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3 years ago

Triangle inequality theorem

1 answer:

6 0

Triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side because if not you don't have a triangle.

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If g(x)=4x^2-16 we’re shifted 9 united to the right and 1 down, what would the new equation be?

Inessa05 [86]

Shown in the graph

<h2>Explanation:</h2>

Using graph tools we can graph the function:

$g(x)=4x^2-16$

which is the red graph shown below. As you can see, this is a parabola. The rule for vertical and horizontal shifts is as follows:

$Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:$

$\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)$

Therefore, If we shift the red graph 9 units to the right and 1 down, our new function (let's call it $h(x)$ ) will be:

$h(x)=4\left(x-9\right)^{2}-16-1 \\ \\ Simplifying: \\ \\ h(x)=4\left(x-9\right)^{2}-17$

This graph is the blue graph below. Let's verify the transformation taking the vertex of the red graph:

$(0,-16)$

By translating the 9 units to the right and 1 down the vertex is also translated by the same rule, so:

$New \ vertex: \\ \\ (0+9,-16-1) \\ \\ (9,-17)$

<h2>Learn more:</h2>

Cubic function: brainly.com/question/13773618#

#LearnWithBrainly

5 0

3 years ago

Which equation is graphed here?

Oxana [17]

The equation graphed is

y = -3x + 3

5 0

3 years ago

The graph shows the amount of a medicine min milligrams, remaining in a patient's body hours after receiving an injection . The

aksik [14]

An exponential function is a function defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>(a) The factor at which the medicine decreased, in 1.5 hour</h3>

From the graph, we have the following ordered pairs

(x,y) = (0,270) and (1.5,80)

Given that:

$y = ab^x$

At point (0,270), we have:

$ab^0=270$

$a= 270$

At point (1.5,80), we have:

$ab^{1.5} = 80$

Substitute 270 for a

$270b^{1.5} = 80$

Divide both sides by 270

$b^{1.5} = 0.2963$

Take 1.5th root of both sides

$b =0.44$

Hence, the medicine decrease in the hour and half at a factor of 0.44

<h3>(b) The factor at which the medicine decreased in the first half hour, and the first hour</h3>

In (a), we have:

The decay factor (b) to be 0.44

This represents the factor at which the medicine decreased throughout.

Hence, the medicine decrease in the first half hour, and the first hour at a factor of 0.44

<h3>(c) The exponential equation</h3>

In (a), we have:

$a= 270$

$b = 0.44$

So, the exponential equation is:

$y =270 * 0.44^x$

In terms of m and h, we have:

$m =270 * 0.44^h$

Hence, the equation relating m to h is $m =270 * 0.44^h$

Read more about exponential equations at:

brainly.com/question/11832081

6 0

2 years ago

HELP ME HOW MANY STARS ARE THERE

s344n2d4d5 [400]

Answer:

9,096

Step-by-step explanation:

and no this is not the wrong answer I have the same answer on my homework I did last week and its correct

8 0

2 years ago

Read 2 more answers

What is the exact value for the expression the square root of 56. − the square root of 14. + the square root of 126.? Simplify i

Olenka [21]

Sqr root of 56 - sqr root of 14 + sqr root of 126= sqr root of (4x14) - sqr root of 14 + sqr root of (9x14)= 2(sqr root of 14) - (sqr root of 14) + 3(sqr root of 14)= 4(sqr root of 14)
The right answer will be B.

6 0

3 years ago

Read 2 more answers