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OverLord2011 [107]

2 years ago

5

The price of the bicycle that someone wants to buy is $282. How much will they pay for the bicycle, in total, if the sales tax i

s 4%? *

1 answer:

andrezito [222]2 years ago

7 0

Answer:

$293.28

Step-by-step explanation:

282 increase 4% =

282 × (1 + 4%) = 282 × (1 + 0.04) = 293.28

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URGENT HELP PLEASE!

Vaselesa [24]

Answer:

(a) $x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}$

(b) $x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}$

Step-by-step explanation:

It is given that $0\leq x\leq 2\pi$ .

(a)

$\sqrt{2}\sin 2x=1$

$\sin 2x=\dfrac{1}{\sqrt{2}}$

$\sin 2x=\dfrac{\pi}{4}$

$2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}$ $[\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]$

$x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}$

(b)

$\csc^2 x-\csc x-2=0$

$\csc^2 x-2\csc x+\csc x-2=0$

$\csc x(\csc x-2)+1(\csc x-2)=0$

$(\csc x+1)(\csc x-2)=0$

$\csc x=-1\text{ or }\csc x=2$

$\sin x=-1\text{ or }\sin x=\dfrac{1}{2}$ $[\because \sin x=\dfrac{1}{\csc x}]$

$x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}$

Therefore, $x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}$ .

5 0

2 years ago

if you were asked to express the weight in ounces of a ladybug in scientific notation, would the exponent of the 10 be positive

Nat2105 [25]

The <em><u>correct answer</u></em> is:

Negative.

Explanation:

Scientific notation is used to express very small or very large numbers.

Very small numbers are written in scientific notation using negative exponents.

Very large numbers are written in scientific notation using positive exponents.

Since a ladybug is very small, we would use the very small scientific notation, which uses negative exponents.

8 1

3 years ago

Read 2 more answers

5c+4(dt6c) HELP ME !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

inysia [295]

The answer is 5c+24ctd

3 0

2 years ago

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The picture frames shown are both squares. The area of the smaller frame is 1/4 the area of the larger frame. Find the side leng

baherus [9]

Area of smaller frame =1/4×36=9sq.in
side of smaller frame =
$\sqrt{9 } = 3in$
side of larger frame
$= \sqrt{36} = 6in$

4 0

3 years ago

Solve the equation 2cosA = 3tanA

zavuch27 [327]

$\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)
\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\\\\
-----------------------------\\\\

2cos(A)=3tan(A)\implies 2cos(A)=3\cfrac{sin(A)}{cos(A)}
\\\\\\
2cos^2(A)=3sin(A)\implies 2[1-sin^2(A)]=3sin(A)
\\\\\\
2-2sin^2(A)=3sin(A)\implies 2sin^2(A)+3sin(A)-2$

$\bf \\\\\\
0=[2sin(A)-1][sin(A)+2]\implies 
\begin{cases}
0=2sin(A)-1\\
1=2sin(A)\\
\frac{1}{2}=sin(A)\\\\
sin^{-1}\left( \frac{1}{2} \right)=\measuredangle A\\\\
\frac{\pi }{6},\frac{5\pi }{6}\\
----------\\
0=sin(A)+2\\
-2=sin(A)
\end{cases}$

now, as far as the second case....well, sine of anything is within the range of -1 or 1, so -1 < sin(A) < 1

now, we have -2 = sin(A), which simply is out of range for a valid sine, so there's no angle with such sine

so, only the first case are the valid angles for A

8 0

2 years ago