Add: 5(0.5k−1)+2(0.4−k) . Answer should be in decimal form.(1 point
To solve the expression, we will distribute the coefficients:
5(0.5k - 1) + 2(0.4 - k)
= 2.5k - 5 + 0.8 - 2k
Now, let's combine like terms:
= 2.5k - 2k - 5 + 0.8
= 0.5k - 4.2
Thus, the answer is 0.5k - 4.2.
Subtract 1/2(z+4)−3(1/4z+1) . Use fractions in final form.(1 point)
First, let's distribute the coefficients:
1/2(z + 4) - 3(1/4z + 1)
= 1/2z + 2 - 3/4z - 3
Now, let's combine like terms:
= (1/2z - 3/4z) + (2 - 3)
To combine the fractions, we need a common denominator, which is 4.
= (2/4z - 3/4z) + (8/4 - 12/4)
= (-1/4z) + (-4/4)
= -1/4z - 4/4
= -1/4z - 1
Thus, the final answer is -1/4z - 1.
Subtract: (3b−2c)−(6c+2b)−(b+c) .(1 point)
Let's simplify the expression step by step:
(3b - 2c) - (6c + 2b) - (b + c)
First, let's remove the parentheses by changing the signs inside:
= 3b - 2c - 6c - 2b - b - c
Next, let's combine like terms:
= (3b - 2b - b) + (-2c - 6c - c)
= 0b - 9c
Since any number multiplied by 0 is 0, the coefficient of b becomes 0.
Therefore, the final simplified expression is -9c.
What value of z would make the expressions 4x−5y and (3y+2x)−z(4y−x) equivalent?(1 point)
To find the value of z that would make the expressions equivalent, we need to set them equal to each other and solve for z.
First, let's set the expressions equal to each other:
4x - 5y = (3y + 2x) - z(4y - x)
Next, let's simplify the right side:
4x - 5y = 3y + 2x - 4zy + zx
Now, let's group like terms:
4x - 5y = (2x + zx) + (3y - 4zy)
Since the expressions are equivalent, the coefficients of x and y on both sides should be equal.
Setting the coefficients equal to each other, we have:
4 = 2 + z (for x coefficients)
-5 = -4z + 3 (for y coefficients)
Now, let's solve the first equation for z:
4 = 2 + z
Subtracting 2 from both sides:
4 - 2 = z
z = 2
Substituting this value of z into the second equation:
-5 = -4(2) + 3
-5 = -8 + 3
-5 = -5
Therefore, the value of z that would make the expressions equivalent is z = 2.
What is the expression 4+8(3x−2)−7x when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work.(4 points)
To simplify the expression 4 + 8(3x - 2) - 7x, let's start by applying the distributive property:
4 + 8(3x) + 8(-2) - 7x
Next, let's simplify the multiplication:
4 + 24x + (-16) - 7x
Now, let's combine like terms:
(24x - 7x) + (4 - 16)
= 17x + (-12)
= 17x - 12
So the simplified expression is 17x - 12.