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Alex17521 [72]
2 years ago
14

Determine if the three side lengths given can create a triangle or not. Prove it by working out the inequality.

Mathematics
1 answer:
Soloha48 [4]2 years ago
7 0

Hello, I Am BrotherEye

Answer:

A. Yes a triangle can be constucted

Step-by-step explanation:

All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle.

~

BrotherEye

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Given that tan^2 theta=3/8,what is the value of sec theta?
algol [13]

Answer:

The value of SecФ is  \pm \sqrt{\frac{11}{8}} .

Step-by-step explanation:

Given as for trigonometric function :

tan²Ф = \frac{3}{8}

Or, tanФ = \sqrt{\frac{3}{8} }

∵ tanФ = \frac{Perpendicular}{Base}

So,  \frac{Perpendicular}{Base} =  \sqrt{\frac{3}{8} }

So, Hypotenuse² = perpendicular² + base²

or, Hypotenuse² = ( \sqrt{3} )² + ( \sqrt{8} )²

Or,  Hypotenuse² = 3 + 8 = 11

Or,  Hypotenuse = ( \sqrt{11} )

Now SecФ = \frac{Hypotenuse}{Base}

or, SecФ = \frac{\sqrt{11}}{\sqrt{8}} = \sqrt{\frac{11}{8} }

<u>Second Method</u>

Sec²Ф - tan²Ф = 1

Or, Sec²Ф = 1 +  tan²Ф

or, Sec²Ф = 1 +  \frac{3}{8}

Or, Sec²Ф = \frac{11}{8}

Or,  SecФ = \pm \sqrt{\frac{11}{8}}

Hence The value of SecФ is  \pm \sqrt{\frac{11}{8}} . Answer

7 0
3 years ago
Read 2 more answers
Clare subscribes to an online music streaming service
xeze [42]

Answer:

She should go with service 2 because it is, cheaper. Service 1 cost $107.52, but service 2 cost only $105.

Step-by-step explanation:

Cost now+increase$=new cost

(Part=percent*whole)

Increase=percent increase*cost now

i=12%*$96

i=0.12*96=$11.52

$96+11.52=107.52

Service two⬇️

8.72*12=$105

5 0
2 years ago
How many grams are in 8 kilograms?
shutvik [7]
I believe it is 8,000 grams :).
5 0
2 years ago
A. [4 marks]
storchak [24]

The value of d is -2

Step-by-step explanation:

The nth term of the arithmetic sequence is u_{n}=u_{1}+(n-1)d , where

  • u_{1} is the first term
  • d is the common difference between each 2 consecutive terms

The nth term of the geometric sequence is u_{n}=u_{1}r^{n-1} , where

  • u_{1} is the first term
  • r is the common ratio between each two consecutive terms r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}

∵ u_{1} of an arithmetic sequence is 1

∵ The common difference is d, where d ≠ 0

∵ u_{2} , u_{3} , u_{6} are the first 3 terms of a geometric sequence

∵ u_{2} = 1 + (2 - 1)d

∴ u_{2} = 1 + d

∵ u_{3} = 1 + (3 - 1)d

∴ u_{2} = 1 + 2d

∵ u_{6} = 1 + (6 - 1)d

∴ u_{2} = 1 + 5d

∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,

   (1 + 5d)

∵ The common ratio in the geometric sequence is r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}

∴ r=\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}

- Use cross multiplication with the equal fractions

∵ \frac{1+2d}{1+d}=\frac{1+5d}{1+2d}

∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)

∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²

- Add like terms in each side

∴ 1 + 4d + 4d² = 1 + 6d + 5d²

- Subtract 1 from both sides

∴ 4d + 4d² = 6d + 5d²

- Subtract 4d from both sides

∴ 4d² = 2d + 5d²

- Subtract 4d² from each side

∴ 0 = 2d + d²

- Take d as a common factor

∴ 0 = d(2 + d)

- Equate each factor by 0

∴ d = 0 but we will reject it because d ≠ 0

∴ 2 + d = 0

- Subtract 2 from both sides

∴ d = -2

The value of d is -2

Learn more:

You can learn more about the sequence in brainly.com/question/1522572

#LearnwithBrainly

7 0
3 years ago
Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed StartFraction 4 over 17 End
IgorC [24]

Answer:

\approx \frac{11}{40}

Step-by-step explanation:

Juice squeezed from first orange = \frac{4}{17} = 0.235

Juice squeezed from second orange = \frac{3}{10} = 0.3

Juice squeezed from third orange = \frac{9}{20} = 0.45

Juice squeezed from fourth orange = \frac{3}{11} = 0.27

Juice squeezed from fifth orange = \frac{7}{15} = 0.47

Total juice squeezed from all the five oranges = 0.235 + 0.3 + 0.45 + 0.27 + 0.47 = 1.725

Total juice to be squeezed = 2 cups

More juice required = 2 - 1.725 = 0.275 \approx \frac{11}{40}

Therefore, to make it 2 cups of orange juice for the family, about \approx \frac{11}{40} cups of more juice is required.

8 0
3 years ago
Read 2 more answers
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