Answer:
p = 4
Step-by-step explanation:
The usually recommended procedure for solving a proportion is to "cross multiply", then divide by the coefficient of the variable. (Solve the remaining one-step equation.)
<h3>Cross multiply</h3>
This means multiply both sides of the equation by the product of the denominators:
(15/6)(6p) = (10/p)(6p) . . . . "cross multiply"
15p = 60 . . . . . . simplify
<h3>Second step</h3>
Now, divide by the coefficient of the variable.
15p/15 = 60/15
p = 4
The solution is p = 4.
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<em>Additional comment</em>
If the variable is in the <em>numerator</em> of the proportion, using cross multiplication, you will find that you end up multiplying and dividing by the other denominator. To solve it in that case, you only need to multiply by the denominator under the variable.
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For example, to solve ...
2/5 = p/10
you only need to multiply by 10. You don't need to multiply by 50, then divide by 5.
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Any proportion can be written 4 ways:
This suggests another strategy: invert the whole proportion, then solve it as one with p in the numerator:
6/15 = p/10 ⇒ p = 10(6/15) = 4
Answer: $2,833.47
Step-by-step explanation:
Part 1:
n = [lnA - lnP] / ln(1 + i)
n = [ln15000 - ln10000] / ln(1 + 0.03)
n = [9.6158 - 9.2103] / 0.0296
n = 13.70
13 years, 8 months, and 12 Days
Part 2:
P = A / [(1 + i)n]
P = 15000 / [(1.03)4]
P = 15000 / 1.1255
P = $13,327.31
Part 3:
A = 10000 (1 + 0.04)5
A = $12,166.53
The amount of money you need to save to buy a car at $15,000 would be;
$15,000 - $12,166.53
=> $2,833.47
Answer:
8 gallons
Step-by-step explanation:
Each rectangular face of the monument has an area of ...
A = bh = (9 ft)(39 ft) = 351 ft^2
The triangular face on top of that rectangle has an area of ...
A = (1/2)bh = (1/2)(9 ft)(10 ft) = 45 ft^2
So, one side of the monument has an area of ...
one side = (351 ft^2) +(45 ft^2) = 396 ft^2
The total area of all four identical sides is ...
surface area = (4)(396 ft^2) = 1584 ft^2
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Each gallon covers 199 ft^2, to the number gallons required is ...
(1584 ft^2)/(199 ft^2/gal) ≈ 7.96 gal
Since only whole gallons can be purchased, 8 gallons of paint must be bought.
Answer:
Step-by-step explanation:
In representing mixed numbers on a number line, we need first to pay attention to the denominators. Here, denominators are 8 and 5, their least common multiple is 40, so, we will need to cut up space between two numbers on the number line on 40 pieces. Also, we have 5 and 3 wholes at these mixed numbers, so, our answer is going to be greater than 8.
We will cut the space between 8 and 9 on a number line on 40 pieces, and we will add 
and 
and get :
So, on a number line between 8 and 9 we need to count 31 out of 40 pieces and that is the result, 8 wholes and 
.
Answer:
x = 20
Step-by-step explanation:
The 2 given angles are alternate interior angles and are congruent, thus
7x - 3 = 6x + 17 ( subtract 6x from both sides )
x - 3 = 17 ( add 3 to both sides )
x = 20
