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3 years ago

Graph x2 + 9y2 = 25. What are the domain and range? Someone please help me ! (Picture below)

Mathematics

1 answer:

pishuonlain [190]3 years ago

5 0

X^2 + 9y^2 = 25
x^2/5^2 + (3y)^2/5^2 = 1

This represent an equation of an ellipse with cente at the origin, the horizontal major axis running from -5 to 5 and vertical minor axis running from -5/3 to 5/3

The third graph is the correct answer.

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.

Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

$y = 11 + x$

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

$y^2 = x^2 + x^2$

$y^2 = 2x^2$

This gives:

$(11+x)^2 = 2x^2$

Open bracket

$121 + 22x + x^2= 2x^2$

Collect like terms

$2x^2 - x^2 -22x - 121 = 0$

$x^2 -22x - 121 = 0$

Using quadratic formula:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}$

$x = \frac{-(-22)\±\sqrt{968}}{2*1}$

$x = \frac{22\±31.11}{2}$

Split

$x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\$

$x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}$

x can not be negative.

So:

$x = \frac{53.11}{2}$

$x = 26.56$

Recall that:

$y = 11 + x$

$y = 11 + 26.56$

$y = 37.56$

Hence, the dimensions are:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

6 0

2 years ago

Identify the range of the function.

Kryger [21]

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3 years ago

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vitfil [10]

Answer:

b -7/8 > -0.50

Step-by-step explanation:

is your answer

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2 years ago

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Daniel [21]

Answer:

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6 0

2 years ago

Please answer this correctly without making mistakes I want ace expert and genius people to answer this correctly without making

sergejj [24]

Answer: 38

Step-by-step explanation: to evaluate an expression for these variables, plug in those numbers for the variables.

Plugging in -1 for y and -19 for z gets you this:

-2(-1)^2(-19)

Now simplify according to order of operations (PEMDAS - parenthesis exponents multiplication/division addition/subtraction)

-1^2 = 1

-2(1) = -2

-2(-19) = 38

Your answer is 38

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