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Mathematics

1 answer:

xxMikexx [17]3 years ago

7 0

Answer:

this is the answer ................

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The sum of two numbers is 25 and their differences is 7

Flauer [41]

$16 + 9 = 25 \\ 16 - 9 = 7$

4 0

3 years ago

Write the equation of a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2(sqrt5)

Xelga [282]

Answer:

$\frac{x^2}{16}-\frac{b^2}{4}=1$

Step-by-step explanation:

A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.

The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4$

The foci c is at +/-2√5, using c² = a² + b²:

$c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2$

Substituting the value of a and b to get the equation of the hyperbola:

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1$

5 0

3 years ago

*50 POINTS* PLEASE I NEED HELP

Butoxors [25]

Well to make a scatter plot you have to make a table first and record all your data. then plot the points and draw a line between exactly the same amount of points. there should be 5 on top and 5 on the bottom of the line. for the last question say what I said

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3 years ago

Read 2 more answers

What is the eqaution of a vertical line passing through (-5,-2)?

Virty [35]

Answer:

x=-5

Step-by-step explanation:

Vertical lines have the same x value all the time. They are of the form x=

Since it passes through the point (-5,-2) the x value must be -5

x=-5

8 0