For the first question, you will write a ratio of 1/2 oz:10 pounds. Please see the attached picture. There are 9 groups of 10 oz in 90 oz, so you will need 9 groups of the amount of medicine too!
For the second question, you need to understand that the exponent (2^3) must be evaluated first because all forms of multiplication/ groupings comes first before adding or subtracting.
Exponents are a way of showing repeated multiplication, so it is done first.
Remember you can do anything to an equation as long as you do it to both sides
2x+3(x-4)=x-20
first distribute
2x+3(x)+3(-4)=x-20
2x+3x-12=x-20
5x-12=x-20
minus x both sides
4x-12=-20
add 12 to both sides
4x=-8
divide both sides by 4
x=-2
Answer:
f(x) = x3 + 3x2 − 4x − 12
Step-by-step explanation:
A polynomial which falls tot he left and rises to the right is a function with a positive leading coefficient. Its formed by the x-intercepts or zeros x = -3, -2 and 2. The zeros form the factors (x+3)(x+2)(x-2). Multiply the factors using the distributive property to find the function in standard form.
(x+3)(x+2)(x-2)
(x^2 + 3x + 2x + 6)(x-2)
(x^2 + 5x + 6)(x-2)
x^3 + 5x^2 + 6x -2x^2 - 10x - 12
x^3 + 3x^2 - 4x - 12
The measure of the angle ∠PQR is 90 degrees
<h3>How to prove that ∠PQR is 90 degrees?</h3>
The equation of the line PQ is given as:
3x - y - 2 = 0
The coordinates of the QR are given as:
(0, -2) and (6, -4)
Make y the subject in 3x - y - 2 = 0
y = 3x - 2
The slope of the above line is
m1 = 3
Next, we calculate the slope (m2) of points Q and R.
So, we have:
m2 = (y2- y1)/(x2 - x1)
This gives
m2 = (-4 + 2)/(6 - 0)
Evaluate
m2 = -1/3
The slopes of perpendicular lines are opposite reciprocals.
m1 = 3 and m2 = -1/3 are opposite reciprocals.
This means the lines PQ and QR are perpendicular lines.
The angle at the point of perpendicularity is 90 degrees
Hence, the measure of the angle ∠PQR is 90 degrees
Read more about linear equations at:
brainly.com/question/15602982
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