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2 years ago

Solve the system of eqautions y=x2-5x+7 , y=2x+1

Mathematics

1 answer:

IgorC [24]2 years ago

3 0

Answer:

Step-by-step explanation:

The system of equations is given as

y=x^2-5x+7 - - - - - - - - - - 1

y=2x+1 - - - - - - - - - - - - - - 2

We would equate equation 1 to equation 2, it becomes

x^2-5x+7 = 2x+1

x^2-5x+7- 2x - 1 = 0

x^2 - 5x - 2x + 7 - 1 = 0

x^2 - 7x + 6 = 0

We would use the factorization method of solving quadratic equations.

x^2 - 6x - x + 6 = 0

x(x - 6) - 1(x - 6)

(x - 6)(x - 1) = 0

x - 6 = 0 or x - 1 = 0

x = 6 or x = 1

Substituting both values of x into equation 2, it becomes

For x = 6,

y=2×6 + 1 = 12 + 1 = 13

y = 13

For x = 1,

y=2 × 1 +1 = 2 + 1 = 3

y = 3

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Answer:

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x = number of hours

y = mx + b = 0.12(x + 3) + 15.21 {It's (x + 3) because we have to add the 3 hours between 9 and noon}

y = mx + b = -0.11x + 15.96 {The slope is negative because the price is decreasing}

Set them equal to each other

0.12(x+3) + 15.21 = -0.11x + 15.96

Now solve for x

0.12x + 0.36 + 15.21 = -0.11x + 15.96

0.12x + 15.57 = -0.11x + 15.96

0.12x + 0.11x = 15.96 - 15.57

0.23x = 0.39

x = 0.38 / 0.23 = 1.7 hours

Convert 0.7 into minutes

0.7 hours * (60 min / 1 hour) = 42 min

So the prices are the same 1 hour and 42 min after noon, which is 1:42 PM

Step-by-step explanation:

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2 years ago

The information below explains the transformations and translations of a logarithmic function. What is the equation for this fun

maks197457 [2]

The transformed function is y = 1/3(log(x/3 + 4)) + 1

<h3>How to transform the logarithmic function?</h3>

The parent logarithmic function is

y = log(x)

When shifted left by 4 units, we have:

y = log(x + 4)

When shifted up by 3 units, we have:

y = log(x + 4) + 3

When compressed vertically by 1/3, we have:

y = 1/3(log(x + 4) + 3)

This gives

y = 1/3(log(x + 4)) + 1

When stretched horizontally by 3, we have:

y = 1/3(log(x/3 + 4)) + 1

Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1

<h3>The transformation of function f(x)</h3>

We have:

f(x) = log[-(x – 5)] + 4

Set the radicand greater than 0

-(x - 5) > 0

Divide by -1

x - 5 < 0

Add 5 to both sides

x < 5 -- this represents the domain

A logarithmic function can output any real number.

So, the range is $-\infty < f(x) < \infty$

In the domain, we have:

x < 5

This means that the interval of decrease is $-\infty < x < 5$

Rewrite as an equation

x = 5 --- this represents the equation of asymptote

Read more about logarithmic functions at:

brainly.com/question/12708344

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1 year ago

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Lady bird [3.3K]

Answer: 24000

Step-by-step explanation:

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3 years ago

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bogdanovich [222]

Answer:

Step-by-step explanation:

f(1)=−3

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f(2)= 2×1(2-1)+1

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Alika [10]

Check the picture below.

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3 years ago

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