Solve for the base. Round to hundredths when necessary.

Mathematics

1 answer:

Elena-2011 [213]3 years ago

6 0

Answer:

2730.54
18.8%
62.5% (decrease)

Step-by-step explanation:

The applicable formula is ...

rate = portion/base

so ...

base = portion/rate

Of course, a percentage is a fraction that has been multiplied by 100%.

1. base = portion/rate = 456/0.167 ≈ 2730.54

The base is about 2730.54.

2. rate = portion/base = 50/266 ≈ 0.18797 ≈ 18.8%

The rate is about 18.8%.

3. The decrease can be figured from ...

rate of change = (new amount)/(original) -1 = 33/88 -1

= -5/8 = -0.625 = -62.5%

The rate of decrease is 62.5%.

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In the figure above, quadrilateral ABCD is a parallelogram. Let x represent the measure of angle GBF, y represent the measure of

ira [324]

Answers:
measure angle x = 40°
measure angle y = 35°
measure angle z = 55°

Explanation:
Part (a): getting angle x:
In triangle BED, we have:
measure angle BED = 90°
measure angle BDE = 50°
Therefore:
measure angle DBE = 180 - (90+50) = 40°
Now, we have angle DBE and angle GBF vertically opposite angles.
This means that they are both equal. Therefore angle GBF = 40°
Since angle GBF is x, therefore:
x = 40°

Part (b): getting angle y:
We know that the sum of measures of angles on a straight line is 180.
This means that:
angle GBF + angle GBC + angle CBE = 180
We have:
angle GBF = 40°
angle GBC = 105°
angle CBE = y
Therefore:
40 + 105 + y = 180
y = 35°

Part (c): getting angle z:
In triangle BCE, we have:
measure angle BCE = z
measure angle BEC = 90°
measure angle CBE = 35°
Therefore:
z + 90 + 35 = 180
z = 55°

Hope this helps :)