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3 years ago

4, 5, 6 is it a right triangle, acute, or obtuse

Mathematics

2 answers:

Sladkaya [172]3 years ago

8 0

Answer:

Since the lengths of the triangle are 4,5, and 6, which are almost equal, then the triangle cannot be obtuse. It's right triangle

maxonik [38]3 years ago

3 0

Answer:

it is an acute scalene triangle

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Which points on the curve of x^2 - xy - y^2 = 5 have vertical tangent lines?

algol [13]

We need to differentiate this with respect to x to see if we can find an expression for the derivative of y at various points. That will be the slope of the tangent to the curve. Then we want to see where that derivative might be infinite -- i.e., where the tangent is vertical.

It's not written as a function, but it can still be differentiated using the chain rule:

x2 + xy + y2 = 3

(2x) + (x dy/dx + y dx/dx) + (2y dy/dx) = 0

(I used parentheses to show the differentiation of each term in the original equation.)

2x + x dy/dx + y + 2y dy/dx = 0

2x + y = -x dy/dx - 2y dy/dx

2x + y = dy/dx (-x -2y)

-(2x + y)/(x + 2y) = dy/dx

We have the derivative of y, but it's defined partly in terms of y itself. That's OK. Let's go on...

So where would the slope be infinite? That would happen when x + 2y = 0, or y = -x/2

Let's plug that in for y in the original equation to find points where that's the case.

x2 + xy + y2 = 3

x2 + x(-x/2) + (-x/2)2 = 3

x2 - x2/2 + x2/4 = 3

3x2 / 4 = 3

x2 = 4

x = ±2

So we have two x values where the tangent might be vertical. Let's plug them into the equation and see what the y values are. First x = 2...

x2 + xy + y2 = 3

4 + 2y + y2 = 3

y2 + 2y + 1 = 0

(y + 1)2 = 0

y = -1

So at the point (2, -1) the tangent is vertical.

Now try x = -2...

x2 + xy + y2 = 3

4 - 2y + y2 = 3

y2 - 2y + 1 =0

(y - 1)2 = 0

y = 1

So at the point (-2, 1) the tangent is vertical.

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2 years ago

Question 7 of 19

Ierofanga [76]

C, 120 units2 is the answer

5 0

3 years ago

PLZ SOMEONE HELP DONT IGNORE ME!!!!

Dafna1 [17]

1. 2.6

2. 0.9

3. 4.5

if you count the lines on the ruler, you can find the answer

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3 years ago

Art 7

poizon [28]

Answer:

C) 0.4 x (2a - 0.3b) = 0.8a - 0.12b

Step-by-step explanation:

0.4 x (2a - 0.3b)

= 0.4(2a) - 0.4(3b)

= 0.8a - 0.12b

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3 years ago

A party rental company has chair and tables for rent. The total cost to rent 6 chairs and 2 tables is $20. The total cost to ren

liubo4ka [24]

Based on the problem statement you can write two equations for the cost of tables (t) and chairs (c).
.. 6c +2t = 20
.. 3c +5t = 35

You can solve these by your favorite method to find the costs are
.. chairs cost $1.25
.. tables cost $6.25

_____
My favorite method is to use the graphing calculator at Desmos [dot] com. Many graphing calculators will solve equations like these either directly, graphically, or indirectly using matrix functions. If you want to solve them by "elimination," you can double the second equation and subtract the first to get
.. 8t = 50

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3 years ago