Answer:
x° = 149°
Step-by-step explanation:
According to the <u>Triangle Sum Theorem</u>, the sum of the measures of the angles in every triangle is 180°. Since we are given two angles with measures of m < 86° and m < 63°, then the third angle must be:
m < 86° + m < 63° + m < (angle 3) = 180°
149° + m < ? = 180°
Subtract 149° from both sides to solve for m < (angle 3)
149° - 149° + m < (angle 3) = 180° - 149°
m < ? = 31°
Therefore, the measure of the third angle is 31°.
To find x°, we can reference the <u>Triangle Exterior Angle Postulate</u>, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
In other words, the measure of x° = m < 86° + m < 63°
x° = 149°
By the way, m< (angle 3) and x° are also supplementary angles whose sum equal 180°:
x° + m < (angle 3) = 180°
149° + 31° = 180°
Answer:
sqrt(A/pi), -sqrt(A/pi)
Step-by-step explanation:
A=pi*r^2
r^2=A/pi
r=sqrt(A/pi), -sqrt(A/pi)
Answer:
The investor receives $200
Step-by-step explanation:
In order to find this, simply multiply the percentage by the total amount.
$5,000 * 4%
$5,000 * .04
$200
Answer: 20 oranges and 5 mangoes
Step-by-step explanation:
Define the following:
x = number of oranges
y = number of mangoes
Make the following system of equations:
x + y = 25
0.35x + 1.00y = 12.00
Solve for x:
y = 25 - x
⇒ 0.35x + 1.00(25 - x) = 12.00
⇒ 0.35x + 25 - x = 12.00
⇒ -0.65x = -13.00
⇒ x = 20
Solve for y:
20 + y = 25
y = 5
∴ 20 oranges and 5 mangoes were purchased.