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vichka [17]
2 years ago
9

You buy a bicycle helmet for $22.26, which includes 6% sales tax. The helmet is discounted 30% off the selling price. What is th

e original price?
Mathematics
2 answers:
schepotkina [342]2 years ago
8 0
Final cost/1.06 = sale price

\frac{22.26}{1.06} = 21.06

The sales price is $21.06

Sales price/.70 (70% of the original price) = original price

\frac{21.06}{.70} = 30.09

The original price of the helmet was $30.09
Korvikt [17]2 years ago
7 0
6% de 22,26 = 
6*22,26/100 = 
1,3356
22,26 - 1,3356 = 20,9244
70% de 20,9244 = 
70*20,9244/100 = 
14,64708 ~ 14,64
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Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D
Ivahew [28]
Check the picture below.

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\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\
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\begin{cases}
d=10\\
e=18\\
f=22
\end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D

\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D

7 0
3 years ago
NEED ANSWERED ASAP PLEASE<br> sin(0)= -4 sqrt 29 / 29
VladimirAG [237]

Answer:

Is - 4

Step-by-step explanation:

29/29  cancel it out

so it will leave -4 out

3 0
3 years ago
Which function has a removable discontinuity?
sweet-ann [11.9K]
"f(x)=(5x)/(x-x²)" is the one function among the following choices given in the question that <span>has a removable discontinuity. The correct option among all the options that are given in the question is the third option or option "C". It is the only function having a term cancelling out each other at the top and the bottom. </span>
5 0
3 years ago
which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!​
coldgirl [10]

9514 1404 393

Answer:

  (a) -(x+7)/y

  (b) (x+7)/-y

Step-by-step explanation:

There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.

The given expression with -1 factored out is ...

  \dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}

Likewise, the expression of (b) with the minus sign factored out is ...

  \dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}

On the other hand, simplifying expression (c) gives something different.

  \dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}

__

Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).

  Given: (-x-7)/y = (-x/y) +(-7/y)

  (a) -(x+7)/y = (-x/y) +(-7/y)

  (b) (x+7)/(-y) = (-x/y) +(-7/y)

  (c) (-x-7)/(-y) = (x/y) +(7/y) . . . . not the same.

__

Of course, you need to know the use of the distributive property and the rules of signs.

  a(b+c) = ab +ac

  -a/b = a/(-b) = -(a/b)

  -a/(-b) = a/b

__

<u>Summary</u>: The given expression matches (a) and (b).

_____

<em>Additional comments</em>

Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...

  \left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0

Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.

The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.

(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given

(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given

(c) evaluates to (-1-7)/-2 = 4, different from given

3 0
2 years ago
8)Reduce a las unidades indicadas: a)18 cm 3 a dm 3
lys-0071 [83]

Answer:

(a) 0.018 dm^3

(b) 20 x 10^15 ml^3

Step-by-step explanation:

a) 18 cm^3 to dm^3

1 cm = 0.1 dm

So,

1 cm^3 = 0.001 dm^3

So, 18 cm^3 = 18 x 0.001 dm^3 = 0.018 dm^3

b) 20 hl^3 to ml^3

1 hl = 100000 ml

So, 1 hl^3 = 10^15 ml^3

So,

20  hl^3 = 20 x 10^15 ml^3.  

7 0
2 years ago
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