Answer:
p
a
+
q
a
−
r
a
+
r
b
−
q
b
−
p
b
Regroup terms.
p
a
−
p
b
+
q
a
−
r
a
+
r
b
−
q
b
Factor
p
out of
p
a
−
p
b
.
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p
(
a
−
1
b
)
+
q
a
−
r
a
+
r
b
−
q
b
Rewrite
−
1
b
as
−
b
.
p
(
a
−
b
)
+
q
a
−
r
a
+
r
b
−
q
b
Factor out the greatest common factor from each group.
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p
(
a
−
b
)
+
a
(
q
−
r
)
−
b
(
−
r
+
q
)
Factor the polynomial by factoring out the greatest common factor,
q
−
r
.
p
(
a
−
b
)
+
(
q
−
r
)
(
a
−
b
)
Factor
a
−
b
out of
p
(
a
−
b
)
+
(
q
−
r
)
(
a
−
b
)
.
Tap for more steps...
(
a
−
b
)
(
p
+
q
−
r
)
Answer:
a² - 14a - 15 = 0 (quadratic equation)
Emily's age = 15 years
Tuli's age = 15 - 10 = 5 years
Step-by-step explanation:
let
Emily age = a
Tuli age = a - 10
Two years ago their ages will be as follows.
Emily's age = a - 2
Tuli's age = a - 10 - 2 = a - 12
The product of their ages 2 years ago is 39.
(a - 2)(a - 12) = 39
a² - 12a - 2a + 24 - 39 = 0
a² - 14a - 15 = 0 (quadratic equation)
To get a
a² + a - 15a - 15 = 0
a(a + 1) - 15(a + 1)
(a + 1)(a - 15)
a = -1 or 15
we can only use 15 as it is positive.
"interverted" or "inverted?"
The vertical height of an inverted cone with base diameter 6 cm and slant height of 6 cm can be found using the Pyth. Thm. Draw or imagine a triangle whose height is h and whose base is 3 cm (not 6) and whose hypotenuse is 6 cm.
Then h^2 + (3 cm)^2 = (6 cm)^2, or h^2 + 9 cm^2 = 36 cm^2, or h^2 = 27 cm^2.
Then the height of the triangle, as well as of the cone, is h = +√27, or
h = +3√3.
