Given:
In a right angle triangle, two interior angles are 60° and 30°, and their opposite sides are x and 3 respectively.
To find:
The length of side x in simplest radical form with a rational denominator.
Solution:
In a right angle triangle,
Using this formula for the given triangle, we get
On cross multiplication, we get
Therefore, the length of side x in simplest radical form is units.
Answer:
<u>So, the answer is option B: a = −5, b = −9, c = 12</u>
Step-by-step explanation:
The general form of the quadratic Formula is ax² + bx + c = 0
We need to compare the given quadratic equation to the general form
ax² + bx + c = 0
−5x² − 9x + 12 = 0
So, we can deduce that
a = -5 , b = -9 and c = 12
<u>So, the answer is option B: a = −5, b = −9, c = 12</u>
Area of the canvas: 96 = 2 · W² + 2 · W L,
where W is the width and L is the length of a back and a top side. Two square sides have area W².
2 W L = 96 - 2 W² /:2
W L = 48 - W²
L = ( 48 - W² ) / W.
The inside volume of the shelter:
V = L · W · W = L · W²
V = W² · ( 48 - W² ) / W ;
V = 48 W - W³
We have to find the derivative:
V ` = 48 - 3 W²
48 - 3 W² = 0 ( for V max. )
3 W² = 48
W² = 48 : 3
W² = 16; W = √16; W = 4 ft.
L = ( 48 - 16 ) / 4 = 32 / 4 = 8 ft.
Answer: The length of the shelter for which the volume inside is maximized is 8 ft.
9514 1404 393
Answer:
124
Step-by-step explanation:
In the absence of any information about interest compounding, we'll assume that simple interest applies. The balance is ...
A = P(1 +rt) . . . . . principal P, annual rate r, for t years
A = 100(1 +0.03×8) = 100×1.24
A = 124
124 would be in the account after 8 years.
_____
<em>Additional comment</em>
If interest is compounded annually, the amount would be ...
100(1.03^8) ≈ 126.68
Answer:
provides information about the strength of a relationship
Step-by-step explanation:
A numerical measure of strength in the linear relationship between any two variables is called the Pearson's product moment correlation coefficient.
The co efficient of correlation is a pure number denoted by r , independent of the units in which the variables are measured that can range from+1 to -1 .
The sign of r indicates the direction of the cor relation.
When r= 0 it does not mean that there is no relationship . For example if the observed values lie exactly on a circle , there is a relationship between variables but r = 0 as r only measure linear cor relation.
The 2nd statement given is the correct answer.
It is not related to ordinal or nominal properties and it does show direction.