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2 years ago

Turn 25/4 into a mixed number

Mathematics

1 answer:

horsena [70]2 years ago

3 0

Mixed number is 6 1/4

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inysia [295]

$\large \bigstar \frak{ } \large\underline{\sf{Solution-}}$

Consider, LHS

$\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} \\ \\ \text{So, using this identity, we get} \\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered} \\$

So, using this identity, we get

$\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

can be rewritten as

$\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}$

<h2>Hence,</h2>

$\begin{gathered} \\ \rm\implies \:\boxed{\sf{ \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}$

$\rule{190pt}{2pt}$

5 0

2 years ago

A cashier has 26 bills consisting of three times as many ones as fives, one less ten than fives, and the rest twenties. If the v

monitta

Let number of fives = x then number of ones = 3x and number of tens = x - 1

so we can create the equation

x + 3x + x-1 + y = 26 where y = number of twenties
so
5x + y = 27

also we have the equation

5x + 3x + 10(x - 1) + 20y = 120

18x + 20y = 130..................................(1)
5x + y = 27 multiply by -20:-
-100x - 20y = -540..............................(2)
Adding equation (1) and (2)
-82x = -410
x = 5, that is 5 fives

Now plug x = 5 into equation 1:-
18(5) + 20y = 130
20y = 40
y = 2 , that is 2 twenties

So the answer is there are (3x) = 15 ones , 5 fives, 4 tens and 2 twenties

7 0

3 years ago

(-16) - (+12) + (-୨)

Nesterboy [21]

Answer:

-37

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Lindsey's goal is to sell at least 35 candles at each of 15 craft fairs. She makes 24 candles each day for 20 days. Use the drop

valina [46]

Answer:

D.Lindsay makes 480 candles. She divides 480 by 15 to get 32. She does not make enough candles.

Step-by-step explanation:

The explanation of the sufficient candles that are required to check whether she reach her goal or not is as follows:

She makes 480 candles that come from

= 24 candles each days × 20 days

= 480 candles

Now if we divide the 480 candles from 15 so we get 32

This is less than the minimum candles required i.e. 35

So, the option D is correct

7 0

2 years ago

To attend the class field trip, 24 students brought their permission slips.

mario62 [17]

Answer:

There are 30 students in the class

Step-by-step explanation:

we can write a ratio as:

8:10 as 24:x

Writing this as an equation gives:

We can now solve for

while keeping the equation balanced:

240

x = 30

7 0

2 years ago

Read 2 more answers