Hot Shot Electronics is designing a packing box for itsnew line of Acoustical Odyssey speakers. The box is a
rectangular prism of length 45 centimeters, width
30 centimeters, and volume 81,000 cubic centimeters.
What is the height, in centimeters, of the box?
A. 75
B. 60
C. 48
D. 27
E. 18

Answers

Answer 1

Answer: Volume = (length) x (width) x (height)

81,000 = (45) x (30) x (height)

Height = (81,000) / (45 x 30) = 60 cm

Answer 2

Answer: V=81 000cm³

V=Ab *h

Ab=L*w

Ab=45*30
Ab=1350cm²

V=1350*h

1350*h=81 000

h=81 000/1 350
h=60cm answer variant b)

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**I need to find out what the vertex , axis of symmetry, maximum or minimum, and the domain and range for function f(x)=-(x-3)^2+2 HELP ME I DONT UNDERSTAND!!

Answers

Notice that the given equation is a parabola.

a) VERTEX
We need to find out where the parabola opens. You can predict the equation by tabulating any values of x and f(x). The table is shown:
x f(x)
_____
0 -7
1 -2
2 1
3 2
4 1
5 -3
As you plot it, the parabola opens downward. The vertex is (3,2) because that is the maximum point. The rest of the values are lesser than 2.
However, there is an easier technique to find the opening parabola and vertex rather than you plot it.

b) AXIS OF SYMMETRY
The axis of symmetry is a line that divides the parabola into two congruent halves. There is a formula for the axis of symmetry which is x = -b/2a.
Note: That is only applied if the parabola opens upward or downward and their axis of symmetry is a vertical line.
To get a and b, arrange the given equation first.
f(x) = -(x - 3)^2 + 2
= -(x^2 - 6x + 9) + 2
= -x^2 + 6x - 7 + 2
= -x^2 + 6x -5
The general form of the quadratic equation is ax^2 + bx + c. Setting a = -1, b = 6, c = -5, the axis of symmetry is
x = -6/(2*-1) = 3.

But anyway, you find it out the table above. We know that the coordinate of the vertex is (3,2). For instance, that is x = 3.

c) MAXIMUM or MINIMUM
Remember that the maximum refers to a vertex where the parabola opening downward. Otherwise, it is a minimum if the parabola opens upward. The maximum or minimum must have a certain value.
We know the answer will be a maximum. Since the axis is symmetry is a vertical line, the value for a maximum is 2.

d) DOMAIN and RANGE
Based on the given equation, the domain will be (-∞, ∞) because all values of x, the parabola continually spreads out.
The range will be (-∞, 2] because the maximum point is 2 and the rest of the values goes negative.

Write 5 x 10^-3 as an ordinary number.

Answers

5 x 10⁻³ is a scientific notation.

5 is the coefficient
10 is the base
3 is the exponent. The sign of the exponent signifies which direction the decimal point moved.

negative sign means that the decimal point moved from left to right in writing the scientific notation.
positive sign means that the decimal point moved from right to left in writing the scientific notation.

5 x 10⁻³ is 0.005 in standard form.

had the exponent been positive.
5 x 10³ is 5000 in standard form

If both the base and height of a triangle are made nine times as long, how many times the area of the original figure is the area of the new figure?

Answers

To start: A = 1/2bh
Now by increasing both the width and height by 9, you get: A = 1/2(9b)(9h) = 1/2(81)bh

You can see that the increase in area is 81 times the original.

A triangle formed by the sides 3.8cm ,3.7 cm, and 5cm is

Answers

By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides.

The triangle formed by the sides 3.8 cm ,3.7 cm, and 5 cm is acute angle triangle.

How to find the type of triangle?

By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides. Thus,