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Bond [772]
3 years ago
15

27 30 33 36 identify d in this

Mathematics
1 answer:
alex41 [277]3 years ago
7 0

Answer:

d = 3

Step-by-step explanation:

d represents the common difference between consecutive terms in the sequence, that is

d = 30 - 27 = 33 - 30 = 36 - 33 = 3

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If
baherus [9]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Given: cos 330 = \frac{\sqrt3}{2}

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

\text{Scratchwork:}\quad \bigg(\dfrac{\sqrt3 + 2}{2\sqrt2}\bigg)^2 = \dfrac{2\sqrt3 + 4}{8}

Proof LHS → RHS:

LHS                          cos 165

Double-Angle:        cos (2 · 165) = 2 cos² 165 - 1

                             ⇒ cos 330 = 2 cos² 165 - 1

                             ⇒ 2 cos² 165  = cos 330 + 1

Given:                        2 \cos^2 165  = \dfrac{\sqrt3}{2} + 1

                              \rightarrow 2 \cos^2 165  = \dfrac{\sqrt3}{2} + \dfrac{2}{2}

Divide by 2:               \cos^2 165  = \dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \dfrac{2\sqrt3+4}{8}

Square root:             \sqrt{\cos^2 165}  = \sqrt{\dfrac{4+2\sqrt3}{8}}

Scratchwork:            \cos^2 165  = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2

                             \rightarrow \cos 165  = \pm \dfrac{\sqrt3+1}{2\sqrt2}

             Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

                             \rightarrow \cos 165  = - \dfrac{\sqrt3+1}{2\sqrt2}

LHS = RHS \checkmark

4 0
4 years ago
A recipe needs 4/5 cups of butter for every 2 cups of flour. If you plan to use 3 cups of flour, how much butter will you need?
DedPeter [7]

Answer:

1 1/5 cups of butter

Step-by-step explanation:

4/5=2

      =3

 4/5 x 3=12/5

12/5 / 2

12/5 x 1/2=1 1/5

7 0
3 years ago
Read 2 more answers
If f(x) = x^3 – 2x^2, which expression is equivalent to f(i)?
arsen [322]
I=√-1 and all the steps are there

6 0
4 years ago
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What is the slope of the two points given?
kvasek [131]
It is 7-7-77-8-7-7-7777-75a
3 0
3 years ago
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Points C and D are equidistant from point A. Complete the following table to prove that AEC≅ AED
inna [77]
To prove that <span>AEC≅ AED, we need to write following proofs or statement reasons.

It is given that points C and D are equidistant to point A. Hence,
</span><span>AD ≅ AC

Next, </span><span>CAE ≅ DAE. AE is the common side or the included side. 
</span><span>
Then, </span><span>AE ≅ EA by Reflexive Property of Congruence as it is congruent to itself.

Lastly, </span><span>EAD ≅ EAC by Symmetric Property of Congruence as these triangles are mirror image of each other.
</span>
Therefore, we can conclude that AEC≅ AED by SSS or Side-Side-Side. That is when all sides of triangles are congruent then both triangles are deemed to be equal.

3 0
3 years ago
Read 2 more answers
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