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Brums [2.3K]
1 year ago
6

NO LINKS!! Please help me with this problem​

Mathematics
2 answers:
Vinil7 [7]1 year ago
7 0

Answer:

\dfrac{y^2}{36}-\dfrac{x^2}{16}=1

Step-by-step explanation:

<u>Standard form equation of a vertical hyperbola</u>

\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1

where:

  • center = (h, k)
  • vertices = (h, k±a)
  • co-vertices = (h±b, k)
  • foci = (h, k±c) where c² = a² + b²
  • \textsf{asymptotes}: \quad y =k \pm \left(\dfrac{a}{b}\right)(x-h)
  • Transverse axis: x = h
  • Conjugate axis: y = k

From inspection of the graph:

  • center = (0, 0)  ⇒ h = 0, k = 0
  • vertices = (0, 6) and (0, -6)  ⇒  a = 6
  • co-vertices = (4, 0) and (-4, 0)  ⇒  b = 4

Substitute the found values into the formula:

\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1

\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1

iogann1982 [59]1 year ago
5 0

{\qquad\qquad\huge\underline{{\sf Answer}}}

The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :

Length of transverse axis is :

\qquad \sf  \dashrightarrow \: 2b = 12

\qquad \sf  \dashrightarrow \: b = 6

length of conjugate axis is :

\qquad \sf  \dashrightarrow \: 2a = 8

\qquad \sf  \dashrightarrow \: a = 4

Equation of hyperbola ~

\qquad \sf  \dashrightarrow \:    \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{  {x}^{2} }{ {a}^{2} }  = 1

plug in the values ~

\qquad \sf  \dashrightarrow \:    \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{  {x}^{2} }{ {4}^{2} }  = 1

\qquad \sf  \dashrightarrow \:    \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{  {x}^{2} }{ {16}^{} }  = 1

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Elizabeth bought lemons (l) and apples (a). Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons an
Zina [86]

Step-by-step explanation:

<u>Given:</u>

  • Lemons - l and apples - a
  • a = 35¢, l = 15¢
  • Number of apples and lemons = 17
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<u>System as per question:</u>

  • a + l = 17
  • 35a + 15l = 395

Or

  • a + l = 17
  • 0.35a + 0.15l = 3.95
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DIA [1.3K]

Answer:

She can make cookies for 4.95 weeks

Step-by-step explanation:

2 x 1 2/3 = 3.333333333

16.5/ 3.333333333 = 4.95

Since Jordan is making two batches of Cookies per week, you need to multiply 2 by the amount of resources needed to bake one batch of cookies. So you multiply 1 and 2/3 by 2 to get the amount of resources neccesary for one week of making cookies. Then, you take the full amount of resources that she has, and divide that by the amount she uses per week, that number will give you the number needed to figure out how many weeks she has to bake cookies.

To figure out the number that is being divided to get the whole number in weeks, you would take the 16.5 cups of flour. The reason why this is, is because that Is the starting number of cups that she has. So here you would need to divide the amount you are taking from it each week. This will result in the amount of weeks that she is able to bake cookies with her flour.

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2 years ago
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Serjik [45]

Answer:

The graph of the system of equations solves the equation  -\frac{1}{4} x + 2 = 2x - 7 ⇒ C

Step-by-step explanation:

<em>Let us revise some important notes about the slope and y-intercept of a line</em>

The form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

  • If the line has a positive slope then its direction will be to the right
  • If the line has a negative slope then its direction will be to the left

The y-intercept (0, b) is the the point of intersection between the line and the y-axis

  • If the line cuts the y-axis at a point above the x-axis, then b is positive
  • If the line cuts the y-axis at a point down the x-axis, then b is negative

<em>To solve our question without any calculation, let us find the direction of the slopes and their y-intercepts</em>

∵ The direction of the blue line is to the left

→ That means m in the equation is negative

∴ Its slope is negative

∵ The line intersects the y-axis at point (0, 2)

→ That means b in the equation = 2

∴ The number in the equation is 2

→ Look at the answer we have two answers have negative slope and

   y-intercept 2 in the left hand side ⇒ C and D

∴ The equation of the blue line is represented by the left side -\frac{1}{4} x + 2

→ that means the equation of the red line is represented by the right side

∵ The direction of the red line is to the right

→ That means m in the equation is positive

∴ Its slope is positive

→ Only C has a positive slope in the right side

∴ The equation of the red line is represented by 2x - 7

The graph of the system of equations solves the equation  -\frac{1}{4} x + 2 = 2x - 7

<u><em>Another way:</em></u>

<em>You can solve each equation to find the value of x, then substitute it in one side of the equation to find y , the values of x and y must be (4, 1) as the point of intersection of the two lines in the graph</em>

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Explanation:

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F=32+\frac{9}{5} C

Where, F is temperature in degree fahrenheit and C is temperature in degree celsius.

Since it is given that the temperature is -62 degree celsius. So put c=-62 in the above formula.

F=32+\frac{9}{5} (-62)

F=32+\frac{(-558)}{5}\\F=32-111.6\\F=79.6

Hence the value of temperature is -79.6 degree fahrenheit.

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There is a </span><span>1,563 feet difference between the height of the bird and the depth of the fish</span>
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3 years ago
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