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Delicious77
3 months ago
12

[GEOMETRY] If m∠DEG= 5x - 4 m∠GEF=7x - 8 m∠DEH= 9y + 5 find the values of x and y

Mathematics
1 answer:
Zina [12.3K]3 months ago
9 0

Given:

Line DEF is straight, so the angles on it sum to 180°.

Thus, angle(DEG) + angle(GEF) = 180°.

Substitute the provided values:

5x-4+7x-8=180

12x-12=180

12x=192

x=16 — Answer

Since vertically opposite angles are equal,

angle(GEF) = angle(DEH).

Substitute in known expressions:

9y+5=7x-8

Plug in x = 16:

9y+5=7*16-8

9y+5=104

9y=99

y=11 — Final Answer

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3400 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 25 years, to t
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=3400(1+0.0825/1)^1*25
=3400(1.0825)^25
=3400(7.2560058)
=24670.41

Hope this assists!!!
6 0
2 months ago
Which product is modeled by the number line below? A number line going from negative 8 to positive 8. An arrow goes from 0 to ne
Svet_ta [12734]
The formula modeling this scenario is (-2)(4). The breakdown of the process shows that shifting from 0 to -2 represents -2 units, and similar deductions follow through other steps reaching -8, with a total change of -2 units per step. Thus, the model results in (-2) × 4.
6 0
1 month ago
A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function? y = –4/3x y = –3/4
Zina [12379]

Answer:

First, we must calculate the slope

m=Y2-Y1/X2-X1

= 9 - (-6) / 12 - (-8)

= 15/20

= 3/4

Therefore, the equation with the slope of 3/4 is Y=3/4x

8 0
3 months ago
Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.
lawyer [12517]

Answer:

6.75g

Step-by-step explanation:

The initial step is to convert all values to grams using rules of three, followed by summation.

In a rule of three calculation, the first step is identifying the measures and how they interrelate; whether their connection is direct or inverse.

In direct relationships, as one measure increases, so does the other.

In inverse relationships, as one measure increases, the other decreases.

Problems involving unit conversion, like this, illustrate a direct relationship between measures.

First step: convert 0.0025kg to grams

One kilogram equals 1000 grams, so:

1kg - 1000g

0.0025kg - xg

x = 1000*0.0025 = 2.5g

Thus, 0.0025kg is equal to 2.5g

Second step: handle 1750 mg

One gram consists of 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

x = \frac{1750}{1000}

x = 1.75g

Therefore, 1750 mg converts to 1.75g

2.25g is fine

Third step: convert 825,000 μg to grams

One gram consists of 1,000,000 micrograms, so:

1g - 1,000,000 μg

xg - 825,000 μg

1,000,000x = 825,000

x = \frac{825,000}{1,000,000}

x = 0.25g

So, 825,000 μg equals 0.25g

Final step: sum all values

0.25g + 2.25g + 1.75g + 2.50g = 6.75g

8 0
3 months ago
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