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2 years ago

Simplify. Remove all perfect squares from inside the square root.

Mathematics

1 answer:

nexus9112 [7]2 years ago

7 0

Answer:

$2z^{3} \sqrt{14z}$

Step-by-step explanation:

$\sqrt{56x^{7} } =\sqrt{(14)(2^{2} )(z^{2})(z^{2})(z^{2})(z) }$

$=2(z)(z)(z)\sqrt{14z} =2z^{3} \sqrt{14z}$

Hope this helps

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A 10ft by 20ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 216ft^

Dmitry [639]

check the picture below.

so, we know the dimensions of the pool, is a 20x10, so its area is simply 200 ft², and we know the walkway is 216 ft², so the whole thing, including pool and walkway is really 200 + 216 ft².

now, as you see in the picture, the dimensions for the combined area is 20+2x and 10+2x, since the walkway is "x" long, therefore,

$\bf \stackrel{length}{(20+2x)}\stackrel{width}{(10+2x)}=200+216\implies \stackrel{FOIL}{4x^2+60x+200}=200+216 \\\\\\ 4x^2+60x=216\implies \stackrel{dividing~by~4}{x^2+15x=54} \\\\\\ x^2+15x-54=0\implies (x+18)(x-3)=0\implies x= \begin{cases} -18\\ \boxed{3} \end{cases}$

notice, it cannot be -18, since is a positive length unit.

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2 years ago

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3 is subtracted from a number.<br> What is the algebraic expression?

Stels [109]

Answer:

Naruto and luffy and Goku will kill you.

Step-by-step explanation:

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3 years ago

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Arlo invested $4000 in an account that earns 5.5% interest, compounded annually. The formula for compound interest is A(t)=P(1+i

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$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=4000\left(1+\frac{0.055}{1}\right)^{1\cdot 4}\implies A=4000(1.055)^4\implies A\approx 4955.2986$

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3 years ago

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Plz help

Sergio039 [100]

2(5*4)+2(4*3)+2(3*5)=94 sq.m (Orginial SA)
2(4*5)+2(5*6)+2(6*4)=148 sq.m (Total SA)

148-94=54 (New SA)

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2 years ago

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A model car is made to a scale of 1:50 (model: real). If the model has a length of 10 cm, calculate the length of the real car (

Alex_Xolod [135]

Answer:

5 m

Step-by-step explanation:

A model car is made to a scale of 1:50 (model: real).

If the model has a length of 10 cm, calculate the length of the real car (answer in meters).

We have a scale of :

model: real = 1:50

The model has a length of 10cm

Hence:

1 cm = 50 cm

10 cm = x cm

Cross Multiply

x cm × 1cm = 10 cm × 50 cm

x cm = 10 cm × 50 cm/1cm

x cm = 500 cm

The length of the real car is 500cm

Converting the length of the real car to meters

100cm = 1 m

500 cm = x m

Cross Multiply

100cm × x m = 500 cm × 1 m

x m = 500 cm × 1 m/100 cm

x m = 5 m

The Length of the real car in meters is 5m

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2 years ago