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Shalnov [3]
3 years ago
13

1.)The original price of a pair of shoes is $29.95. The shoes are on sale for 30% off. Which expression would calculate the sale

price of the shoes?
Question 1 options:

29.95 – 0.30


0.70(29.95)


29.95 – 0.70


0.30(29.95)

2.) A lawn mower is on sale for $284.99 before sales tax. Georgia state sales tax is 4%. Which equation could be used to find the total cost (c) of the mower?

Question 2 options:

0.04(284.99)= c


1.04c = 284.99


1.04(284.99)= c


0.04c = 284.99

3.) All coats are on sale for 25% off the original price. Michael is buying a coat that is originally priced at $49. Sales tax is 6%. Which expression would calculate the final price of a coat?

Question 3 options:

49(0.25)(0.06)


49(0.75)(1.06)


49(0.25)(1.06)


49(0.75)(0.06)

4.) To rent a moving truck, Jennifer must pay a fee of $35.00 per day (d), then $0.80 for each mile driven (m). Which expression could be used to find the total cost to rent a moving truck for d days and driving the truck m miles?

Question 4 options:

0.80m + 35d


35 + 0.80m


0.80d + 35


35.80dm

5.) Erin earns a 12% commission on the furniture she sells. On Monday, she sold $4,500 worth of furniture. Which expression could Erin use to calculate the amount of money she earned?

Question 5 options:

4,500(0.12)


4,500(1.12)


4,500(0.88)
Mathematics
1 answer:
LekaFEV [45]3 years ago
4 0
1. 0.7(29.95)
2. 1.04(284.99)
3. 49(0.75)(1.06)
4. 35+ 0.80m
5. 4500 (1.12)

Hope this helps!
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Answer: C . 147π / 4 mi²

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<u>Given variable</u>

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<u>Given formula</u>

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4 0
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Cos ( α ) = √ 6/ 6 and sin ( β ) = √ 2/4 . Find tan ( α − β )
Zina [86]

Answer:

\purple{ \bold{ \tan( \alpha  -  \beta ) = 1.00701798}}

Step-by-step explanation:

\cos( \alpha ) =  \frac{ \sqrt{6} }{6}  =  \frac{1}{ \sqrt{6} }  \\  \\  \therefore \:  \sin( \alpha )  =  \sqrt{1 -  { \cos}^{2} ( \alpha ) }  \\  \\  =  \sqrt{1 -  \bigg( {\frac{1}{ \sqrt{6} } \bigg )}^{2} }  \\  \\ =  \sqrt{1 -  {\frac{1}{ {6} }}}  \\  \\ =  \sqrt{ {\frac{6 - 1}{ {6} }}}   \\  \\  \red{\sin( \alpha ) =  \sqrt{ { \frac{5}{ {6} }}} } \\  \\  \tan( \alpha ) =  \frac{\sin( \alpha ) }{\cos( \alpha ) }  =  \sqrt{5}  \\  \\ \sin( \beta )  =  \frac{ \sqrt{2} }{4}  \\  \\  \implies \: \cos( \beta )  =   \sqrt{ \frac{7}{8} }  \\  \\ \tan( \beta )  =  \frac{\sin( \beta ) }{\cos( \beta ) } =  \frac{1}{ \sqrt{7} }   \\  \\  \tan( \alpha  -  \beta ) =  \frac{ \tan \alpha  -  \tan \beta }{1 +  \tan \alpha .  \tan \beta}  \\  \\  =  \frac{ \sqrt{5} -  \frac{1}{ \sqrt{7} }  }{1 +  \sqrt{5} . \frac{1}{ \sqrt{7} } }  \\  \\  =  \frac{ \sqrt{35} - 1 }{ \sqrt{7}  +  \sqrt{5} }  \\  \\  \purple{ \bold{ \tan( \alpha  -  \beta ) = 1.00701798}}

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