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ValentinkaMS [17]
3 years ago
13

Can someone help me with these two proof questions?

Mathematics
1 answer:
timurjin [86]3 years ago
6 0

The proofs of above Questions is in attachment !

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∠E and ∠F are vertical angles with m∠E=8x+8 and m∠F=2x+38 .<br><br> What is the value of x?
Zigmanuir [339]
We know that ∠E = ∠F because of the vertical angle theorem.

Using substitution we get 8x + 8 = 2x + 38

Solve for x.

8x + 8 = 2x + 38
8x = 2x = 30 <-- Subtract 8 from each side
6x = 30 <-- Subtract 2x from each side
x = 5 <-- Divide both sides by 6

So, x is equal to 5.
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What is an equation that passes through the point (-2,-3) and is parallel to the line 5x+2y=14
Alekssandra [29.7K]

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5x-2y=16

Hope this helps! If you need an explanation, I've got you.

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Are these proportional? <br> Yes | No
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Answer:

yes

Step-by-step explanation:

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Radioactive Decay Beginning with 16 grams of a radioactive element whose half -life is 30 years ,the mass y(in grams) remaining
Flura [38]

Answer:

the equation should be corrected to fit the data of the problem.  With the corrected equation a mass of 0.5 grams remains after 150 years

Step-by-step explanation:

for the mass y( in grams)

y=23* (1/2)^(t/45), t ≥ 0.

the initial mass is at t=0 , then

y= 23 grams  → should be 16 grams

half-life from the equation = 45 years → should be 30 years

the correct equation should be

y=16*(1/2)^(t/30), t ≥ 0

then after 150 years  → t= 150

y=16*(1/2)^(150/30)= 16*(1/2)^5 = 16/32 = 0.5 grams

then a mass of 0.5 grams remains after 150 years

5 0
3 years ago
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