a. The shape οf the distributiοn οf the sample mean time is nοrmal.
b. The standard error is 0.5345.
What is the standard deviatiοn?Standard deviatiοn is: It is a measure οf hοw spread οut numbers are. It is the square rοοt οf the Variance, and the Variance is the average οf the squared differences frοm the Mean.
Given that:
μ =35
σ = 2
n = 14
a. The shape of the distribution of the sample mean time is normal.
b. To calculate the standard error of the mean time, we would apply this formula,
Standard error :
[tex]$ \rm SE = \frac{ \sigma}{\sqrt{(n)} }[/tex]
[tex]$ \rm SE = \frac{ 2}{\sqrt{(14)} }[/tex]
SE = 0.5345
Thus, the standard error is 0.5345.
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Complete question:
Majesty Videο Prοductiοn Inc. wants the mean length οf its advertisements tο be 30 secοnds. Assume the distributiοn οf ad length fοllοws the nοrmal distributiοn with a pοpulatiοn standard deviatiοn οf 2 secοnds. Suppοse we select a sample οf 16 ads prοduced by Majesty.
a. What can we say abοut the shape οf the distributiοn οf the sample mean time?
b. What is the standard error of the mean time?
si tengo 3657 manzanas y me quitan 84648 pero juan me regala otras 8469 cuantas me quedan para comer?
Answer:
0 (-72522)
Step-by-step explanation:
ahora tienes negativo manzanas
For problems 6 and 7 set up a proportion and solve.
pleaseeeee helpppp i’ll give brainlist
Using proportions we can find,
6. The weight of the adult bear = 750 pounds.
7. The measure of each angles are: 10°, 75° and 95°
Define proportions?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.
Here in the question,
The weight is in the ratio = 3:1000
The average birth weight = 12 ounces = 3/4 pounds.
Now the weigh of adult bear = 1000 × 3/4 = 750 pounds.
In the second part the angles are in the ratio, 2:15:19.
So, 2x+ 15x + 19x = 180
x = 180/36
x = 5
Hence, the measure of each angles are: 10°, 75° and 95°
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Each cell in the crossnumber below contain a single non-zero digit. The answer
two-digit number.
What is the value of x?
A 1
21 UK Mathematics Trust
Clues
ACROSS
1. A square
3. An odd square
B 3
Down
1. A square
2. A square
C 5
www.ukmt.org.uk
1
3
D 7
2
X
The answer to the crossnumber is 25.
What is number?Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics and is used to describe sets, groups, and other mathematical objects. Numbers are used to measure quantities, such as length, area, time, and weight. They are also used to represent relationships between objects, and to describe the properties of those objects. Numbers can be represented in various forms, such as integers, fractions, and decimals.
This can be determined by examining the clues and their corresponding digits. Across, the clue is "A square", so the digit in the corresponding cell must be a perfect square, in this case 1. The next clue is "An odd square", so the digit must be an odd perfect square, which is 3. Down, the first clue is "A square", so the digit must be a perfect square, which is 5. The last clue is "A square", so the digit must be a perfect square, which is 7. When all the digits are put together, the resulting two-digit number is 25.
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write 9 minutes and 25 seconds to 9 in the evening In analogue time
Answer:
9 minutes and 25 seconds to 9 in the evening in analogue time is represented as:
8:50:35 PM
a package contains 6 blue, 4 red, and 5 yellow gumballs. You randomly choose a gumball from the bag, and you do not replace it. Then you randomly choose another gumball. What is the propobility of both gumballs not being red?
The probability of both gumballs not being red is 11/21.
What is the probability?
The probability of the first gumball not being red is:
P(first gumball not red) = P(blue) + P(yellow)
= (6/15) + (5/15)
= 11/15
After removing the first gumball, there are 14 gumballs left in the bag. The probability of the second gumball not being red depends on what color the first gumball was.
Case 1: The first gumball was blue
If the first gumball was blue, there are 5 blue, 4 red, and 5 yellow gumballs left in the bag. The probability of the second gumball not being red is:
P(second gumball not red | first gumball was blue) = P(blue or yellow)
= P(blue) + P(yellow)
= (5/14) + (5/14)
= 5/7
Case 2: The first gumball was yellow
If the first gumball was yellow, there are 6 blue, 4 red, and 4 yellow gumballs left in the bag. The probability of the second gumball not being red is:
P(second gumball not red | first gumball was yellow) = P(blue or yellow)
= P(blue) + P(yellow)
= (6/14) + (4/14)
= 5/7
The probability of both gumballs not being red is the product of the probabilities of each event:
P(both gumballs not red) = P(first gumball not red) * P(second gumball not red | first gumball not red)
P(both gumballs not red) = (11/15) * (5/7)
P(both gumballs not red) = 55/105
P(both gumballs not red) = 11/21
Therefore, the probability of both gumballs not being red is 11/21.
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Find the area of a square that has a side length of 2x + 4. Write your answer in standard
form without any spaces and use ^ to indicate an exponent, if necessary.
As given:
The side of the Square= (2x+
As we know:
The area of a square = Side × side
Putting the values of side in above formula we get:
Area = (2x+4) ×(2x+4)
on solving we get:
Area= 2x×2x + 2x×4 +4×2x + 4×4
Area= 4x^2 + 8x + 8x + 16
Area= 4x^2 + 16x + 16
Hence,The Area of the Square is (4x^2+ 16x +16)
The perimeter of the base of a square pyramid is 48 inches. The height of the pyramid is 8 inches. What is the surface area of the pyramid? Responses
Answer:
To find the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces, and then add them together.
First, let's find the length of one side of the base of the pyramid:
Perimeter of the square base = 4 x side length
48 inches = 4 x side length
Side length = 12 inches
Now we can find the area of the base:
Area of the base = side length squared
Area of the base = 12 inches x 12 inches
Area of the base = 144 square inches
Next, we need to find the area of each triangular face. To do this, we need to find the length of the slant height of the pyramid. We can use the Pythagorean theorem to do this:
Slant height squared = height squared + (1/2 base length) squared
Slant height squared = 8 inches squared + (6 inches) squared
Slant height squared = 64 inches squared + 36 inches squared
Slant height = square root of (64 + 36) inches
Slant height = 10 inches
Now we can find the area of each triangular face:
Area of a triangular face = (1/2 base length) x slant height
Area of a triangular face = (1/2 x 12 inches) x 10 inches
Area of a triangular face = 60 square inches
Finally, we can add the area of the base and the area of the four triangular faces together to find the total surface area of the pyramid:
Total surface area = Area of the base + (4 x Area of a triangular face)
Total surface area = 144 square inches + (4 x 60 square inches)
Total surface area = 384 square inches
Therefore, the surface area of the pyramid is 384 square inches.
1.2541 rounded to nearest tenth
Answer:
1.3
Step-by-step explanation:
look at the hundredths place to decide how to round (1.2541).
when a digit is greater than or equal to 5, we round up
in this number, the hundredths place is 5, meaning we round up to get 1.3
i hope this helps :D
HELPPPPP MEEEEEE!!! PLEASEEEEE
1.
Factor:
2x^2 + 9x + 18
What multiples to get 18 and adds to get 9?
a. (X+9) (x+2)
b. (X+6) (x+3)
c. (X-6) (x-3)
d. (X-9) (x-2)
2.
Factor:
X^2 - 20x + 36
What multiples to get 36 and adds to get -20?
a. (x-6) (x-6)
b. (x+3) (x+12)
c. (x-9) (x-4)
d. (x-18) (x-2)
3.
factor:
2x^2 - 5x -3
STEPS.
STEP 1* - Slide and Multiply the First Number to the Last
STEP 2 - Factor - What Multiplies to get the Last Number and Adds to get the
Middle Number?
STEP 3 - Divide and Reduce - The number we divide by is the same number we slid.
STEP 4 - Bottoms Up - If a fraction remains, move bottom number in front of the
variable.
*Unless there is a GCF. If there is, pull that out first.
a. (x-3)(x+1)
b. (2x+1)(x-3)
c. (2x-1)(x+3)
d. (x-3)(2x-3)
4.
what is the greatest common factor?
8x^2 + 18x + 4
a. 2
b. 4
c. 2x
d. 4x
5.
factor:
8x^2 + 18x + 4
STEPS.
STEP 1* - Slide and Multiply the First Number to the Last
STEP 2 - Factor - What Multiplies to get the Last Number and Adds to get the
Middle Number?
STEP 3 - Divide and Reduce - The number we divide by is the same number we slid.
STEP 4 - Bottoms Up - If a fraction remains, move bottom number in front of the
variable.
*Unless there is a GCF. If there is, pull that out first.
a. (x-2)(4x+1)
b. 2(x-2)(4x-1)
c. 2(x+2) (4x+1)
d. (x+2)(x+4)
The answer to the all questions was solved by the methods of factoring:
b. (x+6)(2x+3)c. (x-2)(x-18)a. (2x-3)(x+1)2b. 2(x-2)(4x+1)What is factoring?Factoring is the process of breaking down a mathematical expression or equation into simpler components, such as factors that when multiplied together give the original expression.
In the given questions,
1.Factoring 2x² + 9x + 18:
First, we need to find two numbers that multiply to 2×18=36 and add up to 9.The numbers are 6 and 6, since 6×6=36 and 6+6=12, but we need to adjust them to fit the middle term, which is positive.Therefore, we use 6 and 3: 6×3=18 and 6+3=9.We can write the expression as: 2x²+ 6x + 3x + 18.Now we can factor by grouping: (2x+6)(x+3).The answer is (a) (2x+6)(x+3).2.Factoring x² - 20x + 36:
First, we need to find two numbers that multiply to 36 and add up to -20.The numbers are -2 and -18, since -2×(-18)=36 and -2+(-18)=-20.We can write the expression as: x² - 2x - 18x + 36.Now we can factor by grouping: (x-2)(x-18).The answer is (d) (x-2)(x-18).3.Factoring 2x² - 5x - 3:
We can start by multiplying the first and last coefficients: 2×(-3)=-6.We need to find two numbers that multiply to -6 and add up to -5.The numbers are -6 and 1, since -6×1=-6 and -6+1=-5.We can write the expression as: 2x² - 6x + x - 3.Now we can factor by grouping: (2x-3)(x+1).The answer is (a) (2x-3)(x+1).4.Finding the greatest common factor of 8x² + 18x + 4:
We can start by factoring out any common factors of the coefficients, which is 2.Then we need to find the greatest common factor of the terms with x.The terms are 8x^2 and 18x, and the greatest common factor is 2x.The constant term, 4, is a factor of 2, so we can factor out another 2.The greatest common factor is 2(2x² + 9x + 2).The answer is (d) 4x.5.Factoring 8x² + 18x + 4:
First, we need to factor out any common factors, which is 2.Then, we can follow the steps:STEP 1* - Slide and Multiply the First Number to the Last: (2x+1)(4x+2).STEP 2 - Factor - What Multiplies to get the Last Number and Adds to get the Middle Number? The last number is 2, and the only factors are 1 and 2, which add up to 3, not 9. Therefore, the expression is prime and cannot be factored further.The answer is none of the given options.To know more about factoring expression, visit:
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23 x _ = 23 x 4
(help me)
Answer:
4
Step-by-step explanation:
To solve for the missing value in 23 x _ = 23 x 4, you can use the property of equality to divide both sides by 23. This will give you _ = 4. Therefore the missing value will be 4.
Hope this helped :)
Answer: the answer is 4
Step-by-step explanation: u can divide both sides with 23 and that leaves u with x=4
The ships kitchen stocks 1 3/5 quarts of ice cream for every 1/4 cake. There are 10 cakes in the kitchen. How many quarts of ice cream are there?
Please explain if you really really know the answer
Therefore , the solution of the given problem of unitary method comes out to be the pantry has 16 quarts of ice cream.
What is an unitary method?The goal can be achieved by making use of what has expression learned to date, utilizing this global access, and incorporating all crucial elements from previous changeable study that employed a specific technique. It is going to be equation possible to get in touch with the entity again if the expected claim result actually happens, or both crucial processes will surely miss the statement. A Rs ($1.21) redeemable fee may be needed for fifty pens.
Here,
Finding the overall quantity of cake in the kitchen is a good place to start. If there are 10 pastries, each measuring 1/4 inch, then there will be:
=> 10 desserts divided by 1/4 each equals the total cake.
=> Cake total equals 10/4 cakes.
=> 2.5 pastries altogether
=> 1 3/5 pints of ice cream for every 1/4 cake.
=> 8 and a half pints of ice cream per 1/4 cake
To determine the total amount of ice cream, we can multiply the ice cream per cake by the total number of cakes:
=> Total ice cream equals the sum of the cakes' ice cream.
=> Total ice cream = (8/5 quarts per 1/4 cake) * (10/4 cakes)
=> Total ice cream = 16 quarts
Consequently, the pantry has 16 quarts of ice cream.
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Mason’s pumpkin had a weight of 3 kg 250 g in August and 4 kg 125 g in October. What was the difference in weight from August to October?
Divide (-18) by (3). Then multiply the quotient by (-4).
Answer:
1.5
Step-by-step explanation:
-18/3 = -6
-6/-4 = 3/2 or 1.5
Answer: 24
Step-by-step explanation:
I need help asap!!!!!
Answer:
8x - 58 ≤ 500
8x ≤ 500 + 58
8x ≤ 558
x ≤ 69.74
What is the standard equation of a circle whose center is (-3, 5) and radius is 2?
Answer:
Step-by-step explanation:
The standard equation of a circle with center (a, b) and radius r is:
(x - a)^2 + (y - b)^2 = r^2
Using the given values, we have:
(x - (-3))^2 + (y - 5)^2 = 2^2
Simplifying:
(x + 3)^2 + (y - 5)^2 = 4
Therefore, the standard equation of the circle is (x + 3)^2 + (y - 5)^2 = 4.
Answer:
[tex] (x + 3)^2 + (y - 5)^2 = 4 [/tex]
Step-by-step explanation:
[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]
[tex] (x - (-3))^2 + (y - 5)^2 = 2^2 [/tex]
[tex] (x + 3)^2 + (y - 5)^2 = 4 [/tex]
Estimate!
16 3/4 divided by 2 1/2
Answer:7
Step-by-step explanation:
6.7 to the 10 is 7
Number 5 Please look at image
The solutions to the quadratic equations are as follows
4a. The rocket was launched from an initial height of 10 meters.
b. The maximum height of the rocket was 55 meters.
c. The rocket reaches its maximum height at 3 seconds
d. the rocket is in the air for t = 6.316 seconds
5. when the horizontal distance is 1 foot, the height of the balloon is 8.875 feet
b. when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet.
How do we solve the quadratic equation?The function is a quadratic equation, and here is how we solve each problem;
a. The initial height of the rocket is the value of h when t=0. So we substitute t=0 into the equation to find:
h = -5(0)² + 30(0) + 10 = 10 meters
b. & c. The maximum height of a projectile launched upward occurs at the vertex of the parabola represented by the quadratic function. For a quadratic function in the form y = ax² + bx + c, the time at which the maximum (or minimum) occurs is -b/2a. In this case, a = -5 and b = 30. So:
t = -b/2a = -30 / (2×-5) = 3 seconds
So, the rocket reaches its maximum height at t=3 seconds. We can find this maximum height by substituting t=3 into the equation:
h = -5(3)² + 30(3) + 10 = -5×9 + 90 + 10 = 45 meters
The rocket is in the air from the time it was launched until it hits the ground. The time when it hits the ground is when h = 0. So we can set the equation to 0 and solve for t:
0 = -5t² + 30t + 10
This is a quadratic equation and can be solved using the quadratic formula: t = [-b ± √(b² - 4ac)] / (2a)
Let's calculate the roots:
t = [-30 ± √((30)² - 4×-5×10)] / (2×-5)
= [-30 ± √(900 + 200)] / -10
= [-30 ± √(1100)] / -10
= 6.316 or -0.32
5. a. To find the height of the balloon when d=1, we substitute d=1 into the equation:
h = -1/8(1)²+ 4(1) + 5 = -1/8 + 4 + 5 = 8.875 feet
b. To determine whether the balloon hits your enemy, we need to see if the balloon's height (h) is above ground level (h > 0) when d=33. So, we substitute d=33 into the equation:
h = -1/8(33)² + 4(33) + 5
h = -1/8×1089 + 132 + 5
h = -136.125 + 132 + 5
h = 0.875 feet
when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet. This means the balloon is above ground level and therefore would indeed hit your nemesis standing 33 feet away.
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ASTORY OF RATIOS
Lesson 8 Problem Set 6.5
Plot the points for each shape, determine the area of the polygon, and then write an expression that could be used to
determine the area of the figure. Explain how each part of the expression corresponds to the situation..
1 A(1,3), B(2.8), C8, 8), D(10,3), and E(5,-2)
y
#D what is the area of this shape
Thus, the area of the pentagon formed by the given coordinates is:
A = 28.5 sq. units.
Explain about the pentagon?A pentagon is just a five-sided polygon in geometry having five straight sides and five inner angles totaling 540 degrees. A pentagon is a five-sided, flat (two-dimensional), plane geometric form.
The coordinates of polygon are:
A(1,3), B(2,8), C(8, 8), D(10,3), and E(5,-2).
Plot the points on the graph as shown.
The area of a pentagon calculation is used to determine the area of a pentagon with apothem, a, but one side length, s:
A = 1/2 * a * (5s)
a = apothem, of perpendicular distance from the centre.
s = length of side.
From graph:
s = 6 units.
a is calculated using the tan function.
each interior angle of pentagon = 54 degrees.
So,
tan (54/2) = a/ (s/2)
tan (36) = a/3
a = 3*tan (36)
a = 1.90 units
A = 1/2 * 1.90 * (5*6)
A = 28.5 sq. units.
Thus, the area of the pentagon formed by the given coordinates is:
A = 28.5 sq. units.
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Do you guys know the answer please help?
The value of x in the figure such that Ray YU is an angle bisector is 18 degrees
How to determine the value of x in the figureGiven
The figure
Such that Ray YU is an angle bisector
An angle bisector is a line or a ray that divides an angle into two equal parts or halves.
In other words, an angle bisector divides an angle into two smaller angles with equal measures.
The point where the angle bisector intersects the opposite side is the angle bisector point
This means that
2x = 36
So, we have
x = 18
Hence, the value of x in the figure is 18
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Explore Part 2
Using the numbers -4 to 4 without repeating, fill in the blanks to make a true statement.
One number will be unused. Use the sketch tool if it helps you with your thinking.
(N = unknown number)
N/N • N < N - N/N < N - N
4 number was not used in the statement. we can use -3 as the other value.
What is a statement?A simple statement is a single assertion that can be classified as true or false, while a compound statement is formed by combining two or more simple statements using logical operators such as "and", "or", and "not".
According to question:To explain the statement mathematically:
First, we evaluate N/N:
N/N = 1
Next, we simplify the inequality using this value:
1•N < N - 1 < N - N
Simplifying further, we get:
N < N - 1 < 0
We can then substitute the values of -4 to 4 for N and see which value(s) satisfy the inequality.
If N = -4, then we have:
-4 < -5 < 0
This is true, so we can use -4 as one of the values.
If N = -3, then we have:
-3 < -4 < 0
This is also true, so we can use -3 as the other value.
Therefore, the completed statement is:
-4/-4 • -4 < -4 - (-4/-4) < -4 + 4/-4 <br>
which simplifies to:
1 < -3 < 5/2
Note that one number, 4, was not used in the statement.
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100 Points!!! Algebra question, only looking for answer to last two. Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Photo attached. Thank you!
1) y = -3x and y = -3x + 2: inconsistent system of equations.
2) y = x - 5 and -2x + 2y = - 10: consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.
Explain about the consistent and inconsistent system of equations?If there is at least one solution, an equation system is considered consistent. If there is no solution, a system is inconsistent.If one equation is a multiple of the other in a pair of equations that have two variables, both equations are dependant. Every point in dependent systems is a potential solution, giving them an endless number of solutions.The given equation are:
The graph for each system of equations is plotted.
1) y = -3x and y = -3x + 2
From the graph 1 it is shown that the lines for the each equation form the parallel lines.
Thus, system of equations are inconsistent.
2) y = x - 5 and -2x + 2y = - 10
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
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let f(x)=x+2 and g(x)=2x2 + 1
look at picture
The values of x such that f(x) = x + 2 and g(x) = 2^x + 1 if f(x = g(x) are x =0 and x = 1
Calculating the values of xGiven that
f(x) = x + 2
g(x) = 2^x + 1
To find x when f(x) = g(x), we need to set the two expressions equal to each other and solve for x:
f(x) = g(x)
x + 2 = 2^x + 1
Subtracting 1 from both sides:
x + 1 = 2^x
We can solve for x by using trial and error or by using numerical methods.
One solution to this equation is x = 1.
To see why, we can plug x = 1 into both sides of the equation:
x + 1 = 2^x
1 + 1 = 2^1
2 = 2
Another solution is x = 0
0 + 1 = 2^0
0 + 1 = 1
1 = 1
Hence, the solutions are x = 0 and x = 1
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I need some help please
Answer:
question where is the question?
The following ordered pairs are found on the graph of the same line.
(-3,9), (-1,4), (1, -1)
Which one of the following points would NOT be found on the line?
A.(-7,19)
B.(7,-16)
C.(-8,20.5)
D.(8,-18.5)
the point that would not be found on the line is option A, (-7,19).
How to calculate the line?
We can use the equation of the line that passes through these three points to determine which of the given points would not be on the line.
First, we can find the slope of the line using the first two points:
slope = (y₂ - y₁)/(x₂- x₁) = (4 - 9)/(-1 - (-3)) = 5/2
Now, we can use the point-slope form of the equation of a line with the slope we just found and the first point (-3,9):
y - y₁= m(x - x₁)
y - 9 = (5/2)(x + 3)
Simplifying this equation gives us:
y = (5/2)x + (27/2)
We can check that the third point (1,-1) also lies on this line by plugging in the values of x and y into the equation above.
Now, we can check which of the given points would not be on this line by plugging in the values of x and y into the equation above.
A. (-7,19): y = (5/2)(-7) + (27/2) = 5.5, which does not equal 19, so this point is not on the line.
B. (7,-16): y = (5/2)(7) + (27/2) = 22.5, which does not equal -16, so this point is not on the line.
C. (-8,20.5): y = (5/2)(-8) + (27/2) = 4.5, which does not equal 20.5, so this point is not on the line.
D. (8,-18.5): y = (5/2)(8) + (27/2) = 25.5, which does not equal -18.5, so this point is not on the line.
Therefore, the point that would not be found on the line is option A, (-7,19).
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Pleaseeeeeee HELP!!!!!!
A piece of farm machinery clears 2/15 acre of land in 1/5 of an hour
Answer: D. 2/3
Step-by-step explanation:
If it is 1/5 of an hour, we times it by 5, to get full hour, right?
So, we also do ×5 for the acre of land, so we can get the amount of acres in a full 1 hour.
5 is the same as 5/1 as a fraction
1/5 × 5 = 5/5 ......1 hour
2/15 × 5/1 = 10/15
So we get, 10/15 acre of land cleared in 1 hour
We simplify 10/15,
Which becomes,
2/3.
In conclusion, this is the working out =
2/15 × 5 = 10/15 = 2/3
Mark my answer as the brainliest!Factor by substitution: (3y−2)2−(3y−2)−2.
The simplification of the polynomial using factor by substitution is: ((3y - 2)⁴ - 1)/(3y - 2)²
How to factor Polynomial by substitution?Factoring polynomials simply means separating a polynomial into its component polynomials.
Sometimes, in the event that polynomials are particularly complicated, it is usually easiest to substitute a simple term and factor down.
We have the equation:
(3y - 2)² - (3y - 2)⁻²
Let 3y - 2 be denoted by S and as such we have:
S² - S⁻²
= S² - 1/S²
Using the denominator as factor, we have:
= (S⁴ - 1)/S²
Plugging 3y - 2 for S gives us:
((3y - 2)⁴ - 1)/(3y - 2)²
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Complete the square to write an equation in general form of 4x2 – 9y2 + 24x + 18y – 9 = 0 in the standard form shown below, and then identify the key features of the graph.
h = center: (, )
k =
a = slope of asymptote:
b =
The equation is now in the standard shape of a hyperbola, as per the provided assertion. [(x - h)² / a²] - [(y - k)² / b²] = 1
What, in plain words, is a hyperbola?A curve formed by the junction of a double right-angled cone and a plane that slices one half of the cone. a plane curve produced by a point so mobile that the difference between its distance from two fixed locations is a constant.
To complete the square for the given equation, we will group the x and y terms and complete the square separately for each.
4x² + 24x - 9y² + 18y - 9 = 0
4(x² + 6x) - 9(y² - 2y) = 9
4(x² + 6x + 9 - 9) - 9(y² - 2y + 1 - 1) = 9
4(x + 3)² - 9(y - 1)² = 36
Dividing by 36, we get:
(x + 3)² / 9 - (y - 1)² / 4 = 1
So, the equation is now in the standard form of a hyperbola:
[(x - h)² / a²] - [(y - k)² / b²] = 1
where h and k are the coordinates of the center, a is the distance from the center to the vertices along the x-axis, b is the distance from the center to the vertices along the y-axis, and the slope of the asymptotes is b/a.
Comparing with the standard form, we can see that:
h = -3, k = 1, a = 3, b = 2, and the slope of the asymptotes is b/a = 2/3.
The center is (-3, 1). The hyperbola opens horizontally, and its vertices are located at (-3 + a, 1) and (-3 - a, 1). So, the vertices are (-6, 1) and (0, 1).
The asymptotes are two straight lines passing through the center with a slope of ±(b/a) = ±2/3. So, the equations of the asymptotes are y - 1 = (2/3)(x + 3) and y - 1 = -(2/3)(x + 3), which simplify to y = (2/3)x + 5/3 and y = -(2/3)x + 1/3.
The distance between the center and the foci is c = sqrt(a² + b²) = √(13). The foci are located at (-3 + c, 1) and (-3 - c, 1). So, the foci are approximately (-0.16, 1) and (-5.84, 1).
The graph of the hyperbola looks like two mirrored U-shaped curves, with the vertices being the endpoints of the transverse axis.
The asymptotes intersect at the center and divide the hyperbola into four parts, called branches. The foci are located on the transverse axis, inside the branches.
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A sphere has a surface area of 60 square feet. Which choice is the best approximation of its radius? Use 3.14 to approximate pi.\
Answer:
Step-by-step explanation:
The surface area of a sphere is given by the formula:
S = 4πr^2
where S is the surface area and r is the radius of the sphere.
We are given that the surface area of the sphere is 60 square feet. Using the formula above, we can solve for the radius:
60 = 4πr^2
Dividing both sides by 4π, we get:
15/π = r^2
Taking the square root of both sides, we get:
r = sqrt(15/π)
Using 3.14 as an approximation for π, we can evaluate this expression:
r ≈ sqrt(15/3.14)
r ≈ 2.20
Therefore, the best approximation for the radius of the sphere is 2.20 feet.
Answer:
Radius is 2.18
Step-by-step explanation:
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Write (Picture) as a fraction. Show your work.
23/200
Hope it helped
20 points answer for brainlist
Multiply, Final answer needs to be in Standard Form.
−5m (−2m + m^2 − 4m^3 + 9)
Answer:
Using the distributive property, we can multiply -5m by each term inside the parentheses:
-5m(-2m + m^2 - 4m^3 + 9) = (-5m)(-2m) + (-5m)(m^2) + (-5m)(-4m^3) + (-5m)(9)
Simplifying each term:
= 10m^2 - 5m^3 + 20m^4 - 45m
The terms are arranged in descending powers of m, so this is already in standard form. Therefore, the final answer is:
20m^4 - 5m^3 + 10m^2 - 45m.