What is the 6th term in the arithmetic sequence below?

The diagram shows a 3 cm x 5 cm x 4 cm cuboid

Rainbow [258]

Answer:

a) The length of segment AC is approximately 5.83 centimeters.

b) The angle ACD is approximately 34.5º.

Step-by-step explanation:

a) Since $AB \perp BC$ , the length of segment $AC$ is determined by Pythagorean Theorem, that is:

$AC = \sqrt{(5\,cm)^{2}+(3\,cm)^{2}}$

$AC \approx 5.831\,cm$

The length of segment AC is approximately 5.831 centimeters.

b) Since $AB \perp BC \perp AD$ , the length of segment $AD$ is determined by this Pythagorean identity:

$AD = \sqrt{(3\,cm)^{2}+(5\,cm)^{2}+(4\,cm)^{2}}$

$AD \approx 7.071\,cm$

The angle ACD is determined by the following trigonometric expression:

$\cos C = \frac{AC}{CD}$

$\cos C = \frac{5.831\,cm}{7.071\,cm}$

$\cos C = 0.825$

$C = \cos^{-1} 0.825$

$C \approx 34.448^{\circ}$

The angle ACD is approximately 34.448º.

4 0

3 years ago

Rectangle LMNO is rotated 90° clockwise around the origin to create rectangle L'M'N'O'. Which statement would best describe the

mel-nik [20]

Answer:

Segment LL' and segment OO' are congruent (same length) and parallel (same inclination).

hope this helps! :)

Explanation:

The transformation described by the rule (x, y) → (x + 2, y + 2) is a translation two units to the right and two units up.

That means that, to create rectangle L'M'N'O', every point of the reactangle LMNO is translated the same amount in the same direction; thus, this is a rigid transformation where angles, lengths, size, shape, and orientation are kept.

Then a segment drawn from point L to L' will have the same length and the same orientation (inclination) of a segment drawn from the point O to O'. Thus, these two segments are parallel and congruent.

3 0

3 years ago

Please help me with this-

bija089 [108]

Answer and Step-by-step explanation:

Section the figure into two 3D shapes.

We get both figures to be a rectangular prism.

The Volume of a rectangular prism is length times width times height.

V (of top Rectangular Prism) = 2 × 2 × 4 = 16

V (of bottom Rectangular Prism) = 6 × 4 × 2 = 48

Now, we add those two volumes together to get the volume of the irregular figure.

16 + 48 = 64.

The volume of the irregular figure is 64 $cm^3$

#teamtrees #PAW (Plant And Water)

4 0

3 years ago

Michelle made 26 more sales calls last month than Allen. Together, they made 120 calls. How many calls were made by Michelle?

arlik [135]

Answer:

Step-by-step explanation: OK so Allena and micheal has 120 all together right

and micheal made 26 more right

So they had the same number but its changed when micheal made 26 more calls

so 120-26=73

so they both cant have 73

So we would divided 73 by 2

since its 2 of them

So its M=47 and A=47

than add the 26 calls to Michael

and it would be 73

and than you add 47 (when they say add them all together)

from allen

and get 120

so the answer is 73 calls by micheal.

7 0

3 years ago

Read 2 more answers

If each lap in a pool is 100 meters long, how many laps equal one mile? Round to the nearest tenth. (Hint: 1 foot ≈0.3048 meter)

aalyn [17]

If each lap in a pool is 100 meters long,how many laps equal one mile Round to the nearest tenth.(Hint:1 foot=0.3048 meter) 1 mile = 5280 ft lets do a ratio: 1ft/.3034m = x ft/100m the ft and meters sybols cancel, so 1/.3048 =x/100 so 100/.3038 = x = 329.164 so there are 329.164 ft for every 100 meters to find the number of laps to get to a mile which is 5280, do another ratio 329.164ft/100 m =5280 ft/xm the left side reduces to 3.29164 =5280/x you can compute this and see that 5280/3.29164 = 1604.064 meters 1604.064 meters *1 lap / 100m = 16.04064 laps are required to make a mile

7 0

3 years ago