You can add and subtract radicals by ensuring that they have same radical parts.
<h3>What's radical?</h3>
It should be noted that a radical expression is an expression that contains the radical symbol which is ✓.
The necessary steps to add or subtract radicals include:
Identify the radical parts.
Add them together.
If there's unlike radical parts, one will manipulate the parts involved before solving.
Example: Add ✓63 + 5✓7
It should be noted that ✓63 = ✓9 × ✓7 = 3✓7
Therefore, ✓63 + 5✓7 will be:
= 3✓7 + 5✓7
= 8✓7.
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Answer:
<h2>Any point on the purple region.</h2>
<em>Look at the picture.</em>
Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below a line
>, ≥ - shaded region above a line
y = 3x
for x = 0 → y = 3(0) = 0 → (0, 0)
for x = 2 → y = 3(2) = 6 → (2, 6)
y < 3x - dotted line, shaded region below the line
y = 5 - it's a horizontal line passes througth points (x, 5) <em>/x - any real number/</em>
y < 5 - dotted line, shaded region below the line
Answer:
See proof below
Step-by-step explanation:
We will use the hint. The statement of the hint holds true, as the linear span of a set of vectors T is equal to the set of linear combinations of vectors in T.
Denote the linear span of vectors with the curly brackets < >, that is,
Let , then u is a linear combination of v1,v2,v3, that is, there exist scalars such that . Multiply by 3 in both sides to get , with
Since , as real numbers are closed under multiplication. Therefore 3u is a linear combination of the vectors , that is,
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. A parabola intersects its axis of symmetry at a point called the vertex of the parabola. You know that two points determine a line.
Hope it helps!
Answer:
1.) 8.09g ; 2) 206.7 years
Step-by-step explanation:
Given the following :
Half-life(t1/2) of Uranium-232 = 68.9 years
a) If you have a 100 gram sample, how much would be left after 250 years?
Initial quantity (No) = 100g
Time elapsed (t) = 250 years
Find the quantity of substance remaining (N(t))
Recall :
N(t) = No(0.5)^(t/t1/2)
N(250) = 100(0.5)^(250/68.9)
N(250) = 100(0.5)^3.6284470
N(250) = 100 × 0.0808590
= 8.0859045
= 8.09g
2) If you have a 100 gram sample, how long would it take for there to be 12.5 grams remaining?
Using the relation :
N / No = (1/2)^n
Where N = Amount of remaining or left
No = Original quantity
n = number of half-lifes
N = 12.5g ; No = 100g
12.5 / 100 = (1/2)^n
0.125 = (1/2)^n
Converting 0.125 to fraction
(1/8) = 1/2^n
8 = 2^n
2^3 = 2^n
n = 3
Recall ;
Number of half life's (n) = t / t1/2
t = time elapsed ; t1/2 = half life
3 = t / 68.9
t = 3 × 68.9
t = 206.7 years