Answer:
a. Fraction of earnings that Mariano put into each piggy bank is 1/12
b. Mariano earns $28.8
Step-by-step explanation:
Mariano divides his earning in a saving account and 3 piggy banks.
First , we have to know the fraction that we divide in the 3 piggy banks.
Piggy banks =Total earning-Saving account
Saving account 3/4,
Total earning is 1
to rest both term we have to get the same denominator , so we can say that the total earning is 4/4
Piggy banks =4/4-3/4=( 4-3)/4=1/4
Piggy banks =1/4
Each piggy bank will be 1/3 of that 1/4
1/3 x 1/4=
For fraction multiplication, multiply the numerators and then multiply the denominators to get
1×1/3×4=1/12
This fraction cannot be reduced.
b. Mariano adds $2.40
1/12 is 2.40
total earning is ?
We use cross-multiplication
a/b=c/d replacing (1/12)/2.40 = 1/ ?
So, the total earning (?) is 1 x 2.40/ (1/12)
= 2.40 x 12=$28.8
Answer as a fraction: 17/6
Answer in decimal form: 2.8333 (approximate)
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Work Shown:
Let's use the two black points to determine the equation of the red f(x) line.
Use the slope formula to get...
m = slope
m = (y2-y1)/(x2-x1)
m = (4-0.5)/(2-(-1))
m = (4-0.5)/(2+1)
m = 3.5/3
m = 35/30
m = (5*7)/(5*6)
m = 7/6
Now use the point slope form
y - y1 = m(x - x1)
y - 0.5 = (7/6)(x - (-1))
y - 0.5 = (7/6)(x + 1)
y - 0.5 = (7/6)x + 7/6
y = (7/6)x + 7/6 + 0.5
y = (7/6)x + 7/6 + 1/2
y = (7/6)x + 7/6 + 3/6
y = (7/6)x + 10/6
y = (7/6)x + 5/3
So,
f(x) = (7/6)x + 5/3
We'll use this later.
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We ultimately want to compute f(g(0))
Let's find g(0) first.
g(0) = 1 since the point (0,1) is on the g(x) graph
We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.
We now use the f(x) function we computed earlier
f(x) = (7/6)x + 5/3
f(1) = (7/6)(1) + 5/3
f(1) = 7/6 + 5/3
f(1) = 7/6 + 10/6
f(1) = 17/6
f(1) = 2.8333 (approximate)
This ultimately means,
f(g(0)) = 17/6 as a fraction
f(g(0)) = 2.8333 as a decimal approximation
Answer:
the point (-3, 5) would be plotted in the second quadrant, quadrant ||
Step-by-step explanation:
The answer is: " 5/2 ; or, write as: "2 ½ " ; or, write as: "2.5" .
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15/ (3x - 6) ;
Substitute "4" for "x" ; and solve:
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Note: (3x -6) = 3(4) - 6 = 12 - 6 = 6 ;
Rewrite the expression:
15/6 = (15 ÷ 3) / (6 ÷ 3) = 5/2 ; or, write as: "2 <span>½ " ; or, write as: "2.5" .
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Answer:
a = -12
b = 3
Step-by-step explanation:
second term = a + 6b
to find the 5th term, notice the pattern (since this is a linear equation, each term increases by the same amount) and each term increases by 4b: 2b -> 6b -> 10b.
therefore, the 4th term would be a+14b and the 5th would be a+18b
so a + 6b = 8
and a + 18b = 44
u now have two simultaneous equations, which can be solved through substitution or elimination. I'm gonna use elimination because it's quicker in this case:
steps: (since the a would cancel out by subtracting, subtract then solve for b. divide by -12 on both sides to isolate the b)
now that u know the value of b, substitute it into an equation to solve for a:
a + 6b = 8
a + 6(3) = 8
a + 24 = 8
a = 8 - 24
a = -16
hope this helps!
