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3 years ago

Points F(3, 3), K(6, 5), J(8, 2) and L(5, 0) lie in a coordinate plane. Which lines are perpendicular?

1 answer:

8 0

To determine if a line is perpendicular to another, you must first determine the slope...
m = y1-y2/x1-x2
m of FK = 3-5/3-6 = -2/-3 = 2/3
m of FJ = 3-2/3-8 = 1/-5
m of FL = 3-0/3-5 = 3/-2
m of KJ = 5-2/6-8 = 3/-2
m of KL = 5-0/6-5 = 5
m of JL = 2-0/ 8-5 = 2/3

In order for two lines to be perpendicular, their slopes must be opposite reciprocals...
FK is perpendicular to FL
FK is perpendicular to KJ
JL is perpendicular to FL
JL is perpendicular to KJ
FJ is perpendicular to KL

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3 years ago

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An old bone contains 80% of its original carbon-14. Use the half-life model to find the age of the bone. Find an equation equiva

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Answer:

An old bone contains 80% of its original carbon-14 in 1844.6479 years

Step-by-step explanation:

We know that

half life time of C-14 is 5730 years

so, h=5730

now, we can use formula

$P(t)=P_0(\frac{1}{2})^{\frac{t}{h} }$

we can plug back h

and we get

$P(t)=P_0(\frac{1}{2})^{\frac{t}{5730} }$

An old bone contains 80% of its original carbon-14

so,

P(t)=0.80Po

we can plug it and then we solve for t

$0.80P_0=P_0(\frac{1}{2})^{\frac{t}{5730} }$

$0.80=(\frac{1}{2})^{\frac{t}{5730} }$

$\ln \left(0.8\right)=\ln \left(\left(\frac{1}{2}\right)^{\frac{t}{5730}}\right)$

$t=-\frac{5730\ln \left(0.8\right)}{\ln \left(2\right)}$

$t=1844.6479$

So,

An old bone contains 80% of its original carbon-14 in 1844.6479 years

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2 years ago

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What is the square root of 4

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Answer:

√4 = 2

Because 2 × 2 = 4

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2 years ago

15/30 = n/34 round to the nearest tenth.

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The equation given in the question has to be answered to the nearest tenth. The only thing that one should be careful about is the cross multiplication part. Other than that there is no difficulty in the given problem. Now let us get down to the equation in the question.
15/30 = n/34
30 * n = 15 * 34
30n = 510
n = 510/30
= 51/3
= 17
So the value of the unknown variable "n" comes out to be 17.

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3 years ago

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For one Geometry test, Nancy correctly answered 18 questions. These correct answers gave her a percent score of 72%. In total, h

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Answer:

25 questions.

Step-by-step explanation:

Correct answer = 18

The percent score of the correct answers is 72%.

Let there are x questions in the test. So,

According to the given condition,

$72\%\ of\ x=18\\\\\dfrac{72}{100}x=18\\\\x=\dfrac{18\times 100}{72}\\\\x=25$

Hence, there were 25 questions in the geometry test.

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