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3 years ago

A newspaper reports the following changes in the temperature of a city over 4 days:

Mathematics

1 answer:

Pie3 years ago

6 0

Answer:

The expression to show the average daily change in temperature can be given by :

⇒ $\frac{2.64-0.22-0.35+0.63}{4}$ °C

Step-by-step explanation:

Changes in the temperature of city as reported by newspaper :

Day 1: 2.64° C

Day 2: $-\frac{2}{9}$ °C

Day 3: -0.35°C

Day 4: $\frac{5}{8}$ °C

The average daily change in temperature can be calculated as

⇒ $\frac{2.64-\frac{2}{9}-0.35+\frac{5}{8}}{4}$ °C

The fractions can be written in decimals

⇒ $\frac{2.64-0.22-0.35+0.63}{4}$ °C

⇒ $\frac{2.7}{4}$ °C

⇒ $0.675\°C\approx 0.68$ °C [Average daily change in temperature.]

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1. Write the slope-intercept form of the equation that passes through the point (0, 1) and is parallel to the line y = 3x - 5

gregori [183]

Answer:

y = 3x + 1

Step-by-step explanation:

If two lines are parallel to each other, they have the same slope.

The first line is Y = 3X - 5. Its slope is 3. A line parallel to this one will also have a slope of 3.

Plug this value (3) into your standard point-slope equation of y = mx + b.

y = 3x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (0, 1). Plug in the x and y values into the x and y of the standard equation.

1 = 3(0) + b

To find b, multiply the slope and the input of x (0)

1 = 0 + b

Now, add 0 to both sides to isolate b.

1 = b

Plug this into your standard equation.

y = 3x + 1

This equation is parallel to your given equation (y = 3x - 5) and contains point (0, 1)

Hope this helps!

3 0

3 years ago

4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail

Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

$h^{-1}(x)=\sqrt{\frac{x+1}{3}}$ ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = $f^{-1}(x)$

* Lets use these steps to solve the problems

∵ $f(x)=\sqrt{x-3}$

∵ f(x) = y

∴ $y=\sqrt{x-3}$

- Exchange x and y

∴ $x=\sqrt{y-3}$

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by $f^{-1}(x)$

∴ $f^{-1}(x)=x^{2}+3$

∵ g(x) = x² + 3

∴ $f^{-1}(x)=g(x)$

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ $f(x)=\sqrt{x-3}$

∵ g(x) = x² + 3

∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ $\frac{x + 1}{3}=y^{2}$

- Take √ for both sides

∴ ± $\sqrt{\frac{x+1}{3}}=y$

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

∴ $h^{-1}(x)=\sqrt{\frac{x+1}{3}}$

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3 years ago

I need help on this problem!?

nata0808 [166]

156/4=39 miles per gallon. 39*12 gallons is 468 miles, and 6 gallons is 234.

6 0

3 years ago

Well... I think you get the point

Mariana [72]

Answer:

Choice B

Step-by-step explanation:

USE PEMDAS

First do the things in the parenthesis. 2 1/3- 3/4 is 19/12

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Hope this helps!

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3 years ago

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VashaNatasha [74]

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3 years ago

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