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ohaa [14]
1 year ago
6

4. If mZDEF = 3x +1 and mZDEG = 5x +19, find the value of x.The image attached isn't the right interpretation of the question.

Mathematics
1 answer:
cestrela7 [59]1 year ago
4 0

Answer

x = 17

Step-by-step Explanation

The question gives us Angle DEF as (3x + 1) and Angle DEG as (5x + 19).

Note that G is the lower end of the diagram.

What isn't evident from the diagram is that Line EF is a bisector for the DEG.

If Line EF is the bisector, this means that it divides the angle into two equal parts.

(Angle DEG) = (Angle DEF) + (Angle FEG)

Angle DEG = (5x + 19)

Angle DEF = (3x + 1)

Angle FEG = Angle DEF (Since we already established that line EF being a bisector means it divides Angle DEG into two equal parts)

So,

Angle FEG = Angle DEF = (3x + 1)

(Angle DEG) = (Angle DEF) + (Angle FEG)

Substituting the parameters

(5x + 19) = (3x + 1) + (3x + 1)

5x + 19 = 3x + 3x + 1 + 1

5x + 19 = 6x + 2

Collecting like terms by bringing all the coefficients of x to the same side

6x + 2 = 5x + 19

6x - 5x = 19 - 2

x = 17

Hope this Helps!!!

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A rectangular garden's length is 5 feet longer than its width. If its perimeter can be represented using the function P(x) = 4x
Ainat [17]
Let
y----------> the length of the rectangle
x---------> the width of the rectangle
P--------> perimeter of a rectangle

we know that
P=38 ft
[P]=2*[x+y]------> 38=2*[x+y]------> equation 1
y=5+x-------> equation 2
<span>substitute 2 in 1
</span>P=2*[x+(5+x)]---------> P=4x+10---------> the given equation
4x=38-10--------> 4x=28----> x=7 ft
y=5+7-----> y=5+7------> y=12 ft

the answer is
the width is 7 ft


3 0
3 years ago
Maia and John both earn $15 an hours their job. This week Mais worked three hours more than John. If "h" represents the number o
drek231 [11]

Answer:

John: 5 Mais :8

Step-by-step explanation:

h = 195 ÷ 15, so they both worked a total of 13 hours.

13 - 3 as Mais worked 3 hours more than John and then divide 10 by 2, so John worked 5 hours are Mais worked 5+3 [8] hours.

6 0
4 years ago
Read 2 more answers
Sum of Two Dice
stellarik [79]

Answer:

a) Most frequent outcome of the experiment is 7

b) Least frequent is 2

Step-by-step explanation:

a)

x= value of dice =7  is with highest frequency = 21  

(b)

x = Value of dice = 2 is with least frequency = 1

5 0
3 years ago
Michael Miller is paid twice a month and had total gross earnings as of 10/15 of $116,800. His gross earnings for the period end
leva [86]

Answer:

1.medicare tax paid by Michael=0

2.medicare tax paid by employer=1780.5

Step-by-step explanation:

total earning of michael as of 10/15=$116,800

earning of michael as of 10/31=$6,000

Total Earning as of 10/31=$116,800+$6,000=$122,800

security tax=6.25%

6.25%of  $122,800 is

security tax=\frac{6.25}{100}×122,800

security tax=7675 dollar

earning of michael after deducting security tax=122800-7675=115125

Medicare tax will be 1.45% on $122,700 earning or more

since michael earning after payment of security tax is 115125

that's why michael will pay zero medicare tax

medicare tax paid by michael =0

while his  employer will pay medicare tax of 1.45% 0f 12,800

medicare tax paid by employer=\frac{1.45}{100}×122,800

medicare tax paid by employer=1780.5



8 0
4 years ago
Use the distributive property to rewrite as an expression<br> 5(x+3)
padilas [110]

Answer:

5x+15

Step-by-step explanation:

you mulityply 5*x and 5*3

8 0
3 years ago
Read 2 more answers
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