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3 years ago

Put this equation in standard form Y+5=-(x+3)?

Mathematics

1 answer:

lisabon 2012 [21]3 years ago

4 0

Answer: y = x - 2

Step-by-step explanation:

Subtract 5 from both sides.

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The width of a container is 5 feet less than its height. Its length is 1 foot longer than its height. The volume of the containe

juin [17]

The height of container is 8 feet

Solution:

Let "w" be the width of container

Let "l" be the length of container

Let "h" be the height of container

The width of a container is 5 feet less than its height

Therefore,

width = height - 5

w = h - 5 ------ eqn 1

Its length is 1 foot longer than its height

length = 1 + height

l = 1 + h ---------- eqn 2

The volume of container is given as:

$v = length \times width \times height$

Given that volume of the container is 216 cubic feet

$216 = l \times w \times h$

Substitute eqn 1 and eqn 2 in above formula

$216 = (1 + h) \times (h-5) \times h\\\\216 = (h+h^2)(h-5)\\\\216 = h^2-5h+h^3-5h^2\\\\216 = h^3-4h^2-5h\\\\h^3-4h^2-5h-216 = 0$

Solve by factoring

$(h-8)(h^2+4h+27) = 0$

Use the zero factor principle

If ab = 0 then a = 0 or b = 0 ( or both a = 0 and b = 0)

Therefore,

$h - 8 = 0\\\\h = 8$

Also,

$h^2+4h+27 = 0$

Solve by quadratic equation formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\mathrm{For\:} a=1,\:b=4,\:c=27:\quad h=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:27}}{2\cdot \:1}$

$h = \frac{-4+\sqrt{4^2-4\cdot \:1\cdot \:27}}{2}=\frac{-4+\sqrt{92}i}{2}$

Therefore, on solving we get,

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

Thus solutions of "h" are:

h = 8

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

"h" cannot be a imaginary value

Thus the solution is h = 8

Thus the height of container is 8 feet

8 0

3 years ago

15pts f(x)=(x+6)/2 g(x)=2x - 6 Show your work to evaluate g(f(x)).

notsponge [240]

Answer:

g(f(x)) = -x - 18

Step-by-step explanation:

2x - 6( (x + 6) / (2) )

2x - 3( x + 6)

2x - 3x - 18

-x - 18

4 0

2 years ago

Can anybody help me with this?

mihalych1998 [28]

Answer:

Cost = 17.08

Step-by-step explanation:

The cost is 4.88 per pound.

We buy 3.5 pounds

Cost = number of pounds * cost per pound

Cost = 3.5 * 4.88

Cost = 17.08

6 0

2 years ago

Which of the following is the equation 6^4 = 1,296 written in logarithmic form?

masya89 [10]

Given $6^4 = 1,296$

To write in logarithmic form we convert exponential form to logarithmic form

We apply the following rule

$b^x = a$ can be written as $log_b(a) = x$

here b = 6 , x=4 and a = 1296

$6^4 = 1,296$ can be written as $log_6(1,296) = 4$

option A is correct

8 0

3 years ago

Read 2 more answers

Please help asap I’m so lost

Simora [160]

what are the other answers

4 0

2 years ago