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3 years ago

In the circle above, Line EF and CD intersect at G. Determine the measure of arc DE.

Mathematics

1 answer:

Aliun [14]3 years ago

6 0

Answer:

100

Step-by-step explanation:

It is a rule that for two opposite arcs, with intersecting lines, between them, the average of the arcs is equivalent to the inside angle. Given this, we can say that:

(CF + ED)/2 = angle G

plug values in

(12x+9x+10)/2 = 110

multiply both sides by 2

21x + 10 = 220

subtract 10 from both sides

21x = 210

divide both sides by 21

x=10

Plug this into DE

10*9+10 = 100

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alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS

serious [3.7K]

Answer:

$k=\frac{-11}{2}$ .

Step-by-step explanation:

We are given $\alpha$ and $\beta$ are zeros of the polynomial $x^2-(k+6)x+2(2k-1)$ .

We want to find the value of $k$ if $\alpha+\beta=\frac{1}{2}$ .

Lets use veita's formula.

By that formula we have the following equations:

$\alpha+\beta=\frac{-(-(k+6))}{1}$ (-b/a where the quadratic is ax^2+bx+c)

$\alpha \cdot \beta=\frac{2(2k-1)}{1}$ (c/a)

Let's simplify those equations:

$\alpha+\beta=k+6$

$\alpha \cdot \beta=4k-2$

If $\alpha+\beta=k+6$ and $\alpha+\beta=\frac{1}{2}$ , then $k+6=\frac{1}{2}$ .

Let's solve this for k:

Subtract 6 on both sides:

$k=\frac{1}{2}-6$

Find a common denominator:

$k=\frac{1}{2}-\frac{12}{2}$

Simplify:

$k=\frac{-11}{2}$ .

7 0

3 years ago

LOOK AT THE PICTURE PLEASE HELP A GIRL OUT IM STUCK ON THIS QUESTION AND I DONT HAVE A LOT OF TIME!!

Tomtit [17]

Answer:

How much time do i have?

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

3x +-11 >-20<br> Which is greater than or less than

SpyIntel [72]

Hey babe I’m going to be at home;)

4 0

2 years ago

Among cases of heart pacemaker malfunctions, were found to be caused by firmware, which is software programmed into the device.

alex41 [277]

Complete question is;

Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

Answer:

P(All three are not caused by firmware) = 83.84%

Probability that the entire batch will be accepted = 0.8384

Step-by-step explanation:

We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.

Thus,

Cases not caused by firmware = 8834 - 504 = 8330

So, probability of the first case not being affected by firmware is;

P(first case not caused by firmware) = 8330/8834

Also,

Probability of second case not being affected by firmware is given as;

P(second case not caused by firmware|first case not affected by firmware) = 8329/8833

Similarly,

Probability of third case not being affected by firmware is given as;

P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832

Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.

Thus, we will make use of the general multiplication rule which is;

P(A & B) = P(B) × P(A|B)

Thus;

P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)

Plugging in the relevant values, we have;

P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)

P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%

6 0

3 years ago

What is y=4/5x+4 in standard form

HACTEHA [7]

5y = 4x + 20
- 4x + 5y = 20

5 0

2 years ago