Find the equation (in terms of xx and yy) of the tangent line to the curve r=3sin2θr=3sin2θ at θ=π/6θ=π/6
Which expression is equal to 728‾‾‾√−563‾‾‾√ ?
−11√ 7
√7
- √7
−37√7
Answer:
The correct option is 3.
Step-by-step explanation:
The given expression is
[tex]7\sqrt{28}-5\sqrt{63}[/tex]
It can be written as
[tex]7\sqrt{4\times 7}-5\sqrt{9\times 7}[/tex]
[tex]7\sqrt{2^2\times 7}-5\sqrt{3^2\times 7}[/tex]
Using product property of radical expressions, we get
[tex]7(\sqrt{2^2}\times \sqrt{7})-5(\sqrt{3^2}\times \sqrt{7})[/tex] [tex][\because \sqrt{ab}=\sqrt{a}\sqrt{b}][/tex]
[tex]7(2\times \sqrt{7})-5(3\times \sqrt{7})[/tex]
[tex]14\sqrt{7}-15\sqrt{7}[/tex]
Taking out common factors.
[tex]\sqrt{7}(14-15)[/tex]
[tex]\sqrt{7}(-1)[/tex]
[tex]-\sqrt{7}[/tex]
Therefore the correct option is 3.
Suppose there is 1.1*f drop in temperature for every thousand feet that an airplane climbs in to the sky if the temperature on the ground is 59.7°F what will the temperature be at an altitude of 11,000 feet
Answer:47.6
Step-by-step explanation:
Penny uses 3/4 yard fabric for each pillow she makes. How many pillows can she make using 6 yards of fabric. Please show your work
Select a rule for the following pattern. 44; 440; 4,400; 44,000 . . .
The rule for the following pattern is to multiply 10 with a constant number 44 everyu sequence.
What is mathematical sequence ?Explanation;
44; 440; 4,400; 44,000.
44
44*10 = 440
440*10 = 4400
4400*10 =44000 and so on
A series is an ordered listing of numbers or other factors like geometric items, that often comply with a specific pattern or characteristic. Sequences can be both finite and limitless. A series is a listing of numbers in a sure order. each number in a series is known as a term . every time period in a series has a role.
Sequences are useful in a number of mathematical disciplines ... specially, sequences are the idea for series, which might be crucial in differential equations and evaluation. Sequences are also of hobby of their own proper and can be studied as styles or puzzles, including in the look at of prime numbers.
A number series is a fixed of numbers that observe a selected pattern or rule to get from time period to time period. There are foremost kinds of exclusive sequences, they are mathematics sequences, geometric sequences, quadratic sequences and special sequences. It assists with comprehension, specially for narrative texts. series structures assist college students of various abilities organize information and ideas successfully.
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What value is added to both sides of the equation x2 − 8x = −10 in order to solve by completing the square?−816−44?
Answer:
The correct option is 2. 16 is added to both sides of the equation.
Step-by-step explanation:
The given equation is
[tex]x^2-8x=-10[/tex]
If an expression is defined as [tex]x^2+bx[/tex], then we need to add [tex](\frac{b}{2})^2[/tex] in the expression to make it perfect square.
In the given equation b=-8.
[tex](\frac{b}{2})^2=(\frac{-8}{2})^2=(-4)^2=16[/tex]
We need to add 16 on both the sides to solve by completing the square.
Therefore the correct option is 2. 16 is added to both sides of the equation.
In order to select the new board members. The French club held an election 9 out of 18 club in the election voted in the election . What percentage of the members voted
Based on a survey, 3 out of 8 households have a pet. Mike's neighborhood has 192 households.
Based on the survey, how many households in Mike's neighborhood ,begin emphasis,most,end emphasis, likely have a pet?
A.24
B.64
C.72
D.116
72 households in Mike's neighborhood ,begin emphasis, most, end emphasis, likely have a pet.
What is Fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
According to question, based on a survey, 3 out of 8 households have a pet. Mike's neighborhood has 192 households.
We have to find how many households in Mike's neighborhood ,begin emphasis, most, end emphasis, likely have a pet.
We get the number of households by following equations:
[tex]\frac{3}{8}[/tex]×[tex]192=72[/tex]
Hence we can conclude that Option C is correct answer.
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What are the next 2 terms of 0.3, -0.09, 0.0027
The next two terms of the sequence 0.3, -0.09, and 0.0027 are -0.00027 and 0.000027, achieved by continuously multiplying each term by -1/10.
Explanation:To find the next terms of the sequence 0.3, -0.09, and 0.0027, you need to understand the pattern in the sequence. Here, each term is multiplied by -1/10 (or -0.1) to get the next term. So, to find the next term, we multiply the last given term (0.0027) by -1/10, which gives -0.00027. Therefore, the fourth term of the sequence is -0.00027. For the fifth term, we do the same process and multiply -0.00027 by -1/10, to get 0.000027. So, the next two terms in the sequence are -0.00027 and 0.000027.
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Rita earned $20 each day. lauren earned $2 the first day, $3 the second day, $4 the third day, and so on. richard earned $25 a day. lisa earned $1 the first day, $2 the second day, $4 the third day, and $8 the fourth day, and so on. who earned the most money in 10 days?
Lisa earned $385 in 10 days, which is highest among others.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
Given that,
Money earned by Rita in one day = $20,
Therefore, money earned by Rita in 10 days = 10 x 20 = $200
Money earned by Lauren on first day = $2
Second day = $3,
Third day = $4, and so on....
Total money earned in 10 day by Lauren = 2 + 3 + 4 + .....11 = $65
Money earned by Richard in one day = $25,
Therefore, money earned by Richard in 10 days = 25 x 10 = $250
Lisa earned $1 for first day, $2 for 2nd day, $4 for 3rd day and $8 for 4th day and so on..
Total money earned by Lisa in 10 days = 1 + 2 + 4 + 8 + ........
= 10 x (10+1) x (20+1) / 6 = 385
Maximum amount is earned by Lisa, which is $385.
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A ballroom has a square dance floor. The area of the floor is 400 square feet. If the length of each side of the square increased by one foot, would its area be a rational number? explain
Answer:
The area is a rational number.
Step-by-step explanation:
Consider the provided information.
A ballroom has a square dance floor. The area of the floor is 400 square feet.
Area of square = (side)²
Substitute the respective value in above formula.
400 = (side)²
√400 = side
20 feet = side
Ignore the negative value as side cannot be a negative number.
Now it is given that the length of each side of the square increased by one foot,
Thus, the new side is 20 + 1 = 21 feet
Now find the area of new square = (side)²
A = 21²
A = 21×21
A = 441 square feet
The number 441 is a rational number.
Hence, the area is a rational number.
We have that If the length of each side of the square increased by one foot,
Yes, Area will be a rational number
From the question we are told that
. The area of the floor is 400 square feet
the length of each side of the square increased by one foot,
Generally the equation for the Area of a square is mathematically given as
a=LxB
a=400
Rational Numbers
This simply means expressible as a ratio of whole numbers.
Therefore
If the length of each side of the square increased by one foot then the value will still be expressible as a ratio of whole numbers.
Hence
Yes, Area will be a rational number
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Why is it preferable to measure a penny in millimeters?
Millimeters are preferred for measuring a penny because they offer greater precision and accuracy, enabling us to measure the dimensions of small objects like a penny with closer to exact measurements.
It is preferable to measure a penny in millimeters because millimeters provide a more precise and accurate measurement due to their smaller size compared to centimeters. The standard width of a penny is 1.9 cm, which is equivalent to 19 mm. Since scientists have established the convention of using the degree of precision dependent on the measuring device, millimeters are more appropriate for small objects like a penny to get an accurate measurement. A millimeter allows us to report the size of the penny to the nearest millimeter, facilitating a precise estimation.
When choosing a unit of measurement, one must consider the object's size and the necessary precision. For very small objects like a paper clip or a penny, millimeters would give the most accurate measurement, compared to centimeters, which are 10 times bigger and could provide a less accurate measurement. Therefore, for tasks requiring precise measurements of small dimensions, millimeters are preferred.
So far this semester, Zachary has test scores of 92, 98, 65, 77, 91, and 85. He has one more test to take before the semester ends. What must he score on the last test to earn an average of 85 for the semester? Type a numerical answer in the space provided.
77 pints= ___gal ___qt ___pt
If other factors are held constant, the bigger the sample is, the greater the likelihood of rejecting the null hypothesis.
a. True
b. False
Justin purchased a 20 pound pumpkin for $9.80. How much did he pay per pound.
Justin paid $0.49/pound for his 20 pound pumpkin.
This is determined by dividing the total amount paid ($9.80) by the pound total (20lbs).
9.80 / 20= 0.49
YZ has endpoints Y(0,5) and Z (12,3). Find the length of YZ to the nearest tenth.
Answer: The answer is 2√37 units.
Step-by-step explanation: Given that the line segment YZ has endpoints Y(0, 5) and Z(12, 3). We are to find the length of the line segment YZ.
The length of YZ will be the distance between the endpoints Y and Z.
The distance between Y and Z will be given by
[tex]YZ=\sqrt{(0-12)^{2}+(5-3)^2}=\sqrt{144+4}=\sqrt{148}=2\sqrt{37}=12.16\sim 12.1.[/tex]
Thus, the length of YZ is 12.1 units.
QUICK HELP! How many terms are in the simplified expression? How many of the terms in the simplified expression are negative?
Expression: 2x^2 - y^2 +5xy - 2y
Final answer:
The simplified expression '2x² - y² + 5xy - 2y' contains four terms, of which two are negative.
Explanation:
The expression given is 2x² - y² + 5xy - 2y To determine how many terms are in this simplified expression, we simply count the distinct variables and constant groupings. In this case, there are four terms: 2x², -y², 5xy, and -2y. Among these, two terms have a negative sign in front of them, indicating that they are negative. Thus, there are two negative terms in the simplified expression.
Karen buys 8.5 pounds of flour. She uses 2.5 pounds to bake bread. She keeps the rest of the flour in small storage bags. If each storage bag contains ⅖ pound of flour, how many storage bags does she use?
ALGEBRA 2- If f(x)= √x-3 , which inequality can be used to find the domain of f(x)?
a. √x-3 ≥ 0
b. x-3 ≥ 0
c. √x-3 ≤ 0
d. x-3 ≤ 0
Answer:
Option B
Step-by-step explanation:
The given equation function is f(x) =[tex]\sqrt{x-3}[/tex]
Domain of this function will be determined by (x-3) ≥ 0
because square root of negative numbers is not defined.
Option B is the answer.
Michael pays $30 to enter a state fair, plus $4 for each ride. Which of the following equations represents his total cost? A. y=34x. B. y=4x+30 C. y=30x+4. D. y=4x+34
The correct mathematical equation representing Michael's total cost at the state fair, considering his base fee and cost per ride, is y=4x+30.
Explanation:The question centers around linear equations, a subject in mathematics. In this context, Michael's total cost of his trip to the state fair is calculated by his base fee, 30 dollars, plus the number of rides he goes on multiplied by the cost per ride, 4 dollars. The correct equation representing this situation would be y=4x+30, where y is the total cost, x is the number of rides he goes on, and 30 is the flat entry fee.
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Analyze the function f(x) = - 2 cot 3x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes
The difference between one-half of a number and one-sixth of the number is equal to ten more than one-eighth of that number. Which equation could be used to find the number?
Answer with explanation:
It is given that, the difference between one-half of a number and one-sixth of the number is equal to ten more than one-eighth of that number.
Let the number be x.
Writing the statement in terms of equations
[tex]\frac{x}{2}-\frac{x}{6}=10+\frac{x}{8}[/tex]
This equation can be used to find the number.
In 4 hours, a car travels 200 miles. What is the speed of the car
Answer:
50 miles per hour
Step-by-step explanation:
200 ÷ 4 = 50
200 = miles in 4 hours
50 = miles in 1 hour
Final answer:
The speed of the car is calculated by dividing the distance traveled (200 miles) by the time taken (4 hours), resulting in a speed of 50 miles per hour.
Explanation:
To determine the speed of the car, we use the formula for speed, which is distance traveled divided by the time taken. In this case, the car travels 200 miles in 4 hours. Plugging in numbers, we calculate the speed as follows:
Divide the distance by the time:Therefore, the speed of the car is 50 miles per hour (mph).
given that EB bisects <CEA , which statement must be true
Answer: A:<CED is a right angle
B: <CEA is a right angle
D: m<CEB=m<BEA
E: m<DEB=135
Step-by-step explanation
Help. What is the slope.
WILL MARK BRAINLIEST!
A sample was taken of dogs at a local dog park on two random days. The counts are displayed in the table below. If there are estimated to be 50 dogs at the park at any given time, which proportion could be used to find the average number of shepherd mixes at the park at any given time?
Answer:
⇒[tex]\frac{8}{21} =\frac{x}{50}[/tex]
Step-by-step explanation:
Let average no. of shepherds be x
there are estimated to be 50 dogs
Thus average no. of dogs / estimated no. of dogs =x/50
Since in sample 1 there are 7 shepherd mix
In sample 2 there are 9 shepherd mix
So total shepherd mix = 9+7=16
Total dogs according to table = 4+7+3+1+2+5+9+5+2+4=42
Thus total shepherd / total dogs = 16/42
A.T.Q
[tex]\frac{16}{42} =\frac{x}{50}[/tex]
⇒[tex]\frac{8}{21} =\frac{x}{50}[/tex]
This proportion could be used to find the average number of shepherd mixes at the park at any given time
Thus option A is correct
The average number of shepherd mixes at the park at any given time is equal to [tex]\frac{8}{21} =\frac{x}{50}[/tex].
Let the average number of shepherd mixes be x.Given the following data:
Estimated population = 50 dogs.To determine the average number of shepherd mixes at the park at any given time:
How to calculate the shepherd mixes.First of all, we would determine the total number of shepherd mixes in sample 1 and sample 2.
Total shepherd mixes = [tex]7 + 9[/tex] = 16 dogs.
For the total dogs:
Total dogs = [tex]4+1+7+3+2+5+9+5+2+4[/tex] = 42 dogs.
The average number of shepherd mixes is given by this mathematical expression:
[tex]\frac{16}{42} =\frac{x}{50}[/tex]
Simplifying further, we have:
[tex]\frac{8}{21} =\frac{x}{50}[/tex]
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What is the greatest common factor of 20a^2, 12a^2 and 8a
What is the truth value for the following conditional statement?
p: true
q: true
p → q
T T → F
F T → T
T T → T
T F → T
Answer:
T T → T
Step-by-step explanation:
Boolean table,
p q p → q
T T T
T F F
F T T
F F T
Given, the conditional statement:
p : True
q : True,
Then by using above table,
p → q is true,
Hence, the correct answer is,
T T → T
⇒ Third option is correct.
Satellites KA-1212 and SAL-11 have spotted a UFO. Scientists want to determine its distance from KA-1212 so they can later determine its size. The distance between the satellites is 900 km. If KA-1212's camera is focused on SAL-11 , it must rotate 60° to see the UFO. If SAL-11's camera is focused on KA-1212, it must rotate 75° to see the UFO. How far is the UFO from KA-1212? Round your answer to the nearest kilometer.
Answer:
The distance of UFO from KA-1212 is 1229.7 km.
Step-by-step explanation:
We are given that,
Distance between the satellites = 900 km
Angle made by the satellite KA-1212 = 60°
Angle made by the satellite SAL-11 = 75°
So, from the figure below,
The third angle is given by = 180° - (60°+75°) = 180° - 135° = 45°
Then, using the law of sines, we have,
[tex]\dfrac{x}{\sin 75}=\dfrac{900}{\sin 45}\\\\x=\dfrac{900\times \sin 75}{\sin 45}\\\\x=\dfrac{900\times 0.966}{0.707}\\\\x=\dfrac{869.4}{0.707}\\\\x=1229.7[/tex]
Thus, the distance of UFO from KA-1212 is 1229.7 km.Satellites KA-1212 and SAL-11 have spotted a UFO. Scientists want to determine its distance from KA-1212 So, it is 1229.7 km.
What is a law of sine?Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.
It is given that
Distance between the satellites KA-1212 and SAL-11 = 900 km
Angle made by the satellite KA-1212 = 60°
Angle made by the satellite SAL-11 = 75°
So, the third angle is given by
= 180° - (60°+75°)
= 180° - 135°
= 45°
Using the law of sines, we get
x/sin75° = 900/sin 45°
x = 900 × sin75°/ sin 45°
x = 900 × 0.966/ 0.707
x = 1229.7
Thus, the distance of a UFO from KA-1212 is 1229.7 km.
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