This is an equation representing the ellipse
Explanation:
The general equation for an ellipse is [tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex] so, when you simplify it according to the characteristics of a and b, you would end up in the similar form of the equation givenwhere a represents half the length of the major axis and b represents half the length of the minor axis. The easiest method to identify, look at whether both the variables are squared, and also the coefficient of x and y should be positive but different.which inequality represents the graph below ?
the regular shipping fee (in dollars) for an online computer store is given by the expression 0.5w + 4.49 where w is the weight (in pounds) of the item. the fee (in dollars) for rush delivery is given by 0.99w + 6.49. You purchase a 26.5 pound computer. How much do you save by using regular shipping instead of rush delivery?
By calculating the shipping fees for regular and rush delivery for a 26.5 pound computer, we find that regular shipping saves approximately 14.90 dollars.
Explanation:We must first calculate the fee for each method and then subtract the regular "shipping fee" from the rush delivery fee to find the savings.
Using the given expression, the regular shipping fee for a 26.5 pound computer is: 0.5*26.5 + 4.49 = 17.74 dollars. Meanwhile, the rush delivery fee for the same computer, using the other given expression, would be: 0.99*26.5 + 6.49 = 32.635 dollars.
Subtracting the regular fee from the rush fee, we find: 32.635 - 17.74 = 14.895 dollars. Therefore, you save about 14.90 dollars by choosing regular shipping over rush delivery.
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The circumference of a circle is 43.96 millimeters. What is the circle's radius?
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
What is the vertical asymptote of the function f(x) = 3 log(x + 3)?
The vertical asymptote of the function f(x) = 3 log(x + 3) is x =
.
The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3
Step-by-step explanation:
A symptote is a line that a curve approaches but never touches
The vertical asymptote of a logarithmic function is at the zero of the argumentf(x) = log(argument) has vertical aymptotes at argument = 0∵ f(x) = 3 ㏒(x + 3)
∵ The argument is (x + 3)
- Equate the argument by zero
∵ x + 3 = 0
- Subtract 3 from both sides
∴ x = -3
- The vertical asymptote of a logarithmic function is at the zero
of the argument
∴ The vertical asympotote of f(x) is x = -3
The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3
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Answer:
-3
Step-by-step explanation:
plato
what did the harlem renaissance celebrate accomplished and lead to in the early 1900’s
Answer:
The migration of the African-Americans to Harlem in the USA empowered the African-Americans in the society in the early 1900s. This was one of the greatest accomplishments of the African-Americans in history.
Explanation:
The "Harlem Renaissance" was originally called the "New Negro Movement." During the "Reconstruction Era," many of the African Americans felt a newfound empowerment in the society. They started leaving the South, where most of them were enslaved and maltreated. Many of them moved to other places such as "Harlem" in New York City. It became an ideal destination for many "Negros" and their number increased over time. This then became an African-American neighborhood.
African-Americans started producing plays with actors of their descent. Several Negro poets emerged describing the life of the African-Americans. Negros became more literate and able when it comes to expressing themselves in the society. They even had their own newspaper known as "The New Negro Movement."
100 POINTS!!! Need answer NOW! only correct answers! don't answer if you don't know how to work the problem!!
1.) Mr. Smith’s class sold wrapping paper for $3.50 each and Mr. Davis’ class sold magazines for $2.75 each. Together, the classes sold 72 items and earned $222 for their school.
Write and solve a system of equations that model the problem. Show all your work.
Which class earned more money?
How much more money did that class earn?
Answer:
Mr. Smith's class earned more money.They earned $2 more than Mr. Davis' class.Step-by-step explanation:
[tex]\text{Let}\\\\x-\text{number of wrapping paper of Mr. Smith's class}\\y-\text{number of magazines of Mr. Davis' class}\\\$3.50x-\text{the amount obtained from the sale of wrapping paper}\\\$2.75y-\text{the amount obtained from the sale of magazines}[/tex]
[tex]\bold{SYSTEM\ of\ EQUATIONS:}\\\\\left\{\begin{array}{ccc}x+y=72&\text{subtract}\ y\ \text{from both sides}\\3.5x+2.75y=222\end{array}\right\\\\\left\{\begin{array}{ccc}x=72-y&(1)\\3.5x+2.75y=222&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3.5(72-y)+2.75y=222\qquad\text{use the distributive property}\\\\(3.5)(72)+(3.5)(-y)+2.75y=222\\\\252-3.5y+2.75y=222\qquad\text{substract 252 from both sides}\\\\-3.5y+2.75y=222-252\qquad\text{combine like terms}[/tex]
[tex]-0.75y=-30\qquad\text{divide both sides by (-0.75)}\\\\\boxed{y=40}\\\\\text{Put it to (1):}\\\\x=72-40\\\\\boxed{x=32}\\\\\$3.5x=\$3.5\cdot32=\$112\\\\\$2.75\cdot40=\$110\\\\\$112-\$110=\$2[/tex]
Find the equation of a line with the given points.
(0, -2) (-2, 10)
Oy=-2x + 10
Oy = 4x + 10
Oy=x-2
Oy=-6x - 2
Answer:
y=-6x-2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(10-(-2))/(-2-0)
m=(10+2)/(-2)
m=12/-2
m=-6
y-y1=m(x-x1)
y-(-2)=-6(x-0)
y+2=-6(x)
y+2=-6x
y=-6x-2
5 6/7-1 1/2
difference?
Answer: 4 5/14
Step-by-step explanation:
Write down the total and the mean for each of the sets below.
a 4, 6, 8, 10 and 12
Answer:
Total: 40
Mean: 8
Step-by-step explanation:
To find the total, we add the numbers together and get 40. Then, to find the mean, we take the total and divide by the number of numbers, which is 5, to get our answer: 8
-AXZ
what is the equation of the following line? (7,2) (0,0)
A) y=2/7x
B) y=-2x
C)y=-7x
D)y=2x
E)y=1/7x
F) y=7x
Answer:
Step-by-step explanation:
(7,2) , (0,0)
slope = (y2 - y1) / (x2 - x1) = (0 - 2) / (0 - 7) = -2/-7 = 2/7
y = mx + b
slope(m) = 2/7
(0,0)...x = 0 and y = 0
now sub
0 = 2/7(0) + b
0 = b
ur equation is : y = 2/7x + 0.....same as y = 2/7x <====
The equation of the line is y = ( 2/7 )x where the slope is m = 2/7
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 7 , 2 )
Let the second point be Q ( 0 , 0 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 2 - 0 ) / ( 7 - 0 )
m = 2/7
Now , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - 0 = ( 2/7 ) ( x - 0 )
y = ( 2/7 )x
Hence , the equation of line is y = ( 2/7 )x
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A baker baker 40 cookies in and hour . What is the repentant and independent variable
Final answer:
The independent variable in the scenario is the time spent baking, and the dependent variable is the number of cookies baked. The size of the oven might be another independent variable if comparing productivity between different bakeries.
Explanation:
In the context of the question where a baker bakes 40 cookies in an hour, we are being asked to identify the dependent and independent variables in this scenario. First, let's define these terms:
The independent variable is the variable that you change or control in an experiment to test the effects on the dependent variable.The dependent variable is what you measure in the experiment and what is affected during the experiment.In this particular case, the independent variable could be the time spent baking, because it is what the baker controls. The dependent variable is the number of cookies baked, which depends on the amount of time the baker spends baking. If, for example, the baker decides to bake for two hours instead of one, we would expect the number of cookies baked to potentially double, assuming productivity remains constant.
In a different scenario, where comparing the productivity of bakers with different oven sizes – such as a Canadian worker with an industrial-size oven versus a U.S. worker with a smaller oven – the size of the oven could be seen as the independent variable affecting the dependent variable of productivity measured by the output of loaves of bread in an hour.
A hemispherical tank is filled with water and has a diameter of 6 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?
Answer:
The total weight of the water in a full tank, to the nearest pound is 3527 pounds per cubic foot
Step-by-step explanation:
Given:
Diameter of the hemispherical tank = 6 feet
Weight of water per cubic foot = 62. 4 pounds
To Find:
The total weight of the water in a full tank, to the nearest pound?
Solution:
We know that the volume of a sphere is:
[tex]V =\frac{4}{3}\pi r^3[/tex]
where
r = is the radius
In the question we are given with diameter,
So
[tex]radius = \frac{diameter}{2}[/tex]
radius = [tex]\frac{6}{2}[/tex]
Radius = 3
We need the volume of the hemisphere
So the volume of the hemisphere will be half of the volume of teh sphere
[tex]\frac{V}{2} = \frac{2}{3}\pi r^3[/tex]
Thus the volume of the hemisphere is
[tex]V =\frac{2}{3} \pi r^3[/tex]
Now substituting the values
[tex]V = \frac{2}{3} \pi(3)^3[/tex]
[tex]V = \frac{2}{3}\pi(27)[/tex]
[tex]V = \frac{54 \pi}{3}[/tex]
[tex]V = \frac{169.56}{2}[/tex]
V= 56.52 cubic foot
Now, the total weight of water of:
W = 56.52 x 62.4
W= 3526.848 pounds per cubic foot
To the nearest pounds
W= 3527 pounds per cubic foot
Answer:
3529
Step-by-step explanation:
If you are here from delta math this is the Answer
3. At the beginning of the day, a water tank contained 526.8 gallons of water. During the day,
some of the water was used to water a garden. At the end of the day, the water tank contained
318.05 gallons of water.
What was the total amount of water used that day?
a. 202.75 gallons
b. 208.75 gallons
C. 208.85 gallons
d. 210.80 gallons
Answer:
208.85
Step-by-step explanation:
It is 208.85 because when you have .8 + .05 =.85
Answer:
Step-by-step explanation:
the total amount of water used that day = 526.80 - 318.05 = 208.75 gallons.
A 50-foot tree casts a shadow 9 feet long. The sine of the angle between the ground and the line that connects the top of the shadow to the top of the tree is approximately
Final answer:
The sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given a 50-foot tree and a 9-foot shadow, is approximately 0.984, calculated using the definition of sine in a right triangle and the Pythagorean theorem.
Explanation:
The question involves finding the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given that a 50-foot tree casts a 9-foot long shadow. In this scenario, we can visualize a right triangle where the tree represents the opposite side (height), the shadow represents the adjacent side (base), and the hypotenuse is the line from the top of the tree to the end of the shadow on the ground.
To find the sine of the angle, we use the definition of sine in a right triangle, which is sine(angle) = opposite / hypotenuse. However, before we can do that, we need to determine the length of the hypotenuse using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).
Let's calculate:
a (opposite) = 50 feet (Height of the tree)
b (adjacent) = 9 feet (Length of the shadow)
c (hypotenuse) = √(50² + 9²) = √(2500 + 81) = √2581 = 50.8 feet (approximately)
Now, we can calculate the sine of the angle:
sine(angle) = opposite / hypotenuse = 50 / 50.8 ≈ 0.984
Therefore, the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree is approximately 0.984.
What is the solution to the equation
?
Answer: [tex]x=9[/tex]
Step-by-step explanation:
Alright, lets get started.
[tex]log_{6}4x^2-log_{6}x=2[/tex]
Using the property of logs : [tex]log (m) - log(n)=log\frac{m}{n}[/tex]
[tex]log_{6}\frac{4x^2}{x}=2[/tex]
[tex]log_{6}4x=2[/tex]
Using the property of logs : [tex]if \ log_{a}m=n, \ then \ a^n=m[/tex]
So,
[tex]6^2=4x[/tex]
[tex]4x=36[/tex]
Dividing 4 in both sides
[tex]x=9[/tex] ...................... Answer
Hope it will help :)
Answer:
x = 9
Step-by-step explanation:
Determine the defined range
[tex]log^6 (4x^2) - log^6 (x) = 2, x = (0, + ∞)[/tex]
Use log^a (x) - log^a (y) = log^a (x/y) to simplify the expression
[tex]log6 (\frac{4x^{2} }{x} )= 2[/tex]
Simplify the expression
log^6 (4x) = 2
Convert the logarithm into an exponential form using the fact that log^a (x) = b is equal to x = a^b
[tex]4x=6^{2}[/tex]
Evaluate the power
4x = 36
Divide both sides of the equation by 4
x = 9, x = (0, + ∞)
Check if the solution is the defined range
x = 9
(9x + 25) (13x - 19) (17y + 5)
Answer:
1989xsquared y + 585xsquared+ 2618xy + 770x - 8075y - 2375
Step-by-step explanation:
(9x + 25) x (13x - 19) x (17y + 5)
(117x squared - 171x + 325x - 475) x (17y + 5)
(117x squared + 154x - 475) x (17y + 5)
[tex](9x + 25) (13x - 19) (17y + 5)=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]
We have to simplify the expression:
(9x + 25)(13x - 19)(17y + 5)
Multiply the first two expressions as
[tex][9x(13x - 19)+25(13x - 19)](17y + 5)[/tex]
[tex]=(117x^2 - 171x + 325x - 475)(17y + 5)[/tex]
[tex]=(117x^2 + 154x - 475)(17y + 5)[/tex]
[tex]=17y(117x^2 + 154x - 475) + 5(117x^2 + 154x - 475)\\=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]
Therefore after simplifying , we get
[tex](9x + 25) (13x - 19) (17y + 5)=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]
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64/9 improper fraction
improper fraction
Answer:
If you want the mixed number,it is 7 1/9
Step-by-step explanation:
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
Which is the solution to the inequality?
y+15 <3
y<-12
y>-12
y<18
y > 18
y < –12
Solution:
Step 1: Given inequality is y + 15 < 3.
To find the solution to the inequality.
Step 2: Subtract –15 on both sides to equal the expression.
⇒ y + 15 –15 < 3 –15
Step 2: Using addition identity property, any number adding with zero gives the number itself.
⇒ y + 0 < –12
⇒ y < –12
Hence the solution to the inequality is y < –12.
Answer:
Step-by-step explanation:
It’s b
Complete the inequality statement
7/10 ___ 11/20
> < =
Answer:
The person up there is right just saying:)
Step-by-step explanation:
Evaluate –x + (–7.5) for x = 6.3.
Answer:
Step-by-step explanation:
The answer is 1.2, you want to replace the x with the 6.3 and then the -7.5 ends up turning into a positive. You then add the two together -6.3 + 7.5 = 1.2
Ms.Griffith lives on one of the highest floors in her apartment building. The elevator goes up one floor every 10.2 seconds. Along the way, it stops for a total of 45.8 seconds for people to get out. If it takes her 158 seconds to travel from the lobby to her apartment, what floor does she live on?
Answer:
Ms. Griffiths lives on 3rd floor
Step-by-step explanation:
The elevator moves 10.2 seconds from one floor to another and stops for 45.8 seconds for people to exit. Thus, add: 10.2 seconds + 45.8 seconds = 56 seconds
If it takes her 158 seconds to travel from the lobby to her apartment, then 158 seconds/56 seconds = 2.8 = 3 (approximately).
Therefore, she lives on 3rd floor.
Mathematically, the values ought to be 168 seconds /56 seconds = 3.
Evaluate 2(x-4) + 3x - x2 for x = 3.
O
A. -6
O
B. 2
a
O c. 6
OD. -2
Answer:
D. -2.
Step-by-step explanation:
2(x-4) + 3x - x2 for x = 3
= 2(3-4) + 3(3) - 3^2
= 2(-1) + 9 - 9
= -2 + 9 - 9
= -2.
a wave has a wavelength of 5m and a frequency of 68 hertz what is the speed
Answer:
Therefore the Speed of a wave is 340 m/s.
Step-by-step explanation:
Given:
Wave Length = 5 m
Frequency = 68 hertz
To Find:
Speed = ?
Solution:
Wave Speed:
Wave speed is the distance a wave travels in a given amount of time, such as the number of meters it travels per second.
Wave speed is related to wavelength and wave frequency.
The Formula is given by
[tex]Speed = Wavelength\times Frequency[/tex]
Substituting the values we get
[tex]Speed = 5\times 68=340\ m/s[/tex]
Therefore the Speed of a wave is 340 m/s.
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Which statements are true?
A;When triangle ABC is reflected over the y-axis to create triangle A'B'C' , the coordinates for B' are(1, -1) .
B;When triangle ABC is rotated 90 degrees clockwise about point A to create triangle A'B'C' , the coordinates for B' are (3,3]
C When triangle ABC is dilated from the origin by a scale factor of 1\4
to create triangle A'B'C', the coordinates for B'are (4,4)
D When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0)
E When triangle ABC is dilated from the origin by a scale factor of 5 to create triangle A'B'C', the coordinates for B' are (5,5)
The correct answer is: When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0). The true statement is D.
Let's analyze each statement:
A; When triangle ABC is reflected over the y-axis to create triangle A'B'C' , the coordinates for B' are (1, -1) .
To reflect over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. If the coordinates for B are (x, y), then after reflecting, the x-coordinate becomes -x. Since B has coordinates (1, 1), after reflection, B' will have coordinates (-1, 1). So, statement A is false.
B; When triangle ABC is rotated 90 degrees clockwise about point A to create triangle A'B'C' , the coordinates for B' are (3,3]
Rotation of 90 degrees clockwise about a point involves swapping x and y coordinates and negating the new x-coordinate. The point A is not given, but assuming it's (0, 0), if B has coordinates (x, y), then after rotation, B' will have coordinates (y, -x). If A is (0, 0) and B is (3, 1), after rotation, B' will have coordinates (1, -3), not (3, 3). So, statement B is false.
C; When triangle ABC is dilated from the origin by a scale factor of 1/4 to create triangle A'B'C', the coordinates for B' are (4,4)
Dilating by a scale factor of 1/4 means multiplying each coordinate by 1/4. If B has coordinates (x, y), then after dilation, B' will have coordinates (1/4 * x, 1/4 * y). Since B has coordinates (4, 4), after dilation, B' will have coordinates (1, 1). So, statement C is false.
D; When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0)
Translation involves adding/subtracting values to x and y coordinates. If B has coordinates (x, y), then after translation by (-2, -1), B' will have coordinates (x - 2, y - 1). Since B has coordinates (1, 1), after translation, B' will have coordinates (-1, 0). So, statement D is true.
E; When triangle ABC is dilated from the origin by a scale factor of 5 to create triangle A'B'C', the coordinates for B' are (5,5)
Dilating by a scale factor of 5 means multiplying each coordinate by 5. If B has coordinates (x, y), then after dilation, B' will have coordinates (5 * x, 5 * y). Since B has coordinates (4, 4), after dilation, B' will have coordinates (20, 20), not (5, 5). So, statement E is false.
So, the true statement is D.
8. Mr. Gardner is contemplating which shullle service to take lo the airport. Fost
Shullle charges a $5 pick-up fee and $0.25 per mile. Steady Shullle cholges a $2
pick-up fee and $0.50 per mile.
Part A: When will the two plans cost the same amount
Part B: If the airport is 20 miles away, which company should Mr. Gardner choose?
Answer:
Frosts second mile and steadys 6th mike
Step-by-step explanation:
Part A: The two plans will cost the same amount when the distance to the airport is 12 miles.
Part B: For a 20-mile distance, Mr. Gardner should choose Fost Shuttle, costing $10 compared to $12 for Steady Shuttle.
Let's solve Part A first:
Part A:
Let's denote the distance to the airport as d miles.
For Fost Shuttle:
Cost = Pick-up fee + Cost per mile × Distance
Cost = $5 + $0.25 × d
For Steady Shuttle:
Cost = Pick-up fee + Cost per mile × Distance
Cost = $2 + $0.50 × d
Now, we'll set up an equation to find when the two plans cost the same amount:
[tex]\[5 + 0.25d = 2 + 0.50d\][/tex]
Solving for d:
[tex]\[0.25d - 0.50d = 2 - 5\]\[-0.25d = -3\]\[d = \frac{-3}{-0.25}\]\[d = 12\][/tex]
So, the two plans will cost the same amount when the distance is 12 miles.
For Part B:
Given the distance is 20 miles, let's calculate the cost for each company:
For Fost Shuttle:
Cost = $5 + $0.25 × 20 = $5 + $5 = $10
For Steady Shuttle:
Cost = $2 + $0.50 × 20 = $2 + $10 = $12
Comparing the costs, Mr. Gardner should choose Fost Shuttle as it costs $10 compared to $12 for Steady Shuttle.
Hep me ASAP!!!! A.-2 B.4 C.7-3sqrt3 D.7- sqrt3
Answer:
7 - 3[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
3 + [tex]\sqrt{x+7}[/tex] - [tex]\sqrt{3x}[/tex] ← substitute x = 9
= 3 + [tex]\sqrt{16}[/tex] - [tex]\sqrt{27}[/tex]
= 3 + 4 - [tex]\sqrt{9(3)}[/tex]
= 7 - 3[tex]\sqrt{3}[/tex]
Why is important to use mixed numbers in real life
Answer:
It is important to use mixed numbers in real life, because it can help you find the measurements for when you are buying ingredients or baking something.
Hope this helps ;)
Step-by-step explanation:
The information from the settings menu titled "About" for an Apple iPod is given.
About
Songs
3639
Videos
32
Photos
0
Capacity
62.5 GB
Available
35.0 GB
Version
1.1.1
S/N
4H534PG7TY1
Model
MA148LL
Format
Windows
What percent of the memory capacity is still available? Round to the nearest percent. (GB stands for gigabytes.)
Answer:
Step-by-step explanation:
total capacity = 62.5 GB
available capacity = 35.0 GB
35 is what percent of 62.5
35 = x% * 62.5
35 / 62.5 = x%
0.56 = x%
56% = x <=====
56% of the memory capacity is still available.
To calculate the percentage of memory capacity that is still available, we can use the available capacity and total capacity information provided.
Given:
Capacity: 62.5 GB
Available: 35.0 GB
To find the percentage, we divide the available capacity by the total capacity and multiply by 100:
Percentage = (Available / Capacity) x 100
Percentage = (35.0 GB / 62.5 GB) x 100
Percentage ≈ 56%
Therefore, 56% of the memory capacity is still available.
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Is 12=24-y and Y equals 12
Answer: Yes.
Step-by-step explanation: if y=12, then 24-12=24 aka 24-y=12
Please help me guys with this than you
Answer:theres nothimh here to answer
Step-by-step explanation: