Piecewise and Combining Functions
1 answer:
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Step-by-step answer:
Please refer to attached image.
1. Quad PQRS is cyclic (all vertices on the same circle), so opposite angles are supplementary, meaning
that
angles QPS and QRS are supplementary =>
QPS+QRS=180 =>
QRS = 180 - 74 = 106
2. Triangle RSQ is isosceles with RS=RQ =>
angles RSQ and RQS are congruent.
3. Angle RSQ = (180 - 106) /2 = 74 / 2 = 37
4. QP is a diameter => angle QSP is a right-angle.
5. From (3) and (4) above,
angle RSP = 37+90 = 127
6. Since PQRS is cyclic, angles RQP and RSP are supplementary =>
RQP+RSP = 180 =>
x + 127 = 180 =>
x = 180 - 127 = 53 degrees.
Answer:
The solution is .
Step-by-step explanation:
Given:
The inequality given is:
In order to simplify for 'x', we first isolate 'x' on one side.
Adding -4 on both sides, we get:
Now, is an absolute value function which is defined as:
Therefore, the given inequality can be rewritten as:
and
Therefore, the solution is .
Answer:
Step-by-step explanation:
We are given the following in the question:
Volume of cake = 351 cubic inches
Let x inches be the width of cake.
Width of cake, w =
Then, length of cake,l =
Height of cake,h =
Volume of cake = Volume of cuboid
Putting values, we get:
Thus, dimensions of cake are: