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2 years ago

How to solve the following system y=(1/2)x^2+2x-1 and 3x-y=1

Mathematics

1 answer:

ruslelena [56]2 years ago

7 0

Answer:

(0,-1),(2,5)

Step-by-step explanation:

3x-y=1

0.5 $x^{2}$ +2x-1=y

Substitute the equation of y into the other equation

3x-(0.5 $x^{2}$ +2x-1)=1

3x-0.5 $x^{2}$ -2x+1=1

collect like terms

-0.5 $x^{2}$ +x=0

Solve for x

x(-0.5x+1)=0

0=-0.5x+1

-1=-0.5x

x=2 x=0

Back substitute into the other original equation and solve for y

3(2)-y=1

6-y=1

y=5

(2,5)

3(0)-y=1

-1(-y)=-1(1)

y=-1

(0,-1)

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Anvisha [2.4K]

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Step-by-step explanation:

We'll take this step by step. The equation is

$8-3\sqrt[5]{x^3}=-7$

Looks like a hard mess to solve but it's actually quite simple, just do one thing at a time. First thing is to subtract 8 from both sides:

$-3\sqrt[5]{x^3}=-15$

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$x=\sqrt[3]{5^5}$

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3 years ago

Describe how the range of a data set can help describe its variability.

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Answer:

The range is defined as the difference between the term with the highest value and the term with the lowest value. This statistic is used to measure the variability of a series of data because it provides information on how far apart the values of a tail of the distribution are from the values at the other end of the tail.

Imagine that you manufacture a type of spare part for cars that must have a measurement of 10 cm with a margin of error of 1 cm.

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10 ± 1 cm

Then you expect your manufacturing process to produce pieces with identical dimensions, that is, with little variability.

If you randomly select a sample of n pieces and measure them, the variability is expected to be low, so that your process is of quality, then expect a low range preferably less than 1 cm.

{10, 10.1, 10.5, 9.8, 9,6, 10.2} Range= 10.5 - 9.6 = 0.9 cm low variability

But if you find that the range is up to 8 cm, this would mean that not all pieces measure around 10 cm, it means that the variability of the measurements is high.

{14, 12, 11, 8, 7, 11, 12, 15} Range = 15 - 7 = 8 cm high variability

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