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3 years ago

Find the missing angle or side. Round to the nearest tenth.

Mathematics

1 answer:

babymother [125]3 years ago

8 0

Answer:

$x = 19.4$

Step-by-step explanation:

For the 72-deg angle, 6 is the adjacent leg. x is the hypotenuse. The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.

$\cos A = \dfrac{adj}{hyp}$

$\cos 72^\circ = \dfrac{6}{x}$

$x \cos 72^\circ = 6$

$x = \dfrac{6}{\cos 72^\circ}$

$x = 19.4$

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Answer:

3,300 i THINK i used a calculator

Step-by-step explanation:

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3 years ago

Connie Hamm demonstrates microwave ovens. She earn $5.00 per demonstration for the first 10 demonstrations and $6.00 for each de

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4 years ago

Please help thank you

Dvinal [7]

the tale-tell fellow is the number inside the parentheses.

if that number, the so-called "growth or decay factor", is less than 1, then is Decay, if it's more than 1, is Growth.

$\bf f(x)=0.001(1.77)^x\qquad \leftarrow \qquad \textit{1.77 is greater than 1, Growth} \\\\[-0.35em] ~\dotfill\\\\ f(x)=2(1.5)^{\frac{x}{2}}\qquad \leftarrow \qquad \textit{1.5 is greater than 1, Growth} \\\\[-0.35em] ~\dotfill\\\\ f(x)=5(0.5)^{-x}\implies f(x)=5\left( \cfrac{05}{10} \right)^{-x}\implies f(x)=5\left( \cfrac{1}{2} \right)^{-x} \\\\\\ f(x)=5\left( \cfrac{2}{1} \right)^{x}\implies f(x)=5(2)^x\qquad \leftarrow \qquad \textit{Growth} \\\\[-0.35em] ~\dotfill$

$\bf f(t)=5e^{-t}\implies f(t)=5\left( \cfrac{e}{1} \right)^{-t}\implies f(t)=5\left( \cfrac{1}{e} \right)^t \\\\\\ \cfrac{1}{e}\qquad \leftarrow \qquad \textit{that's a fraction less than 1, Decay}$

now, let's take a peek at the second set.

$\bf f(x)=3(1.7)^{x-2}\qquad \leftarrow \qquad \begin{array}{llll} \textit{the x-2 is simply a horizontal shift}\\\\ \textit{1.7 is more than 1, Growth} \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)=3(1.7)^{-2x}\implies f(x)=3\left(\cfrac{17}{10}\right)^{-2x}\implies f(x)=3\left(\cfrac{10}{17}\right)^{2x} \\\\\\ \textit{that fraction is less than 1, Decay} \\\\[-0.35em] ~\dotfill$

$\bf f(x)=3^5\left( \cfrac{1}{3} \right)^x\qquad \leftarrow \qquad \textit{that fraction is less than 1, Decay} \\\\[-0.35em] ~\dotfill\\\\ f(x)=3^5(2)^{-x}\implies f(x)=3^5\left( \cfrac{2}{1} \right)^{-x}\implies f(x)=3^5\left( \cfrac{1}{2} \right)^x \\\\\\ \textit{that fraction in the parentheses is less than 1, Decay}$

6 0

4 years ago

3.2.4 practice modeling slope-intercept Equation of a line

UNO [17]

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.

3 0

3 years ago

What picture shows 1/2 of the rectangle shaded

astra-53 [7]

Answer:

just look at the side of the triangle that is shaded and thats your answer right or left

Step-by-step explanation:

look at the side that is shaded

3 0

3 years ago