If m∠CXP = 106.02°, m∠SYD is 73.98°. Among the given ones the correct option is 1.
What is Transversal?In geometry, a transversal is a line that intersects two or more other lines in a plane.
When a transversal intersects two parallel lines, it forms a set of eight angles, including alternate interior angles, alternate exterior angles, corresponding angles, and consecutive interior angles.
If the lines PQ←→ and RS←→ are parallel, then the alternate interior angles formed by transversal CD←→ are congruent. Therefore, we have:
m∠CXP = m∠DYX (alternate interior angles)
m∠CXD + m∠DXP = 180° (linear pair)
We can use these two equations to find m∠SYD. First, we need to find m∠CXD, which is the same as m∠YXC because they are vertical angles. We know that:
m∠CXP = 106.02°
So, we can use the linear pair equation to find m∠DXP:
m∠CXD + m∠DXP = 180°
m∠DXP = 180° - m∠CXD
Substituting m∠CXD = m∠YXC, we get:
m∠DXP = 180° - m∠YXC
Now, using the alternate interior angles equation, we can replace m∠CXP with m∠DYX:
m∠DYX = m∠CXP = 106.02°
Finally, we can use the linear pair equation again to find m∠SYD:
m∠DYX + m∠SYD = 180°
m∠SYD = 180° - m∠DYX
m∠SYD = 180° - 106.02°
m∠SYD = 73.98°
Therefore, m∠SYD is 73.98°, i.e., option 1.
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EASY QUESTION PLZ HELP
evaluate 10^-7
Final answer:
To evaluate 10⁻⁷, it is understood as 1 divided by 10 to the seventh power, or 0.0000001. This notation is used in scientific measurements, for instance in expressing the hydronium ion concentration based on pH.
Explanation:
To evaluate 10⁻⁷, we must understand the notation of negative exponents.
10 raised to the power of -7 can be written as 1 divided by 10 raised to the power of 7:
10⁻⁷ = 1 / 10⁷
Since 10 raised to any positive power results in a large number, 10 raised to the power of 7 is a very large number (10,000,000). Dividing 1 by this large number is very close to zero:
1 / 10⁷≈ 0.000 000 1
Therefore, 10⁻⁷ is approximately equal to 0.000 000 1. This value is incredibly small, representing one divided by ten million.
This type of notation is commonly used in scientific measurements, such as expressing the concentration of hydrogen ions in a solution with a certain pH level.
(cosx/(secx-tanx)) = 1+senx
i dont know how to prove this! HELP ...?
Rewrite the square-root expression as an imaginary number: sqrt of -64
is it 8i?
Answer:
The square root of -64 is 8i
Step-by-step explanation:
Given the number -64
we have to find the square root of the above number i.e [tex]\sqrt{-64}[/tex]
As
[tex]\sqrt{-64}=\sqrt{-8\times 8}[/tex]
[tex]=\sqrt{-(8)^2}[/tex]
[tex]=\sqrt{(-1)(8)^2}[/tex]
[tex]=\sqrt{-1}\sqrt{8^2}=8i[/tex]
Hence, the square root of -64 is 8i
for a research project, students are asked to study how often students at an online high school look at social media while doing schoolwork
what is a proportional relationship
Find the solutions of the given system of equations: y = x2 – 7x + 16 and y = x - 1.
The solutions of the given system of equations: y = x2 – 7x + 16 and y = x - 1 is 4 + i and 4 - i.
what is quadratic equation?
A quadratic equation in the variable x is an equation of the form
ax² + bx + c= 0, where a, b, c are real numbers, a * 0.
Given equations are:
y= x²-7x+16 and y=x-1
So, x-1= x²-7x+16
or, x²-8x+17=0
or, x²-8x+17 =0
a=1, b=-8, c=17
Using discriminant method,
x= [tex]-b\pm\sqrt{b^{2}-4ac } /2a[/tex]
x= -(-8) ± [√(-8)²- 4*1*17]/2*1
x=8±√(√64-68)/2
x= 8±√(-4)/2
x= 4 ± i
x= 4 + i and x= 4 - i
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What is negative 8 over 12?
Daniel has $25 to spend at the fair. If the admission to the fair is $4 and the rides cost $1.50 each , what is thw greatest number of rides daniel can go in ?
Daniel can go on 14 rides at the fair.
Explanation:To find out the greatest number of rides Daniel can go on, we need to calculate the cost of admission and the cost of the rides. The admission to the fair is $4 and each ride costs $1.50. To determine the number of rides, we subtract the cost of the admission from the total amount Daniel has to spend and then divide that by the cost of each ride. So, Daniel can go on (25 - 4) / 1.50 = 14 rides. Therefore, the greatest number of rides Daniel can go on is 14.
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PLZ HELP ME
What is 3^2/3 equal to?
3 square root of 9
2swuare root of 9
3 square root of 27
2 square root of 27
A pack of gum costs 75 cents. That is 3 cents less than three times what the pack cost 20 years ago. Which equation could be used to find the cost of the gum 20 years ago?
Answer:
the answer is actually 3x - 0.03 = 0.75
Step-by-step explanation:
A spinner used for a game is divided into 4 sections: Yellow, Brown, Red and Orange. The spinner is spun 50 times and lands on brown 18 times. What is the experimental probability that the spinner does NOT land on brown?
Answer:
[tex]\frac{16}{25} =0.64[/tex]
Step-by-step explanation:
Given : A spinner used for a game is divided into 4 sections: Yellow, Brown, Red and Orange. The spinner is spun 50 times and lands on brown 18 times
To Find: What is the experimental probability that the spinner does NOT land on brown
Solution :
Since we are given that the spinner is spun 50 times .
Ans the spinner lands on brown 18 times
Probability of landing on brown = [tex]\frac{18}{50} =\frac{9}{25}[/tex]
Since we know that the sum of probabilities is 1
So, probability that the spinner does NOT land on brown is :
⇒ 1 - prob. of landing on brown
⇒[tex]1-\frac{9}{25}[/tex]
⇒[tex]\frac{25-9}{25}[/tex]
⇒[tex]\frac{16}{25}[/tex]
Thus probability that the spinner does NOT land on brown is 16/25=0.64
4.The point (2, 8) is on the graph of f(x) = x3. What is the value of b if the point (0.5, 8) is on the graph of f(bx)?
X/2+3= 5 its solving equations (with three terms) please help me
Each month, Kaisorn deposits $50.00 onto her public transportation card. It costs her $2.50 per trip to ride the subway. Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway.
If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs?
A 50 − 2.5x = y
40 − 2x = y
B 50 + 2.5x = y
40 + 2x = y
C 50 − 2.5y = x
40 − 2y = x
D50 + 2.5y = x
40 + 2y = x
Answer:
A. 50 − 2.5x = y
40 − 2x = y
Step-by-step explanation:
We know that x represents the number of trips and y represents the amount remaining in each account, then, let's think in an example; after the first trip x = 1, therefore, Kaisorn's account must decrease from $50 to $50 - $2.5 = $47.5 = y, and Thom's account must decrease from $40 to $40 - $2 = $38 = y. Replacing x = 1 in each case gives:
A
50 − 2.5(1) = y
47.5 = y
40 − 2(1) = y
38 = y
B
50 + 2.5(1) = y
52.5 = y
40 + 2(1) = y
42 = y
C
50 − 2.5y = (1)
y = (1 - 50)/(-2.5)
y = 19.6
40 − 2y = (1)
y = (1 - 40)/(-2)
y = 19.5
D
50 + 2.5y = (1)
y = (1 -50)/2.5
y = -19.6
40 + 2y = (1)
y = (1 - 40)/(2)
y = -19.5
As it can be seen, option A is the correct one.
What are two numbers that multiplied equals 4900 but when added equals 140?
Evaluate the function at the given point.
x = –15
x –15 –2 –1 0 13 16 22
y –2 –15 0 3 5 12 13
A.y = –15
B.y = 5
C.= –2
D.y = 13
The value of the tabular function at x = –15 will be –2. Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given in the form of a table.
x –15 –2 –1 0 13 16 22
y –2 –15 0 3 5 12 13
The value of y corresponds to x is the value of the function.
The value of the tabular function at x = –15 will be –2. Then the correct option is C.
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Which of the following is the most accurate definition of a function
The data set represents the number of snails that each person counted on a walk after a rainstorm. 12, 13, 22, 16, 6, 10, 13, 14, 12 The outlier of the data set is .
Answer: 22
Step-by-step explanation:
Given : The data set represents the number of snails that each person counted on a walk after a rainstorm.
The given data : 12, 13, 22, 16, 6, 10, 13, 14, 12
Arrange in order : 6,10 , 12, 12, 13, 13, 14, 16, 22
We can see that all data values are closer to each other except 22.
22 is an extreme value as compare to the entire data values.
Therefore, the outlier of the data set is 22 .
Solve for x.
6(x – 1) = 9(x + 2)
To solve for x in the equation 6(x – 1) = 9(x + 2), expand and simplify the equation, combine like terms, isolate the variable x, and solve for x by dividing both sides by 3.
Explanation:To solve for x in the equation 6(x – 1) = 9(x + 2), we can begin by expanding the equation:
6x - 6 = 9x + 18
Next, we can combine like terms by subtracting 6x from both sides:
-6 = 3x + 18
Then, we can isolate the variable x by subtracting 18 from both sides:
-24 = 3x
Finally, we can solve for x by dividing both sides by 3:
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6. Complete the two-column proof.
Given:x/6+2=15
Prove: x = 78
Statement: x/6+2=15 Reason: A:
x/6=13 B:
x=78 C:
Answer:
Given: [tex]\frac{x}{6} + 2 = 15[/tex] ......[1]
To prove : x =78
Subtraction property states that you subtract the same number to both sides of an equation.
Subtract 2 from both sides of an equation [1];
[tex]\frac{x}{6} + 2 - 2= 15 -2[/tex]
Simplify:
[tex]\frac{x}{6} = 13[/tex] ......[2]
Multiplication property states that you multiply the same number to both sides of an equation.
Multiply 6 to both sides of an equation [2];
[tex]\frac{x}{6} \times 6 = 13 \times 6[/tex]
Simplify:
[tex]x = 78[/tex] proved!
Statement Reason
1. [tex]\frac{x}{6} + 2 = 15[/tex] Given
2. [tex]\frac{x}{6} = 13[/tex] Subtraction property of equality
3. [tex]x = 78[/tex] Multiplication property of equality
Final answer:
To solve for x, subtract 2 from both sides of the equation, then multiply both sides by 6. This yields that x equals 78, completing the proof.
Explanation:
To complete the two-column proof, we start with what is given and use algebraic manipulation to prove that x equals 78. Here are the steps formatted into a proof:
Statement: x/6 + 2 = 15 Is b a linear combination of a1, a2, and a3?
a1= (1, -2, 0); a2= (0,1,2); a3=(5, -6, 8); b= (2,-1,6) ...?
Factor completely 25x2 – 36
Answer
(5x – 6)(5x – 6)
(6x – 5)(6x – 5)
(6x – 5)(6x + 5)
(5x – 6)(5x + 6)
...?
(5X-6)(5X+6) THIA IA THE ANSWER TO THE problem
What is 65 percent of 40?
First, let's write 65% as a decimal. We can do this by moving the decimal point 2 places to the left. When we do this, we will get 0.65.
Next, the word of means "multiply" so we have to multiply 0.65 by 40.
(.65) × (40) = 26.00
To calculate 65 percent of 40, convert 65% to a decimal (0.65) and then multiply by 40 to get the answer, which is 26.
To find what 65 percent of 40 is, you can convert the percentage to a decimal and then multiply by the number. To convert a percentage to a decimal, divide it by 100. In this case, 65% becomes 0.65.
Next, multiply 0.65 by 40 to get the answer.
The calculation process looks like this:
0.65 (converted percentage) × 40 (the number) = 26
Therefore, 65 percent of 40 is 26.
Stephen wants to buy yellow tangs and clown fish for his saltwater aquarium. He wants to spend no more than $77 on fish. At the store, yellow tangs cost $15 each and clown fish cost $11 each. Write and graph a linear inequality to find the number of yellow tangs x and the number of clown fish y that Stephen could purchase. Name a solution of your inequality that is not reasonable for the situation. Explain
What might cause the disappearance of animals in the wild
Various factors cause the disappearance of animals in the wild, including habitat destruction, hunting, disease, and changes in predator-prey relationships.
Explanation:The disappearance of animals in the wild can be caused by various factors, including habitat destruction, hunting, disease, and changes in predator-prey relationships. One of the main factors is habitat destruction, which occurs when natural habitats are altered or destroyed by human activities such as farming, logging, and construction. This leads to a loss of biodiversity as plant and animal populations are destroyed or displaced.
Hunting is another major cause of animal disappearance. Animals are hunted for various purposes including meat, hides, and horns. Large mammals are particularly vulnerable as they are often targeted for their valuable resources. In addition, diseases can spread among animals due to human activities, such as the introduction of domestic animals, leading to population declines and even extinctions.
Changes in predator-prey relationships can also affect animal populations. For example, the decline of predators like cougars, lions, and leopards can result in an increase in the prey population. This can lead to changes in vegetation, stream paths, and overall biodiversity.
Which is a factor of 12x2– 46x – 8 ?
Answer
2
3x – 4
2x + 1
3x – 2
"Calculate cos theta to two decimal places. (Use the pic attached inside!!!)
A. 0.61
B. 1.44
C. 0.72
D. 0.43
If f(x) is an even function, which statement about the graph of f(x) must be true?
-It has rotational symmetry about the origin.
-It has line symmetry about the line y = x.
-It has line symmetry about the y-axis.
-It has line symmetry about the x-axis.
Since f(x) is an even function, the statement which is true is the graph of f(x) has a line of symmetry about the y-axis.
To answer the question, we need to know what an even function is.
What is an even function?An even function is a function f(x) such that f(x) = f(-x). That is f(x) is single valued for both positive and negative values of x.
Now, for an even function, since f(x) = f(-x), both positive and negative values of x give a single value of f(x).
For this to be true, the graph of f(x) is symmetric about the y-axis.
So, since f(x) is an even function, the statement which must be true is graph of f(x) has a line of symmetry about the y-axis.
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Jackson middle school has 6 students in choir for every 1 student in band. if there are 54 students in band, how many students are in choir?
What is the estimated sum? round each number to the nearest hundred before adding. 521,370 26,839
The estimated sum of 521,370 and 26,839, when rounded to the nearest hundred, is 548,200.
To find the estimated sum, you first need to round each number to the nearest hundred before adding them. For the given numbers 521,370 and 26,839, we round them as follows:
521,370 rounds to 521,400 (because the number after the hundreds place, 7, is 5 or greater, so we round up).
26,839 rounds to 26,800 (because the number after the hundreds place, 3, is less than 5, so we round down).
Now we add the rounded numbers:
521,400 + 26,800 = 548,200
So, the estimated sum of 521,370 and 26,839 is 548,200.