The vertices of the hyperbola are the x-intercepts of the hyperbola
The equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]
How to determine the equation of the hyperbola?The equation of a hyperbola is represented as:
[tex]\frac{(y - k)^2}{a^2} -\frac{(x - h)^2}{b^2} = 1[/tex]
The vertices are (20,0) and (-20,0).
So, the center of the hyperbola is:
(h,k) = (0,0).
Also, we have:
a = 20
This gives
[tex]\frac{(y - 0)^2}{a^2} -\frac{(x - 0)^2}{b^2} = 1[/tex]
Evaluate
[tex]\frac{y^2}{a^2} -\frac{x^2}{b^2} = 1[/tex]
Substitute 20 for a
[tex]\frac{y^2}{20^2} -\frac{x^2}{b^2} = 1[/tex]
[tex]\frac{y^2}{400} -\frac{x^2}{b^2} = 1[/tex]
The length of the conjugate axis is:
l = 18 units
So, we have:
[tex]b = \frac{18}2 = 9[/tex]
The equation becomes:
[tex]\frac{y^2}{400} -\frac{x^2}{9^2} = 1[/tex]
[tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]
Read more about hyperbola at:
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A teacher puts five packages of craft paper into a cabinet each package has 80 sheets of paper what is the total number of sheets of craft paper that the teacher put into the cabinet and wears a.40 b.85 c.400 d.450
Answer:
C
Step-by-step explanation:
If we have 5 packages and each contains 80, we are basically doing 80+80+80+80+80 (5 TIMES) which is referred to as 80×5=400
Answer:
1 package contain 80 sheets of paper.
If there is 5 packages, there will be 'x' sheets of paper.
We replace the sheets of paper with 'x', because the value of x is unknown.
Now we set up the equation:
Sheets 80 x__________ _________ = _________, solve for x;
Packages 1 580/1 = x/5
*5 *5
400 = x
Why is math super hard??
Click all the questions that are considered statistical questions. No links please.
Answer:
The first three are not statistical, the last three are.
Use substitution to find the value of y. x =3 x+y=7 step 1 : rewrite the equation step 2 :add or subtract to solve for y
Answer:
[tex]\huge\boxed{\sf y = 4 }[/tex]
Step-by-step explanation:
Given Equations:
x = 3 --------------------(1)
x + y = 7 ---------------(2)
Step 1: Substitute Eq. (1) in (2)
3 + y = 7
Step 2: Subtract 3 to both sides
y = 7 - 3
y = 4
[tex]\rule[225]{225}{2}[/tex]
Which function has a constant additive rate of change of –1/4?.
Mrs. Gomez purchased a pair of sneakers for $32.50 and two shirts for
$13.00 each. If Mrs. Gomez pays 8% in sales tax, then what is the total
cost Mrs. Gomez will pay for the sneakers and shirts? *
Your answer
Answer:
62.86
Step-by-step explanation:
Add the cost of things without sales tax:
32.5+ (13×2)=58.5
Convert percent to decimal:
8/100=0.08
Multiply cost without sales tax by sales tax to get the amount added to the cost:
0.08×58.2=4.656
Add cost and sales tax amount to get total payment:
4.656+58.5=62.856
Round the total payment to the nearest hundredth place:
62.86
1035 divided by 23 hun
Answer:
45
Step-by-step explanation:
A storage compartment is shaped like this hexagonal prism. The prism has a base area of 7.35 cm².
What is the volume of the compartment?
Enter your answer as a decimal in the box.
cm³
The volume of the compartment shaped like this hexagonal prism is 29.4 cm³
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
The volume of a hexagonal prism = area of base * height
Hence:
Volume = 7.35 cm² * 4 cm = 29.4 cm³
The volume of the compartment shaped like this hexagonal prism is 29.4 cm³
Find out more on volume at: https://brainly.com/question/1972490
Answer:
The answer is 29.4 cm^3! The first user has it correct dont worry guys^_^
Step-by-step explanation:
I took the k12 4.12 Unit Test: Three-Dimensional Geometry - and got a 90% ^_^
Good luck with the rest of the questions! If you had question 4 "A minuture connector is shaped like a hexagonal prism. The prism has a base area of 8.15 cm^3. What is the volume of the compartment?"
Then your answer would be 32.6 cm^3
Last year, there were n pies baked for the bake sale. This year, there were 228 pies baked. Using , write an expression for the total number of pies baked in the two years.
Calculate the compound interest on $6 000 if invested for 3 years at 7.5% per annum.
multiple choice answers:
$6000 $7453.78 $1453.78 $7534.87
Question 9 of 14 V
Question 9
Levi was designing a kite. He needs to determine the measure of A before cutting the fabric.
(1100
(6x + 4)º
A А
(4x + 26)
What is the measure of angle A?
The measure of angle A in the kite before cutting the fabric is 42 degrees.
What is a kite?A kite is a quadrilateral with four sides and four angles. Adjacent sides are equal, and the diagonals bisect each other at 90 degrees.
Also, there is a pair of equal opposite angles.
From the diagram:
110 + (6x + 4) + (4x + 26) = 180 (sum of angles in a straight line)
10x + 30 = 70
x = 4
∠A = 4(4) + 26 = 42°
The measure of angle A in the kite before cutting the fabric is 42 degrees.
Find out more on kite at: https://brainly.com/question/386327
8 nickels 12 pennies?
Answer:
52 cents :)
Step-by-step explanation:
Nickel: 5 cents
Penny: 1 cent
5 x 8 = 40
12 x 1 = 12
40 + 12 = 52
Have an amazing day!!!
Please rate and mark brainliest!!
Which value for x makes this inequality true?
−5>x
This inequality says the following:-
-5>x
negative 5 is greater than x, which means x is less than -5:
x<-5
Now, Which values make this inequality true?
Since x is less than -5, then numbers less than -5 will make this inequality true.
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)
On your way to a tournament, you meet six knights, each accomplished by six squires. Each squire leads two horses by reins, and on each horse are seated two young children. How many people and animals are going to the tournament?
Answer:
72
Step-by-step explanation:
Answer: 12 animals 36 people , in total 48 its so easy just adding and multiplying :)
Step-by-step explanation:6 knights 6 squires =12, then animals human people 6 time animals 2 is 12 animals then more humans 2 times 12 the horses is 24 in total add up humans 24+12=36 and animals is 12 so 36 people, and 12 animals in total 36+12 is 48
23.-28. In a manner similar to Example 1, (a) identify input and
output consistent with the general proportional model; (b) write
an equation for the model; (c) determine a numerical value for the
constant k; and (d) solve the problem.
24. The speed of a skidding car is directly proportional to the
square root of the length of the skid. On a snowy road, a car
with good brakes traveling at 40 mph would skid approxi-
mately 178 ft. If the skid marks of a similar car on a similar
road were 400 ft, how fast would this car be traveling?
24. If the skid marks of a similar car on a similar road were 400 ft, how fast would this car be
traveling?
The direct variation that of the speed to the skid length implies that the speed increases as the length increases
The car would be traveling at 59.96 mph
How to determine the speed of the skidding car?A direct variation that illustrates the speed of the skidding car is:
s = k√l
Where:
s represents the speed of the carl represents the length of the skidk represents the proportionality constantMake k the subject in s = k√l
k = s /√l
Rewrite as:
s₁ /√l₁ = s₂ /√l₂
Substitute known values
40 /√178 = s₂ /√400
Evaluate the square root of 40
40 /√178 = s₂ /20
Multiply both sides by 20
800 /√178 = s₂
Evaluate the quotient
s₂ = 59.96
Hence, the car would be traveling at 59.96 mph
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Helppppp!!!!!!!!!
I need this before midnight
Answer:
a) 9am
b) 10am
c) 50 miles
d) 30 minutes
e) 11:30
f) 90 miles
ASAP Please i need this done in the next 20 minutes
cos^2B-sin^2B=3cosB+1
the answer is "Using the trigonometric identity
sin²x + cos²x = 1 , then sin²x = 1 - cos²x
Consider the left side
sin²a - sin²b
= (1 - cos²a) - (1 - cos²b)
= 1 - cos²a - 1 + cos²b
= cos²b - cos²a
= right side , thus verified"
Find the area of the triangle b= 12.4 cm and h= 18 cm
Answer:
111.6 cm
Step-by-step explanation:
The area of a triangle can be calculated using the following formula:
Area = (base x height) / 2
Using this formula we can solve this problem in the following way:
We know base = 12.4, and height = 18(12.4 x 18) / 2 = 111.6Hope this helps!!
Answer:
answer 111.6 cm^2.......
What is the length of side a? Round to the nearest tenth
Answer:
○ [tex]\displaystyle 12,9[/tex]
Step-by-step explanation:
Use the Law of Sines to find the length of the second edge:
Solving for Angles
[tex]\displaystyle \frac{sin\angle{C}}{c} = \frac{sin\angle{B}}{b} = \frac{sin\angle{A}}{a}[/tex]
Use [tex]\displaystyle sin^{-1}[/tex]towards the end or you will throw your result off!
Solving for Edges
[tex]\displaystyle \frac{c}{sin\angle{C}} = \frac{b}{sin\angle{B}} = \frac{a}{sin\angle{A}}[/tex]
Let us get to wourk:
[tex]\displaystyle \frac{a}{sin\:40} = \frac{10}{sin\:30} \hookrightarrow \frac{10sin\:40}{sin\:30} = x; 12,855752194... \\ \\ \boxed{12,9 \approx x}[/tex]
I am joyous to assist you at any time.
23
Hot dogs are sold in packages of 12. Buns are sold in packages of 8. What is
the least number of packages of buns you would have to buy if you want to
purchase an equal number of hot dogs and buns?
А 3
B 4
C5
D 6
Answer:
A) 3
Step-by-step explanation:
12 * 2 = 24
8 * 3 = 24
24 = 24
What is the probability of both coins landing on heads?
Write your answer as a fraction or a whole number. With fractions, use a slash ( / ) to separate the numerator and denominator.
Answer:
and with the fractions and then divide the answer by 2.1
Step-by-step explanation:
Please help!! 155 questions 2 hours in I need help!
Answer:
the first one And the first one only
Step-by-step explanation:
supplementary angles are angles that add up to 180.
Hope this helps! :)
What is the
Height?
Please, asap. If two people answer, I will give one of you a brainlest and ask I will ask another question afterward.
Answer:
the answer is the number 23
help me pls pls bro pls
Identify the value of y.
7(5-5y) = 9y-4-357
Hey there!
Let's solve this equation!
The first step is to use the Distributive Property.
7(5-5y)=9y-4-357
35-35y=9y-361
Combine Like Terms:
-35y-9y=-361-35
-44y=-396
Divide both sides by -44:
y=9
Hence, the answer is:
[tex]\boxed{\boxed{\bold{y=9}}}[/tex]
Hope everything is clear.
Let me know if you have any other questions; if so, please comment.
#LearningDoesn'tEnd
#LearningIsFun
[tex]\rule{200}{2}[/tex]
What will be the sales price of the car if it has a regular price of $16 000 and is on sale for 20% off? Determine the cost of the car including 13% tax.
Answer:
14,464
Step-by-step explanation:
16,000 - 20% = 12,800
12,800 + 13% = 14,464
I hoope this is correct. Have a wonderful day and dream a good dream of good people. :)
The vertices of a quadrilateral drawn in a coordinate plane are (-6,6), (4,6), (2,-5), and (-6,-9). what is the length of the side joining the vertex in quadrant i to the vertex in quadrant 11? a) 2 b) 8 c) 10 d) 12
Using the formula for the distance between two points, it is found that the length of the side joining the vertex in quadrant i to the vertex in quadrant ii is given by:
c) 10
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In quadrant I, both coordinates are positive, hence the vertex is (4,6). In quadrant II, x is negative while y is positive, hence the vertex is (-6,6). Thus, the distance is given by:
[tex]D = \sqrt{(-6 - 4)^2+(6 - 6)^2} = 10[/tex]
Which means that option C is correct.
More can be learned about the distance between two points at https://brainly.com/question/18345417
Find the area of each triangle b= 12.4cm. h= 18 cm
[tex] \frac{1}{2} \times b \times h \\ \frac{1}{2} \times 12.4 \times 18 \\ 6.2 \times 18 \\ 111.6 {cm}^{2} [/tex]
seven less than the product of a number n and 1/3 is no more than 95
Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.
Which statement about the value of x is true?
x > 38
x < 39
x < 77
x > 103
Answer: x>38
Step-by-step explanation:
By the exterior angle theorem, x=39+38=77.