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2 years ago

Which equation has a graph that lies entirely above the x-axis?

Mathematics

2 answers:

Alinara [238K]2 years ago

8 0

Answer:

(Option C) y = (x – 7)2 + 7

Step-by-step explanation:

hope this helps!! have an amazing day <3

kogti [31]2 years ago

4 0

Answer:

Answer:

Option C.

Step-by-step explanation:

The vertex form of a parabola is

where, a is constant, (h,k) is vertex.

If a<0, then it is a downward parabola and if a>0, then it is an upward parabola.

A downward parabola never lies entirely above the x-axis.

First equation is

It is a downward parabola and vertex is (-7,7).

Second equation is

It is an upward parabola and vertex is (7,-7).

Third equation is

It is an upward parabola and vertex is (7,7).

Fourth equation is

It is a linear equation with y-intercept -7.

Only equation 3 is an upward parabola whose vertex lies above the x-axis.

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A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares from the

Stells [14]

Answer:

$\frac{5}{3}$ in

Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

Width of box=15-2x

Height of box=x

Volume of box= $L\times B\times H$

Substitute the values then we get

Volume of box=V(x)= $(8-2x)(15-2x)x=(15x-2x^2)(8-2x)$

$V(x)=120x-30x^2-16x^2+4x^3$

$V(x)=4x^3-46x^2+120x$

Differentiate w.r.t x

$V'(x)=12x^2-92x+120$

$V'(x)=0$

$12x^2-92x+120=0$

$3x^2-23x+30=0$

$3x^2-18x-5x+30=0$

$3x(x-6)-5(x-6)=0$

$(x-6)(3x-5)=0$

$x-6=0\implies x=6$

$3x-5=0\implies x=\frac{5}{3}$

Again differentiate w.r.t x

$V''(x)=24x-92$

Substitute x=6

$V''(6)=24(6)-92=52>0$

Substitute x=5/3

$V''(5/3)=24(5/3)-92=-52$

Hence, the volume is maximum at x= $\frac{5}{3}$

Therefore, the side of the square , $x=\frac{5}{3}$ in cutout that gives the box the largest possible volume.

5 0

2 years ago

Find the perimeter of rectangle PQRS with vertices P(0,0), Q(0,7), R(12,7) & S (12,0).

Andrews [41]

Check the picture below.

you can pretty much just count the units off the grid.

the perimeter is the length of all sides summed up.

7 0

2 years ago

Given a line segment A(16, 8) and B(1, 3) what are the coordinates or the line segment partitioned two-fifths from A to B.

Shalnov [3]

Partitioning means to find the dividing point between two points.
This is done by prorating the difference in x- and y-coordinates, and adding to the first.

We will take the first point (from A to B) as A(16,8).
The difference is B-A, i.e.
(1,3)-(16,8) = (-15,-5)
2/5 of the difference is (2/5)*(-15,-5) = (-6,-2)
Add the difference to the first coordinates (point A) gives
Point of division = (16,8)+(-6,-2) = (16-6, 8-2) = (10,6)

7 0

2 years ago

2= p-3 / 2 linear equation

rewona [7]

The answer to this question is
P= 12

4 0

2 years ago

Pls answer I need help

natali 33 [55]

Answer:

It's 2.

Step-by-step explanation: