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Anestetic [448]
2 years ago
7

Determine the greatest common factor of 28xy^9z and 32x^2y^7z

Mathematics
1 answer:
RSB [31]2 years ago
5 0

Answer:

GCF = 4xy⁷z

Step-by-step explanation:

Do Prime Factorizations for each term and select only those terms common to each:

28xy⁹z = 2·2·7·x·y·y·y·y·y·y·y·y·y·z

32x²y⁷z = 2·2·2·2·2·x·x·y·y·y·y·y·y·y·z

GCF = 2·2·x·y·y·y·y·y·y·y·z

GCF = 4xy⁷z

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A fisherman leaves his home port and heads in the direction N 70 ° W. He travels d1 = 40 mi and reaches Egg Island. The next day
Gnesinka [82]

Answer:

A)82.02 mi

B) 18.7° SE

Step-by-step explanation:

From the image attached, we can see the angles and distance depicted as given in the question. Using parallel angles, we have been able to establish that the internal angle at egg island is 100°.

A) Thus, we can find the distance between the home port and forrest island using law of cosines which is that;

a² = b² + c² - 2bc Cos A

Thus, let the distance between the home port and forrest island be x.

So,

x² = 40² + 65² - 2(40 × 65)cos 100

x² = 1600 + 4225 - (2 × 2600 × -0.1736)

x² = 6727.72

x = √6727.72

x = 82.02 mi

B) To find the bearing from Forrest Island back to his home port, we will make use of law of sines which is that;

A/sinA = b/sinB = c/sinC

82.02/sin 100 = 40/sinθ

Cross multiply to get;

sinθ = (40 × sin 100)/82.02

sin θ = 0.4803

θ = sin^(-1) 0.4803

θ = 28.7°

From the diagram we can see that from parallel angles, 10° is part of the total angle θ.

Thus, the bearing from Forrest Island back to his home port is;

28.7 - 10 = 18.7° SE

4 0
3 years ago
Shade the grid to represent the ratio 9/25. Then find a percent equivalent to the given ratio.
anzhelika [568]
Answers and workings in the attachment below.

3 0
3 years ago
Find the total surface area of the figure
liberstina [14]

Answer:2237

Step-by-step explanation: 22000 +4484

4 0
3 years ago
The perimeter of the rectangle is 30 centimeters. What is the length of side c?
Rainbow [258]
The answer would be 10
8 0
3 years ago
What is the length of segment LP?
Mariana [72]
In the image, as denoted by similar sides OP and MN, we can conclude that the 2 triangles are similar triangles. To look for the value of x (which we can substitute later to find the length of segment LP), we relate the relations of segments LO and LP to segments LM and LN. This relation is shown below:

LO/LP = LM/LN

22 / x+12 = 30 / x+12 + 5
22 / <span>x+12 = 30 / x+17
</span>
Cross-multiplying:
30x + 360 = 22x + 374

Isolating x to one side of the equation by subtracting 22x and 360 from both sides:

30x + 360 - 360 - 22x = 22x + 374 - 360 - 22x
8x = 14
x = 1.75

Since we now have the value of x, we substitute this to the equation of LP:
LP = x + 12
LP = 1.75 + 12
LP = 13.75

Therefore the value of LP is 13.75 in.

8 0
3 years ago
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