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AVprozaik [17]
3 years ago
14

What is a solution to 4x+6<(with a line under it ) 18

Mathematics
1 answer:
JulsSmile [24]3 years ago
7 0

Answer:

\textbf{$x \in (-\infty, 3] $}\\

Step-by-step explanation:

\textup{Given:}\\$ 4x + 6 $\textup{Subtracting $6$ from both the sides }\\$ 4x \leq 18 - 6 \hspace{5mm} (=12) $\\\textup{Dividing by $4$ on both the sides: \hspace{15mm} [Note that the sign of the inequality changes only when we divide it by a negative number]}\\$$ x \leq 3 $$\\\textup{$x$ can be any real number less than or equal to 3.}\\$ \iff x \in R^- \cup \{a : 0 \leq a \leq 3\} $

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Considere a função de oferta como sendo y= 5x - 1/2 e a função de demanda como sendo y= -7x + 47/2 , onde x é a quantidade e y é
swat32

A) Temos que igualar isso a 2,50, que é o valor de y, ou seja, o valor do preço. Façamos isso, então, na função de demanda.

y = -7x + \frac{47}{2}

Substituir.

2,50 = - 7x + \frac{47}{2}

Passar o que é x de um lado e o que é número do outro lado.

-7x  = - \frac{47}{2} + 2,50

A fração 47/2 corresponde a 23,5. É mais interessante para nós, nesse caso, utilizar o valor decimal.

-7x  = - 23,5 + 2,50

Somar logo.

-7x = -21

Podemos multiplicar por -1 para tirar os sinais negativos.

7x = 21

Passar o x dividindo

x = \frac{21}{7}

Dividir

\boxed{x = 3}

Para um preço de R$ 2,50, a quantidade demandada é de 3 unidades.



B) Basta igualar as duas formulinhas.

5x - \frac{1}{2} = -7x + \frac{47}{2}

Passar o que é x de um lado e o que é número do outro lado.

5x + 7x = \frac{47}{2} + \frac{1}{2}

Somar tudo. Como as frações têm o mesmo denominador, <u>nada de </u><u>mmc</u>! Basta somar os numeradores.

12x = \frac{48}{2}

Podemos dividir lá, olha:

12x = 24

Passar o x dividindo

x = \frac{24}{12}

Dividir

\boxed{x = 2}

O ponto de equilíbrio é o valor 2.



C) Basta, então, igualar as fórmulas da oferta e da demanda a 10.

Fórmula da oferta

10 = 5x - \frac{1}{2}

Passar o que é x de um lado e o que é número do outro lado.

5x = 10 - \frac{1}{2}

Se 1/2 = 0,5, dá pra resolver sem fazer mmc:

5x = 10 - 0,5

Subtrair

5x = 9,5

Passar dividindo

x = \frac{9,5}{5}

Dividir.

\boxed{x = 1,9}

Fórmula da demanda

10 = -7x + \frac{47}{2}

Passar o que é x de um lado e o que é número do outro lado.

-7x = \frac{47}{2} - 10

Divide 47/2, vai.

-7x = 23,5 - 10

Subtrair.

-7x = 13,5

Passar o 7 dividindo.

x = - \frac{13,5}{7}

Vamos dividir e transformar em decimal.

\boxed{x = -1,9285714285714285714285714285714}


Subtrair a oferta pela demanda.

x = 1,9 - (-1,9285714285714285714285714285714)

Subtrair.

\boxed{x = 3,8285714285714285714285714285714}

Arredondando, o preço será de R$ 3,83.

8 0
3 years ago
Jerald jumped from a bungee tower. If the equation that models his height, in feet, is h = –16t2 + 729, where t is the time in s
Snezhnost [94]

Answer. First option: t > 6.25


Solution:

Height (in feet): h=-16t^2+729

For which interval of time is h less than 104 feet above the ground?

h < 104

Replacing h for -16t^2+729

-16t^2+729 < 104

Solving for h: Subtracting 729 both sides of the inequality:

-16t^2+729-729 < 104-729

-16t^2 < -625

Multiplying the inequality by -1:

(-1)(-16t^2 < -625)

16t^2 > 625

Dividing both sides of the inequality by 16:

16t^2/16 > 625/16

t^2 > 39.0625

Replacing t^2 by [ Absolute value (t) ]^2:

[ Absolute value (t) ]^2 > 39.0625

Square root both sides of the inequality:

sqrt { [ Absolute value (t) ]^2 } > sqrt (39.0625)

Absolute value (t) > 6.25

t < -6.25 or t > 6.25, but t can not be negative, then the solution is:

t > 6.25



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The values of x and y vary directly
ss7ja [257]

Answer:

y = (1/4)x

Step-by-step explanation:

"Direct variation" here signifies y = kx, where k is the constant of proportionality.

Then y = kx.  Here we are to find k using the info that x = 12 and y = 3:

3 = k(12), or

k = 3/12, or k = 1/4

Then y = (1/4)x

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3 years ago
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help I will fail math class please help doors for the small cabinets are 11.5 inches long . doors for the large cabinet are 2.3
VARVARA [1.3K]
11.5 * 2.3 = large door size
large door size / 12 = large door size in feet
large door size in feet / 10 = how many large doors can be cut from the board. (you have to round it down if there's a decimal- no 1/2 doors.)
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Oliver works 5 days a week. He drives 53 kilometres each day and walks a total of 25 kilometres over the week: He uses the follo
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I think it’s 36 but I’m not good at math so don’t count me on it
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