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3 years ago

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A worm walks 40cm in 8 minutes. Give both unit rates. Make sure you include the unit for each. (Total 8 points: 2 points for eac

h unit rate, 1 point for each of the units labeled and 1 point for each work shown or explanation)

1 answer:

vodka [1.7K]3 years ago

7 0

40/8 = 5 cm per minute

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2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai

nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

$\frac{1}{4} = \frac{15 + x + x}{x(15+x)}$

$\frac{1}{4} = \frac{15 + 2x}{x(15+x)}$

Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

$x^2 + 7x - 60 = 0$

Quadratic equation with $a = 1, b = 7, c = -60$ . So

$\Delta = 7^{2} - 4*1*60 = 289$

$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

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Given that 12 , 3 is on the graph of f(x) find the corresponding point for the function

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(12,24)
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3 years ago

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Bingel [31]

Are you cheating in a exam if you are

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2 years ago

L want to know the sum result.10+67×2=?<br>

Volgvan

Answer:

$144$

Step-by-step explanation:

<u>Step 1: Multiply </u>

$10 + (67 * 2)$

$10 + 134$

<u>Step 2: Combine </u>

$10 + 134$

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Answer: $144$

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3 years ago

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Day 6: Textbook Page 321 Problem 9 When Esteban looks at the puddle, he sees a reflection of the top of the cactus. How tall is

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The given figure can be drawn as,

From the figure,

$\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}$

$\begin{gathered} \tan \theta=\frac{DE}{EC} \\ \tan \theta=\frac{1.5}{2.5} \\ \tan \theta=0.6 \end{gathered}$

Since angle of incidence will be equal to angle of reflection, $\begin{gathered} \text{tan}$ Therefore, the height of cactus is 6 m.

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11 months ago