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3 years ago

The function g(x) = 3x - 12x + 7 written in vertex form is g(x) = 3(x - 2)2 – 5. What is the vertex of g(x)?

1 answer:

3 0

$\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] ~\dotfill\\\\ g(x)=3(x-\stackrel{h}{2})^2+(\stackrel{k}{-5})\qquad \qquad \stackrel{\textit{vertex}}{(2,-5)}$

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Marianna [84]

Answer:

B. {16, 19, 20}

Step-by-step explanation:

The <em>triangle inequality</em> requires for any sides a, b, c you must have ...

a + b > c

b + c > a

c + a > b

The net result of those requirements are ...

the sum of the two shortest sides must be greater than the longest side
the length of the third side lies between the difference and sum of the other two sides

If we look at the offered side length choices, we see ...

A: 8+11 = 19 . . . not > 19; not a triangle

B: 16+19 = 35 > 20; could be a triangle

C: 3+4 = 7 . . . not > 8; not a triangle

D: 5+5 = 10 . . . not > 11; not a triangle

The side lengths {16, 19, 20} could represent the sides of a triangle.

_____

<em>Additional comment</em>

The version of triangle inequality shown above ensures that a triangle will have non-zero area.

The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")

4 0

2 years ago

Choose the model that represents the function

kirill [66]

Answer:

OPTION D

Step-by-step explanation:

We have to determine which option determines the function given above.

To determine the function, just substitute the values and compare LHS and RHS.

we have $f(4) = 18$

$f(-2) = -12$

$f(0) = -2$

$f(-3) = -17$

Here, $x$ is the domain and $f(x)$ is the co-doamin.

Therefore, $x = \{4, -2, 0, -3\}$

Now, OPTION A: $f(x) = 2x - 5$

Substitute x = 4. We get f(x) = 3 $\ne$ 18.

So, OPTION A is rejected.

Similarly, OPTION B: $f(x) = 5x + 2$

Substitute x = 4. We get f(4) = 22 $\ne$ 18.

It is rejected as well.

Now, for OPTION C: $f(x) = \frac{x}{2} - 5$

Substitute x = 4. We get f(4) = -3 $\ne$ 18.

So, OPTION C is also rejected.

OPTION D: $f(x) = 5x - 2$

Substitute x = 4. We get f(4) = 18.

Substitute the remaining points in domain as well. We notice that it exactly matches the given function. So, OPTION D is the answer.

8 0

3 years ago

A circular clock face is stenciled along its edge. The radius of the clock is 12 centimeters, so the stenciling covers about cen

Inessa05 [86]

Answer:

6 srry if dis is wrong sis

Step-by-step explanation:

since the radius is 12 divide that by 2 and you get 6 which is the diameter.

so im guessing the answer is 6 idk i haven't done this inna min. i hope this was helpful <3

4 0

3 years ago

Read 2 more answers

Bag a contains 4 red and 3 blue tickets. bag b contains 3 red and 1 blue ticket. a bag is randomly selected by tossing a coin an

nikdorinn [45]

It's difficult to draw a tree diagram with this software.
Try to do it yourself & you will find the followings:

If A is selected (P(A) =1/2) we can get ether red (p(A & red)=4/7
so P(A∩red)= 1/2 x 4/7 = 4/14
Also we can get P(blue) = 3/7 & P(A∩blue) = 1/2 x 3/7 = 3/14

Same reasoning for B & you will get P(B∩read) 1/2 x 3/4 = 3/8
Also we can get P(B∩blue) = 1/2 x 1/4 = 1/8
Probability of blues is either 3/14 or 1/8
P(blue) = 3/8 +1/8 =19/56 = 0.339

6 0

3 years ago

Helpppp plsss......!!!!!!!!

ioda

Answer:

Step-by-step explanation:

Mower A: 3.25 / 0.3 = 10.83

Mower B: 3.75 / 0.15 = 25

Mower C: 4.25 / 0.24 = 17.71

Mower D: 5.50 / 0.18 = 30.50

Answer: D :)

8 0

3 years ago