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3 years ago

A line can intersect a circle in

Mathematics

1 answer:

juin [17]3 years ago

5 0

Answer:

A line that intersects a circle in exactly one point is called a tangent and the point where the intersection occurs is called the point of tangency.

Step-by-step explanation:

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What is the value of x ??

ruslelena [56]

Answer:

Step-by-step explanation:

The Tangent-Secant Exterior Angle Measure Theorem states that if a tangent and a secant or two tangents/secants intersect outside of a circle, then the measure of the angle formed by them is half of the difference of the measures of its intercepted arcs. Basically, what that means here is that $x$ equals half of the difference of $30\textdegree$ and the measure of the unlabeled arc.

First, we need to find the measure of the unlabeled arc, since we can't find $x$ without it. We know that the measure of the full arc formed by the circle is $360\textdegree$ , so the measure of the unlabeled arc must be $360-30-100-100=130\textdegree$ by the Arc Addition Postulate.

Now, we can find $x$ . Using all of the information known, we can solve for $x$ like this:

$\\x=\frac{1}{2} (130\textdegree-30\textdegree)\\=\frac{1}{2} (100\textdegree)\\=50\textdegree$

Hope this helps!

5 0

3 years ago

A newly established clothing shop analyzed their monthly profit compared to the amount spent on advertising each month. The foll

Reil [10]

The maximum profit is the highest point on the curve at (3, 45), and since the y-value is the profit in hundreds of dollars, the maximum profit is $4500.
The shop is making a profit as long as the curve is above the x-axis, so this is over the given interval (0, 10).
The maximum profit is earned at x = 3, and the x-value is the money spent on advertising in hundreds of dollars, so this means that $300 was spent of advertising.

3 0

3 years ago

Read 2 more answers

Solve for x: 3+x=2x=?

Leokris [45]

Answer:

x=3

Step-by-step explanation:

3+x=2x

Subtract x from each side to get the variable on one side

3+x-x=2x-x

3 = x

4 0

4 years ago

Read 2 more answers

Help!!!! Asap! I’m not understanding this I really need help !!! Please

jenyasd209 [6]

Answer:

Opposite Angles Theorem

Step-by-step explanation:

All opposite angles are congruent, meaning that two angles created by intersecting lines that oppose eachother are equal in size. The theorem goes by different names, so I don't know exactly what your teacher is asking for, but I hope I could help.

5 0

3 years ago

A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specime

Shalnov [3]

Answer:

We conclude that the true average percentage of organic matter in such soil is different from 3%.

Step-by-step explanation:

We are given that the values of the sample mean and sample standard deviation are 2.481 and 1.616, respectively.

Suppose we know the population distribution is normal, we have to test the hypothesis that does this data suggest that the true average percentage of organic matter in such soil is something other than 3%.

Let $\mu$ = true average percentage of organic matter in such soil

SO, Null Hypothesis, $H_0$ : $\mu$ = 3% {means that the true average percentage of organic matter in such soil is equal to 3%}

Alternate Hypothesis, $H_A$ : $\mu \neq$ 3% {means that the true average percentage of organic matter in such soil is different than 3%}

The test statistics that will be used here is One-sample t test statistics because we don't know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{{\frac{s}{\sqrt{n} } } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean amount of organic matter = 2.481%

s = sample standard deviation = 1.616%

n = sample of soil specimens = 30

So, test statistics = $\frac{0.02481-0.03}{{\frac{0.01616}{\sqrt{30} } } }$ ~ $t_2_9$

= -1.759

Now, P-value of the test statistics is given by;

P-value = P( $t_2_9$ > -1.759) = 0.046 or 4.6%

If the P-value of test statistics is more than the level of significance, then we will not reject our null hypothesis as it will not fall in the rejection region.

If the P-value of test statistics is less than the level of significance, then we will reject our null hypothesis as it will fall in the rejection region.

Now, here the P-value is 0.046 which is clearly smaller than the level of significance of 0.05 (for two-tailed test), so we will reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the true average percentage of organic matter in such soil is different from 3%.

3 0

3 years ago