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Brut [27]
2 years ago
15

A local gas station is offering a deal to their customers. If they purchase an $8.00 car wash, the cost per gallon gas is $2.60.

Write and solve a linear equation to find how many gallons you can afford if you have $40.
Mathematics
1 answer:
Rina8888 [55]2 years ago
5 0

Answer:

y = 2.6x + 8

Plug 40 into y

40 = 2.6x + 8 and solve for x

x = 12.3 gallons

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Log(x-2)+log2=2logy<br>log(x-3y+3)=0​
In-s [12.5K]

Answer:

<h2>x = 4 and y = 2 or x = 10 and y = 4</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}\log(x-2)+\log2=2\log y&(1)\\\log(x-3y+3)=0&(2)\end{array}\right

===========================\\\text{DOMAIN:}\\\\x-2>0\to x>2\\y>0\\x-3y+3>0\to x-3y>-3\\=====================\\\\\text{We know:}\ \log_ab=c\iff a^c=b,\\\\\text{therefore}\ \log_ab=0\iff a^0=b\to b=1\\\\\text{From this we have}\\\\\log(x-3y+3)=0\iff x-3y+3=1\qquad\text{add}\ 3y\ \text{to both sides}\\\\x+3=3y+1\qquad\text{subtract 3 from both isdes}\\\\\boxed{x=3y-2}\qquad(*)\\\\\text{Substitute it to (1)}

\log(3y-2-2)+\log2=2\log(y)\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log(3y-4)+\log2=\log(y^2)\qquad\text{subtract}\ \log(y^2)\ \text{from both sides}\\\\\log(3y-4)+\log2-\log(y^2)=0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\ \text{and}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log\dfrac{(3y-4)(2)}{y^2}=0\qquad\text{use}\ \log_ab=0\Rightarrow b=1\\\\\dfrac{(3y-4)(2)}{y^2}=1\iff y^2=(3y-4)(2)\\\\\text{Use the distributive property}\ a(b+c)=ab+ac

y^2=(3y)(2)+(-4)(2)\\\\y^2=6y-8\qquad\text{subtract}\ 6y\ \text{from both sides}\\\\y^2-6y=-8\qquad\text{add 8 to both sides}\\\\y^2-6y+8=0\\\\y^2-2y-4y+8=0\\\\y(y-2)-4(y-2)=0\\\\(y-2)(y-4)=0\iff y-2=0\ \vee\ y-4=0\\\\\boxed{y=2\ \vee\ y=4}\in D

\text{Put the values of}\ y\ \text{to }\ (*):\\\\\text{for}\ y=2:\\\\x=3(2)-2\\\\x=6-2\\\\\boxed{x=4}\in D\\\\\text{for}\ y=4:\\\\x=3(4)-2\\\\x=12-2\\\\\boxed{x=10}\in D

4 0
2 years ago
Plz help I need help
suter [353]

Answer:

7q + 12

Step-by-step explanation:

simply arrange the given expressions into the traditional way of adding numbers like 1 + 1 but vertically like : 1

1 +

which is equivalent to

6q + 1 +

q + 11

______

7q + 12

why? because 6q plus q is equal to 7q and 1 + 11 is equal to 12

good day.

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arsen [322]

the right answer is 12 and if you ever need more help just use the app mathaway

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Fraction from or decimal form but has to be rounded
Alekssandra [29.7K]

Answer:

x = \frac{25}{6}

Step-by-step explanation:

Given expression is,

2x-\frac{11}{4}x=-\frac{25}{8}

\frac{8x}{4}-\frac{11}{4}x=-\frac{25}{8}

\frac{8x-11x}{4}=-\frac{25}{8}

-\frac{3x}{4}=-\frac{25}{8}

\frac{3x}{4}\times 4=\frac{25}{8}\times 4

3x=\frac{25}{2}

\frac{3x}{3}=\frac{25}{2}\times \frac{1}{3}

x = \frac{25}{6}

5 0
2 years ago
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