Which of the following situations could be modeled by the equation 8 + 4x = 12 + 3x?

This question has two parts. First, answer Part A. Then, answer Part B. Part A Fill in the blanks to complete the sentence. A ta

myrzilka [38]

Answer:

85

Step-by-step explanation:

6 0

3 years ago

When temperature is zero degree Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the correspondin

7nadin3 [17]

Answer:

$\\ y = 1.8(x) + 32$ or $\\ y = \frac{9}{5}(x) + 32$

or equivalently:

$\\ F = 1.8(C) + 32$ or $\\ F = \frac{9}{5}(C) + 32$

Step-by-step explanation:

To express the Fahrenheit temperature as a linear function of the Celsius temperature, F(c), we can proceed as follows.

We can use here the two-point form equation of a line:

$\\ y-y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x-x_1)$ [1]

We are asked to express the Fahrenheit temperature as a function of Celsius temperature, so the independent variable, in this case, is x (Celsius temperature) and the dependent variable is y (Fahrenheit temperature).

When temperature is zero degree Celsius ( $\\x_1 = 0$ ), the Fahrenheit temperature is 32 ( $\\y_1 = 32$ ).

When the Celsius temperature is 100 ( $\\x_2 = 100$ ), the corresponding Fahrenheit temperature is 212 ( $\\y_2 = 212$ ).

Then, using [1], we have:

$\\ y-32 = \frac{212 - 32}{100 - 0}(x-0)$

$\\ y-32 = \frac{180}{100}(x)$

$\\ y-32 = 1.8(x)$ .

It could be also be written as:

$\\ y-32 = \frac{18}{10}(x)$ = $\\ y-32 = \frac{9}{5}(x)$ , as it commonly appears in books.

Then the Fahrenheit temperature express as a linear function of the Celsius temperature, F(c) is ( solving the equation for y ) :

$\\ y = 1.8(x) + 32$ or $\\ y = \frac{9}{5}(x) + 32$ .

Or equivalently:

$\\ F = 1.8(C) + 32$ or $\\ F = \frac{9}{5}(C) + 32$

We can check this using the given values from the question:

For 0 Celsius degrees, the Fahrenheit temperature is:

$\\ y = 1.8(0) + 32$ = 32 Fahrenheit degrees.

For 100 Celsius degrees, the Fahrenheit temperature is:

$\\ y = 1.8(100) + 32 = 180 + 32$ = 212 Fahrenheit degrees.

5 0

4 years ago

The delivery ramp at the corner cafe id a right triangle. The hypotenuse is 4 meters long. One leg is 3 meters long. What is the

disa [49]

Answer:

f. sqrt 7 meters

Step-by-step explanation:

we use Pythagoras' theorem here,

let the unknown side be x,

therefore,

=> 3² + x² = 4²

=> x² = 16 - 9

=> x = √7 m

7 0

4 years ago

Read 2 more answers

What is the value of x if y = 4

enyata [817]

Answer:

x is infinite

Step-by-step explanation:

x is a function so

if y=f:x

therefore

$0 < x < \infty$

5 0

3 years ago

when constructing the incenter of a triangle, The inersection of all three of which type of line needs to be found

lesantik [10]

Answer: Angle bisector

The angle bisector is the line that cuts an angle in half. The three angle bisectors all intersect at the same point which is the incenter. The incenter is the center of the circle in which is largest possible, yet it's fully inside the triangle. No part of this circle is outside the triangle.

3 0

3 years ago