How many 3-person committees can be formed in a club with 8 members??

Which equation represents a line which is parallel to the line<br> X + 6y = -24?

horrorfan [7]

Answer:

y = -(1/6)x - 6

Step-by-step explanation:

slope intercept form is

y = mx + b

m is the slope

b is the y-intercept

---------------------------

x + 6y = -24

Subtract x from both sides

6y = -x - 24

Divide both sides by 6

y = -(1/6)x - 4

slope = -1/6

-----------------------------

Parallel lines have the same slope

therefor the parallel line is

y = -(1/6)x - 6

7 0

2 years ago

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalen

lyudmila [28]

x=-9-4y

substitute

2(-9-4y)+5y=-6

-18-8y+5y=-6

-18-3y=-6

-3y=-6+18

-3y=12

-3y÷-3= 12÷-3

y=-4

4 0

3 years ago

One solution to the problem below is 5. What is the other solution? c^2 - 25 = 0

topjm [15]

Answer:

c = -5

Step-by-step explanation:

Plug in -5 to c in the equation:

c² - 25 = 0

(-5)² - 25 = 0

Simplify. First, solve the power, then solve the subtraction:

(-5)² - 25 = 0

(-5 * -5) - 25 = 0

(25) - 25 = 0

0 = 0 (True)

~

4 0

3 years ago

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A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 34.5 ft3. what dimensions

____ [38]

Answer:

$l \approx 3.3\,ft$ , $x = 3.2\,ft$

Step-by-step explanation:

The equations of volume and surface area are presented below:

$34.5 = l^{2}\cdot x$

$A_{s} = 2\cdot l^{2} + 4\cdot l \cdot x$

The length of the tank is:

$x = \frac{34.5}{l^{2}}$

The expression fo the surface area is therefore simplified into an univariable form:

$A_{s} = 2\cdot l^{2} + 4\cdot \left(\frac{34.5}{l} \right)$

$A_{s} = 2\cdot l^{2} + \frac{138}{l}$

The first and second derivatives of the expression are, respectively:

$A_{s}' = 4\cdot l -\frac{138}{l^{2}}$

$A_{s}'' = 4 +\frac{276}{l^{3}}$

The first derivative is equalized to zero and length of the square side is now found:

$4\cdot l -\frac{138}{l^{2}} = 0$

$4\cdot l^{3}-138 = 0$

$l^{3} = \frac{138}{4}$

$l = \sqrt[3]{\frac{138}{4} }$

$l \approx 3.3\,ft$

Now, the second derivative offers a criteria to determine if solution leads to an absolute minimum:

$A_{s}'' = 4 + \frac{276}{(3.3\,ft)^{3}}$

$A_{s}'' = 11.7$ (Absolute minimum)

The depth of the tank is:

$x = \frac{34.5\,ft^{3}}{(3.3\,ft)^{2}}$

$x = 3.2\,ft$

6 0

3 years ago

A tank containing 64 gallons lost 6 1/4 % through leakage. How much remained in the tank?

NemiM [27]

Hey you!

STEP 1: 6 1/4 = 6.25

STEP 2: 64*6.25% = 4 (64*6 1/4 = 4 as well).

STEP 3: 64 - 4 = 60

60 gallons of gas remained in the tank.

4 0

3 years ago

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