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]
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Assessment started: undefined.
Item 1
In this polygon, all angles are right angles.
What is the area of this polygon?
PLEASE HELP ME
An object is attached by a string to the end of a spring. Fang throws the object upwards and starts a stopwatch at t=0t=0t, equals, 0 seconds. The object starts oscillating vertically in a periodic way that can be modeled by a trigonometric function.
The object's average height is -20\text{ cm}−20 cmminus, 20, start text, space, c, m, end text (measured from the top of the spring). It first achieves that average height on the way up at t=0.2t=0.2t, equals, 0, point, 2 seconds, and then again every 222 seconds. The object's maximum and minimum heights are each 5\text{ cm}5 cm5, start text, space, c, m, end text from its average height.
Find the formula of the trigonometric function that models the height HHH of the weight ttt seconds after Fang started the stopwatch. Define the function using radians.
\qquad H(t) =H(t)=H, left parenthesis, t, right parenthesis, equals
What is the height of the object after 0.60.60, point, 6 seconds? Round your answer, if necessary, to two decimal places.
The object attached to a string illustrates a sinusoidal trigonometric function
The trigonometric function is H(t) = 5sin(π/2(t-0.2))-20, and the object's height after 0.6 seconds is -17.06 cm
How to determine the trigonometry function model?The trigonometry model of the object is a sine function represented by:
H(t) = Asin(B(t - c)) + D
The maximum height is 5 cm.
So, we have:
Amplitude, A = 5
The average height is - 20 cm.
So, we have
Vertical shift, D = -20
Its first average height is at t = 0.2.
So, we have:
Horizontal shift, C = 0.2
The period B is then calculated as:
B = π/t
The object reaches the maximum height every 2 seconds.
So, we have:
B = π/2
Substitute these values in H(t) = Asin(B(t - c)) + D
H(t) = 5sin(π/2(t-0.2))-20
Hence, the trigonometric function is H(t) = 5sin(π/2(t-0.2))-20
The height of the object after 0.6 secondsSubstitute 0.6 for t in H(t)
H(0.6) = 5sin(π/2(0.6-0.2))-20
Evaluate
H(0.6) = -17.06
Hence, the object's height after 0.6 seconds is -17.06 cm
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Answer:
What is the importance of biology laboratory?
Biological Science Laboratory Apparatus is essential for meeting our basic needs of food, clothing, shelter, health, energy, clean air, water and soil. Biological Science Laboratory Apparatus enrich the quality of life in numerous ways by providing new solutions to problems in health and materials and energy usage.
if £2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after two years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2\implies A=2121.8[/tex]
Answer:
2,121.8
Step-by-step explanation:
2000(1.03)^2
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Help!!!!!!! v is a vector of magnitude 4 making an angle of 30° with the positive x-axis. find v in component form .
Since v is a vector of magnitude 4 and makes angle 30° with the positive x axis, vector v in component form is v = 2√3i + 2j
To find vector v in component form, we need to know what a vector is
What is a vector?A vector is a physical quantity that has both magnitude and direction.
Component of a vectorA vector can be resolved into perpendicular components along the x, y and z axis.
Components of vector vSince vector v has a magnitude of 4 making an angle of 30 with the positive x - axis, its x-component is V = (vcos30°)i
= (4cos30°)i
= (4 × √3/2)i
= 2√3i.
The y-component of v is V' = (vsin30°)j
= (4 × sin30°)j
= (4 × 1/2)j
= 2j
Vector v in component form
So, vector v in component form is v = V + V'
= 2√3i + 2j
So, since v is a vector of magnitude 4 and makes angle 30° with the positive x axis, vector v in component form is v = 2√3i + 2j
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There are exactly 4 parts to this question so if u can please answer thanks
Part A
Dilate Triangle OPQ with a scale factor of 1/2.
Provide the coordinates of each new vertex.
Part B
How does the size Triangle O'P'Q' compare to the size of Triangle OPQ?
Explain how this relates to the scale factor.
Part C
Are
Part D
If the length of segment OQ measures 9.8 units, what is the length of segment O'Q'? Explain in terms of similarity.
Answer:
see my question and come there now I want to talk with you
Step-by-step explanation:
Goal: illustrates radius, diameter, chord, center, arc, central angle, and
inscribed angle.
Role: Garden Designer/Landscape Architect
Audience: Math Teacher
Situation: A certified plantita and backyard owner plans to have a unique
garden. As a Landscape Architect, you are asked to make a sample layout of
a circular garden. She asks you to include the following on her garden:
● well
● pond
● bridge
● fountain
● walkways
● benches or chairs
● entrance and exit gates.
● trees, ornamental plants, and herbs
Procedure:
1. Draw a circle.
2. Conceptualize a circular garden and layout using the specified
items mentioned above.
What I Can Do
9
DISCIPLINE • GOOD TASTE • EXCELLENCE
3. Label the parts of circle formed on the garden layout
Please I'm looking for a serious answer. I need to pass this on monday. Thank you.
Please Help this is due soon
The table below represents an exponential function.
table represents an exponential function.
What is the interval between neighboring
x-values shown in the table?
1
What is the ratio between neighboring y-values?
4
What is the equation for this pattern?
y = _^x
I only need the last one answered
Answer:
[tex]y = {4}^{x} [/tex]
is the answer
What was the original cost of the jacket.
Answer:
(c) $80
Step-by-step explanation:
Each discounted price corresponds to the original price multiplied by a factor related to the discount. For a discount fraction of 'd', the multiplier is (1 -d).
This means you can use any of the lines in the table to find the original price.
5% disount: (1 -5%)·p = $76 . . . . where p is the original price
p = $76/0.95 = $80 . . . . . . . the original price
10% discount: (1 -10%)·p = $72
p = $72/0.90 = $80
25% discount: (1 -25%)·p = $60
p = $60/0.75 = $80
_____
Additional comment
The table values for 5% and 10% differ by 5% and $4. That means 5% of the original price is $4. There are two things you can do with this:
add back that 5% to the 5%-discounted price: $76 +4 = $80multiply that 5% by 20 to get 100% of the original price: 20(5%) = 20($4) ⇒ 100% = $80.What is the value of k?
Answer:
10°
Step-by-step explanation:
According remote interior angles, 4k + 5 + 6k + 10 = 115.
10k + 15 = 115
10k = 100
k = 10
Hope this helps :)
Have a nice day!
Answer:
k = 10°
Step-by-step explanation:
According to the exterior angle theorem, the exterior angle will be equal to the two opposite inside angles added together. It will look like the following, and we solve for k from there.
115° = (4k + 5)° + (6k + 10)°
115° = 4k° + 5° + 6k° + 10°
115° = 6k° + 4k° + 10° + 5°
115° = 10k° + 15°
100° = 10k°
10° = k
k = 10°
Use the definition of continuity and the properties of limits to show that the function k(x)= √8−x2 2x2−5 is continuous at x = -2
12. A grocery store collects donated canned
food for a food bank. The cans are packed
in boxes that hold 24 cans. The store has
collected 744 cans.
a) Draw a graph to show this situation. Put
the number of boxes on the horizontal
axis and the number of cans on the
vertical axis. 2
b) Use your graph to estimate the number
of boxes needed to hold 744 cans.
c) Write an equation that relates the
number of boxes needed to the number
of cans.
d) Solve your equation to determine the
number of boxes needed.
e) Compare your solution in part (d) with
your estimate in part (b). Do you think
)
your solution is correct? Explain.
Answer:
For the last three years, the National Post has greeted the yuletide season by publishing the video above. With a simple message of maximizing charitable giving by donating money to the food bank instead of canned goods, it is one of our most popular videos of all time, reaching virtually every corner of the English-speaking world.
Step-by-step explanation:
Point c is the center of dilation. line segment b a is dilated to create line segment b prime a prime. the length of c a is 4. the length of a a prime is 16. what is the scale factor of the dilation of line segment ba? one-fifth one-fourth 4 5
The scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.
What is the dilation of the figure?Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.
Point c is the center of dilation. Line segment BA is dilated to create line segment b prime, a prime. The image of the given problem is attached below. The length of CA is 4.
[tex]CA=4[/tex]
The length of a prime is 16.
[tex]AA'=16[/tex]
The new dimension will be,
[tex]CA'=CA+AA'\\CA'=4+16\\CA'=20[/tex]
Now, the scale factor is the ratio of the new dimension to the original dimension. Thus, the scale factor of the dilation is,
[tex]r=\dfrac{20}{4}\\r=5[/tex]
This will be the same for the line segment BA. Thus, the scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.
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Answer:
the answer is 5
Step-by-step explanation:
D
If and , which expression is equivalent to ?
A.
B.
C.
D.
determine if the expressions
are
7. 2 - 2 + 5x; 5x
-5 1/2+6 3/4+(-4 1/4)=
Answer:
-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
that the answer
calculate them
is 48,200 in scientific notation?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \:48200[/tex]
[tex]\qquad \sf \dashrightarrow \:4.82 \times 10 {}^{4} [/tex]
How do solve this
h(x)=1/2x-14; h(4)
Answer:
-12
Step-by-step explanation:
h(x) = ½x - 14 where x = 4:
h(4) = ½(4) - 14
= 2 - 14
= -12
Consider the quadratic function.
f(x)=x^(2)+2x-15
If the line of symmetry of the function is located at x=N, what is the value of N?
HELP ASAP
Answer:
N = -1
explanation:
x = N
solving steps:
[tex]\sf f(x)=x^2+2x-15[/tex]
To find symmetry of a quadratic function.
vertex formula : [tex]\sf x=\dfrac{-b}{2a}[/tex]
[tex]a=1,\:b=2[/tex]
[tex]\sf x=\dfrac{-2}{2\cdot \:1}[/tex]
[tex]\sf x = -1[/tex]
Then,
N = -1
What is the value of X?
A) 17
B) 16
C) 16.5
D) 15
Answer:
answer is 16.5
Step-by-step explanation:
answer is 16.5
The normal price of a television is £1200
It is reduced to £970
Work out the percentage reduction.
Give your answer to 1 decimal place
Answer:80.8%
Step-by-step explanation:
£1200=100%
£970=
£970*100%/£1200=80.8333333
80.8%
Answer:
19.2%.
Step-by-step explanation:
Reduction = 1200-970 = £230,
% reduction = 230*100/ 1200
= 19,2%
If the hypotenuse of a 30°-60°-90° Triangle is 10√2, find the length of the other two sides.
Let us consider a 30°-60°-90°△ABC right angled at B in which ∠C = 30⁰ and ∠A = 60⁰ with hypotenuse AC = 10√2 units.
Solution:-In △ABC,
[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{AB}{AC}[/tex]
[tex]\longrightarrow[/tex]sin 30⁰ = [tex]\sf \dfrac{AB}{10\sqrt{2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf \dfrac{1}{2}= \dfrac{AB}{10\sqrt{2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf AB = \dfrac{10\sqrt{2}}{2}[/tex]
[tex]\longrightarrow[/tex][tex]\sf AB = 5\sqrt{2}\:units[/tex]
[tex]\\[/tex]
In △ABC,
[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{Base}{Hypotenuse}[/tex]
[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{BC}{AC}[/tex]
[tex]\longrightarrow[/tex]cos 30⁰ = [tex]\sf \dfrac{BC}{10\sqrt{2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf \dfrac{\sqrt{3}}{2}= \dfrac{BC}{10\sqrt{2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2}\times \sqrt{3}}{2}[/tex]
[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2\times 3}}{2}[/tex]
[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{6}}{2}[/tex]
[tex]\longrightarrow[/tex][tex]\sf BC = 5\sqrt{6}\: units[/tex]
Thus , the length of other two sides of triangles are 5√2 and 5√6 units.
How much, in total, did Noel spend to cash her three most recent paychecks?
Based on the amount that Noel cashed in each of her most recent paychecks, the amount she spent in total is $10.99.
How much did Noel spend?The bank directory shows that you are charged 1.99% of the amount being cashed as well as a check processing fee of $1.39.
The amount Noel spent is therefore:
= (1.99% x 100.53) + (1.99% x 119.38) + (1.99% x 122.52) + (1.39 x 3 checks)
= 2.00 + 2.38 + 2.44 + 4.17
= $10.99
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Look at these equations.
9 = 7+ a
a + 8 = b + 5
Use both equations to work out the value of B
Answer:
B=5
Step-by-step explanation:
If 7 plus a equals 9 then a would equal 2.
2+8=b+5
10=b+5
Ask yourself what number plus 5 equals 10
B is 5 because 5 plus 5 is 10
An aluminum bar 3 feet long weighs 12 pounds. What is the weight of a similar bar that is 3 feet 4 inches long?
Answer: 13 [tex]\frac{1}{3}[/tex] pounds
Step-by-step explanation:
We will set up a proportion. I will have the weight, in pounds, on the top (numerator) and the length, in inches, on the bottom (denominator).
[tex]\frac{12}{36} =\frac{x}{40}[/tex]
Cross-multiply:
36 * x = 12 * 40
36x = 480
Divide both sides of the equation by 36:
x = 13 [tex]\frac{1}{3}[/tex] pounds
Answer:
Step-by-step explanation:
First find unit weight.
1 foot = 12 inches
3 ft = 3*12 = 36 inches
3ft 4 inches = 36 + 4 = 40inches
Weight of 36 inches long bar = 12 pounds
Weight of 1 inch bar = 12/36
[tex]\text{Weight of 40 inches long bar = $\dfrac{12}{36}*40$}[/tex]
= 13.3 pounds
Suppose the demand d, in units sold, for a company's jeans at price x, in dollars, is d(x)=800−4x.
A. If revenue=price×demand, write the rule for the function r(x), which represents the company's expected revenue in jean sales. Then state the domain of this function.
B. If the price is $30, how much revenue will the company earn?
A. The rule for the function r(x) is r(x)=
Answer:
Sorry let me try to understand the question
Step-by-step explanation:
The domain of the function r(x) is (0, 200).
The revenue earned when the price is $30 is $20400.
The rule for the function r(x) is x(800 - 4x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Demand:
d(x) = 800 - 4x
Price = x
Revenue = Price x demand
Revenue = r(x)
A)
The rule for r(x).
r(x) = x d(x) = x(800 - 4x)
The domain of r(x) is 0 < x < 200 i.e (0, 200).
B)
x = 30
r(x) = 30(800 - 4 x 30)
r(x) = 30(800 - 120) = 30 x 680 = 20400
C)
r(x) = x(800 - 4x)
Thus,
The answers are given above.
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A bus makes 28 stop every 2 hours. How many stops does it make in 5 hours?
Answer:
70 stops
Step-by-step explanation:
To find the amount of stops it makes in an hour, do 28 stops ÷ 2 hours, which will give you 14 stops in one hour.
Then do 14 stops × 5 hours, which would give you 70 stops.
Here's the notation if you want to make it look pretty:
[tex]5(\frac{28}{2} )=70[/tex]
I need help please this is very tricky to me
Answer:
273cm
Step-by-step explanation:
21 times 13 is 217. That is how you find out the area of parallelogram, (base times peperndicular heigh)
help pls first correct answer gets brainleist
n²= 7²+3²
=49+9
=58
n= V58
=7.62m
A 60 cm high cylinder with 14 cm its diameter is cut vertically into two equal halves. what is the volume of a half part
The volume of the half part of a cylinder of 60 cm high and 14 cm in diameter is 1470π cm³.
Volume of a cylindervolume of a cylinder = πr²h
where
r = radiush = heightTherefore,
r = 14 / 2 = 7 cm
h = 60 cm
volume of the cylinder = π × 7² × 60
volume of the cylinder = π × 49 × 60
volume of the cylinder = 2940π cm³
The volume of the half part = 2940π / 2 = 1470π cm³
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cuanto es 4{(-50+-5)÷3]+6}x[-4+-3÷1)÷3]
Answer:
-148/3 or -49.3
Step-by-step explanation:
Use the ordered pairs below. (10,20), (11, 21), (12, 22) What patterns are used to create the ordered pairs?
Answer:
Add 1 unit to the X coordinates and Y coordinates for each new pair.
step-by-step explanation:
X: 10 + 1 = 11 + 1 = 12
Y: 20 + 1 = 21 + 1 = 22