Unknown g (x) = ax + b and g (g (x)) = 16x - 15. Calculate the value of a and b.
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means that when you subsituted g(x) for x in g(x), you got 16x-15
a(ax+b)+b=16x-15
distribute
xa^2+ab+b=16x-15d
we look at the x terms
therefor
xa^2=16x
a^2=16
a=-4 or 4
we will find out
look a constant terms
ab+b=-15
undistribute b
b(a+1)=-15
if a is -4 then
b(-4+1)=-15
b(-3)=-15
b=5
if a=4 then
b(4+1)=-15
b(5)=-15
b=-3
so
g(x)=-4x+5 or
g(x)=4x-3
if a=-4, b=5
if a=4, b=-3
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Answer:
12 quarts of the 90% pure apple juice should be used
Step-by-step explanation:
Here, we want to calculate the number of quarts of the 90% pure apple juice to be used.
Let the number of quarts of the 90% pure apple juice to be used be x;
This brings the total of the 85% result to (4 + x)
By mathematical convention;
4 quarts of 70% + x quarts of 90% = (4 + x) of 85%
70% = 70/100 = 0.7
90% = 90/100 = 0.9
85% = 85/100 = 0.85
Thus, mathematically;
(0.7 * 4) + (0.9 * x) = 0.85(4 + x)
2.8 + 0.9x = 3.4 + 0.85x
Let’s collect like terms
3.4 -2.8 = 0.9x -0.85x
0.6 = 0.05x
x = 0.6/0.05
x = 12
Final answer:
To get an 85% pure mixture, you need to combine 4 quarts of 70% pure apple juice with 4 quarts of 90% pure apple juice. This is obtained by setting and solving an algebraic equation based on percentage purity and volume.
Explanation:
This problem relates to an area of mathematics known as algebra. We are trying to find the amount of 90% pure apple juice needed to achieve an 85% pure mixture with a 4 quart bottle of 70% pure apple juice.
First, let's set up an equation based on the given information:
70%(amount of 70% pure apple juice) + 90%(amount of 90% pure apple juice) = 85%(total amount of apple juice mix)
Since the 70% pure apple juice is 4 quarts, the equation becomes:70%(4 quarts) + 90%(x) = 85%(4 quarts + x)
Next, we will solve for x. To do this, convert the percentages into decimals, multiply through, simplify and solve.
0.7(4) + 0.9x = 0.85(4+x)
2.8 + 0.9x = 3.4 + 0.85x
Solving for x, we get that x = 4 quarts.
So, you would need 4 quarts of the 90% pure apple juice to get an 85% pure mixture with your 4 quart of 70% pure apple juice.
Learn more about algebra here:
#SPJ3
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To find y:
To find z:
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I hope this helps;)
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Divide by 6 on each side and you get the length to be 12 yards.
Now to find the perimeter you find the sum of two times the width and two times the length.
2(6)+2(12)=perimeter
12+24+36
So the perimeter is 36 yards. Hope this helps.
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combine like terms
2x + 2 = 154
subtract 2
2x = 154
divide by 2
x = 76
so the two numbers are 76 and 78
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16x = 10(x + 1)
16x = 10x + 10
6x = 10
x = 10/6 = 1 and 2/3
The solution to the second pair of equal expressions is:
10(x + 1) = 26(+1) - 16
The left side is 10(x + 1) = 10x + 10
The right side is 26(+1) - 16 = 26-16 = 10
The equation now says 10x + 10 = 10
Subtract 10 from each side: 10x = 0
The solution to this pair of equal expressions is x = 0 .
I think I understand the weird question now. It's trying to say that
the first expression is equal to both the second and third expressions.
Let's try the first and the third:
16x = 26(+1) - 16
16x = 26 - 16
16x = 10
x = 10/16 = 5/8 = 0.625
Nope, that wasn't it.
The upshot of all my research is: I have no idea what the question is trying to say,
therefore no clue of what the actual question is, and no direction toward an answer.