Answer:
[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]
Step-by-step explanation:
Since the required hyperbola has its vertex at (5,0), its transverse axis is on the x-axis and center at (0,0).
So, we use the equation in standard form
[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex]
Also, since the path of the space probe gets closer to y = -x, this is the asymptote to the hyperbola.
Our standard asymptote equation is y = ±bx/a taking the negative sign and comparing with y = -x,
-bx/a = -x ⇒ b/a = 1 ⇒ a = b
Also, the coordinate of the vertex (c, 0) = (5, 0) and c² = a² + b²
substituting c = 5 and a = b into the equation, we have
c² = a² + b²
5² = a² + a²
25 = 2a²
a² = 25/2
a = √(25/2)
a = ±5/√2
rationalizing, we have
a = ±5/√2 × √2/√2
a = ±5√2/2
Since a = b, b = ±5√2/2
Inserting a and b into the equation for the hyperbola, we have
[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1\\\frac{x^{2} }{(\frac{5\sqrt{2} }{2} )^{2} } + \frac{y^{2} }{\frac{5\sqrt{2} }{2} ^{2} } = 1\\\frac{x^{2} }{\frac{25 X 2 }{4} } + \frac{y^{2} }{\frac{25X2 }{4} } = 1\\\frac{x^{2} }{\frac{25}{2} } + \frac{y^{2} }{\frac{25}{2} } = 1\\\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]
So, the required equation is
[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]
Complete the square to go to the conic form of the circle. x^{2}+y^{2}+8x-2y+1=0
Answer:
Step-by-step explanation:
[tex]x^2+8x+y^2-2y=-1\\\\x^2+8x+16+y^2-2y+1=-1+16+1\\(x+4)^2+(y-1)^2=16\\\\(x+4)^2+(y-1)^2 = 4^2[/tex]
manuela wants to make a cube from construction paper . if she cuts out the design below and folds it to make a cube , what will be the surface area of the cube?
25 cm2
70 cm2
125 cm2
150 cm2
Answer:
150 cm2
Step-by-step explanation:
one square would simply be base x height our base is 5 and height is 5 so i multiply that and get 25 since this is a cube all sides are equal so I will simply just multiply 25 by the number of sides since a cube has 6 sides our equation to get the answer would be 25 x 6 = 150 so 150 is our answer! Hope this is a good explanation! Have a good day!
PLEASE ANSWER ASAP
no links please
what is xy?
answers: a: ^ 2 b: 5 c: 5^2 d: 10
Answer:
C: 5√2
Step-by-step explanation:
Answer is C, 5[tex]\sqrt{2}[/tex] hope this helps !!!
Explanation: A 45°-45°-90° triangle is a special right triangle that has two 45-degree angles and one 90-degree angle. The side lengths of this triangle are in the ratio of; Side 1: Side 2: Hypotenuse = n: n: n√2 = 1:1: √2. The 45°-45°-90° right triangle is half of a square.
an equation is shown. x + 3 = 8.5 what is the solution to the equation
Answer:
mbcnnb.hhhhjsjsjsnwjwnnwnwnenenebebeneme dcecvejsksmemebeccehsnsnsne evvenekeiekekenbegegevebbehehenebebbebebendhfhhcjcmc d d ecevegjskdkdklxbxbcbfdvvdvdhejrklnssfbmjffbb c
Step-by-step explanation:
nbsnsmsmlslakwj
Write the inequality that represents the number line
Answer:
C)
Step-by-step explanation:
its for 7th grade plss help me
Answer:
x ≤ 40
Step-by-step explanation:
x >= -5x8
x =< 40
This is a pic of my question..
Answer:
The answer is c
Step-by-step explanation:
5x+3y=19
multiply x 2: 10x+6y=38
2x-4y=-8
multiply by -5: -10x+20y=40
now you can add the two equations:
10x+6y=38
-10x+20y=40
add equations 0x+26y=78
Y=3
HELP
Please help me
Answer:
A) [tex]f^{-1} (x)=\frac{5x+3}{2}[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{2x-3}{5}[/tex]
[tex]y=\frac{2x-3}{5}[/tex]
[tex]x=\frac{2y-3}{5}[/tex]
[tex]\frac{5x+3}{2} =y[/tex]
[tex]y=\frac{5x+3}{2}[/tex]
So option (A)
---------------------------
hope it helps...
have a great day!!
[tex]f(x)=1/3(4-x)² what is the value of f(16)[/tex]
Answer:
wheneveryouseeanxonthe
rightputa16thatwhatf(16)
means.
f(16)=
3
1
(4−16)
2
f(16)=
3
1
(−12)
2
f(16)=
3
1
(144)
f(16)=48
[isyouranswer]
Step-by-step explanation:
mark me as brainliest.oky?
I need help please!!
Answer:
1
Step-by-step explanation:
sike i lied this is so easy pls try pls
Please help!! Select the values for the domain & range of the function given below.
Answer:
the first one n second one
Which value of x makes the equation 0.75(x + 20) = 2 + 0.5(x - 2) true?
Answer:
x = -56
Step-by-step explanation:
0.75(x + 20) = 2 + 0.5(x - 2)
0.75x + 15 = 2 + 0.5x - 1
0.25x = -14
x = -14/0.25
x = -56
Find the volume of the triangular prism below 5mm 12mm 3mm
Answer: 90 mm cubed
Step-by-step explanation:
Formula = (L*W*H) / 2
5 * 12 * 3 = 60 * 3 = 180
180 / 2 = 90
HELP... I will give brainliest to the best answer! :))
(a) Write 2500 in expanded notation.
(b) Write the prime factorization of 2500 using exponents
(c) Find 2500.
Answer:
a) (2 x 1000) + (5 x 100)
b) 5^4 × 2²
c) ??
Step-by-step explanation:
b) 2500 = 25 x 100
25 = 5 x 5
100 = 25 x 4 = 5 x 5 x 2 x 2
15 points, needs to be done ASAP! Any joking around will lead to a report.
Answer: The mean is 6.
Step-by-step explanation: First you add all of the numbers together getting a total of 48. Next to find the mean you divide them by the total number of "dots". Lastly, you get the answer of 6 which is your mean.
Answer:
6.
Step-by-step explanation:
First you take the data on the dot plot, and write the numbers down from least to greatest.
The data set:
2,3,6,6,7,8,8,8
Now that you have the data reordered in a easier way to read, add up all the numbers that you got from the dot plot.
2+3+6+6+7+8+8+8=48
Next we count all the number in the data set we made.
2,3,6,6,6,7,8,8,8 = 8
The amount of numbers in this data is 8.
Lastly we then divide 48 by 8.
48/8= 6
So your answer is 6!
A CD player that regularly sells for $79.00 is on sale at a 15% discount.
Find the sale price of the CD player. Show your work.
Answer:65.15
Step-by-step explanation:
Answer:
$67.15
Step-by-step explanation:
100% - 15% = 85%
original price = 79
85% of 79 = sale price
85/100 * 79 = sale price
67.15
Thank for help find a volume
Answer:
117π=367.38
Step-by-step explanation:
r=d/2=3
V=πr2h=π·3²·13=117π=367.38
You make $0.75 for every newspaper you sell. Write and solve an equation to find how many newspapers n you have to sell to buy the soccer cleats. Soccer Cleats cost: $36.00
Answer:
You would need 48
Step-by-step explanation:
divide 36.00/0.75
Please help worth 30 points it’s geometry.
I have a grade check tmr and I have an F in geometry please help!!!
Answer:
everything is in the photo
Kirk Middle School students are trying to make the
largest Italian sub on record. They make an Italian sub
that is 6 feet long. They decide to divide the sub into
smaller portions to share with other students. If each
portion is foot long, how many students would get a
portion of the sub? Justify your work.
Due to delays a company had to extend a project from 28 days to 76 days. What was the percentage increase in time to complete the project. Round your answer to the nearest tenth.
Answer: [tex]171.4\%[/tex]
Step-by-step explanation:
Given
Time is extended from 28 days to 76 days
The percentage increase is given by
[tex]\Rightarrow \dfrac{\text{New-original value}}{\text{original value}}\times 100[/tex]
Putting values
[tex]\Rightarrow \dfrac{76-28}{28}\times 100=\dfrac{48}{28}\times 100\\\\\Rightarrow 171.4\%[/tex]
Thus, the percentage increase in time is [tex]171.4\%[/tex]
The cost of electricity is obtained as follows: A fixed charge of $(a), rent of a meter $(b) and a charge of (c) cents for unit of electricity supplied Determine the total cost of using n units of electricity.
Answer:
$(a + b) + cn cent
Step-by-step explanation:
Given :
Fixed charge = $a
Rent of a meter = $b
Charge per unit of electricity = c cents
The total cost of using n units of electricity :
For n units of electricity ;
Fixed charge is paid once
Meter rent is paid once
The cost of electricity = (number of units * cost per unit) = (n * c) = nc cents
Total cost of n units of electricity :
$(a + b) + cn cent
arrange the following elements according to the increasing atomic size
Ai, P, Si, Mg
Please help me I don’t under stand helpppp ASAP
Answer:
25
Step-by-step explanation:
Answer:
27.7
Step-by-step explanation:
Please help me ASAP!!!
Answer:
the third one (2,-18)
Step-by-step explanation:
If n/12 = 15/36 , then n= ___.
pls help me!
Answer: n=5
have an amazing day <3
Calculate the volume of the shaded space. Round to the nearest tenth, if necessary.
Answer:
Volume of the shaded space = 4480.0 yd³
Step-by-step explanation:
Volume of the shaded space = Volume of cuboid - Volume of Pyramid placed inside
Volume of cuboid = Length × Width × Height
= 28 × 12 × 20
= 6720 yd³
Volume of pyramid = [tex]\frac{1}{3}(\text{Area of the base})(\text{Height})[/tex]
= [tex]\frac{1}{3}(28\times 12)(20)[/tex]
= 2240 yd³
Volume of the shaded space = 6720 - 2240
= 4480.0 yd³
Beth is making fruit saladShe adds 5 grapes for every 2 strawberries she uses 12 strawberries, how many grapes will use? please get back to me !
Answer:
she uses 12×5=60 grapes
Answer:
30
Step-by-step explanation:
5 grapes : 2 strawberries
5 : 2
x : 12
x = (5 × 12) ÷ 2
x = 30
Substitute the values of a = 7 and b = 11. What expression do you get when you substitute these two values? 67 + 311 6 ( 7 ) + 3 ( 11 ) 6 ( 7 ) - 3 ( 11 ) 7 ( 7a) + 3 ( 11b)
Answer:
[tex]6(7) + 7(11)[/tex]
Step-by-step explanation:
Given
The expression is:
[tex]6a + 7b[/tex]
[tex]a = 7[/tex]
[tex]b = 11[/tex]
Required
The corresponding expression when the values are substituted for the variables
We have: [tex]6a + 7b[/tex]
Substitute [tex]a = 7[/tex]
So, the expression becomes:
[tex]6(7) + 7b[/tex]
Substitute [tex]b = 11[/tex]
So, the expression becomes:
[tex]6(7) + 7(11)[/tex]
Rectangle ABCD with vertices A(-8,6), B(-2,8), C(-1,5), and D(-7,3) is reflected over the y-axis. What are the new points?
