Answer:
8 : 24 P.M
Step-by-step explanation:
Data provided in the question:
On December 1 bright star Procyon will just be rising on the eastern horizon at 10 P.M
Now,
we know that Stars rise 4 minutes earlier each night
Therefore,
24 days later i.e after 24 nights the total early time
= 24 days × 4 minutes per day
= 96 minutes
or
= 1 hour 36 minutes early
Hence,
on Christmas Day the star will rise at 1 hour 36 minutes early than 10 P.M
= 8 : 24 P.M
Unfortunately, Katie will be $20 short
She has $40
Plus the $38 x 5 she will be earning which is $190
$190+$40 is $230
Looks like Kate needs one more day of hard work to get her bike ; )
9. You can easily get rid of the decimal fraction by multiplying by 10. This will move the decimal point one place to the right in each number.
However, since all the decimal fractions are even numbers of tenths, you can also turn them to integers by multiplying by 5:
... 3x +24 = 36
_____
10. If you can't describe what the parts of your equation represent, you have no business writing it. Saying you can't describe your equation is the same as saying you don't understand the problem.
It is important to be able to describe the parts of the equation just as it is important to be able to say what the problem is telling you, what it is asking, and what your strategy is for solving it. The parts of the equation are intimately tied with those things: they embody the given information and the strategy of your solution.
Answer:
3. r = -8
4. x = -5
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
2(-5r + 2) = 84
<u>Step 2: Solve for </u><em><u>r</u></em>
- Divide 2 on both sides: -5r + 2 = 42
- Subtract 2 on both sides: -5r = 40
- Divide -5 on both sides: r = -8
<u>Step 3: Check</u>
<em>Plug in r into the original equation to verify it's a solution.</em>
- Substitute in <em>r</em>: 2(-5(-8) + 2) = 84
- Multiply: 2(40 + 2) = 84
- Add: 2(42) = 84
- Multiply: 84 = 84
Here we see that 84 does indeed equal 84.
∴ r = -8 is a solution of the equation.
<u>Step 4: Define equation</u>
264 = -8(-8 + 5x)
<u>Step 5: Solve for </u><em><u>x</u></em>
- Divide both sides by -8: -33 = -8 + 5x
- Add 8 to both sides: -25 = 5x
- Divide 5 on both sides: -5 = x
- Rewrite: x = -5
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in<em> x</em>: 264 = -8(-8 + 5(-5))
- Multiply: 264 = -8(-8 - 25)
- Subtract: 264 = -8(-33)
- Multiply: 264 = 264
Here we see that 264 does indeed equal 264.
∴ x = -5 is a solution of the equation.
