Which graph is the graph for the function? <br><br> y=x^2+x-12

A rectangular prism shaped toy box is 52 centimeters long. The perimeter of one side of the box is 90 centimeters. The height of

Archy [21]

Answer:

The volume of the toy box is 25688 cubic centimetres

Step-by-step explanation:

The 6 faces of a rectangular prism are rectangles, each two opposite faces are equal in dimensions, its dimensions are L, W, H, so two faces has dimensions L , W, two faces L , H and two faces W , H

The formula of the volume of it is V = L × W × H

∵ The toy box is shaped a rectangular prism

∵ The toy box is 52 cm long

∴ H = 52 cm

∵ The perimeter of one side is 90

- Perimeter of any rectangle is twice the sum of its dimensions

∴ Twice the sum of two dimensions of the side = 90 cm

- Divide it by 2 to find the sum of the two dimensions

∴ The sum of two dimensions = 90 ÷ 2 = 45 cm

The sum of two dimensions is less than the height of the box, that means 45 is the sum of the other two dimensions L and W

∵ L + W = 45

∵ The height of the box is is twice as long as it’s width

∴ H = 2 W

∵ H = 52 cm

∴ 52 = 2 W

- Divide both sides by 2

∴ 26 = W

∴ W = 26 cm

Substitute the value of W in the equation of the sum of the two dimensions to find L

∵ L + 26 = 45

- Subtract 26 from both sides

∴ L = 19 cm

∵ V = L × W × H

∴ V = 19 × 26 × 52

∴ V = 25688 cm³

The volume of the toy box is 25688 cubic centimetres

7 0

3 years ago

Use the distributive property to simplify 3 + 5c(2 + 6c) completely.

Charra [1.4K]

Answer:

Distributive property says that:

(A + B)*C = A*C + B*C

Now let's try to use it in our expression:

3 + 5*c*(2 + 6*c)

Here we can take the two terms inside the parentheses as A and B, and the term that multiplies them as C, then distributing we get:

3 + (5*c)*2 + (5*c)*(6*c)

Now remember that the multiplications are associative and commutative, then we can write this as:

3 + (2*5)*c + (5*6)*(c*c)

3 + 10*c + 30*c^2

And we can't simplify it anymore.

7 0

3 years ago

If 2x2 + y2 = 17 then evaluate the second derivative of y with respect to x when x = 2 and y = 3. Round your answer to 2 decimal

Vera_Pavlovna [14]

Answer:

y''=-1.26

Step-by-step explanation:

We are given that $2x^2+y^2=17$

We have evaluate the second order derivative of y w.r.t. x when x=2 and y=3.

Differentiate w.r.t x

Then , we get

$4x+2yy'=0$

$2x+yy'=0$

$yy'=-2x$

$y'=-\frac{2x}{y}$

Again differentiate w.r.t.x

Then , we get

$2+(y')^2+yy''=0$ $(u\cdot v)'=u'v+v'u)$

$2+(y')^2+yy''=0$

Using value of y'

$yy''=-2-(-\frac{2x}{y})^2$

$y''=-\frac{2+(-\frac{2x}{y})^2}{y}$

Substitute x=2 and y=3

Then, we get $y''=-\frac{2+(\frac{4}{3})^2}{3}$

$y''=-\frac{18+16}{9\times 3}=-\frac{34}{27}$

Hence,y''=-1.26

6 0

4 years ago

HELP PLS Match each graph with the logarithmic function it represents

SIZIF [17.4K]

Each graph has been matched with the logarithmic function it represents as follows:

f(x) = 3 - 4In (x-2) = graph 3.

f(x) = 3 - Inx = graph 1.

f(x) = In(x + 1) = graph 4.

f(x) = 2In(x + 3) = graph 2.

<h3>What is a function?</h3>

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.

<h3>The types of function.</h3>

In Mathematics, there are different types of functions and these include the following;

Periodic function

Inverse function

Modulus function

Signum function

Piece-wise defined function.

Logarithm function

<h3>What is a logarithm function?</h3>

A logarithm function can be defined as a type of function that represents the inverse of an exponential function. Mathematically, a logarithm function is written as follows:

y = logₐₓ

In this exercise, you're required to match each graph with the logarithmic function it represents as shown in the image attached below:

f(x) = 3 - 4In (x-2) = graph 3.

f(x) = 3 - Inx = graph 1.

f(x) = In(x + 1) = graph 4.

f(x) = 2In(x + 3) = graph 2.

Read more on logarithm function here: brainly.com/question/13473114

#SPJ1

3 0

2 years ago

20×+4=4(5x+1) how many solution are in this equation

Tomtit [17]

Simplify both sides of the equation

(20)(4)= 4(5x+1)

Simplify

80 = 20x+4

Flip the equation

20x+4 = 80

Subtract 4 from both sides

20x+4-4 = 80-4

20x = 76

Divide both sides by 20

20x/20 = 76/20

x= 3.8

There is one solution in this equation

7 0

4 years ago

Which graph is the graph for the function? y=x^2+x-12