0.91÷-0.13
=-7
hope this helps!
Answer:
r = 24
Step-by-step explanation:
3(r+2)+5(2−r)=−32
Step 1: Simplify both sides of the equation.
3(r+2)+5(2−r)=−32
(3)(r)+(3)(2)+(5)(2)+(5)(−r)=−32(Distribute)
3r+6+10+−5r=−32
(3r+−5r)+(6+10)=−32(Combine Like Terms)
−2r+16=−32
−2r+16=−32
Step 2: Subtract 16 from both sides.
−2r+16−16=−32−16
−2r=−48
Step 3: Divide both sides by -2.
−2r/-2 = -48/-2
r = 24
Answer:
Look at attached image
Step-by-step explanation:
Answer:
b. -84
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<u />
<u />
<u />
<u>Step 2: Solve for </u><em><u>a</u></em>
- Addition Property of Equality:
- [Simplify] Add:

- Multiplication Property of Equality:

- [Simplify] Multiply:

<u>Step 3: Check</u>
<em>Plug in a into the original equation to verify it's a solution.</em>
- Substitute in <em>a</em>:

- [Frac] Divide:

- Subtract:

Here we see that 5 does indeed equal 5.
∴ a = -84 is the solution to the equation.
The height of the <em>water</em> depth is h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours, and the height of the Ferris wheel is h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds. Please see the image to see the figures.
<h3>How to derive equations for periodical changes in time</h3>
According to the two cases described in the statement, we have clear example of <em>sinusoidal</em> model for the height as a function of time. In this case, we can make use of the following equation:
h = a + A · sin (2π · t/T + B) (1)
Where:
- a - Initial position, in meters.
- A - Amplitude, in meters.
- t - Time, in hours or seconds.
- T - Period, in hours or seconds.
- B - Phase, in radians.
Now we proceed to derive the equations for each case:
Water depth (u = 20 m, l = 8 m, a = 14 m, T = 12 h):
A = (20 m - 8 m)/2
A = 6 m
a = 14 m
Phase
20 = 14 + 6 · sin B
6 = 6 · sin B
sin B = 1
B = π/2
h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours.
Ferris wheel (u = 40 m, l = 2 m, a = 21 m, T = 40 s):
A = (40 m - 2 m)/2
A = 19 m
a = 21 m
Phase
2 = 21 + 19 · sin B
- 19 = 19 · sin B
sin B = - 1
B = - π/2
h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds.
Lastly, we proceed to graph each case in the figures attached below.
To learn more on sinusoidal models: brainly.com/question/12060967
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