
[tex]\dfrac{a+13}{2}=6\\\\\\\Rightarrow a+13=12\\\\\Rightarrow a=12-13\\\\\Rightarrow a=-1[/tex]
and
[tex]\dfrac{b-1}{2}=-6\\\\\\\Rightarrow b-1=-12\\\\\Rightarrow b=-12+1\\\\\Righatrrow b=-11.[/tex]
Thus, the other endpoint of the segment is (-1, -11).