Answer:
Step-by-step explanation:
focus distance=9
a=2 f²=a²+b² ==> b²=9²-2²=77 ==> b=√77
[tex]\dfrac{(x-0)^2}{2^2}- \dfrac{(y-0)^2}{77}=1\\\\\\\boxed{\dfrac{x^2}{4}- \dfrac{y^2}{77}=1}\\[/tex]
Equation of hyperbola is [tex]\frac{x^{2} }{4} -\frac{y^{2} }{77} =1[/tex].
What is hyperbola?Hyperbola is defined as an open curve having two branches which are mirror images to each other.
A plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant : a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.
Given
Foci: (-9, 0) and (9, 0)
Foci: (±9, 0)
Vertices: (-2,0) and (2,0)
Vertices: (±2, 0)
So, a = ±2, c = ±9
Now [tex]c^{2} =a^{2} +b^{2}[/tex]
[tex]b^{2} =c^{2} -a^{2}[/tex]
[tex]b^{2} =9^{2} -2^{2}[/tex]
[tex]b^{2} =81-4[/tex]
[tex]b^{2} =77[/tex]
Equation of hyperbola is
[tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} } =1[/tex]
⇒ [tex]\frac{x^{2} }{4} -\frac{y^{2} }{77} =1[/tex]
Hence, equation of hyperbola is [tex]\frac{x^{2} }{4} -\frac{y^{2} }{77} =1[/tex].
Find out more information about hyperbola here
https://brainly.com/question/27799190
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A sphere has radius r unit. Find the following. (a) Circumference of great circle
Answer:
2πr
Step-by-step explanation:
the Circumference of great circle =
2×π×r or 2πr
300 divided by 6 times to the 2nd power divided by 3.14, i need help.
Answer:
Step-by-step explanation:
300÷6x²÷3.14=2.6539278131634819533
please explain if you can
Answer:
Hello again! The answer to this one is C
Step-by-step explanation:
As I said before, a fraction is out of 100, like a percent. Divide 100 by the denominator (in this case, 4). This gives you 75%. However, to convert this into a decimal, we need to multiply it by 0.01. This gives you 0.75.
Answer:
.75
Step-by-step explanation:
there are more that one way to represent numbers..
Roman numerals are quite obsolete, but fractions, decimals and percent's
are the ones that you mainly learn about in a math class...
numbers of one type can be converted to any other...
in this case you want to convert a FRACTION 3/4 to change to a DECIMAL version.... NOTE: at the end I will also show the PERCENT VERSION...
the fraction to decimal conversion is done by "LONG DIVISION"
__.75__
4 | 3.0
2.8
-----
20
20
---
0
Note as a percent it is 75%
What is cos 30°?
604
2.
90'
309
13
O A. /
O B. 1 / 2
O c.
O D. V
O E F
O F. 1
SUB
Answer:
the value of cos 30degree is √3\2 ....
f(x) = x2. What is g(x)?
Answer:
B
Step-by-step explanation:
Looking at the graph, we can see that g(x) is a compressed version of f(x) in the x direction but stretched in the y direction. We know that it is compressed because the values of g(x) are inside of f(x) in the x direction, and that it is streched because the values of g(x) are higher than the values of f(x) in the y direction.
Next, we want to figure out how much g(x) is a compression/stretch of x.
In the y direction, at x=1, y=1. At x=3, y=9. The ratio between the y values is 9/1 = 9, so in the y direction, the graph is streched by 9.
A stretch in the y direction can be represented by kf(x), with k representing how much the graph is stretched. In our example, k=9, so we have
kf(x) = 9f(x) = 9(x²) = 9x². This is equal to (3x)² = 9x², or B
In the x direction, at x=1, y=1. At x=3, y=9. The ratio between the x values is 3/1 = 3, so in the x direction, the graph is compressed by 3.
f(kx) represents a compression by a factor of k in the x direction, and k =3 here, so we have
f(kx) = f(3x) = (3x)² = 9x² = B
Which of the following sets contains multiples of six?
{1, 6}
{2, 3}
{4, 9}
{12, 18}
(4x-3)^2-(2x+5)^2=0 tìm x
Hi
Your question would be better with " Could you help me please ? " at the end. Quite sure your mum told you that some time in the past.
I will show you how to solve but you will do the calculus. Math is all about rules, methods and training. If you dont practice, you will never progress.
rule : you must know by heart your remarkable identities.
Here we have : ( 4x-3)² - (2x+5)² = 0
It 's of the form A² -B² = ( A+B) ( A-B)
here A is : 4x-3 and B is 2x+5
Now let's apply rule : ( 4x-3)² - (2x+5)² = ( (4x-3) +( 2x+5) ) ( (4x-3) - (2x+5)
= ( 4x-3 +2x+5 ) ( 4x-3 -2x-5 )
= ( 6x +2) ( 2x-8)
so : ( 4x-3)² - (2x+5)² = ( 6x +2) ( 2x-8)
so ( 4x-3)² - (2x+5)² = 0 means : ( 6x +2) ( 2x-8) = 0
Rule A*B = 0 if A = 0 or B = 0
A is 6x+2 and B = 2x-8
So I let you now work :
You have to solve : 6x+2 = 0
and 2x-8 = 0
Solutions of this two calculus will be the solutions of ( 4x-3)² - (2x+5)² = 0
Have fun !
solve for w 3w + 6w - 19 = -91
please
Hi ;-)
[tex]3w+6w-19=-91\\\\3w+6w=-91+19\\\\9w=-72 \ \ /:9\\\\\huge\boxed{x=-8}[/tex]
Answer:
w = -8Step-by-step explanation:
Given:
3w + 6w - 19 = -91Isolate w, add 19 to both sides:
3w + 6w = -91 + 19Simplify both sides:
9w = -72Divide both sides by 9:
w = -72/9w = -8Q. An Umbrella is made by stitching 10 triangular peices of cloth to two different colours, each piece measuring 20cm, 50cm & 50cm. Show much cloth of each colour is required for the umbrella?
Plz answer fast for thanks and brainliest.
Answer:
1000
[tex]1000 \sqrt{6} [/tex]
Step-by-step explanation:
Given: Dimensions of each triangular piece used in umbrella.
Reasoning: By using Heron’s formula, we can calculate the area of a triangle.
Heron's formula for the area of a triangle, Area = √s(s - a)(s - b)(s - c)
Where a, b, and c are the sides of the triangle, and
s = Semi-perimeter = Half the Perimeter of the triangle = (a + b + c)/2
We know that umbrella is made of 10 triangular pieces of cloth of two different colours.
Let us calculate the area of one triangle.
For each triangle, a = b = 50 cm, c = 20 cm
Semi Perimeter
s = (a + b + c)/2
= (50 + 50 + 20)/2
= 120/2
= 60 cm
By using Heron’s formula,
Area of triangle = √s(s - a)(s - b)(s - c)
= √s(s - a)(s - b)(s - c)
= √60(60 - 50)(60 - 50)(60 - 20)
= √60 × 10 × 10 × 40
= 200√6 cm2
Therefore,
Area of 10 triangular pieces = 10 × 200√6 cm2 = 2000√6 cm2
Hence, cloth required for each colour = (Total area of the cloth)/2
= (2000√6)/2
= 1000√6 cm2
Thus, 1000√6 cm2 cloth of each colour is required for the umbrella
The length of a sandbox is three feet longer than its width. Write the expression that would represent the perimeter of the sandbox.
Answer:
4w + 6
Step-by-step explanation:
Let width = w
Length = w + 3
Perimeter = 2*length + 2* width
= 2(w +3) + 2w {Use distributive property}
= 2w + 2*3 + 2w
= 2w + 6 + 2w {Combine like terms}
= 4w + 6
10 fewer than the difference of 8 and w? PLEASE HELP GETS BRAINLY 5 STARS AND A LIKEEEE!!!!!!!!!
Answer:
(8-w)-10
so -w-2
if w is a variable... sorry this answer is just for reference
Step-by-step explanation:
Can anyone help?
If f(x)=3^x, prove that f(x) + f(x+1)= 4f(x)
Answer:
[tex]f(x) = {3}^{x} \\ f(x +1) = {3}^{(x + 1)} \\ f(x) + f(x + 1) \\ = {3}^{x} + {3}^{(x + 1)} \\ = {(1 \times 3}^{x} ) +( 3 \times {3}^{x} ) \\ By \: taking \: {3}^{x} \: common, \: we \: get \\ (1 + 3) \times {3}^{x} \\ = 4 \times {3}^{x} \\ = 4f(x)[/tex]
f(x)+f(x+1)=4f(x), when f(x)=3^x Hence provedFind the slope of the line that passes through the points (0,-11) and (8,-8).
To find the slope of a line, we can use the following formula:
[tex] \displaystyle \large{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
m-term stands for slope or gradient. The formula is useful whenever you want to find a slope of two points.
Let these be the following:
[tex] \displaystyle \large{(x_1,y_1) = (0, - 11)} \\ \displaystyle \large{(x_2,y_2) = (8, - 8)}[/tex]
Substitute the points in formula:
[tex] \displaystyle \large{m = \frac{ - 8 -( - 11)}{ 8 - 0} }[/tex]
Negative multiply negative always come out as positive.
[tex] \displaystyle \large{m = \frac{ - 8 + 11}{ 8 - 0} } \\ \displaystyle \large{m = \frac{ 3}{ 8 } } \\ [/tex]
Since m stands for slope, we can say that:
[tex] \displaystyle \large \boxed{ \tt{slope = \frac{3}{8} }}[/tex]
Answer:
Step-by-step explanation:
(x₁ ,y₁) = (0,-11) & (x₂ , y₂) = (8,-8)
Slope = [tex]\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]=\dfrac{-8-[-11]}{8-0}\\\\=\dfrac{-8+11}{8}\\\\=\dfrac{3}{8}[/tex]
7b + 2 = 23
Help pls
Answer:
3
Step-by-step explanation:
7b + 2 = 23
Subtract 2 from both sides,
=> 7b = 21
=> b = 21/7
=> b = 3
(-786)+(-923)=(-923)+(-786)
verify
Answer:
[tex] - 786 + - 923 = - 923 + - 786 \\ - 786 - 923 = - 923 - 786 \\ - 1709 = - 1709 \\ thank \: you[/tex]
what is n (AUB) if (A)=25,n(B) = 10 and BCA
Answer:
35
Step-by-step explanation:
It is in the above photo .
What is 1,025 divided by 68
Answer:
15.07352941
Step-by-step explanation:
in short 15.07
2 questions
***************
Step-by-step explanation:
1) As U is the mid point of TV ,it divides the whole line in two equal parts:
TV=TU+UV
TU=UV
Subtitute values:
5x+6=23+23
5x+6=46
5x=46-6
5x=40
x=40/5
x=8
2) Q is mid point of PR so PQ=QR
PR=PQ+QR
15x-29=6x-1+6x-1
15x-29=12x-2
15x-12x=29-2
3x=27
x=27/3
x=9
Note:if you need to ask any question please let me know.
Please no links because they dont work :).
Answer:
semoga jawapan ini dapat membantu
-2(-6n-3)-8=82 solve for n
Answer:
n = 7
Step-by-step explanation:
-2(-6n-3)-8=82,
12n + 6 - 8 = 82,
12n -2 = 82,
12n = 84,
n = 7
Answer:
n=7
Step-by-step explanation:
-2(-6n-3)-8=82
Add 8 to both sides
-2(-6n-3)-8+8=82+8
Simplify
-2(-6n-3)=90
Divided both sides by -2
-2(-6 -3) = 90
2 -2
Simply
-6n-3=-45
Add 3 to both sides
-6n-3+3=-45+3
Divided both side by -6
-6n = -42
-6. -6
Simply
n=7
What is the answer to
5 - ( - 12 )
Answer: 17
Step-by-step explanation:
since there are two minuses, you change them to a plus and add, ending up with 5+12 to get 17
250 ÷ [5(3 • 7 + 4)]
Answer:
2
Step-by-step explanation:
6) find HJ
8)find IK
Answer:
HJ = 17
IK = 30
Step-by-step explanation:
to find HI :
GH : 2
HI : ?
IJ : 12
GI : 7
HI = GI - GH
HI = 7- 2
HI = 5
HI + IJ = HJ
5 + 12 = HJ
17 = HJ
To find IK
IJ = ?
JK = 12
KL = ?
IL = 49
JL = 31
To find IK we need to find KL and IJ
KL = JL - JK
KL = 31 - 12
KL = 19
IJ = IL - (JK + KL)
IJ = 49 - 31
IJ = 18
IK = IJ + JK
IK = 18 + 12
IK = 30
select the correct answer
Answer:
B
Step-by-step explanation:
This is a linear function that continues both ways infinitely.
Answer:
B
Step-by-step explanation:
The domain of the function is all real numbers.
A rectangular block has square base of area 64 cm². If the thickness of the block is 5 cm, find its total surface area.
Answer:
total surface area of cube is 6 * area of one side
therefore area of one side is given 64cm^2
thickness is also given 5cm .
TSA is 64*5 = 320cm^2
hope it is helpful
Answer:
288 cm²
Step-by-step explanation:
The square base has an area of 64 cm².
That means the sides of the square base measure 8 cm.
The perimeter of the base is P = 4 * 8 cm = 32 cm.
The lateral area is Ph = 32 cm * 5 cm = 160 cm².
The two bases are congruent, and their combined area is 2 * 64 cm² = 128 cm².
The total surface area equals the sum of the lateral area and the area of the bases.
SA = 160 cm² + 128 cm²
SA = 288 cm²
-3, 31, 11, 5.5, -60/-11
Order From least to greatest
Answer:
-60,-11,-3,5.5,11,31
Solve. x-6=-18
A x=-24
B x=-12
C x= 12
D x= 6
x - 6 = -18
x = -18 + 6
x = -12 ← the end
Answer: B)
[tex]\boxed{\underline{\bf \: ANSWER}}[/tex]
[tex] \sf \: x - 6 = - 18 [/tex]
Add 6 to both sides.
[tex] \sf \: x=-18+6 [/tex]
Add -18 and 6 to get -12.
[tex] \boxed{\underline{ \bf \: x=-12 }}[/tex]
=> The correct answer will be Option B - x = - 12
_______
Hope it helps.
╰☆☆RainbowSalt2222☆☆╮
PLS HELP!!!! I solved these but i dont know how to show my work...
Find the difference between temperatures of 17 degrees celcius above zero and 12 degrees celcius below zero
Answer:
29° C
Step-by-step explanation:
-17(-12)
=29
Hope this helps
Answer:
29C
Step-by-step explanation:
Above zero temperature = +17C
Below zero temperature = -12C
Difference= 17 - (-12C)
= 17 + 12 C
=29C
What is the sum of all the positive integers from √24 to √102
Answer:
[tex] \sqrt{24} = 4.9[/tex]
[tex] \sqrt{102} = 10.1[/tex]
positive integers = x
4.9 < x < 10.1
x = 5, 6, 7, 8, 9, 10
sum = 5 + 6 + 7 + 8 + 9 + 10
= 45