Answer:
Step-by-step explanation:
You'd have to be really familiar with conic sections to know what to do with this. Good thing I am! ; )
Begin by grouping the x terms together and the y terms together, and getting the constant on the other side of the equals sign:
[tex]25x^2+200x-9y^2+18y=-166[/tex]
Now we need to complete the square on the x terms and the y terms. Do this by first factoring out the leading coefficient from each, the 25 from the x's and the 9 from the y's:
[tex]25(x^2+8x)-9(y^2+2y)=-166[/tex]
Now take half the linear term in each set of parenthesis, square it, and add it in to both sides, remembering the multiplier outside (the 25 and the 9). Our x linear term is 8. Half of 8 is 4, and 4 squared is 16, so we add a 16 into the parenthesis with the x's; our y linear term is 2. Half of 2 is 1 and 1 squared is 1, so we add a 1 into the parenthesis with the y's:
[tex]25(x^2+8x+16)-9(y^2+2y+1)=-166+400-9[/tex]
Note the 400 and -9 on the right side now. 25 times 16 is 400; we didn't just add in a 16, we have to multiply the scalar number into it before we know what we REALLY added in. And the -9 comes from multiplying the -9 times 1.
The reason we do this is to get the perfect square binomials on the left that we created while completing the square:
[tex]25(x+4)^2-9(y+1)^2=225[/tex]
Now, finally we will divide both sides by 225 to get this conic into standard form:
[tex]\frac{(x+4)^2}{9} -\frac{(y+1)^2}{25} =1[/tex]
This is a hyperbola with a horizontal transverse axis and a center of (-4, -1). The reason we know it's not an ellipse is because an ellipse will always have a + sign separating the x-squared from the y-squared whereas a hyperbola always has a - sign separating them. And we also know it's not a circle because the values of the leading coefficients weren't the same.
Geometric mean between 2 and 24
Choose the correct name for the polygon.
VRUST
SRVUT
SRTUV
RSVUT
The name of polygon is SRVUT.
What is Polygon?In geometry, a polygon is any closed curve made up of a collection of continuous line segments (sides) without any intersections. Triangles (three sides), quadrilaterals (four sides), and pentagons are the three simplest polygons (five sides).
Given:
Usually while naming the polygon we have to focus on the letter to which each vertex is allotted.
and, the name of any geometrical shape should be in a flow, it should be like which letter come after the previous in clockwise or anticlockwise order.
Here, the polygon will have name:
VRSTU
RSTUV
STUVR
TUVRS
UTVRS
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Three bowls and four mugs can hold a total of 2.52 litres of water. Each bowl can hold
70 ml more than a mug. How much water can a mug hold? Give your answer in litres.
(with full working)
9514 1404 393
Answer:
0.33 litres
Step-by-step explanation:
If a mug can hold a volume of m litres, then a bowl can hold a volume of m+0.07 litres. The total volume held by the given containers is ...
3(m +0.07) +4m = 2.52
7m +0.21 = 2.52 . . . . . . . . simplify
7m = 2.31 . . . . . . . . . . . . . subtract 0.21
m = 0.33 . . . . . . . . . . . . . divide by 7
Each mug can hold 0.33 litres.
please hellp meeee :D
a) 20 ft
b) 32 mm
Step-by-step explanation:
a) The legs of the smaller triangle are 6-6-3. The larger triangle is 1/3 larger than the other triangle so the lengths of the legs are 8-8-4 so the perimeter is 20 ft.
b) Since one side of the larger square is 8 mm, this means that the perimeter is 4×8mm = 32 mm.
Answer:
i dont know what the answerris
Step-by-step explanation:
SOMEONE PLEASE HELP!
I dont know Im sorry
Step-by-step explanation:
I just want points in not that smart
PLEASE HELPS ASAP!! ILL GIVE BRAINLIEST AND A THANKS!!
What is the area of a circle with a radius of 3/8 meters?
Answer:
3/8^2 = 9/64
9/64 x 3.14 = 0.4415625 rounded = 0.44
Formula area of a circle:
pi(3.14 or 22/7 or any other number depending what they tell you to use for pi) x radius(half of your diameter or given radius)^2(squared, to the power of 2)
pi x radius being squared
Which coordinate point represents the y -intercept of the equation 3x + 2y = 18
Answer:
(-6,18)
Step-by-step explanation:
3x + 2y = 18
2y= -3x + 18
y=-3/2 x + 18
give x=0
y=-3/2 *0+18
y=18#
y=18
3x+2(18)=18
3x+36=18
3x=18-36
3x=-18
x=-18/3
x=-6
The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored greater than 700.
a. 95%.b. 2.5%.c. 5%.d. 97.5%.
Using the Empirical Rule, the percentage of students who scored greater than 700 is:
b. 2.5%
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.700 is two standard deviations above the mean. 5% of the measures are more than two standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of these measures are below 300 and 2.5% are above 700, hence option B is correct.
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What is the fractional equivalent of the repeating decimal n=0.2727…?
Answer: 3/11 would be the answer
Round 27346 to 2 significant figures i need a step by step expansion
Answer:
27000
Step-by-step explanation:
We want to round 27346 to 2 significant figures.
Now, the number already has 5 significant figures, so to reduce it to 2 sig figures, we will have to reduce the 3 digits from the right to zero so that we can have just 2 significant figures by approximating.
Thus, 3 is less than 5 and so 7 cannot increase. Thus, we will have 27000 as the number when reduced to 2 significant figures.
What is the range of the data set 1 2 3 4 5 6 7
Answer:
6
Step-by-step explanation:
Range = Highest number - Smallest number
From the data
Highest number = 7
Lowest number= 1
Range = 7 - 1
RAnge = 6
Hence the range of the dataset is 6
A chocolate milk container in the form of a rectangular prism is 5 cm long, 3 cm wide, and 9 cm high. How many cubic centimeters of chocolate milk can it hold?
WITH SOLUTION PLEASE
Hello there I hope you are having an great day :) A chocolate milk container in the form of a rectangular prism is 5 cm long, 3 cm wide, and 9 cm high. How many cubic centimetres of chocolate milk can it hold?
V = L x W x H
Volume = length x Width x Height.
V = (5cm) (3cm (9cm)
V = 135cm^3
Therefore, the chocolate milk container can hold 135 cubic centimetres. Hopefully that helps you :)
Magdeline wants to know if the number of words on a page in her art book is generally more than the number of words on a page in her science book. She takes a random sample of 25 pages in each book and then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.
Book Mean Median Mean Absolute Deviation
Art 68.7 50 15.4
Science 54.2 55 7.9
She claims that because the mean number of words on each page in the art book is greater than the mean number of words on each page in the science book, the art book has more words per page. Based on the data, is this a valid inference?
Answer:
Yes
Step-by-step explanation:
Because the mean is the total of all the words divided by the number of pages, so if the mean is higher, that means that there are more pages on average in the art book than the science book.
Answer:
no
Explanation:
there is a lot of variability in the art book data
A school has 500 students. 340 are boys
a student is chosen at random. find the probability that student is a girl
Answer:
p = 8/25
Step-by-step explanation:
500 - 340 = 160 girls
p = 160/500
p = 8/25
solve the equation
f(n)=10⋅2n for n = -2
Answer:
f(n)= -40.
Step-by-step explanation:
Polynomial is a combination of O constants O variables O exponents O all of the choices
Answer:
It would be all of the above.
Step-by-step explanation:
An example of a polynomial is:
2x^3 - 4x^2 +1x -8
Note how there are exponents, such as ^3 for example. There is also a variable, in this case x. Lastly, there are constants, which are numbers by themselves.
Define the variables and translate the following statements into
algebraic inequalities.
"You buy hamburgers at a fast food restaurant. A
hamburger costs $0.49. You have at most $3 to spend.
Write an inequality for the number of hamburgers (6) you
can buy."
The variable should be on the left side of the inequality.
Etion
Check
nikal bhosdike gaand mara
Suppose you have a bag containing 2 black marbles and 3 red marbles. You reach into the bag, select a marble, see what color it is and replace it in the bag. Then you repeat this process. What is the probability of first selecting a black marble, replacing it and then selecting a red marble?
one clothing truck visits avas place every 3 days and another clothing truck visits noahs place every 5 days if both clothing trucks visited today when is the next time both trucks visit on the same day
Answer:
15 days
Step-by-step explanation:
Given
[tex]Truck\ 1: 3\ days[/tex]
[tex]Truck\ 2: 5\ days[/tex]
Required
Next time they both visit
First, list out days of visitation of each truck
[tex]Truck\ 1: 3, 6, 9, 12, 15, 18, 21\ days.....[/tex]
[tex]Truck\ 2: 5, 10, 15, 20, 25, \ days.....[/tex]
Write out the common days;
[tex]Day = 15[/tex]
The next time they both visit is the after 15 days
Wanda Frey insured her home for $156,400. Her annual insurance rate is $0.83
per $100. What annual premium did she pay?
Answer:
$1,298.12
Step-by-step explanation:
there are 1564 hundreds in 156,400
so 1564 x .83 = 1298.12
Find the area of an 11-gon with side length 5 inches.
Answer:
234.141
Step-by-step explanation:
The formula is [tex]\frac{11}{4} *(s)^2*cot(\frac{\pi }{11})[/tex]. If you substitute 5 in, you get [tex]\frac{275}{4} *cot(\pi /11)[/tex] or 234.141
Please I need this ASAP
Answer:
Step-by-step explanation:
Always work from the inside out. That means we will deal with the parenthesis first: (4 - 1)
That gives us
2[32 - (3)³]. Next deal with the exponents. That gives us
2[32 - 27]. Next, the last set of parenthesis, which are actually brackets:
2[5] which then, finally, becomes 10
Order of operations...PEMDAS
The graph below shows Ariana's pay as a painter. How much does Ariana charge per painting?
30 ft.
6 ft.
4 ft.
20 ft.
?
25 ft.
PLEASE HELP QUICK
Answer:
5 ft
Step-by-step explanation:
30/6 = 5
20/4 = 5
25/x = 5
25/5 = 5
x = 5
Answer:
5 feet
Step-by-step explanation:
the triangles are scaled by the factor of 5
Problem #4:
and one
sum of
A gumball machine contains 15 green gumballs, 6 yellow gumballs, and
11 pink gumballs.
The gumball machine dispenses 1 gumball at a time.
a) What is the probability of getting a pink gumball?
b) What is the probability of getting three pink gumballs in a
row?
c) If the machine was refilled, and you purchased 4
gumballs, what is the theoretical probability of the machine
dispensing 4 green gumballs?
d) If we add 8 orange gumballs to the machine, what is the probability
of getting two orange gumballs and then a yellow gumball.
be closest
at 18.
Answer:
Step-by-step explanation:
Prepare closing entireties for the concert hall bond fund
PLEASE HELP!! IM BEGGING !!
Answer:
0
Step-by-step explanation:
P(starts with M wins presidency) = required outcome / Total possible outcomes
Number of names which starts with M = 1
Total number of names = 5
P(starts with M wins presidency) = 1/ 5
For vice presidency :
Number of names which starts with M = 0
Total number of names = 4
P(starts with M wins vice presidency) = 0/4
P(name which starts with M wins presidency and vice presidency) = 1/5 * 0/4 = 0
Find the area of the composite figure
Answer:
area of semicircle=76.969 inches
triangle is=10 in so 20 since there is 2 triangles made
rectangle=140 in
236.969 inches is the total
hope this helps
have a good day :)
Step-by-step explanation:
Can someone please help me?
Answer:
yes i can
Step-by-step explanation:
Answer:
(2,7)
Step-by-step explanation:
A 30 ft ladder is leaning against a wall making a 48 angle with the ground. Approximately how far from the wall is the base of the ladder?
Determine the mode of the following data set:
-- 3, 12, 5, 12, 11, 2, 3, 10, 7, 6, 1, 4
a. 12
b. 3 and 12
c. no mode
d. 5
Step-by-step explanation:
3 AND 12 MAY BE
HOPE IT HELP U ...