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3 years ago

Write an absolute value equation that has the solution x=-10 and x=-5

1 answer:

5 0

The last step of an equation whose solutions are x=-10 and x=-5 is:

(x+10)(x+5)=0

We need to add some previous steps, which make the equation an absolute value equation.

A way to do this, is writing |(x+10)(x+5)|=0,

the only solutions are still x=-10 and x=-5

Answer: |(x+10)(x+5)|=0

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A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s

Setler [38]

Answer:

$310\text{ feet and }210\text{ feet}$

Step-by-step explanation:

GIVEN: A farmer has $520 \text{ feet}$ of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is $310 \text{ feet}$ .

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be $x$ and $y$

perimeter of rectangular pen $=2(x+y)=520\text{ feet}$

$x+y=260$

$y=260-x$

area of rectangular pen $=\text{length}\times\text{width}$

$=xy$

putting value of $y$

$=x(260-x)$

$=260x-x^2$

to maximize $\frac{d \text{(area)}}{dx}=0$

$260-2x=0$

$x=130\text{ feet}$

$y=390\text{ feet}$

but the dimensions must be lesser or equal to than that of barn.

therefore maximum length rectangular pen $=310\text{ feet}$

width of rectangular pen $=210\text{ feet}$

Maximum area of rectangular pen $=310\times210=65100\text{ feet}^2$

Hence maximum area of rectangular pen is $65100\text{ feet}^2$ and dimensions are $310\text{ feet and }210\text{ feet}$

5 0

2 years ago

Rosa spent $11.52 on 8 candy necklaces for each of her two friends. How much did each necklace cost?

Liono4ka [1.6K]

Answer:

i don't wanna tell u the wrong answer but I think it is A

Because it says 8 neclaces for EACH of her two friends

So i divided 11.52 by 16

So i got 0.72 I am sorry if it is wrong Have a great day!

3 0

2 years ago

Evaluate the spherical coordinate integral

expeople1 [14]

Rewrite the equations of the given boundary lines:

y = -x + 1 ==> x + y = 1

y = -x + 4 ==> x + y = 4

y = 2x + 2 ==> -2x + y = 2

y = 2x + 5 ==> -2x + y = 5

This tells us the parallelogram in the x-y plane corresponds to the rectangle in the u-v plane with 1 ≤ u ≤ 4 and 2 ≤ v ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

$J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3$

Rewrite the integrand:

$-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3$

The integral is then

$\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}$

5 0

3 years ago

0.032 0.90 0.088 from greatest to least

ioda

Answer:

0.9 , 0.088 , 0.032

Step-by-step explanation:

0.9 --> 1st greatest

0.088 --> 2nd greatest

0.032 --> 3rd greatest

So, 0.9 , 0.088 , 0.032

5 0

2 years ago

boxes of a whole wheat linguine are on sale this week for 30% off the original price. they cost $1.50 when they are not on sale.

allochka39001 [22]

30% of $1.50 is 0.45 and if it's on sale you subtract from original price
so 1.50 - 0.45
and your answer would be $1.05

4 0

2 years ago