Answer: To clear an equation of decimals, multiply each term on both sides by the power of ten that will make all the decimals whole numbers. In our example above, if we multiply .25 by 100, we will get 25, a whole number. Since each decimal only goes to the hundredths place, 100 will work for all three terms.
So let's multiply each term by 100 to clear the decimals:
(100)0.25x + (100)0.35 = (100)(-0.29)
25x + 35 = -29
Now we can solve the equation as normal:
25x + 35 - 35 = -29 - 35
25x = -64
x = -2.56 Since the original was in decimal form, the answer should most likely also be in decimal form.
Let's look at one more:
1.75x + 4 = 6.2
We have to think a little more carefully about what multiple of ten to use here. 6.2 only needs to be multiplied by 10, but 1.25 needs 100, so we will multiply every term by 100. Don't forget to multiply the 4 by 100 as well.
(100)(1.75x) + (100)(4) = (100)(6.2)
175x + 400 = 620
We had to be extra careful as we multiplied by 100. Now we can solve the equation as normal:
175x + 400 - 400 = 620 - 400
175x = 220
x = 1.26
Step-by-step explanation:
Step-by-step explanation:
1. We we can split 4p into 9p - 5p, and now we have 3p² + 9p - 5p - 15 = 0. We can take out 3p from the first 2 terms and -5 from the last 2 terms. This gets us 3p (p + 3) -5 (p + 3) = 0. These two terms have (p + 3) as a common facor, so we can take that out as well, which give us (p + 3)(3p - 5) = ). Using Zero Product Property, p + 3 = 0 and 3p - 5 = 0, and when we solve each equation, we get p = -3, p= 5/3.
2. We will use the same process.
6x² + 14x - 3x - 7 = 0
2x (3x+7) - 1 (3x+7) = 0
(3x + 7)(2x - 1) = 0
3x + 7 = 0, 2x - 1 = 0
x = -7/3, x=1/2
Hope this helps!
Answer:
$541.67 per month
Step-by-step explanation:
Tuition and other expenses = $8,250 per semester.
There are two semesters in a year
She has 4 years to spend
Total semester=4years*2semesters
=8 semesters
4 years in college which is a total of 8 semesters.
Total Tuition and other expenses = $8,250 * 8
= $66,000
She needs a total of $66,00 to complete her college
Assistance from parents=$15,000
Financial aid(per semester)=$4750
Total financial aid=$38,000
Total assistance=
Assistance from parents+ financial aid
=$15000+$38,000
=$53,000
Total savings=Total amount needed - Total assistance
=$66,000 - $53,000
=$13,000
She needs to save $13,000 in two years
There are 12 months in one year
2 years=2*12=24 months
Monthly savings=Total savings/24 months
=$13,000/24
=$541.666666
To the nearest cent
=$541.67
Answer:
The area of the unpainted region on the four inch board = 160·√3 in.²
Step-by-step explanation:
Here we have that the boards are crossing each other on their flat sides Therefore, when the boards are separated, the area of the unpainted region is the area of a parallelogram
The dimensions of the formed parallelogram are;
Interior angles = 60° and 120° (adjacent angles of a parallelogram)
Height, h of parallelogram formed = 4 inches
From the angle of crossing of the parallelogram, we have;
Angle between the width or perpendicular cross section of the 6 inches board and the angle of crossing of the two boards = 90° - 60° = 30°
Therefore, length of base, b of the parallelogram formed by the unpainted region is given as follows;

Therefore, the area of the parallelogram = b × h = 4 × 40·√3 = 160·√3 in.²
Hence, the area of the unpainted region on the four inch board = 160·√3 in.².
Answer:
- 3x + 6 = 12; Distributive Property
Step-by-step explanation:
<u>The next step is:</u>
- 3*x + 3*2 = 12
- 3x + 6 = 12
This is a distributive property
Correct choice is A