Answer:
x = 105.4
Step-by-step explanation:
We are given;
Log 3 + log x = 5/2
We are required to find x;
We are going to use the laws of logarithms to solve for x
That is;
log a + lob b = log(ab)
Therefore;
Log 3 + log x = 5/2
we get;
log 3x = 2.5
But;
Given, logₐb= x , then b = a^x
In this case;
log 3x = 2.5
we get , 3x = 10^2.5
That is , 3 x = 316.227
x = 105.4
Thus, the value of x is 105.4
Answer:x=4 y=3
Step-by-step explanation:
Let's solve your system by substitution.
2x−1=y+4;3y+1=3x−2
Step: Solve2x−1=y+4for y:
2x−1=y+4
2x−1+−y=y+4+−y(Add -y to both sides)
2x−y−1=4
2x−y−1+−2x=4+−2x(Add -2x to both sides)
−y−1=−2x+4
−y−1+1=−2x+4+1(Add 1 to both sides)
−y=−2x+5
−y
−1
=
−2x+5
−1
(Divide both sides by -1)
y=2x−5
Step: Substitute2x−5foryin3y+1=3x−2:
3y+1=3x−2
3(2x−5)+1=3x−2
6x−14=3x−2(Simplify both sides of the equation)
6x−14+−3x=3x−2+−3x(Add -3x to both sides)
3x−14=−2
3x−14+14=−2+14(Add 14 to both sides)
3x=12
3x
3
=
12
3
(Divide both sides by 3)
x=4
Step: Substitute4forxiny=2x−5:
y=2x−5
y=(2)(4)−5
y=3(Simplify both sides of the equation)
Answer:
what's the question
Step-by-step explanation:
#1
Lets x = number of adult tickets
Lets y = number of children tickets
equation 1: 8x + 4y = 5040
equation 2: x + y = 680
solve them by using substitution
x + y = 680
x = 680 - y
substitute x = 680 - y into 8x + 4y = 5040
8(680 - y) + 4y = 5040
5440 - 8y + 4y = 5040
-4y = 5040 - 5440
-4y = -400
y = 100
x = 680 - y
x = 680 - 100
x = 580
Answer:
There were 580 adults and 100 children at the last Miller's home basketball game.
#2
Similar to the #1
Lets x is the number of people riding school bus
Lets y is the number of people riding luxury charter bus
equation 1: x + y = 65
equation 2: 8x + 15y = 611
We need to write the equation in its vertex form so we have to know the general equation for the vertex form. It is written as:
y = (x - h)^2 + k
where h and k represents the point of the vertex.
We go as follows:
y = (x^2 + 4x) – 3
y +4= (x^2 + 4x+4) – 3
y = (x + 2)^2 - 7
Therefore, the correct answer from the choices is option B.
