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3 years ago

13

Javier is cooling a liquid in a science lab. The liquid starts at 85 degrees, and he cools it 3.5 degrees every minute for 12 mi

nutes. Create a number sentence to model this scenario.

1 answer:

bija089 [108]3 years ago

7 0

85- (3.5*12)

* means times

I think this is correct.

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Solve The Equation <br> 4x×9y=7<br> 4x-9y=9

hoa [83]

Answer:

$\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$(4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}$

$4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}$

8 0

3 years ago

What is the domain of the square root function graphed below?

Nikolay [14]

The domain of a function is the set of all values x can have.
From the graph, we see the least value of x is 3. x can be any value greater than or equal to 3.

The domain is

$x \ge 3$

5 0

4 years ago

(picture included) brainliest

Temka [501]

The answer is 2.5 (B)

4 0

3 years ago

passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to ?

goblinko [34]

Answer:

Equation of line , 5x + 3y = 0

Step-by-step explanation:

The slope of a line passing through points (x₁,y₁) and (x₂,y₂) is given by $\frac{y_2-y_1}{x_2-x_1}$

Here points are given by (-3,0) and (-6,5)

Slope $=\frac{5-0}{(-6)-(-3)}=\frac{-5}{3}$

The slope of parallel lines are same. So slope of required line $=\frac{-5}{3}$

Equation of a line with slope m passing through origin is given by

y =mx

So equation of line, $y=\frac{-5}{3}x\\\\3y=-5x\\\\5x+3y=0$

Equation of line , 5x + 3y = 0

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3 years ago

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Find the missing length for a right triangle with hypotenuse of 18 and a leg length of 6

yaroslaw [1]

$\sqrt{18^2-6^2}$
$\sqrt{256-36} = \sqrt{220} = 2 \sqrt{55}$

4 0

3 years ago

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