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3 years ago

13

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −6y2 − 9y = −1

1 answer:

Tomtit [17]3 years ago

8 0

$-6y^2 - 9y = -1$

$y= \dfrac{-9+ \sqrt{9^2-4*-6} }{2*6}, \dfrac{-9-\sqrt{9^2-4*-6}}{2*6}$

$y= \dfrac{-9+ \sqrt{105} }{12}, \dfrac{-9- \sqrt{105} }{12}$

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A chemical manufacturer wishes to obtain 700 litres of a 24% acid solution by mixing a 40% acid solution with a 15% solution. Ho

vekshin1

00 x 0.24 = a x 0.40 + ( 700 -a ) x 0.15 = 0.40 a - 0.15 a + 105.00
<span>168.00 = 0.25a + 105.00 </span>
<span>a = 252 </span>
<span>Solution with 40% ....................252 liters........................ans </span>

<span>Solution with 15 % ...................700 - 252= 448 liters.........................ans</span>

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3 years ago

Lucy went to Chik Fil A. She bought a meal that cost $9.27. If the tax rate is 6% how

borishaifa [10]

Answer:

$9.83

Step-by-step explanation:

Tax= 6% of 9.27

$=\frac{6}{100}*9.27\\\\=\frac{55.62}{100}\\\\=0.5562$

Amount paid by her = 9.27 + 0.5562 = 9.8262 = $9.83

4 0

3 years ago

(x-3y+ 3z=-4<br><br> 2x+3y-z =15<br><br> (4x-3y- z=19<br><br> - What is the solution to the system?

lesya [120]

Answer:

x=5,y=1 and z=-2

Step-by-step explanation:

We are given that system of equation

$x-3y+3z=-4$ (I equation)

$2x+3y-z=15$ (II equation )

$4x-3y-z=19$ (III equation )

Equation II multiply by 3 then add with equation I

Then, we get

$7x+6y=41$ ....(Equation IV)

Subtract equation II from equation III then we get

$2x-6y=4$ (equation V)

Adding equation IV and equation V then, we get

$9x=45$

$x=5$

Substitute x=5 in equation V then, we get

$2(5)-6y=4$

$10-6y=4$

$6y=10-4=6$

$y=1$

Substitute x=5 and y=1 in equation then, we get

$5-3(1)+3z=-4$

$2+3z=-4$

$3z=-4-2=-6$

$z=\frac{-6}{3}=-2$

Hence, the solution for the given system of equation is given by

x=5,y=1 and z=-2

7 0

3 years ago

Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = ta

Irina-Kira [14]

Answer:

The inner function is $u = \pi x$ .

The outer function is $f(u) = \tan{u}$ .

$\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}$

Step-by-step explanation:

The inner function is the one we apply the outer function to.

So

$y = \tan{\pi x}$

We apply the outer function tangent to $\pi x$ .

So, the inner function is $u = \pi x$ .

The outer function is $f(u) = \tan{u}$ .

The derivative of a compositve function

$y = f(u)$ in which $u = g(x)$ is given by the following function.

$y^{\prime} = f^{\prime}(u)*g^{\prime}(x)$

So

$f(u) = \tan{u}$

$f^{\prime}(u) = \sec^{2}{u}$

$u = g(x) = \pi x$

$g^{\prime}(x) = \pi$

So

$y^{\prime} = f^{\prime}(u)*g^{\prime}(x)$

$\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}$

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Archy [21]

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3 years ago