Answer:
this seems like an interesting story
Answer:
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
Step-by-step explanation:
Let x represent the number of 30-day periods.
Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used.
Therefore the equation =
$165 -$4 × x
= 165 - 4x.......... Equation 1
He has another gift card for $145 that loses $3.50 for each 30-day period it is not used.
$145 -$3.50 × x
= 145 - 3.50x........... Equation 2
Hence, an equation for the number of 30-day periods until the value of the gift cards will be equal is obtained by equating Equation 1 and Equation 2 together
So, we have
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
We simplify further:
165 - 145 = -3.50 + 4.0x
20 = 0.5x
x = 20/0.5
x = 40
Therefore, number of each 30-day periods until the value of the gift cards will be equal is 40
Answer:
6.1° and 83.9°
Step-by-step explanation:
Complementary angles sum 90°
a+b = 90°
a = b - 77.8
then:
(b - 77.8) + b = 90
2b - 77.8 = 90
2b = 90 + 77.8
2b = 167.8
b = 167.8/2
b = 83.9°
a = b - 77.8
a = 83.9 - 77.8
a = 6.1°
Answer:
a. 29.3 units²
Step-by-step explanation:
The area of a circle is A = πr².
The area of each triangle is A = ½bh.
The vertex angle of each triangle is 360/5 = 72°. If we cut the triangle in half, we can use trig to write:
sin 36° = (½b) / r
b = 2r sin 36°
And:
cos 36° = h / r
h = r cos 36°
Substituting, we get the area of each triangle is:
A = r² sin 36° cos 36°
A = ½ r² sin 72°
The radius of the circle is 8. So the area of the circle minus the area of the 5 triangles is:
A = π (8)² − 5 (½) (8)² (sin 72°)
A ≈ 48.9 units²
Three fifths of the area is shaded, so:
⅗ A ≈ 29.3