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2 years ago

HELP! ASAP!

Mathematics

1 answer:

Novosadov [1.4K]2 years ago

5 0

Step-by-step explanation:

Part A:

So the height is going to be x when you fold the sides up. So that's one part of the volume but for the width it was going to be 4 but since two corners were cut out with the length x the new width is going to be (4-2x). The same thing applies for the length which should be 8 inches but since two corners were removed with the length x it's now (8-2x)

v = x(4-2x)(8-2x)

Part B:

The volume can be graphed although there must be a domain restriction since the height, width, or length cannot be negative. So let's look at each part of the equation

so for the x in front it must be greater than 0 to make sense

for the (4-2x), the x must be less than 2 or else the width is negative.

for the (8-2x) the x must be less than 4 or else the length is negative

so the domain is going to be restricted to 0 < x < 2 so all the dimensions are greater than 0

By using a graphing calculator you can see the maximum of the given equation with the domain restrictions is 0.845 which gives a volume of 12.317

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HELP PLEASE!!!!!!!!!!!!

Bogdan [553]

Answer:

See the explanation.

Step-by-step explanation:

We are given the function f(x) = x² + 2x - 5

Zeros :

If f(x) = 0 i.e. x² + 2x - 5 = 0

The left hand side can not be factorized. Hence, use Sridhar Acharya formula and

$x= \frac{-2+\sqrt{2^{2}-4\times(-5)\times1 } }{2}$ and

$x= \frac{-2-\sqrt{2^{2}-4\times(-5)\times1 } }{2}$

⇒ x = -3.45 and 1.45

Y- intercept :

Putting x = 0, we get, f(x) = - 5, Hence, y-intercept is -5.

Maximum point :

Not defined

Minimum point:

The equation can be expressed as (x + 1)² = (y + 5)

This is an equation of parabola having the vertex at (-1,-5) and axis parallel to + y-axis

Therefore, the minimum point is (-1,-5)

Domain :

x can be any real number

Range:

f(x) ≥ - 6

Interval of increase:

Since this is a parabola having the vertex at (-1,-5) and axis parallel to + y-axis.

Therefore, interval of increase is +∞ > x > -1

Interval of decrease:

-∞ < x < -1

End behavior :

$f(x) = x^{2} +2x-5 =x^{2} (1+\frac{2}{x} -\frac{5}{x^{2} } )$

So, as x tends to +∞ , then f(x) tends to +∞

And as x tends to -∞, then f(x) tends to +∞. (Answer)

7 0

3 years ago

Solve the system of equations x+y=-8 and -9x-6y=60 by combining the equations

TiliK225 [7]

Answer:

x = - 4 y = - 4

Step-by-step explanation:

x+y= - 8

-9x-6y=60

First, solve for x in the first equation:

x+y = - 8 Subtract y from both sides

x + y - y = -8 - y y cancels on the left

x = - 8 - y

Now plug in what you found for x into the 2nd equation and solve for y.

- 9x - 6y = 60

-9(- 8 - y) - 6y = 60 Multiply out

72 + 9y - 6y = 60

72 + 3y = 60 Subtract 72 from both sides

72 - 72 + 3y = 60 - 72 72 cancels on the left

3y = - 12 Divie both sides by 3

3y/3 = -12/3 3 cancels on the left because 3/3 = 1

y = -4

Now plug your answer for y back into the first equation to get x.

x + y = -8

x + (-4) = - 8 Add 4 to each side

x - 4 + 4 = - 8 + 4 4 cancels on the left

x = -4

x = - 4 and y = - 4

8 0

3 years ago

Which of the following is the statement of the triangle inequality theorem?

kupik [55]

we know that

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

a,b,c------> the length sides of a triangle

The theorem states that three conditions must be met

case 1)

$a+b > c$

case 2)

$a+c > b$

case3)

$c+b > a$

therefore

the answer is the option

B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

5 0

3 years ago

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304 students went on a field trip .7 buses were filled and 17 students traveled in cars. How many students were in each bus?? Sh

Gemiola [76]

304-17= 287.
287 divided by 7= 41 students per bus.

8 0

3 years ago

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REALLY NEED HELP

artcher [175]

Answer:

Y=-5/3x

Step-by-step explanation:

Use the slope formula and slope-intercept form y=mx+b to find the equation.

3 0

2 years ago