Algebra<span><span>Introduction to Algebra
</span>Variables<span>
</span>Expressions<span>
</span>Equations<span>
</span>Solution of an equation<span>
</span>Simplifying equations<span>
</span>Combining like terms<span>
</span>Simplifying with addition and subtraction<span>
</span>Simplifying by multiplication<span>
</span>Simplifying by division<span>
</span>Word problems as equations<span>
</span>Sequences VariablesA variable is a symbol that represents a number. Usually we use letters such as n, t, or x for variables. For example, we might say that s stands for the side-length of a square. We now treat s as if it were a number we could use. The perimeter of the square is given by 4 × s. The area of the square is given by s× s. When working with variables, it can be helpful to use a letter that will remind you of what the variable stands for: let n be the number of people in a movie theater; let t be the time it takes to travel somewhere; let d be the distance from my house to the park. ExpressionsAn expression is a mathematical statement that may use numbers, variables, or both.Example:The following are examples of expressions:2x3 + 72 × y + 52 + 6 × (4 - 2)z + 3 × (8 - z<span>)</span></span>
A.) False
b.) True
c.) True
d.) True
<h3>
Answer: 35</h3>
A prime number is one where the only factors are one and itself. A composite number has other factors.
You'll have to look at the list of numbers from 1 to 50
In that list, 47 is the largest prime less than 50, and 12 is the smallest composite number greater than 10.
So 47-12 = 35
Angle D is 180° -75° -45° = 60°. Drawing altitude MX to segment DN divides the triangle into ΔMDX, a 30°-60°-90° triangle, and ΔMNX, a 45°-45°-90° triangle. We know the side ratios of such triangles (shortest-to-longest) are ...
... 30-60-90: 1 : √3 : 2
... 45-45-90: 1 : 1 : √2
The long side of ΔMDX is 10√3, so the other two sides are
... MX = MD(√3/2) = 15
... DX = MD(1/2) = 5√3
The short side of ΔMNX is MX = 15, so the other two sides are
... NX = MX(1) = 15
... MN = MX(√2) = 15√2
Then the perimeter of ΔDMN is ...
... P = DM + MN + NX + XD
... P = 10√3 +15√2 + 15 + 5√3
... P = 15√3 +15√2 +15 . . . . perimeter of ΔDMN
It’s true!! Hope this helped!!!!
