Answer:
20
Step-by-step explanation:
We write what we know.
Jimmy
$50/mo app 65¢ or .65
Lisa
$55/mo app 40¢ or .40
a = number of apps
The difference will come from the number of apps, a.
We need them to equal each other so let's write an equation.
$50 + .65a = $55 + .40a
We need to solve for a.
$50 + .65a = $55 + .40a subtract $50 for each side.
$50 - $50 + .65a = $55 - $50 + .40a
.65a = $55 - $50 + .40a
.65a = $5 + .40a subtract .40a from each side
.65a - .40a = $5 + .40a - .40a
.65a - .40a = $5
.25a = $5 Divide each side by .25
.25a/.25 = $5/.25
a = $5/.25
a = 20
So Jimmy and Lisa need to download 20 apps for their bill to be the same.
Answer:
rhombus; Measure of angle B = 70 degrees
Step-by-step explanation:
The shape is a rhombus. Angle B and angle A are supplementary, so they add up to 180 degrees.
110 + B = 180
B = 180 - 110
B = 70
It is a rhombus because all sides are equal.
1 cup is 8 fluid ounces.
1 cap is 6 oz, 2 caps is 12 oz, is that greater than 8 oz? well, surely you'd know.
Answer:
(- 1, 8 ) and (5, 2 )
Step-by-step explanation:
Given the 2 equations
y = - x + 7 → (1)
y = 0.5(x - 3)² → (2)
Substitute y = 0.5(x - 3)² into (1)
0.5(x - 3 )² = - x + 7 ← expand and simplify left side
0.5(x² - 6x + 9) = - x + 7 ( multiply both sides by 2 )
x² - 6x + 9 = - 2x + 14 ( subtract - 2x + 14 from both sides )
x² - 4x - 5 = 0 ← in standard form
(x - 5)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 5 : y = - 5 + 7 = 2 ⇒ (5, 2 )
x = - 1 : y = 1 + 7 = 8 ⇒ (- 1, 8 )
