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3 years ago

Which system of equations is represented by this graph?y= _ x+3 y= _ x-3

Mathematics

1 answer:

navik [9.2K]3 years ago

5 0

I believe the first one is -1/2
And other one 1/2
Like 80% sure:)

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

For carolina's birthday her mom took her and her friends to a water park.Carolina mom paid 42.50 for 5 students tickets. What wa

Sophie [7]

Answer:

8.5 for each student ticket

Step-by-step explanation:

Simply divide the total cost 42.5 by the amount of students 5 to get your answer.

42.5 / 5 = 8.5

7 0

2 years ago

Helppppp me plss, I’ll mark u as brainlest

Marina86 [1]

$\large\color{lime}\boxed{\colorbox{black}{Answer : - }}$

We know that, in ∆ABC,

∠A+∠B+∠C = 180°

But the triangle is right angled at C

ie., ∠C = 90°

Therefore, ∠A+∠B+ 90° = 180°

⇒ ∠A + ∠B = 90°

Therefore, <u>cos(A + B) = cos 90º = 0</u>

6 0

3 years ago

Help please look below

Gwar [14]

A is located, as you look A is past -2 almost hitting -3 making the mark 2.8 so the answer is A

3 0

2 years ago

Eliza is two years younger than half her brother, Juan’s age. Write an equation to represent Eliza’s age. If Juan is 6 how old i

Natalka [10]

X = Juan's age
y = Eliza's age

Some key words/phrases we can use to help us make the equation are:

-is (whatever comes after this word usually equals the end result, or what it equals)
-two years younger
-than
-half her brother's age
.
just break it down :)

x/2 (half her brother's age) - 2 (two years younger) = y (Eliza is...)

| basically,
v

x/2 - 2 = y
So if Juan is 6, then we need to plug in 6 for x.

6/2 - 2 = y

3 - 2 = y

1 = y

ANSWER: Eliza is one year old.

6 0

3 years ago

Which system of equations is represented by this graph?y= _ x+3 y= _ x-3​

Which system of equations is represented by this graph?y= _ x+3 y= _ x-3