Given: ∠ DEF
To construct: ∠TSZ ≅ ∠DEF
Construction: Consider the attachment
Step-01: Draw a line XY and choose a point S on it as a vertex of the required angle. Further marks point T such that DE = ST
Step-02: Take an arc AB from point E in ∠DEF of any length and draw at point S which cuts at point P on XY line.
Step-03: Take another arc of length AB from point B in ∠DEF and draw from point P which cuts to the previous arc at Q.
Step-04: Now, join the point SQ and extend up to Z such that EF = SZ
Hence, ∠ TSZ will be the required congruent constructed angle to∠DEF
Answer:
Width of the box = 2 inches
Step-by-step explanation:
Volume of a box = length × width × height
Volume of the box = 240 cubic inches
Length of the box = (x + 8) inches
Width of the box = x inches
Height of the box = 12 inches
Volume of a box = length × width × height
240 = (x + 8) * x * 12
240 = (x² + 8x) * 12
240 = 12x² + 96x
12x² + 96x - 240 = 0
x² + 8x - 20 = 0
Solve quadratic equation using factorization method
x² + 10x - 2x - 20 = 0
x(x + 10) -2(x + 10) = 0
(x + 10) (x - 2) = 0
x + 10 = 0 OR x - 2 = 0
x = -10 OR x = 2
Width of the box can not be a negative value
Therefore,
Width of the box = 2 inches
Hello!
your answer is:
<span>using the distributive property of multiplication, the equivalent expression is:</span>
12m-15
<em>I hope this helps, and have a nice day!</em>
Answer:
Step-by-step explanation:
These exponential forms can be written into radicals very easily as long as you remember the rule: The denominator of the rational exponent serves as the index of the radical and the numerator serves as the exponent on the radicand. Let's look at a rational exponent. 3/4 4 would be the index on the radical (the number that sits in the little dip of the radical sign) and 3 is the power on the base. So
can be written in radical form as
![\sqrt[4]{x^3}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E3%7D)
Let's do 3^3/2 in your problem. 2 is the index (which is a "normal" square root and you don't need to write a 2 there cuz it's understood that it's a 2 if nothing is there), and 3 is the power on the base, which in our case is a 3. Bases can be numbers OR letters.
![3^{\frac{3}{2}}=\sqrt[2]{3^3}=\sqrt{3^3}](https://tex.z-dn.net/?f=3%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%3D%5Csqrt%5B2%5D%7B3%5E3%7D%3D%5Csqrt%7B3%5E3%7D)
That does in fact have an actual number answer, but I don't think you are simplifying them yet, only learning to write them from one form to another, so there you go!
