F(x)<0 over (- infinity, -3) and what other interval? (-2.4,-1.1)

The base of an open rectangular box is of length (2x+5) cm and width x cm. The area of this base is 58cm^2. The height of the op

andreev551 [17]

B) $x =4.28$

C) volume = $135.25cm^3$ .

Step-by-step explanation:

Here we have , The base of an open rectangular box is of length (2x+5) cm and width x cm. The area of this base is 58cm^2. The height of the open box is (x-2) cm. We need to find the following :

a) show that 2x^2+5x-58=0

We know that area of rectangle = $length(width)$

⇒ $Area = length(width)$

Putting values according to question we get :

⇒ $58 = (2x+5)(x)$

⇒ $58 = (2x^2+5x)$

⇒ $2x^2+5x - 58 = 0$

b) solve the equation in the question above, giving your answer to 2 decimal places

Solving this equation :

⇒ $2x^2+5x - 58 = 0$

By quadratic formula

⇒ $x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $x = \frac{-5 \pm \sqrt{5^2-4(2)(-58)} }{2(2)}$

⇒ $x = \frac{-5 \pm 22.11}{4}$

⇒ $x = \frac{-5 + 22.11}{4} , x = \frac{-5 - 22.11}{4}$ { Since side can't be negative ! }

⇒ $x =4.28$

c) calculate the volume of the box, stating units of you answer

Since x = 4.28 , other sides are

$2x+5=2(4.28)+5=13.56\\x-2=4.28-2=2.28$

We know that volume is given by :

⇒ $length(width)(height)$

⇒ $13.86(4.28)(2.28)$

⇒ $135.25cm^3$

Therefore , volume = $135.25cm^3$ .

7 0

3 years ago

Help what is the answer for this

grandymaker [24]

Answer:

A) <SQT = 36 degrees

B) <QRW = 36 degrees

C)<PRV = 72 degrees

Step-by-step explanation:

A) <SQT = 36 degrees (< SQT and < PQR are vertically opposite angles, and vertically opposite angles are equal)

B) <QRW = 36 degrees ( <QRW and < SQT are corresponding angles since they lie on the same side of the transversal across the parallel lines. Corresponding angles are equal)

C)<PRV = 72 degrees( <PRV is the exterior base angle to < PQR and exterior base angles, are always twice their interior correxpondents)

8 0

3 years ago

Help please! Thanks!

Gemiola [76]

Answer: 2/3
1/3 * 2= 2/ 3

8 0

3 years ago

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An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using d for distance in kilometers and

uranmaximum [27]

We are given relation between distance( in kilometers) travelled and number of hours taken by an Albatross bird.

Distance in kilometers taken by variable d.

Number of hours by t.

And situation is given d=50t.

We know, direct relation formula y= kx read as y is directly proportional to x. And k is the constants of proportionality.

In the given fuction y is taken by variable d and x is taken by variable t.

If we compare d=50t by y = mx, the value of k is 50.

Therefore, constant of proportionality is 50.

Constant is a number that never change it's value.

Therefore, constant of proportionality is just 50.

But we can say variables d and t are two variables those are directly proportional to each other.

Constant of proportionality is actually unit rate of change.

For the given situation constant of proportionality is the number of km travelled in per unit time (in 1 hour.)

If we divide 400km 8 hours, we get 400/8 = 50 km per hour.

Therefore, variables of proporation are d and t and relation between them is " they are directly proportional to each other".

And the constants of proportionality is just 50.

7 0

3 years ago

What is the vertex of y=x² – 8x + 14

ozzi

Answer:

-2

Step-by-step explanation:

Get the equation in the form y = ax2 + bx + c.
Calculate -b / 2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.

4 0

3 years ago

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