Choose a variable to represent one of the unknowns. Express the remaining unknowns in terms of the variable you chose in step 1.
Look for a relationship between the unknowns given in the problem. Write an equation. (Look for the other relationship given in the problem.) Two sides of a triangle are equal in length and double the length of the shortest side. The perimeter of the triangle is 35 inches.
1 answer:
Let's just choose "x" as our variable for the length of a side of the triangle.
Two sides of a triangle are equal in length and double the length of the shortest side.
A triangle has 3 sides. Make the smallest side x then the two equal sides that are double the smallest side are both equal to 2x
The perimeter of the triangle is 35 inches. Perimeter is the sum of all sides.
x + 2x + 2x = 35
5x = 35
x = 7
So the smallest side is 7, and the other two sides are 14.
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Answer:
Step-by-step explanation:
The equation for a circle is , where
is the vertex of the circle and
is the radius. Immediately, since the center of the circle is given, we know what
and
are.
is 230 and
is 220.
The only thing we need to find is the radius, which will just be the distance from the center (230,220) to a point on the circumference (170,170). The distance between them can be calculated using the <u>distance formula</u>, which is really just the <u>Pythagorean Theorem</u> rearranged. The formula states that , where
is the change in the x-coordinates of the two points and
is the change in the y-coordinates of the two points. Plug-in
for 60 and
for 50 to get
. Solve for
, arriving at
. Therefore, the radius of the circle is
.
Finally, we have all of the components to create the equation of the circle. Plug-in 230 for , 220 for
, and
for
.
The equation of the circle will be .
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Answer:
a₇ = 2.375
Step-by-step explanation:
There is a common ratio r between consecutive terms, that is
r = =
=
= -
This indicates the sequence is geometric with nth term
= a₁
where a₁ is the first term and r the common ratio
Here a₁ = 152 and r = - , then
= 152
, so
a₇ = 152 = 152 ×
= 2.375