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2 years ago

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Roberto has $200 in spending money. He wants to buy some video games that cost $25.50 each. Write and solve an inequality to fin

d the number of games that Roberto can buy.

2 answers:

Mekhanik [1.2K]2 years ago

4 0

Step-by-step explanation: Each game is $25.50 which in math means it has an "x"

So if x=1 then 25.50x says that 1 video game is $25.50

Set up the equation:

200 = 25.50x (divide both sides by 25.50 to isolate the x)

200/25.50 = 7.84

x = 7.84

You can't have 0.84 of a video game, so Roberto can only buy 7 of them. The answer is correct good job!

Veseljchak [2.6K]2 years ago

3 0

Answer:

f(x) = 25.50x Roberto can buy 7 video games

Step-by-step explanation:

Each game is $25.50 which in math means it has an "x"

So if x=1 then 25.50x says that 1 video game is $25.50

Set up the equation:

200 = 25.50x (divide both sides by 25.50 to isolate the x)

200/25.50 = 7.84

x = 7.84

You can't have 0.84 of a video game, so Roberto can only buy 7 of them.

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<img src="https://tex.z-dn.net/?f=prove%20that%5C%20%20%5Ctextless%20%5C%20br%20%2F%5C%20%20%5Ctextgreater%20%5C%20%5Cfrac%20%7B

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

1 year ago

Which Two Numbers Add Up To Negative 26 And Multiply To 11?

Fynjy0 [20]

Xy=11
x+y=-26

x+y=-26
minus x both sides
y=-26-x

sub for y
x(-26-x)=11
-26x-x^2=11
add 26x+x^2 both sides
x^2+26x+11=0

ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

a=1
b=26
c=11

x= $\frac{-26+/-\sqrt{26^{2}-4(1)(11)} }{2(1)}$
x= $\frac{-26+/-\sqrt{676-44} }{2}$
x= $\frac{-26+/-\sqrt{632} }{2}$
x= $\frac{-26+/-2\sqrt{158} }{2}$
x= $-13+/-\sqrt{158}$

x= $-13+\sqrt{158}$ or $-13-\sqrt{158}$

aprox

x=-0.420195 or -25.5698

those are the numbers

5 0

2 years ago

Divide the fractions and simplify the answer 60 / 2 2/3

balu736 [363]

2 2/3 as a decimal is 2.66666667. 60 divided by 2.66666667 is 22.5.
As a fraction, the answer will be 22 5/10

Please mark my answer as the brainliest answer, I'd really appreciate it, thanks!

6 0

2 years ago

Read 2 more answers

Once again lol, plz help a dummy at mathhhh

USPshnik [31]

Answer:

1) x-axis 2) y-axis

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Lauren has a bouquet of flowers. 1/5 of the flowers are red. 3/10 of the flowers are white. The rest are yellow. Lauren’s bouque

ss7ja [257]

Answer:

36 flowers

Step-by-step explanation:

Given

$Red = \frac{1}{5}$

$White = \frac{3}{10}$

$Yellow = 18$

Required

Determine the number of flowers

First, we need to determine the fraction of flowers that are yellow;

$R + W + Y = 1$

$\frac{1}{5} + \frac{3}{10} + Y = 1$

$\frac{2+ 3}{10} + Y = 1$

$\frac{5}{10} + Y = 1$

$Y = 1 - \frac{5}{10}$

$Y = \frac{10 -5}{10}$

$Y = \frac{5}{10}$

$Y = \frac{1}{2}$

Let the number of flowers by N;

The yellow flowers can be represented as;

$18 = \frac{1}{2} * N$

Solve for N

$N = \frac{18 * 2}{1}$

$N = \frac{36}{1}$

$N = 36$

5 0

2 years ago