The answer would be C.) The way you group numbers in a series of multiplication problems doesn't change the final product.
A. is invalid because any whole number x 1 would be that whole number as the product.
B. Is invalid because any number x 0 will be 0.
D. is invalid because you can multiply in any way as long as the number's value (example, 1 turning into -1 without any multiplication of -1) does not change during the process.
F(x) = 4 - x² g(x) = 6x
(g - f)(x) = g(x) - f(x)
(g - f)(3) = g(3) - f(3)
g(x) = 6x
g(3) = 6*3 = 18
f(x) = 4 - x²
f(3) = 4 - 3² = 4 - 9 = -5
(g - f)(3) = g(3) - f(3) = 18 - (-5) = 18 + 5 = 23
(g - f)(3) = 23
No guarantee that there will enough hotdogs for the buns, we must find the common multiple between the usual number of hot dogs and buns in each package.
Since we're looking for the smallest common multiple between 8 and 10, we can use the method shown below to compute for the least common multiple.
8 = 2³
10 = 2 x 5
LCM = 2³ x 5 = 40
To purchase 40 hot dogs and buns, you need to buy 5 packages of buns and 4 packages of hot dogs.
Answer:
Hotdog: 4 packages
Buns: 5 packages
Answer: x = 2.65, y = 3.81
Step-by-step explanation:
ABC similar to PQR
1) Find the ratio of corresponding sides
2) Use that ratio to find values for x & y
1) Side AB = 2.76cm & Side PR = <em>y</em><em> </em>cm
Side BC = <em>x</em> cm & Side RQ = 3.66 cm
Side CA = 3 cm & Side QP = 4.14 cm (both lengths given)
Can match 3 to 4.14 & ratio of sides in ABC to PQR= 3 /4.14
Length of sides ABC = 3/4.14 times the length of sides PQR
2) x = (3 / 4.14) * 3.66 = 2.65
Now solve for y, ABC to PQR: 2.76 = (3 / 4.14) (<em>y </em>)
<em>equality property</em> (both sides) & inverse operation to isolate <em>y : </em> . 2.76 ÷ (3 / 4.14) = (3 / 4.14 ) ÷ (3 / 4.14) (<em>y</em><em>)</em>
2.76 * (4.14 / 3) = 3 / 4.14 * (4.14 / 3) (<em>y</em><em>)</em>
(2.76 * 1.38 ) = 3.81 = <em>y</em>
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<em>Scale Factor Method: Determine the Multiplier</em>
Small to Big or Big to Small ➜ Be sure not to switch
