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skelet666 [1.2K]

3 years ago

12

Louis wants to carpet the rectangular floor of his basement. The basement has a area of 768 square feet. The width of the baseme

nt is 1/3 it’s length. What is the length of Louis’s basement

1 answer:

pentagon [3]3 years ago

5 0

Area=width*length. Let width=x ft, then length=3x ft, given the information in the problem. The area of basement=x*3x=768, 3x^2=768, x^2=256, x=16. The width is 16 feet. Therefore, length=3x=3*16=48 feet.

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Two cities are building bicycle paths. Charles City has built 5km of bicycle paths by the end of the first month, and the total

sergey [27]

Answer:

Month 4

Step-by-step explanation:

To solve this problem we must propose an equation that models the number of kilometers of bicycle trails made monthly in Charles City and in Tinsel Town

<em>For Charles City </em>we know that the number of kilometers built in the first month is 5, and it doubles every month. Then we have an exponential equation, in base 2, whose initial value is 5.

This equation has the following form:

$y = C_1 (2^{x-1})$

Where:

$C_1$ is the number of kilometers built in month 1

x is the number of months: {1, 2, 3, 4, 5 ... x}

x = 1 represents month 1.

So:

$Charles\ City\ (km) = 5(2^{x-1})$

<em>For Tinsel Town</em> we know that the number of kilometers built in the first month is 21 and increases at a fixed rate of 5 kilometers per month. This can be modeled by a linear equation.

$Tinsel\ Town\ (km) = 21 + 5(x-1)$

Where x is the number of months. x: {1, 2, 3, 4, 5 ...}

We want to know at the end of what month the total length of the cycle lanes in Charles City first exceeds the length in Tinsel Town

Then we equal both equations and clear x.

$5 (2^{x-1}) = 21 + 5(x-1)\\\\5 (2^{x-1}) - (21 + 5(x-1)) = 0$

Clearing x from this equation is very difficult, so to find x, we iterate until we get the value of x that causes the equation to approach 0.

For x = 3

$5(2^{3-1}) - (21 +5(3-1)) = 0\\\\20- 31= -11$

For x = 4

$5(2^{4-1}) - (21 +5(4-1)) = 0\\\\40 - 36 = 4$

<em>The value must be between x = 3 and x = 4</em>

For x = 3.8

$5 (2^{3.8-1}) - (21 +5(3.8-1)) = 0\\\\34.82 - 35 = 0.18$

Then x ≈ 3.8 months.

Finally we have that By the end of the fourth month the total length of the cycle lanes in Charles City exceeds the length in Tinsel Town

6 0

3 years ago

In the after school Dena, Shawn, and Amanda knit scarfs that are the same size with yellow, white, and blue yarn. Denas scarf is

jenyasd209 [6]

Answer:

$\frac{8}{20}$

Step-by-step explanation:

We have been given that in the after school Dena, Shawn, and Amanda knit scarfs that are the same size with yellow, white, and blue yarn. Denas scarf is 2/5 yellow, Shawn's scarf is 3/5 , and Amanda's scarf is 3/4 yellow.

To make Amanda's argument true, let us compare each fraction by making a common denominator.

We can see that least common denominator of each fraction would be 20.

$\text{Dena's scarf}=\frac{2}{5}\Rightarrow\frac{2*4}{5*4}=\frac{8}{20}$

$\text{Shawn's scarf}=\frac{3}{5}\Rightarrow\frac{3*4}{5*4}=\frac{12}{20}$

$\text{Amanda's scarf}=\frac{3}{4}\Rightarrow\frac{3*5}{4*5}=\frac{15}{20}$

Since $\frac{8}{20}$ , therefore, Amanda's scarf has the most yellow.

8 0

3 years ago

What is 25 divided by 82?

Murrr4er [49]

In decimal form it’s 0.3048.. so basically 0.3

6 0

3 years ago

How to find the point-slope form for the slope of 6 and passing through(-7,1)

MariettaO [177]

Answer: y-1=6(x+7)

Step-by-step explanation:

The formula for point-slope form is $y-y_1=m(x-x_1)$ . Since we are given the point and slope, we can directly plug them in.

$y-1=6(x-(-7))$ [distribute by -1]

$y-1=6(x+7)$

Now, we know that the point-slope form is y-1=6(x+7).

8 0

3 years ago

You have just isolated a new radioactive element. If you can determine its half-life, you will win the Nobel Prize in physics. Y

Troyanec [42]

Staals half
1 gram left
0.3 grams left
half lives are normally written in years
it goes likt this

$A=P( \frac{1}{2})^ \frac{t}{h}$
A=final amount
P=initila amount
t=time elapsed
h=time half life is (same units as time)

let's use days as the units of time

we are given
initial amount=1gram
final amount=0.3gram
time=4 days

so
$0.3=1( \frac{1}{2})^ \frac{4}{h}$
solve for h
$0.3=( \frac{1}{2})^ \frac{4}{h}$
take the ln of both sides
$ln(0.3)=ln( \frac{1}{2})^ \frac{4}{h}$
$ln(0.3)=\frac{4}{h}ln( \frac{1}{2})$
times both sides by h
$hln(0.3)=4ln( \frac{1}{2})$
divide both sides by ln(0.3)
$h= \frac{4ln( \frac{1}{2}) }{ln(0.3)}$
use calculator
h=2.30287
3 sig figs
h=2.303 days

6 0

4 years ago