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2 years ago

Helppppp please 100 points and ill give brainliest!!!

Mathematics

2 answers:

Arturiano [62]2 years ago

7 0

F(x)=4x .............

krok68 [10]2 years ago

4 0

Answer:

f(x)=4x

Step-by-step explanation:

Let's look at the progression of f(x) values as the x value goes up. The x value goes up in steps of 1, but the f(x) value goes up in steps of 4. This means that the f(x) value grows 4 times faster than the x value. Comparing them side by side, you can see that each f(x) value is indeed 4 times larger than the corresponding x value. Therefore, the descriptive function is f(x)=4x.

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A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by

V = $V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x$

First, we differentiate V(x) with respect to x, to get,

$\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450$

Equating the first derivative to zero, we get,

$\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0$

Solving, with the help of quadratic formula, we get,

$x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2}$ ,

Again differentiation V(x), with respect to x, we get,

$\frac{d^2(V(x))}{dx^2} = 24x - 180$

At x =

$\displaystyle\frac{5(3-\sqrt{3})}{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Thus, by double derivative test, the maxima occurs at

x = $\displaystyle\frac{5(3-\sqrt{3})}{2}$ for V(x).

Thus, largest volume the box can have occurs when $x = \displaystyle\frac{5(3-\sqrt{3})}{2}}$ .

Maximum volume =

$V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}$

8 0

3 years ago

Tony is training to run a marathon. He has already run 2 miles today and is running additional miles at 6 miles per hour. Write

Minchanka [31]

I think its 8m/h or somethan but idrk. Like it doesnt specify how long it took him the run the 2 hours so idrk. Or it would be 2m/d + 6m/h with d=day

3 0

3 years ago

J has coordinates (-2,8) R has coordinates (-7,-3) find the coordinates of point A that partition (JR) in the ratio 5:2 and sket

kolbaska11 [484]

J Coordinates: (-2,8)

R Coordinates: (-7,-3)

A cuts JR in the ratio of 5:2

We have to find out the coordinates for A. Let coordinates of A be (x,y)

The section formula helps us determine a point (x,y) that divides the line joining two points (x1,y1) and (x2,y2) in the ratio of m:n

x1, y1 represents the point which is more on the left side of the x axis, while x2,y2 represents the point which is more on the right side of the x axis

So here x1 = -7, y1 = -3, x2 = -2, y2 = 8, m = 5, n = 2

As per section formula, x = (mx₂ + nx₁) / (m + n), and y = (my ₂ + ny₁) / (m + n))

⇒ x = ((5*-2) + (2*-7)) / (7)

⇒ x = (-10+ (-14)) / (7)

⇒ x = -24 / 7

⇒ x = -3.43

and y = ((5*8) + (2*-3)) / (7)

⇒ y = (40 - 6) / 7

⇒ y = 4.86

So coordinates of A are (-3.43,4.86)

Please see the attached image for seeing the points and line on chart.

4 0

2 years ago

If 2 angles are both right angles then they are congruent. Would the converse of this statement be true?

yKpoI14uk [10]

Given:

The statement is: If 2 angles are both right angles then they are congruent.

To find:

The converse of the given statement and then check whether it is true or not.

Solution:

We know that,

Statement: If p, then q.

Converse : If q, then p.

The statement is: If 2 angles are both right angles then they are congruent.

So, the converse of this statement is:

If 2 angles are congruent then both are right angles.

This statement is not true because if 2 angles are congruent then it is not necessary that the angles are right angles.

Therefore, the converse of this statement is not true.

4 0

3 years ago

A website recommends that you should have 3 gallons Of water for every inch of goldfish in your tank , if you have one billion g

Natalija [7]

Answer:

9,000,000,000 gallons of water.

Step-by-step explanation:

We have been given that a website recommends that you should have 3 gallons of water for every inch of goldfish in your tank. We are asked to find the gallons of water needed for one billion goldfish that are each 3 inches.

First of all, we will find gallons of water needed for each fish.

$\text{Gallons of water needed for each fish}=3\cdot 3=9$

$\text{1 billion}=10^9=1,000,000,000$

Now, we will multiply number of gallons of water required for 1 fish by 1 billion to find required gallons of water.

$\text{Gallons of water needed for 1 billion fish}=9\cdot 1,000,000,000$

$\text{Gallons of water needed for 1 billion fish}=9,000,000,000$

Therefore, you need 9,000,000,000 gallons of water for 1 billion fish.

7 0

3 years ago