Which expressions are equivalent

Mathematics

1 answer:

Kazeer [188]3 years ago

5 0

Step-by-step explanation:

The first set is equivalent.

We obtain the right-hand side by swapping places of the terms.

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The pipe fitting industry had 546.5 thousand jobs in 2015 and is expected to decline at an average rate of 3 thousand jobs per y

lesya692 [45]

Answer:

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

Step-by-step explanation:

Due to the assumption of a yearly average rate, a linear function model shall be used. The expected amount of jobs ( $n$ ) after a certain amount of years (t) is given by the following formula:

$n = n_{o} + \frac{\Delta n}{\Delta t}\cdot t$

Where:

$n_{o}$ - Initial amount of jobs in pipe fitting industry, measured in thousands.

$\frac{\Delta n}{\Delta t}$ - Average yearly rate, measured in thousands per year. (A decline is indicated by a negative sign)

If $n_{o} = 546.5$ , $t = 2025-2015 = 10\,years$ and $\frac{\Delta n}{\Delta t} = -3\,\frac{1}{years}$ , then:

$n = 546.5+\left(-3\,\frac{1}{year}\right)\cdot (10\,years)$

$n = 516.5$

The percent change in jobs from pipe fitting industry is calculated as follows:

$\%n = \left(1-\frac{n}{n_{o}}\right)\times 100\,\%$

$\% n = \left(1-\frac{516.5}{546.5}\right)\times 100\,\%$

$\%n = 5.5\,\%$

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

4 0

3 years ago

A car completes a journey at an average speed of 40km/h.At what speed must it travel on the return journey if the average speed

nalin [4]

The distance, s = 40t₁ where t₁ is the time to complete the outward journey.
The same distance = vt₂ where t₂ is the time to complete the return journey at speed v.
For the whole journey, 2s=60(t₁+t₂). Therefore s=30(t₁+t₂)=40t₁=vt₂.
30t₁+30t₂=40t₁, 10t₁=30t₂, t₁=3t₂, so s=120t₂=vt₂ and v=120kph.

5 0

3 years ago

Benjamin threw a rock straight up from a cliff that was 48 ft above the water. If the height of the rock h, in feet, after t s

fomenos

Answer: It will take 4 seconds for the rock to hit the water.

Step-by-step explanation:

Given : Benjamin threw a rock straight up from a cliff that was 48 ft above the water.

If the height of the rock h, in feet, after t seconds is given by the equation

$h = -16 t^2+ 52 t + 48$