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3 years ago

How does labeling the diagram help us show that we can use right triangle congruency (SAS in this case)?

Mathematics

1 answer:

dem82 [27]3 years ago

4 0

Answer:

Step-by-step explanation:

S A S congruence rule: Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of other triangle.

If two triangles are congruent by SAS, and the angle is 90, then by CPCT{corresponding part of congruent triangle) the hypotenuse of the two triangles will be congruent.

Now, as hypotenuse and one leg are congruent in both triangles, we can apply RHS congruent

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Consider the surface f (x comma y comma z )f(x,y,z)equals=negative 2 x squared plus 2 y squared minus 3 z squared plus 3 equals

trapecia [35]

Answer:

a) (8,8,-6)

b) 4x+4y+3z = -3

Step-by-step explanation:

The surface is given by the equation

f(x,y,z) = 0 where

$f(x,y,z)=-2x^2+2y^2-3z^2+3$

The gradient of this function is the vector

$(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})=(-4x,4y,-6z)$

If we evaluate it in the point P = (-2,2,1) we obtain the point

(8,8,-6)

The vectors with their tails at P are of the form

(-2,2,1)-(x,y,z) = (-2-x, 2-y, 1-z)

as they must be orthogonal to the gradient, they must be orthogonal to the vector (8,8,6) so their inner product is 0

$(-2-x,2-y,1-z)\cdot(8,8,6)=0\Rightarrow -16-8x+16-8y+6-6z=0\Rightarrow 4x+4y+3z=-3$

and the equation of the desired plane is

4x+4y+3z = -3

3 0

4 years ago

What is the turning point of the graph of f(x) = |x| + 4 ?

leva [86]

F(x) = |x| + 4

f(0) = I 0 I + 4===> (0,4)

f(0) = - 0 +4 ===> (0,4)

3 0

3 years ago

Divide use partial quotients 36 divided by 540

Blizzard [7]

Answer and explanation;

= 1/15 is the answer get when 36 is divided by 540 .

We can use the partial quotients to divide 540 by 36 then we get the reciprocal of the answer;

540 ÷ 36

We can take 360 ÷ 36 = 10

Then the remainder is ; 540 -360 = 180

But ; 180 ÷36 = 5

Then we get the sum of the quotients which is 10 +5 = 15

Thus; 540 ÷ 36 = 15

However; the question was 36 ÷ 540 , so we get the reciprocal of 15;

= 36 ÷ 540 = 1/15

8 0

3 years ago

Read 2 more answers

How to solve slope intercept form with fractions

Sedaia [141]

If the fraction is for example 1/4, try to graph it at before the half by a little.

5 0

3 years ago

Graph each function for the given domains F(x) = -|x| D: -5, -3, 0, 3, 5

Nikitich [7]

Ok, so what this means is if it's negative, leave it. if it's positive, make it negative

so the range would be -5,-3,0,-3,-5

point are

(-5,-5)
(-3,-3)
(0,0)
(3,-3)
(5,-5)

7 0

3 years ago