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2 years ago

3.2.4 practice modeling slope-intercept Equation of a line

Mathematics

1 answer:

UNO [17]2 years ago

3 0

Answer:

this is from apex

Step-by-step explanation:

1. Which option did you choose? Discuss with another student why you made the choice you made. (1 point)

Troposphere (above the surface) because it looks simpler.

what do you know? the upper crust of the Earth is the layer extending 10 to 40 km beneath the surface. The surface temperature averages 15 degrees Celsius and increases 25 degrees Celsius with each kilometer of depth

what do you want to find out? The range of temperatures I would expect to encounter while traveling within the boundaries of the upper crust.

what answers do you expect to find? a range of temperatures (duh).

Writing an Equation

2. Define the variables you will use in your equation. (1 point)

Let one variable be the distance away from the surface and the other variable be the temperature.

D for distance and T for temperature.

The y-intercept is the starting position at Earth's surface. The coordinates of the y-intercept are (0, the temperature at Earth's surface).

3. What is the b-value of the y-intercept for your equation? (1 point)

15, I finally figured it out after 2 days lol.

The slope is the rate of change for temperature.

If the temperature increases (gets hotter) as the distance from the surface increases, then the slope is positive.

If the temperature decreases (gets colder) as the distance from the surface increases, then the slope is negative.

4. What is the slope of your equation? (1 point)

the slope of my equation is... positive!

5. Write an equation that models the relationship between your variables. (1 point)

umm, let's see... y= 25x+15 with x being each kilometer down from the surface temp. (15).

or if you just need the "equation" equation, then its y=mx+b

Interpreting the Equation

6. Identify and explain what each term represents in the temperature model.

a) The slope (1 point)

b) The y-intercept (1 point)

Graph the line

7. Identify three points on your line. (1 point)

(10,265) (11,290) (12,315)

8. Using the coordinates from question 7, calculate the slope of your line. Does it match the slope from your model? (2 points)

the slope of my line is 25, just like in my model. (wow magical)

Graph the Equation

9. On the graph below, plot the points and sketch your line. (4 points: 1 for each graphed point, 1 for the line)

see attachment.

Find the Temperature Range

10. Complete the sentence for your layer. (1 point)

The upper crust is the region that starts at Earth's surface and ends between 10 km and 40 km below the Earth's surface.

Use the temperature equation to find the temperature range for your layer.

range: between 265 degrees Celsius and 1015 degrees Celsius. (10km - 40 km)

11. What is the temperature at the end of your layer that is farthest from the surface? (1 point)

1015 degrees celsius.

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Camille stopped at the grocery store to buy milk. While at the store, she spotted cans of soup on sale for $2.25 each. If the mi

Mrrafil [7]

$2.25x+$3.50=$35

so, $35-$3.50=$31.50

Then you divide $31.50 by $2.25

That equals 14

So, x=14

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2 years ago

A local sorority sold hot dogs and bratwursts at the spring fling picnics. The first day they sold 8 dozen hot dogs and 13 dozen

Sergeu [11.5K]

Answer: Cost of each hot dog and bratwursts would be $1.1 and $1.35 each.

Step-by-step explanation:

Since we have given that

Cost of each dozen hot dogs be 'x'.

Cost of each dozen bratwursts be 'y'.

The first day they sold 8 dozen hot dogs and 13 dozen bratwursts for $316.20.

So, the equation would be

$8x+13y=\$316.20$

.The second day they sold 10 dozen hot dogs and 15 dozen bratwursts for a total of $375.00.

So, the equation would be

$10x+15y=\$375.00\\\\2x+3y=\$75$

So, the equations becomes

$8x+13y=316.20--------------(2)\\\\(2x+3y=75)\times 4\\\\\implies 8x+12y=300------------(1)$

So, by elimination method, we get that

$8x+13y=316.20\\\\(-)8x+(-)12y=(-)300\\\\--------------\\y=\$16.20$

Put the value of y in the eq(1), we get that

$2x+3y=75\\\\2x+3(16.20)=75\\\\2x+48.6=75\\\\2x=75-48.60\\\\2x=26.4\\\\x=\dfrac{26.4}{2}\\\\x=\$13.2$

Hence, the cost of hot dogs would be $\dfrac{13.2}{12}=\$1.1$

And the cost of bratwursts would be $\dfrac{16.2}{12}=\$1.35$

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2 years ago

Use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle. Show all work for full credit.

diamong [38]

Answer: The given triangle LMN is an obtuse-angled triangle.

Step-by-step explanation: We are given to use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle.

From the figure, we note that

in ΔLMN, LM = 5 units, MN = 13 units and LN = 14 units.

We know that a triangle with sides a units, b units and c units (a > b, c) is said to be

(i) Right-angled triangle if $b^2+c^2=a^2,$

(ii) Acute-angled triangle if $b^2+c^2>a^2,$

(iii) Obtuse-angled triangle if $b^2+c^2$

For the given triangle LMN, we have

a = 14, b = 13 and c = 5.

So,

$b^2+c^2=13^2+5^2=169+25=194,\\\\a^2=14^2=196.$

Therefore, $b^2+c^2$

Thus, the given triangle LMN is an obtuse-angled triangle.

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2 years ago

Point b has coordinates (3,-4) and lies on the circle whose equation is x^2 + y^2= 25. If angle is drawn in a standard position

lakkis [162]

Point B has coordinates (3,-4) and lies on the circle. Draw the perpendiculars from point B to the x-axis and y-axis. Denote the points of intersection with x-axis A and with y-axis C. Consider the right triangle ABO (O is the origin), by tha conditions data: AB=4 and AO=3, then by Pythagorean theorem:

 $BO^2=AO^2+AB^2 \\ BO^2=3^2+4^2 \\ BO^2=9+16 \\ BO^2=25 \\ BO=5$ .

{Note, that BO is a radius of circle and it wasn't necessarily to use Pythagorean theorem to find BO}
The sine of the angle BOA is
$\sin \angle BOA= \dfrac{AB}{BO} = \dfrac{4}{5} =0.8$

Since point B is placed in the IV quadrant, the sine of the angle that is drawn in a standard position with its terminal ray will be 


 $\sin \theta=-0.8$ .

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2 years ago

A local library claims it has 2.73x103 books. If there are 42 people in the building, how many books per capita are there?

sveticcg [70]

Answer:

$Per\ Capita = 64$