Suspecting that his parents are going to give him $1,300 continually you would solve like this
$120,000-$100= $19,900
$19,900/$1,300= 92.23
92.23 is the amount of $1,300 donations it would take from his parents, so if he was getting $1,300 month it would take 92.23 months
Step-by-step explanation:
Write the prime factorization of each term:
9r⁵s = 3² × r⁵ × s
6r⁴s² = 2 × 3 × r⁴ × s²
12r²s = 2² × 3 × r² × s
The greatest common factor will have all the common factors raised to their lowest exponent.
So all three terms have 3, r, and s as factors. The lowest exponent of 3 is 1. The lowest exponent of r is 2. The lowest exponent of s is 1.
GCF = 3 × r² × s
GCF = 3r²s
Factor out the GCF:
9r⁵s + 6r⁴s² − 12r²s
3r²s (3r³ + 2r²s − 4)
L x W = 105
L + W = 26 so L = 26 - W
substitute L = 26 - W into L x W = 105
(26 - W) x W = 105
26W - W^2 = 105
W^2 - 26W + 105 = 0
(W - 21)(W - 5) = 0
W - 21 = 0; W = 21
W - 5 = 0; W = 5
The the dimensions of the rectangle are 5 ft and 21 ft.
Double check:
The sum of the length and the width is 26 feet: 21 + 5 = 26 feet
A rectangle has an area of 105 square feet: 21 x 5 = 105 square feet
Answer: 2 hr.
Explanation: Think back to rate of change. <em>d</em> = <em>rt</em>, <em>r</em> = <em>d/t</em>, <em>t</em> = <em>d/r</em>. In this case, we will be using <em>d</em> = <em>rt</em>. Mph would be <em>r</em>, rate, so you would categorize 15 mph and 8 mph under rate. <em>t</em> should represent the time each cyclist traveled. Tracey's and Emma's distance, <em>d</em>, would be the same as their mph, hence Tracey's being 15<em>t</em> and Emma's would be 8<em>t</em>. When you add Tracey's distance plus Emma's distance, you end up with 46 mi. Now, you need to combine like terms, which should look like 15<em>t</em> + 8<em>t </em> = 46. Add 15 and 8 to get 23, so it should be 23<em>t</em> = 46 now. Then, divide both sides of the equation by 23 and now you should have your answer, <em>t</em> = 2 hr.
