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solniwko [45]
3 years ago
13

Delfina is moving to a new house, and she is packing some books in a box that measures 12 inches tall by 12 inches wide by 12 in

ches deep. Write the measurements of the box in exponential notation, in standard form,and in expanded form
Mathematics
1 answer:
VLD [36.1K]3 years ago
5 0
Exponential form:12^3
Standard form:1728
Expanded form:12x12x12
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Cuboid ABCDEFGH is shown
gtnhenbr [62]

Answer:

The angle formed between CF and the plane ABCD is approximately 47.14°

Step-by-step explanation:

The given parameters are;

BC = 6.8

DE = 9.3

∠BAC = 52°

We note that the angles formed by the vertex of a cuboid are right triangles, therefore, by trigonometric ratios, we get;

sin∠BAC = BC/(The length of a line drawn from A to C)

∴ The length of the line drawn from A to C = BC/sin∠BAC

The length of the line drawn from A to C = 6.8/sin(52°) ≈ 8.63

∴ AC = 8.63

By trigonometry, we have;

The angle formed between CF and the plane ABCD = Angle ∠ACF

tan\angle X = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length}

tan\angle ACF = \dfrac{FA}{AC}

In a cuboid, FA = BG = CH = DE = 9.3

\therefore tan\angle ACF = \dfrac{9.3}{8.63}

\therefore \angle ACF = arctan \left(\dfrac{9.3}{8.63} \right) \approx 47.14^{\circ}

The angle formed between CF and the plane ABCD = Angle ∠ACF ≈ 47.14°

4 0
3 years ago
The function y=x²-4x+8 approximates the height, y, of a bird, and its horizontal distance, x, as it flies from one
trapecia [35]

When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet  , Minimum at (2,4)

Therefore Option C and D is the correct answer.

<h3>What is a Quadratic Function?</h3>

The equation for a quadratic function is given by

y = a(x-h)² +k²

where (h,k) is the extreme value(vertex).

Here the equation given is

y = x²-4x +8

y = x²-4x+4+4

y = (x-2)² +4

Here the value of a = 1 , h = 2 and k = 4

The extreme value is at (2,4)

Therefore When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet  , Minimum at (2,4)

Therefore Option C and D is the correct answer.

To know more about Quadratic Function

brainly.com/question/5975436

#SPJ1

7 0
2 years ago
30 poins on he line hurr
Evgen [1.6K]

Answer:

(6(4) + 5) / 6 = 29/6

Step-by-step explanation:

3 0
3 years ago
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Javier bought 8 seeds in order to plant an herb garden for his grandma. Of the seeds he bought, 6 were sage seeds. If Javier cho
drek231 [11]

Answer

4/5

Step-by-step explanation:

if i'm wrong let me know

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3 years ago
(03.01)
Troyanec [42]
Number 1s answer would be 2. and number 2s answer would be 2
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