Multiplying both sides of <span>−1/3x≤−6 by -3 results in "x is equal to or greater than 18."
Note that multiplying such an inequality requires reversing the direction of the inequality symbol.
I subst. 18 for x in </span><span>−1/3x≤−6 as a check, and found that the resulting inequality is true.</span>
Answer:
first number(x) = 2 second number(y)= 6
Step-by-step explanation:
This is an example of a simultaneous equation.
First write this word problem as equations, where x is the "first number" that you've mentioned and y is the "second number".
x + 2y = 14 (equation 1)
2x + y = 10 (equation 2)
This is solved using the elimination method.
We need to make one of the coefficients the same - in this case we can make y the same. In order to do this we need to multiply equation 2 by 2, so that y becomes 2y.
2x + y = 10 MULTIPLY BY 2
4x + 2y = 20 (this is now our new equation 2 with the same y coefficient)
Now subtract equation 1 from equation 2.
4x - x + 2y - 2y = 20 - 14 (2y cancels out here)
3x = 6
x = 2
Now we substitute our x value into equation 1 to find the value of y.
2 + 2y = 14
2y = 12
y = 6
Hope this has answered your question.
What is the equivalent value of 1/3×(−15)
Answer: -5x
Answer:
x = 10 , EF = 8 , FG = 15.
Step-by-step explanation:
Given : If EF = 2x – 12, FG = 3x – 15, and EG = 23.
To find : find the values of x, EF, and FG.
Solution : We have given EF = 2x – 12, FG = 3x – 15, and EG = 23.
Let the line E ___F___G.
Here F is the mid point of EG . ( mid point divide the line EG cut the line EG in two equal parts)
We can say EF = FG.
EF + FG = EG -------(1)
Plug tha values EF = 2x -12 and FG = 3x - 15 , EG = 23 in equation (1).
2x - 12 + 3x -15 = 23 .
On combine like terms
2x + 3x -12 -15 = 23 .
5x - 27 + 23 .
on adding both side by 27.
5x = 23 +27.
5x = 50 .
On dividing both sides by 5.
x = 10.
Them, EF = 2 (10) -12
20 -12
EF = 8
FG = 3 (10) -15 .
FG = 30 -15 .
FG = 15.
EG = 5 +18 = 23 .
Therefore, x = 10 , EF = 8 , FG = 15.
G(x) = f(x+1) - f(x)
=[ a(x+1)^2+b(x+1)+c ] - [ax^2+bx+c]
=[ a(x^2+2x+1) +bx + b + c ] - [ax^2 + bx + c]
=[ ax^2 + 2ax + a + bx + b + c ] - [ax^2 + bx + c]
= ax^2 + 2ax + a + bx + b + c - ax^2 - bx - c
= 2ax + a + b
Therefore g(x) = 2ax + a + b
h(x) = g(x+1) - g(x)
=2a (x+1) + a + b - [2ax+a+b]
=2ax + 1 + a +b - 2ax - a - b
Therefore h(x) = 1