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2 years ago

How would I solve this

Mathematics

2 answers:

kondor19780726 [428]2 years ago

5 0

The formula of the area of a rectangle is A = LW
You have been given the length and width as (x+1) and (x+3). You've also been given the area, 80 ft2

So we can substitute what we have in the formula as follows

80 = (x+1)(x+3)

If we FOIL the right side of the equation, we have

80 = x2+4x+3

Let's bring the 80 to the right side of the equation so that we have an equation equal to 0.

x2+4x-77 = 0

We can factor this as
(x+11)(x-7) = 0

So,
x+11 = 0 This gives us x=-11 which would yield dimensions of -10 and -8. Since we can't have negative dimensions, let's check the other factor.
x-7=0, giving us x=7
So the dimensions of the porch are
(7+1) and (7+3)

The porch is 8 x 10

Feliz [49]2 years ago

3 0

What are you solving for???

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PilotLPTM [1.2K]

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3 years ago

A researcher wishes to estimate the proportion of X-ray machines that malfunction. A random 275 sample of machines is taken, and

Dominik [7]

Answer:

Following are the solution to the given question:

Step-by-step explanation:

$95\%$ Confidence Interval for both the percentage of all x-ray machines

p = the machinery's share is not working:

$= \frac{228}{275}\\\\ = 0.829$

$\text{Margin of Error} = Z_{(\frac{\alpha}{2})} \times \sqrt{( p \times (1-p)}{n})$

$= 1.96 \times \sqrt{(0.829 \times \frac{0.171}{275})} \\\\= 1.96 \times 0.023 \\\\= 0.045$

Lower $95\%$ Confidence interval = p - error margin $= 0.829 - 0.045 = 0.784$

Upper $95\%$ Confidence Interval = p + error margin $= 0.829 + 0.045 = 0.874$

So, $95\%$ Confidence Interval $= ( 0.78 , 0.87 )$

4 0

2 years ago

N=r (A-s) what is s

Lerok [7]

$r(A-s)=N\ \ \ \ |\text{use distributive property}\\\\rA-rs=N\ \ \ \ |-rA\\\\-rs=-rA+N\ \ \ \ |:(-r)\neq0\\\\\boxed{s=\dfrac{rA-N}{r}}$

4 0

3 years ago

Joey is running an experiment with a mass on a spring. Joey models the height of the mass above the table he is working on using

galben [10]

Answer: 1.8 s

Step-by-step explanation:

Given

The height of the spring mass system above the table is given by

$h(t)=6.85\cos (3.42t)+9$

The mass is performing S.H.M with frequency $\omega =3.42$

and $\omega T=2\pi$

$\therefore T=\dfrac{2\pi }{\omega}$

time when mass returns to its original position

$T=\dfrac{2\pi }{3.42}\\\\T=1.8\ s$

5 0

2 years ago

21. In 4 + In(4x - 15) = In(5x + 19)

Alexxx [7]

Answer:

$x=-30;\quad \:I\ne \:0$

Step-by-step explanation:

$In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)$

$\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\$

$\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\$

$\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\ne \:0\\\frac{-nxI}{-nI}=\frac{30nI}{-nI};\quad \:I\ne \:0\\\mathrm{Simplify}\\\frac{-nxI}{-nI}=\frac{30nI}{-nI}\\\mathrm{Simplify\:}\frac{-nxI}{-nI}:\quad x\\\frac{-nxI}{-nI}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{nxI}{nI}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{xI}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}\frac{30nI}{-nI}:\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:$

$\quad \frac{a}{-b}=-\frac{a}{b}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{30I}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\ne \:0$

3 0

3 years ago