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2 years ago

2 people working at the same rate will take 9 hours to paint a room.

Mathematics

1 answer:

Lera25 [3.4K]2 years ago

6 0

Answer:

a)6 hrs

b)faster

Step-by-step explanation:

a) 9*2/3=6

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The width of a field is 3 miles less than the length. The square mileage of the plot is 18 miles squared. Find the dimensions.

kherson [118]

LW = A
L(L - 3) = 18
L^2 - 3L - 18 = 0
(L - 6) (L + 3) = 0
L could be 6 or -3 ( -3 cannot be a length of a side of a rectangle since it’s negative.)
So L = 6 and W= 3

6 0

3 years ago

Use the distributive property to write an equivalent expression.<br> 8(10n-8p+9)

LenKa [72]

Answer:

80n - 64p + 72

Step-by-step explanation:

8(10n) + 8(-8p) + 8(9)

80n - 64p + 72

8 0

2 years ago

A boat has a speed of 15 mph in still water. It travels downstream from Greentown to Glenavon in g hours. It then goes back upst

Lerok [7]

Step-by-step explanation:

We want to find two things-- the speed of the boat in still water and the speed of the current. Each of these things will be represented by a different variable:

B = speed of the boat in still water

C = speed of the current

Since we have two variables, we will need to find a system of two equations to solve.

How do we find the two equations we need?

Rate problems are based on the relationship Distance = (Rate)(Time).

Fill in the chart with your data (chart attached)

The resulting speed of the boat (traveling upstream) is B-C miles per hour. On the other hand, if the boat is traveling downstream, the current will be pushing the boat faster, and the boat's speed will increase by C miles per hour. The resulting speed of the boat (traveling downstream) is B+C miles per hour. Put this info in the second column in the chart. Now plug it into a formula! <u>Distance=(Rate)(Time) </u>Now solve using the systems of equations!

6 0

3 years ago

Solve 73 make sure to also define the limits in the parts a and b

Aleks04 [339]

73.

$f(x)=\frac{3x^4+3x^3-36x^2}{x^4-25x^2+144}$

$\lim_{x\to\infty}f(x)=\lim_{x\to\infty}(\frac{3+\frac{3}{x}-\frac{36}{x^2}}{1-\frac{25}{x^2}+\frac{144}{x^4}})=3$ $\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}(\frac{3+\frac{3}{x}-\frac{36}{x^2}}{1-\frac{25}{x^2}+\frac{144}{x^4}})=3\cdot\frac{1}{2}=3$

Since we can't divide by zero, we need to find when:

$x^4-2x^2+144=0$

But before, we can factor the numerator and the denominator:

$\begin{gathered} \frac{3x^2(x^2+x-12)}{x^4-25x^2+144}=\frac{3x^2((x+4)(x-3))}{(x-3)(x-3)(x+4)(x+4)} \\ so: \\ \frac{3x^2}{(x+3)(x-4)} \end{gathered}$

Now, we can conclude that the vertical asymptotes are located at:

$\begin{gathered} (x+3)(x-4)=0 \\ so: \\ x=-3 \\ x=4 \end{gathered}$

so, for x = -3:

$\lim_{x\to-3^-}f(x)=\lim_{x\to-3^-}-\frac{162}{x^4-25x^2+144}=-162(-\infty)=\infty$ $\lim_{x\to-3^+}f(x)=\lim_{x\to-3^+}-\frac{162}{x^4-25x^2+144}=-162(\infty)=-\infty$

For x = 4:

$\lim_{x\to4^-}f(x)=\lim_{n\to4^-}\frac{384}{x^4-25x^2+144}=384(-\infty)=-\infty$ $\lim_{x\to4^-}f(x)=\lim_{n\to4^-}\frac{384}{x^4-25x^2+144}=384(-\infty)=-\infty$

4 0

1 year ago

A positive integer is 4 more than 12 times another. Their product is 5896. Find the two integers.

maksim [4K]

X = integer one
y = integer 2

x = 12y + 4

x * y = 5896

Solve the system of equations

8 0

3 years ago

Read 2 more answers