Answer: Option C (
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)
Step-by-step explanation:
1. To solve this problem you must use the Quadratic formula, which is used to solve quadratic equation. This formula is shown below:
2. Substitute values. Then, you have:
3. Then,you obtain the following result:
±
<h3>
Answer:</h3>
System
Solution
- p = m = 5 — 5 lb peanuts and 5 lb mixture
<h3>
Step-by-step explanation:</h3>
(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.
For the total amount of mix:
... p + m = 10
For the quantity of peanuts in the mix:
... p + 0.2m = 0.6·10
For the quantity of almonds in the mix:
... 0.8m = 0.4·10
For the ratio of peanuts to almonds:
... (p +0.2m)/(0.8m) = 0.60/0.40
Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.
So, your system of equations could be ...
___
(b) Dividing the second equation by 0.8 gives
... m = 5
Using the first equation to find p, we have ...
... p + 5 = 10
... p = 5
5 lb of peanuts and 5 lb of mixture are required.
The equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
<h3>How to determine the equation?</h3>
The attached table of values represents the missing piece in the question.
Start by calculating the rate of change using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (14.77 - 10.55)/(7- 5)
Evaluate
m = 2.11
The equation is then calculated using:
y = m(x - x1) + y1
This gives
y = 2.11(x - 5) + 10.55
Evaluate
y = 2.11x - 10.55 + 10.55
y = 2.11x
Hence, the equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
Read more about linear equations at:
brainly.com/question/14323743
#SPJ1
Answer:
∠ B = 60°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
(10x - 45)° is an exterior angle of the triangle , then
10x - 45 = 3x + 4x = 7x ( subtract 7x from both sides )
3x - 45 = 0 ( add 45 to both sides )
3x = 45 ( divide both sides by 3 )
x = 15
Then
∠ B = 4x = 4 × 15 = 60°
For example, lets say:
L = 10
H = 6
W = 4
Imagine the shape is facing slightly towards your left
A left vertical cross section (perpendicular to the base) of the cuboid would result in a 10 by 6 rectangle
A right vertical cross section (perpendicular to the base) of the cuboid would result in a 6 by 4 rectangle
A horizontal cross section (parallel to the base) of the cuboid would result in a 10 by 4 rectangle
An angled cross section (through the middle) would also give a rectangle but the dimensions would be different. If the cut went from one '4' edge to the one in the opposite corner, the length of that would be found using Pythagoras
a² + b² = c²
6² + 10² = c²
36 + 100 = 136
√136 ≈ 11.66cm
11.66 by 4 rectangle
The shows that the resulting shape will always be a rectangle for these cross sections.
<em>The only case in which it would not, would be if one of the faces of the cuboid was a square - in which case one of the cross sections would also be a square.</em>
