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2 years ago

Quinn is playing video games at a virtual reality game room. The game room charges 20 dollars for every 30 minutes of play time.

Mathematics

2 answers:

bija089 [108]2 years ago

8 0

Answer:

Step-by-step explanation:

20 dollars for 30 minutes

you want to find out

_____ dollars for 150 minutes

150/30=5

20 x 5= 100

she needs 100 dollars

Colt1911 [192]2 years ago

5 0

Answer:

3000$

Step-by-step explanation:

20 x 150=3000

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Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

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3 years ago

Using the information given, select the correct ending balance.

klemol [59]

Step-by-step explanation:

Simple first we will add previous balance and total deposit

498.03 + 604.28

= 1102. 31

Then we will subtract it by total withdrawals

1102.31 - 599.49

= 502. 82

The ending balance is 502.82

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2 years ago

Multiply using the distributive property

ludmilkaskok [199]

What grade is that is that 4th or 5th grade

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2 years ago

Math<br><br><br> is my answer correct??

matrenka [14]

$▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪$

Here's the solution ~

The given points are : (-7 , -4) and (1 , 1)

now, let's use distance formula to find the distance between them !

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:\sqrt{(x_2 - x_1)² +( y_2 - y_1)² }$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: \sqrt{( - 7 - 1) {}^{2} + ( - 4 - 1) {}^{2} }$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: \sqrt{( - 8)² +( - 5)² }$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: \sqrt{64 + 25}$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: \sqrt{89}$

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2 years ago

2rods whose length are 21 cm & 14cm are to be cut length equal

Allushta [10]

7cm each. reason: the rod of 21cm lenght will be cut into 3pieces of 7cm each, while that of 14cm will be cut into 2 pieces of 7cm each. Therefore, there 5 pieces of rods of 7cm each. Thanks.

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3 years ago