All categories

2 years ago

Simplify your answer as much as possible

Mathematics

1 answer:

Roman55 [17]2 years ago

8 0

You said - 1/3 - 3/5 x = 1/2

Multiply each side by 3 :

- 1 - 9/5 x = 3/2

Multiply each side by 5 :

- 5 - 9x = 15/2

Multiply each side by 2 :

- 10 - 18x = 15

Add 10 to each side :

- 18x = 25

Divide each side by -18 :

or x = - 1 and 7/18 (same thing)

You might be interested in

What is the measure in radians for the central angle of a circle whose radius is 9 cm and intercepted arc length is 7.2 cm? Ente

DaniilM [7]

Answer:

0.8

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

1. Judy took $30 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each ba

Pavel [41]

Answer:

Step-by-step explanation:

The relationship between the number of popcorn and drinks is linear relationshipThe responses are;(a) Please find attached the required graph created with MS Excel(b) From the graph, we have that as the number of bags of popcorn Judy buys increases, the number of drinks decreases linearlyReasons:The given parameter are;Amount Judy took with her to spend on popcorn and drinks = $30Price of each bag of popcorn = $5Price of each drink = Half the price of a bag of popcorn∴ The price of each drink = (a) Let X represent the number of bags of popcorn Judy buys and let Y represent the number of drinks she buys, we have;5·X + 2.5·Y = 302.5·Y = 30 - 5·XWhich gives;Y = 12 - 2·XUsing the above equation, the graph of popcorn and drinks bought by Judy is plotted with MS Excel and attached here(b) The data in the graph are presented as followsThe point corresponding to the y-intercept is the point that gives the maximum number of drinks Judy can buy if she does not buy popcorn is 12 drinks. The number of drinks she can buy reduces by 2 for each bag of popcorn she buys, such that she can buy 6 bags of popcorn and no drinks which is the x-intercept.

3 0

2 years ago

Read 2 more answers

PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS

nlexa [21]

Answer:

third option

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Cam is 3 years older than Lara, If there combined age is 63, determine their ages by solving simultaneous elmination.

dem82 [27]

Answer:

30 and 33 years

Step-by-step explanation:

Let Lara be x years

Cam =x+3

x+x+3=63

2x+3=63

2x=63-3

2x=60

x=60/2

x=30

Lara=30years and Cam =30+3+33years

5 0

3 years ago

Read 2 more answers

Explain the steps to finding the vertex of g(x) = 3x2 + 12x + 15

RUDIKE [14]

Answer:

The vertex of this parabola, $(-2, 3)$ , can be found by completing the square.

Step-by-step explanation:

The goal is to express this parabola in its vertex form:

$g(x) = a\, (x - h)^2 + k$ ,

where $a$ , $h$ , and $k$ are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at $(h,\, k)$ .

The vertex form can be expanded to obtain:

$\begin{aligned}g(x)&= a\, (x - h)^2 + k \\ &= a\, \left(x^2 - 2\, x\, h + h^2\right) + k = a\, x^2 - 2\, a\, h\, x + \left(a\,h^2 + k\right)\end{aligned}$ .

Compare that expression with the given equation of this parabola. The constant term, the coefficient for $x$ , and the coefficient for $x^2$ should all match accordingly. That is:

$\left\lbrace\begin{aligned}& a = 3 \\ & -2\,a\, h = 12 \\& a\, h^2 + k = 15\end{aligned}\right.$ .

The first equation implies that $a$ is equal to $3$ . Hence, replace the " $a\!$ " in the second equation with $3\!$ to eliminate $\! a$ :

$(-2\times 3)\, h = 12$ .

$h = -2$ .

Similarly, replace the " $a$ " and the " $h$ " in the third equation with $3$ and $(-2)$ , respectively:

$3 \times (-2)^2 + k = 15$ .

$k = 3$ .

Therefore, $g(x) = 3\, x^2 + 12\, x + 15$ would be equivalent to $g(x) = 3\, (x - (-2))^2 + 3$ . The vertex of this parabola would thus be:

$\begin{aligned}&(-2, \, 3)\\ &\phantom{(}\uparrow \phantom{,\,} \uparrow \phantom{)} \\ &\phantom{(}\; h \phantom{,\,} \;\;k\end{aligned}$ .

8 0

3 years ago