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3 years ago

Identify the ventez of the graph. Tell whether it is a minimum or maximum.

Mathematics

1 answer:

kotegsom [21]3 years ago

3 0

Answer:

2nd option: the lowest point on the graph is (-2, -2). this is where both sides of the parabola converge. from this point, both lines go up. this means the vertex is a minimum.

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Triangle HIJ has coordinates H(-3,5), (8,2), and J(-3,-5). Find

Vlad1618 [11]

Answer:

H (x= -3 , y=5)

I (x=8 , y=2)

J (x= -3 , y= -5)

D is the distance between the 2 points so just plug in the x and y cords of each of the corresponding points

so for (HI)

you plug in 2 on the red x

and 8 on the red y

then -3 in the blue x

and 5 in the blue y

5 0

2 years ago

PLEASE HELP ME ASAP!!!! My entire grade depends on these questions and I need to show the work that go me there

Marizza181 [45]

Answer:

Answers are in bold

Step-by-step explanation:

Part 1A

Use the Zero Product Property to find the x-intercepts:

0=-(x+4)(x-1)

0=(x+4)(x-1)

0=(x+4)

-4=x

x=-4

0=(x-1)

1=x

x=1

So the x-intercepts are x=-4 and x=1 which is also (-4,0) and (1,0)

For the y-intercepts, plug in x=0:

f(x)=-(0+4)(0-1)

f(x)=(-4)(-1)

f(x)=4

So the y-intercept is y=4 which is also (0,4)

Part 1B

In general, the axis of symmetry is equal to x=h in the equation y=(x-h)^2+k

For a parabola, the axis of symmetry is equal to x=-b/2a, so we expand the given equation and then plug in the values of "a" and "b" to get the axis of symmetry:

f(x)=-(x+4)(x-1)

f(x)=-(x^2+3x-4)

f(x)=-x^2-3x+4

So now we know a=-1 and b=-3, therefore we can plug them in:

x=-b/2a

x=-(-3)/2(-1)

x=3/-2

x=-3/2

x=-1.5

So the equation of the axis of symmetry is x=-1.5

Part 1C

We'll use the equation x=-b/2a to get the x-coordinate for the vertex (which we already know is x=-1.5), then plug in that value of x in the original equation to get the y-coordinate for the vertex:

f(x)=-(-1.5+4)(-1.5+1)

f(x)=-(2.5)(-0.5)

f(x)=-(-1.25)

f(x)=1.25 <-- y-coordinate

So the coordinates of the vertex are (-1.5,1.25)

Part 1D

See the image below

I'll let someone else do the last 4 questions as I am unable to answer them.

8 0

3 years ago

Simplify: (2+7x)/(x^(2)-4x)-(3)/(x-1)

Rina8888 [55]

Answer:

I need points please forgive me :(

3 0

4 years ago

I need help asap im timed

Iteru [2.4K]

Answer:-

Refer to attachment for the required solution.

8 0

3 years ago

Read 2 more answers

The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu

rjkz [21]

The balloon has a volume $V$ dependent on its radius $r$ :

$V(r)=\dfrac43\pi r^3$

Differentiating with respect to time $t$ gives

$\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}$

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

$10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}$

The surface area of the balloon is

$S(r)=4\pi r^2$

and differentiating gives

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi r\dfrac{\mathrm dr}{\mathrm dt}$

so that at the moment the radius is 3 m, its area is increasing at a rate of

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi(3\,\mathrm m)\left(\dfrac5{18\pi}\dfrac{\rm m}{\rm s}\right)=\dfrac{20}3\dfrac{\mathrm m^2}{\rm s}$

4 0

3 years ago