Answer:
5%
Step-by-step explanation:
1. We assume, that the number 48 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 48, so we can write it down as 100%=48.
4. We know, that x% equals 2.4 of the output value, so we can write it down as x%=2.4.
5. Now we have two simple equations:
1) 100%=48
2) x%=2.4
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=48/2.4
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for 2.4 is what percent of 48
100%/x%=48/2.4
(100/x)*x=(48/2.4)*x - we multiply both sides of the equation by x
100=20*x - we divide both sides of the equation by (20) to get x
100/20=x
5=x
x=5
now we have:
2.4 is 5% of 48
x: 13.8924439894498
y: 6
B) (12,0) (6,0) .....
Answer:
(-6,9,-3)
Step-by-step explanation:
-3x -y +z=6
-3x-y+3z =0
x-3z =3
Multiply the second equation by -1
-1 *(-3x-y+3z) =0*-1
3x +y -3z =0
Add this to the first equation
-3x -y +z=6
3x +y -3z =0
----------------------
0 + 0 + -2z = 6
Divide by -2
-2z/-2 = 6/-2
z = 6/-2
z=-3
Take the third equation to find x
x-3z=3
x-3(-3) = 3
x+9=3
Subtract 9 from each side
x+9-9 =3-9
x=-6
Now we need to find y
3x +y -3z =0
3(-6) +y -3(-3) =0
-18 +y +9=0
-9+y =0
Add 9 to each side
-9+9+y = 0+9
y=9
(-6,9,-3)
From the given word problem, the smaller number is 5
Let's assume the smaller number is represented by x and the larger number is represented by y.
According to the given information in the word problem, the difference between the two numbers is 25. This can be expressed as:
y - x = 25 (Equation 1)
It is also stated that the smaller number is 1/6th of the larger number:
x = (1/6) * y (Equation 2)
To find the value of the smaller number (x), we can substitute Equation 2 into Equation 1:
y - (1/6) * y = 25
Multiplying through by 6 to eliminate the fraction:
6y - y = 150
5y = 150
Dividing both sides by 5:
y = 30
Substituting the value of y back into Equation 2:
x = (1/6) * 30 = 5
Therefore, the value of the smaller number is 5.
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Answer:
x = 2 is a zero of f(x)
Step-by-step explanation:
if x = 2 is a zero of f(x) , then f(2) = 0
given
f(x) = - 4x³ + 2x² - 3x + 14 , then
f(2) = - 4(2)³ + 2(2)² - 3(2) + 14
= 16 - 4(8) + 2(4) - 6 + 14
= 16 - 32 + 8 - 6 + 14
= 0
since f(2) = 0 then x = 2 is a zero of f(x)
Using substitution, we can determine whether 2 is a zero of the given function.
To determine whether 2 is a zero of the function f(x)=x^(4)-4x^(3)+2x^(2)-3x+14, we can use substitution. We substitute x = 2 into the function and check if the resulting expression equals zero.
f(2) = (2)^(4)-4(2)^(3)+2(2)^(2)-3(2)+14 = 16-32+8-6+14 = 0
Since the result is zero, we can conclude that 2 is indeed a zero (root) of the function.
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