Answer:
IJ = 6
Step-by-step explanation:
This is a 30-60-90 triangle.
The ratio of the lengths of the sides is:
1 : sqrt(3) : 2
The short leg is the length of the long leg divided by sqrt(3).
The hypotenuse is twice the length of the short leg.
IK = JK/sqrt(3) = 3sqrt(3)/sqrt(3) = 3
IJ = 2IK = 2(3) = 6
<span>△RST is a right triangle because RS¯¯ is perpendicular to RT¯¯ .</span>
11) Since the triangle has a pair of congruent base angles, it is an isosceles triangle which means that the two pairs of legs are congruent.
Make them equal to each other in an equation.
5x = x + 20
Subtract x from both sides.
4x = 20
Divide both sides by 4.
x = 5
12) The two legs are congruent so that means the base angles must be congruent. First find the measure of the base angles. Create an equation:
x + x + 50 = 180
Combine like terms.
2x + 50 = 180
Subtract 50 from both sides.
2x = 130
Divide both sides by 2.
x = 65
Now make the base angle plus x equal 180, because they form a straight line.
65 + x = 180
Subtract 65 from both sides.
x = 115
13) You know the vertex angle (top angle) is 90 degrees because it is supplementary to a right angle. The triangle is isosceles because the two legs are congruent, so make the base angles plus 90 add up to 180 in an equation.
x + x + 90 = 180
Combine like terms.
2x + 90 = 180
Subtract 90 from both sides.
2x = 90
Divide both sides by 2.
x = 45
Given:
Total amount for investment = $32000
Rate of interest for Stock A = 4%
Rate of interest for Stock B = 7%
Jim is hoping to earn $2,000 in interest.
To find:
The amount of investments in Stock A and Stock B.
Step-by-step explanation:
Let amount of investments in Stock A = $x
Amount of investments in Stock B = $y
Total amount for investment = $32000
...(i)
Rate of interests in Stock A and Stock B are 4% and 7%. Total interests is $2000.
...(ii)
From (i) and (ii), we get
Divide both sides by -0.03.
Put x=8000 in (i).
Therefore, the amount of investments in Stock A and Stock B are $8000 and $24000 respectively.
