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3 years ago

8

Given that △DEF is a right triangle and that ∠E=90° with sides DE¯¯¯¯¯=3, DF¯¯¯¯¯=5, and FE¯¯¯¯¯=4, which ratio would be equal t

o sin(D)?

1 answer:

aniked [119]3 years ago

4 0

9514 1404 393

Answer:

sin(D) = 4/5

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation ...

Sin = Opposite/Hypotenuse

sin(D) = FE/DF

sin(D) = 4/5

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Kitty [74]

Answer:

no

Step-by-step explanation:

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3 years ago

Log16^*+log4^*+log2^*=7

ale4655 [162]

Answer:

$x = 16$

Step-by-step explanation:

Given

$log_{16}(x) + log_4(x) + log_2(x) = 7$

Required

Solve for x

$log_{16}(x) + log_4(x) + log_2(x) = 7$

Change base of 16 and base of 4 to base 2

$\frac{log_2(x)}{log_2(16)} + \frac{log_2(x)}{log_2(4)} + log_2(x) = 7$

Express 16 and 4 as 2^4 and 2^2 respectively

$\frac{log_2(x)}{log_2(2^4)} + \frac{log_2(x)}{log_2(2^2)} + log_2(x) = 7$

The above can be rewritten as:

$\frac{log_2(x)}{4log_22} + \frac{log_2(x)}{2log_22} + log_2(x) = 7$

$log_22 = 1$

So, we have:

$\frac{log_2(x)}{4*1} + \frac{log_2(x)}{2*1} + log_2(x) = 7$

$\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x) = 7$

Multiply through by 4

$4(\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x)) = 7 * 4$

$log_2(x) + 2}log_2(x) + 4log_2(x) = 28$

$7log_2(x) = 28$

Divide through by 7

$\frac{7log_2(x)}{7} = \frac{28}{7}$

$log_2(x) = 4$

Apply the following law of logarithm:

<em>If </em> $log_ab = c$ <em> </em><em>Then </em> $b = a^c$ <em></em>

So, we have:

$x = 2^4$

$x = 16$

6 0

3 years ago

Raymond claims that 55 * 52 = 53. Rose argues that 55 * 52 = 5'.

boyakko [2]

Answer:

Step-by-step explanation:

8. Harry, Louis and Niall are working with exponents. Harry claims 4

2

∙ 4

5 = 4

10

. Louis

claims 4

2

∙ 4

5 = 4

7

. Niall claims 4

2

∙ 4

5 = 167

. Which student has the correct answer?

Explain why.

9. Raymond and Rose were working with exponents.

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4 years ago

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Shtirlitz [24]

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3 years ago

Read 2 more answers

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astra-53 [7]

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For reference, the absolute value of -20 is also just 20.

Hope the explanation helps :)

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3 years ago

Read 2 more answers