Answer:
(x-2)^2/4 - (y+1)^2/16 = 1
Step-by-step explanation:
The first thing you want to do is find the center of the hyperbola. Since you have the two equations of the asymptotes, their intersection must be what you want. setting 2x - 5 equal to -2x + 3, you get that x = 2, meaning that 2 is the x-coord of your center. Plugging this value of x into the equations, you get that y = -1. Now that you have your center, you have the information that one of the vertices is on the y-axis. Since the distance from the center to the vertice must be a straight line, you know for sure that this hyperbola is a horizontal one (a vertical one would not have a vertice on the y-axis given this center). Knowing this, you have the equation form (x-2)^2/a^2 - (y+1)^2/b^2 = 1. I got a little confused here, but remember that you now know the center and the equations of the asymptotes. y = 2x - 5 is equal to 2(x - 2) - 1. The form of the asymptotes of a horizontal hyperbola is b/a(x-h) + k, which means that b/a must be equal to 2. This also means that 2a = b, and 4a^2 = b^2. Now you can substitute b^2 for 4a^2, leaving you with the equation (x-2)^2/a^2 - (y+1)^2/ 4a^2 = 1. Remember that vertice on the y-axis? Since it must be at the same y-coordinate (since you know that it must be a horizontal line from the center to the vertice), you know the vertice has to be (0, -1). You can plug these values into the previous equation, which gives you (0 - 2)^2 / a^2 - 0 = 1. This leaves you with 4/a^2 = 1, which means that a must be 2. Since you already know that b is 2a, b must be equal to 4. Plugging those values into the equation, you get your final answer, (x-2)^2/4 - (y+1)^2/16 = 1.
3.
Calculate 7.561 – 2.37
Answer:
7.561 – 2.37=5.191 if you wanted me to show work, comment and ill change it.
Step-by-step explanation:
what is equivalent to 2(-6c+3)+4c
Answer:
-8c + 6
Step-by-step explanation:
2 (-6c + 3) + 4c
Distribute the 2 with the expression in the parenthesis:
-12c + 6 + 4c
*Parenthesis are no longer needed
Combine Like terms:
-8c + 6
*Ask yourself is it in its simplest form? If no, continue your work. If yes, you have your answer.
3x+7+56=90 what is this
Answer:
X=9
Hope this helps! :)
All of the points in the picture are on the same line.
1. Find the slope of the line. Explain or show your reasoning.
because
2. Write an equation for the line.
3. What is the value ofe
CE
4. Is the point (0.-2) on this line? Explain how you know.
because
Bella only u answer
Answer:
The slope equals the rise divided by the run
Step-by-step explanation:
Find the coordinates of the midpoint of segment Hl with endpoints: H(-5, 5) and 1(7,3).
Answer:
Midpoint is (1,4)
What is the volume of the sphere?
Use \mathrm{\pi } = 3 . 14π=3.14 and round your answer to the nearest hundredth.
Answer:
cubic inches
The volume of the sphere that has a radius of 3 inches is: 113.1 in.³
What is the Volume of a Sphere?Volume of a sphere is found using the formula, V = 4/3 πr³, where r is the radius of the sphere.
Given the following:
π = 3.14r = 3 inchesPlug in the values into V = 4/3 πr³:
Volume of the sphere = 4/3 (3.14)(3)³
Volume of the sphere = 113.1 in.³
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Find the Derivative y’ implicitly.
[tex]e^{x^2y} - e^y = e^y(e^{x^2} - 1) = x[/tex]
We should ISOLATE x
[tex]e^y= \frac{x}{e^{x^2} - 1}[/tex]
Find the Natural Log of Both Sides to Make the Left Side "y"
[tex]y = ln(\frac{x}{e^{x^2}-1})[/tex]
Now, FIND THE DERIVATIVE Using Chain Rule!!!
[tex]y' = \frac{1}{\frac{x}{e^{x^2}-1}} * \frac{(1(e^{x^2}-1) - x(2x*e^{x^2})}{(e^{x^2}-1)^2}= {\frac{e^{x^2}-1}{x}}* \frac{(1(e^{x^2}-1) - x(2x*e^{x^2})}{(e^{x^2}-1)^2} = {\frac{1}{x}}* \frac{(1(e^{x^2}-1) - x(2x*e^{x^2})}{(e^{x^2}-1)} = {\frac{1}{x}}* \frac{(e^{x^2}-1 - 2x^2e^{x^2})}{(e^{x^2}-1)}[/tex]
on saturday mark have 20 apples and his mom took 2
They are ordering 120 pounds of seafood for the week. How many should be fish?
Answer:
43.2 pounds of fish :)
Step-by-step explanation:
120 x 0.36 = 43.2
Have a great day!!
Please rate and mark brainliest!!!
Help?? I'm so confused
Answer:
0.10
Step-by-step explanation:
If one meter is 100 centimeters and you're trying to find how much of a meter is in 10 centimeters all you need to do is divide the meter by 10, just like they did to get the amount of centimeters.
A man deposits $45 000 in a savings account.
Compound interest is paid at 3.5% calculated
at the end of each year.
How much will be in the bank account at
the end of 2 years?
Answer:
3150
Step-by-step explanation:
principal =45000
compound interest =3.5%
Time =2years
then,
3.5/100*45000=1575
2years
1575*2=3150
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP
Answer:
(-3, 3)
explanation:
original coordinate of C: (3, 5)if reflected over y axis, use the formula: (x,y) → (-x, y)
new coordinate: (-3, 5)If translated vertically, there will be change in y axis
then vertically -2 units:(-3, 5-2) → (-3, 3)
Answer:
-3,3
Step-by-step explanation:
I really dont know how to explain
PLEASEEE HELP!!! Let f and g be differentiable functions such that f' (1) = 2 and g’ (1) = 6. If h (x) = 5 f(x) - 4g (x) + 3x^2 - 2, what is the value of h’ (1) ?
The value of h'(1) is -8
Given the following expression;
[tex]h (x) = 5 f(x) - 4g (x) + 3x^2 - 2[/tex]
Differentiating the function above:
[tex]h' (x) = 5 f'(x) - 4g' (x) + 6x[/tex]
Given the following parameters
[tex]f' (1) = 2\\g' (1) = 6[/tex]
Get h'(1)
[tex]h' (1) = 5 f'(1) - 4g' (1) + 6(1)\\h' (1)=5 (2) - 4(6) + 6(1)\\h' (1)= 10-24+6\\h' (1)=-8[/tex]
Hence the value of h'(1) is -8
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To avoid a service fee, your checking account balance must be at least $500 at the end of each month. Your current balance is $525.17. You use your debit card to spend $117.08. What possible amounts can you deposit into your account by the end of the month to avoid paying the service fee?
Answer: At least $91.91
Step-by-step explanation:
From the question, we are informed that to avoid a service fee, the checking account balance must be at least $500 at the end of each month.
Since the current balance is $525.17 and $117.08 has been spent, the balance will now be:
= $525.17 - $117.08
= $408.09
Since the checking account balance must be at least $500 at the end of each month and we currently have $408.09, this means that there will still be a need to add $91.91.
= $500 - $408.09
= $91.91
At least $91.91 must be added to avoid the fee.
deals with three-dimensional objects, such as cubes and spheres.
Step-by-step explanation:
Length, width and height are three dimensional objects.
I hope this will help you.
Ashley has ridden 32 miles of a bike course. The course is 80 miles long. What percentage of the course has Ashley ridden so far?
Answer:
40%
Step-by-step explanation:
divide 80 by 100 80/100= 0.8 then divide 32 by 0.8 to get 40%
PLS HELP !!
What is cos 30°?
Answer:
E
Step-by-step explanation:
[tex]cos30 = \frac{ \sqrt{3} }{2} [/tex]
At a birthday party for 20 people each person could order a hot dog or chips. If there were four times as many hot dogs as chips ordered, calculate how many hot dogs and how many chips were bought.
Call the amount of chips ordered : x
-> The amount of hot dogs ordered : 4x
Since there are a total of 20 chips and hot dogs orders, x + 4x = 20 -> 5x = 20
-> x = 20/5 = 4
-> 4x = 4 x 4 = 16
So, there are 16 hot dogs and 4 chips ordered.
Answer:
16 hot dogs
4 chips
Step-by-step explanation:
Let h = number of hot dogs ordered
Let c = number of chips ordered
Given:
Total number of orders = 20Four times as many hot dogs as chips ordered⇒ h + c = 20
⇒ h = 4c
Substitute h = 4c into h + c = 20 and solve for c:
⇒ 4c + c = 20
⇒ 5c = 20
⇒ c = 4
Substitute found value for c into h = 4c and solve for h:
⇒ h = 4 × 4
⇒ h = 16
Therefore, 16 hot dogs and 4 chips were ordered.
This table shows data collected by a runner.
A three column table with 7 rows. The first column, Time in minutes, has the entries, 1, 2, 3, 4, 5, 6. The second column, Distance in miles, has the entries, 0.19, 0.38, 0.57, 0.76, 0.95, 1.14. The third column, Elevation in meters, has the entries, 12, 28, 67, 98, 124, 145.
Answer:
the answer is B
Step-by-step explanation:
The elevation is a nonlinear function because it does not have a constant rate of change.
Answer:
B
Step-by-step explanation:
pls help asap if you can
what is the answer? I'll give brainiest to whoever is right
Answer:
5) 0 6 ) 1/4
Step-by-step explanation:
So the slope ( gradient ) of line E is 0 because it is straight and it as no slope
The slope of line F is 1/4 because:
Gradient = y^2 - y^1 / x^2 - x^1
Gradient = 2-0 / 6- -2
Gradient= 2 / 8
2/8 in lowest term is 1/4
YOU MIGHT AVE A DIFFERENT METHOD BUT ANSWERS MUST BE THE SAME.
HOPE IT HELPED
A parabola can be drawn given a focus of (-11, -2) and a directrix of x= -3
Write the equation of the parabola in any form.
Check the picture below, so the parabola looks more or less like that.
now, the vertex is half-way between the focus point and the directrix, so that puts it where you see it in the picture, and the horizontal parabola is opening to the left-hand-side, meaning that the distance "P" is negative.
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\begin{cases} h=-7\\ k=-2\\ p=-4 \end{cases}\implies 4(-4)[x-(-7)]~~ = ~~[y-(-2)]^2 \\\\\\ -16(x+7)=(y+2)^2\implies x+7=-\cfrac{(y+2)^2}{16}\implies x=-\cfrac{1}{16}(y+2)^2-7[/tex]
Mary is saving money to buy a game.So far she has saved $36,which is three-fourths of the total cost of the game.How much does the game cost?
Answer:
48 i think
Step-by-step explanation:
Answer:
$48
Step-by-step explanation:
please help thank youuu
Answer:
What color does the letter purple taste like?
Step-by-step explanation:
Enter the first 4 terms of the sequence defined by the given rule. Assume that the domain of each function is the set of whole numbers greater than 0.
f(1) = 390,625, f (n) = f (n − 1)
The first 4 terms of the sequence are ____, ____, ____, and ____.
Answer:
The first four terms is: 390625, 625, 25, 5
Step-by-step explanation:
Given
[tex]f(n) = \sqrt{f(n-1)}[/tex]
To determine the first 4 terms.
We have
[tex]f(1) = 390625[/tex]
[tex]f(2) = \sqrt{f(2 - 1)}[/tex]
[tex]f(2) = \sqrt{f(1)}[/tex]
Substitute 390625 for f(1)
[tex]f(2) = \sqrt{390625}[/tex]
[tex]f(2) = 625[/tex]
For f(3), we have
[tex]f(3) = \sqrt{f(3-1)}[/tex]
[tex]f(3) = \sqrt{f(2)[/tex]
[tex]f(3) = \sqrt{625[/tex]
[tex]f(3) = 25[/tex]
For f(4), we have
[tex]f(4) = \sqrt{f(4-1)[/tex]
[tex]f(4) = \sqrt{f(3)[/tex]
[tex]f(4) = \sqrt{25[/tex]
[tex]f(4) = 5[/tex]
Hence, the first four terms is:
390625, 625, 25, 5
show that
[tex]3 \frac{3}{4} \div 1 \frac{1}{3 } = 5 \frac{1}{12} [/tex]
write down all the steps in your working
Write the sum of O.31 (repeating 31 )and 0.125 (repeating 125)
Answer: 0.435 repeating
Step-by-step explanation:
if a:b=3:4 find the value of 15a+9b:16a+5b
Answer :
81 : 68⠀
Step-by-step explanation:
⠀
[tex] {\longrightarrow \: \sf \: Let \: \: a : b\: = 3: 4 = \dfrac{a}{b} \: = \: \dfrac{3}{4} = k}[/tex]
⠀
Therefore,
⠀
[tex] \dashrightarrow \qquad \sf \: a = 3k[/tex]
[tex] \dashrightarrow \qquad \sf \: b = 4k[/tex]
⠀
Now, Substituting the values :
⠀
[tex]\longrightarrow \qquad \sf \: 15a+9b:16a+5b[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{15(3k)+9(4k)}{16(3k)+5(4k)}[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{45k+36k}{48k+20k}[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{81k}{68k}[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{81 \cancel{k}}{68 \cancel{k}}[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{81}{68}[/tex]
⠀
[tex]\longrightarrow \qquad \bf \: {81} : {68}[/tex]
⠀
Therefore ,
⠀
[tex]{ \pmb{ \sf{\longrightarrow \qquad \: 15a+9b:16a+5b = 81 : 68}}}[/tex]
⠀
When the speed of the bottle is 2 m/s, the KE is kg m2/s2. When the speed of the bottle is 3 m/s, the KE is kg m2/s2. When the speed of the bottle is 4 m/s, the KE is kg m2/s2. When the speed of the bottle is 5 m/s, the KE is kg m2/s2. When the speed of the bottle is 6 m/s, the KE is kg m2/s2.
The answers to the Speed question are:
0.5 1.1252 3.125 4.5What is a speed?Speed is known to be the distance that is said to be traveled and it is per unit of time. It is seen as the rate of which an object is said to be moving.
Note that Speed is calculated in this case as 1/2mv².
Therefore, to calculate the variables are:
If the speed of the bottle is 2 m/s, then
= ½ (0.250) (2) ^2
= 0.5
If the speed of the bottle is 3 m/s, then
= ½ (0.250) (3) ^2
=1.125
If the speed of the bottle is 4 m/s, then
= ½ (0.250) (4) ^2.
= 2
If the the speed of the bottle is 5 m/s, then
= ½ (0.250) (5) ^2
= 3.125
= ½ (0.250)(6)^2
=4.5
Therefore, the answer given above are correct.
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#SP9
Answer:
0.5, 1, 2, 3, & 5
Step-by-step explanation:
did it on edgeinuity
What is the answer to this question I can’t work it out Ni=n02(yi-yo)/t2
Changing the subject of an equation involves solving for another variable in the equation
The equation of t is [tex]t=\frac{\sqrt{y_i-y_o}}{N}[/tex]
How to change the subject of the equationThe equation is given as:
[tex]N=\sqrt[2]{\frac{y_i-y_o}{t^2}}[/tex]
Rewrite the equation as:
[tex]N=\sqrt{\frac{y_i-y_o}{t^2}}[/tex]
Evaluate the square root of t^2
[tex]N=\frac{\sqrt{y_i-y_o}}{t}[/tex]
Multiply both sides by t
[tex]Nt=\sqrt{y_i-y_o}[/tex]
Make t the subject, in the above equation
[tex]t=\frac{\sqrt{y_i-y_o}}{N}[/tex]
Hence, the equation of t is [tex]t=\frac{\sqrt{y_i-y_o}}{N}[/tex]
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