Answer:
Step-by-step explanation:
1). x² - 8x
To convert this expression into a perfect square trinomial,
x² - 2(4x) + 4² = (x - 2)²
Therefore , 4² = 16 should be added.
Option (4) is the answer.
2). x² + 2x = 3
x² + 2(1)(x) = 3
x² + 2(1)(x) + 1 = 3 + 1 [By adding 1 on both the sides]
(x + 1)² = 4
x + 1 = ±2
x = -3, -1
Option (1) is the answer.
3). 3x²- 18x = 21
x² - 6x = 7
x² - 2(3x) = 7
x² - 2(3x) + 3² = 7 + 3²
(x - 3)² = 7 + 9
(x - 3)² = 16
x - 3 = ±4
x = -1, 7
X means everything in algebra. It is a variable, which means that its meaning changes based on context. For example, x could be time, but it could also be cars. x is what all Mathematicians chase after and it is also the greatest tool at their disposal. x is generally called an independent variable because its value determines the output of a function. y, on the other hand, is the result of fooling around with x. It's a dependent variable, which means that y changes when x changes.
Take, for instance, the following function:
y = x + 3
Let's set x = 3.
y = (3) + 3
y = 6
As you can see, what we input as x determines what y outputs.
Diffusion- The process by which molecules spread themselves out evenly in a given area. This happens by natural molecular movement.How do particles move across membranes?- by osmosis, active transport, simple diffusion and facilitated diffusionSimple/Passive Diffusion<span>- No energy
- Happens across cell membrane
- From high to low concentration ("down the concentration gradient")</span>Controlled/Facilitated Diffusion- diffusion across a membrane through specific protein channels in the membrane, with no energy costOsmosis- Simple diffusion of waterActive Transport<span>- Requires energy
- Happens only at specific channels
- From low to high concentration ("against the concentration gradient")</span>Concentration Gradient- difference in concentration of a substance between one area and anotherGradient- Different or unevenSemi-Permeability<span>- a type of biological membrane that will allow certain molecules or ions to pass through it by diffusion
(- maintain a balance of water in the cell
- ability to differentiate materials that are needed and those that are not needed in the cell, keeping the cell healthy
- ability to control the amount and kind of substances through the cell membranes )</span>What must we understand? (homeostasis- cells)- Cells constantly change concentrations to their benefit and to maintain stable internal conditions.Endocytosis- the movement of bulk liquids or solids into a cell, by the indentation of the plasma membrane to form vesicles containing the substance; active process requiring ATPEndo--means 'inside'Exocytosis- the movement of bulk liquids or solids out of a cell by fusion of vesicles containing the substance with the plasma membrane; active process requiring ATPExo--means 'outside'How many types of Endocytosis are there?- 3 types of endocytosis-- phagocytosis, pinocytosis and receptor mediated endocytosisPhagocytosis- In endocytosis, if the substances being taken in are particles, such as bacteria, then process is called phagocytosisPinocytosis- In endocytosis, if the substances are in solution, such as the end products of digestion, then the process is called pinocytosisReceptor-Mediated Endocytosis- is an endocytotic mechanism in which specific molecules are ingested into the cell.Water Potential- the tendency of water molecules to move from an area of higher concentration to an area of lower concentrationPlasmolysis- Shrinkage of protoplasm away from the cell wall of a plant or bacterium due to water loss from osmosis, therefore resulting in gaps between the cell wall and cell membrane.Protoplasm- the fluid living content of the cell-- composed mainly of nucleic acids, proteins, lipids, carbohydratesTypes of Solutions<span>- hypotonic
- isotonic
- hypertonic</span>Hypotonic<span>- concentration of dissolved substances is greater INSIDE the cell
- through osmosis, H2O diffuses INTO the cell
- hippos get fat, so will the cell
[a less concentrated solution (one with a more negative water potential) than the cell solution]</span>Isotonic<span>- concentration of dissolved substances is EQUAL INSIDE and OUTSIDE the cell
- H2O diffuses INTO the cell and OUT of the cell at the same rate</span>Hypertonic<span>- concentration of dissolved substances is greater OUTSIDE the cell
- through osmosis, H2O diffuses OUT of the cell
- this cell will shrink
[a more concentrated solution (one with a less negative water potential) than the cell solution]</span>Gene- a length of DNA at a specific location on a chromosome that controls a specific heritable characterisicStandard Deviation (SD)<span>- measures the spread of the data in a set by describing how far the numbers are from the mean
(- a valuable method of analysis
- it takes into account all values & it's not affected by extreme values
- gives you a hint on how accurate the data is- if the method is good- if you can draw a valid conclusion)</span>Equation for Standard Deviationn= # of data pointsHow do you find the mean?- in a data set, add all the values together then divide by the total number of values in the setHigh SD- the data is widely spread (less reliable)Low SD- the data is clustered closely around the mean (more reliable)Cell Membrane- controls what comes in and out of the cellCell Wall- composed of cellulose and other carbohydrates, giving plant cells further support and a more rigid structure than animal cellsNucleus<span>- the brain and control center of the cell:
contains DNA
controls all cellular functions in the cell</span>Nucleolus- small body found in the nucleus of eukaryotic cells where ribosomal RNA is synthesisedCytoskeleton<span>- in the structural support; </span>
