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3 years ago

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Simplify the expression 49

2} " alt=" \frac{1}{2} " align="absmiddle" class="latex-formula">

1 answer:

dimaraw [331]3 years ago

8 0

To convert a mixed fraction into an improper fraction:

$a\frac{b}{c} =\frac{(a\cdot c)+b}{c}$

$49 \frac{1}{2} = \frac{(49\cdot 2)+1}{2} = \frac{98 +1}{2} = \boxed{\bf{\frac{99}{2}}}$

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Log 15 (2x − 2) = log 15 (x+9)

notka56 [123]

Answer:

$x=11$

Step-by-step explanation:

Given the equation

$\log_{15}(2x-2)=\log_{15}(x+9)$

Note that

$2x-2>0\\ \\2x>2\\ \\x>1$

and

$x+9>0\\ \\x>-9$

Combined, $x>1$

Solve the equation:

$2x-2= x+9\\ \\2x-x=9+2\\ \\x=11$

Since $11>1,$ this is the solution to the equation.

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3 years ago

Directions: Find the indicated trigonometric ratio as a fraction in simplest form. 1. Sin L =

Rainbow [258]

Answer:

$\sin L = 0.60$

$tan\ N = 1.33$

$\cos L = 0.80$

$\sin N = 0.80$

Step-by-step explanation:

Given

See attachment

From the attachment, we have:

$MN = 6$

$LN = 10$

First, we need to calculate length LM,

Using Pythagoras theorem:

$LN^2 = MN^2 + LM^2$

$10^2 = 6^2 + LM^2$

$100 = 36 + LM^2$

Collect Like Terms

$LM^2 = 100 - 36$

$LM^2 = 64$

$LM = 8$

Solving (a): $\sin L$

$\sin L = \frac{Opposite}{Hypotenuse}$

$\sin L = \frac{MN}{LN}$

Substitute values for MN and LN

$\sin L = \frac{6}{10}$

$\sin L = 0.60$

Solving (b): $tan\ N$

$tan\ N = \frac{Opposite}{Adjacent}$

$tan\ N = \frac{LM}{MN}$

Substitute values for LM and MN

$tan\ N = \frac{8}{6}$

$tan\ N = 1.33$

Solving (c): $\cos L$

$\cos L = \frac{Adjacent}{Hypotenuse}$

$\cos L = \frac{LM}{LN}$

Substitute values for LN and LM

$\cos L = \frac{8}{10}$

$\cos L = 0.80$

Solving (d): $\sin N$

$\sin N = \frac{Opposite}{Hypotenuse}$

$\sin N = \frac{LM}{LN}$

Substitute values for LM and LN

$\sin N = \frac{8}{10}$

$\sin N = 0.80$

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3 years ago

Blaine buys 2 books and the total cost is $24.18. What is the constant of proportionality that relates the cost in dollars, y, t

cestrela7 [59]

Answer:

$ 12.09

Step-by-step explanation:

formula Y = KX

Where; y = $ 24.18

x = 2 books

k = constant of proportionality

Step 1. Do the equation based on the formula

Y = kx

$24.18 = k2

Step 2. Divide by 2

$24.18/2 = k2/2

k = $12.09 (answer)

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Answer

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Step-by-step explanation:

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2 years ago

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