Identify the length, width, and height of the figure formed.

There is no restriction upon the domain, the x values, and is all real numbers or (-oo,+oo)

From such it is clear that the domain also contains all real numbers.

The range of f(x) is (-oo,+oo)

8 0

3 years ago

Which of the equations below could be the equation of this parabola?

BARSIC [14]

Parabolas like $y=ax^2$ have the y-axis as their symmetry axis, so options B and D are surely wrong.

Moreover, parabolas like $x=ay^2$ have the x-axis as their symmetry axis. If $a>0$ the parabola is concave rightwards, if $a$ the parabola is concave leftwards.

Since your parabola is concave leftwards, the only feasible option is $x=-2y^2$

7 0

3 years ago

Find the distance between the points (4,-8) and (7-10).

Anastaziya [24]

Answer:

$\displaystyle d = \sqrt{13}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Point (4, -8)

Point (7, -10)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [DF]: $\displaystyle d = \sqrt{(7-4)^2+(-10+8)^2}$
(Parenthesis) Subtract/Add: $\displaystyle d = \sqrt{(3)^2+(-2)^2}$
[√Radical] Exponents: $\displaystyle d = \sqrt{9+4}$
[√Radical] Add: $\displaystyle d = \sqrt{13}$

6 0

3 years ago

Read 2 more answers

A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 60 p

boyakko [2]

Answer:

large: 40 lbs
small: 20 lbs

Step-by-step explanation:

A system of equations can be written for the weights of the boxes based on the relationships given in the problem statement. One equation will be for the total weight of 1 large and 1 small box; the other will be for the total weight of 70 large and 60 small boxes.

Let L and S represent the weights of Large and Small boxes, respectively. The system of equations is ...

L + S = 60 . . . . . . combined weight is 60 lbs

70L +60S = 4000 . . . . weight of boxes in the truck

__

We can solve this by substituting for s in the second equation.

70L +60(60 -L) = 4000

10L = 400 . . . . . . . . . subtract 3600, simplify

L = 40

S = 60 -L = 20

A large box weighs 40 pounds; a small box weighs 20 pounds.

7 0

3 years ago

A bacteria population is 2000 at time t = 0 and its rate of growth is 1000 · 5t bacteria per hour after t hours. what is the pop

natima [27]

Since you are given the rate of growth, the population must be computed from the integral ...

$\displaystyle p(t)=2000+\int_{0}^{t}{\left(1000\cdot 5^{t}\right)}\,dt=2000+\frac{1000}{\ln{(5)}}\cdot \left(5^{t}-1\right)\\\\=2000+\frac{1000}{\ln{(5)}}\cdot 4\approx 4485\qquad\mbox{after 1 hour}$

5 0

4 years ago