In triangle ABC, the perpendicular bisector of side AB intersects the extension of side AC at point D. If ∠CBD = 16° and ∠ACB = 118°, find the measure of ∠ABC. A. 16 degrees B. 44 degrees C. 62 degrees D. 74 degrees

Answers

Answer 1

Answer:

Answer:A

Step-by-step explanation:

To find the measure of angle ABC in triangle ABC, we can use the properties of perpendicular bisectors.

Since the perpendicular bisector of side AB intersects the extension of side AC at point D, we know that AD = DB. Therefore, triangle ABD is an isosceles triangle.

In an isosceles triangle, the angles opposite the equal sides are also equal. So, we have:

∠ABD = ∠ADB

Since ∠CBD = 16° and ∠ACB = 118°, we can find ∠ADB as follows:

∠ADB = 180° - ∠CBD - ∠ACB

= 180° - 16° - 118°

= 46°

Since ∠ABD = ∠ADB, we have:

∠ABD = 46°

Now, we can find ∠ABC:

∠ABC = 180° - ∠ABD - ∠ACB

= 180° - 46° - 118°

= 16°

Therefore, the measure of ∠ABC is 16 degrees. So, the correct answer is A. 16 degrees.

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Logan saves the same amount of money each month for college. His current total savings is 300m2 + 120m + 180 dollars. Which factorization could represent the number of months and amount of a monthly deposit in dollars?

Answers

If we let x as the amount of money saved per month and m be the number of months:

xm = 300m2 + 120m 180

The quadractic equation would result to:
300m2 + (120-x)m + 180 = 0

Using the quadratic formula we have the following factorization:
(m - ( -120 + x + sqrt (x2 - 240x - 2145600) ) / 600) (m - ( -120 +x - sqrt (x2 - 240x - 2145600) ) / 600) = 0

60(5m2 +2m +3) the answer is d

At the end of one day, the value of a share of a certain stock was $12. Over the next three days, the change in the value of the share was $-1, then, $-1, and then $3. Write an expression that descrines the situation.

Answers

12-13=-1+4(after 2 days)=3

The ratio of boys to girls in history class is 4 to 5. How many girls are in the class if there are 12 boys in the class?

Answers

$4x-\ amount\ of\ boys\n5x-\ amount\ of\ girls\n\n4x=12\ \ \ | fivide\ by\ 4\nx=3\n\n5x=5*3=15\n\nThere \ are\ 15 \ girls \ in\ class.$

Final answer:

In a class where the ratio of boys to girls is 4 to 5, if there are 12 boys, there would be 15 girls.

Explanation:

The subject of this question is mathematics, specifically the topic of ratios and proportions. To answer your question, the ratio of boys to girls is 4 to 5, this means that for every 4 boys in the class, there are 5 girls. If there are 12 boys, you simply multiply each side of the ratio by the same factor to keep the ratio the same. Since 12 divided by 4 equals 3, we also have to multiply 5 by 3. Hence, there are 15 girls in the class.

Learn more about Ratio and Proportion here:

brainly.com/question/31776433

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Kaitlin paid $16.60 for 33.2 centimeters of wire.Find the unit price in dollars per centimeter.
If necessary, round your answer to the nearest cent.

Answers

Answer:

Step-by-step explanation:

$0.50 per centimeters i think

Final answer:

To find the unit price, you divide the total price by the total quantity. The unit price of the wire is approximately $0.50 per centimeter, after rounding to the nearest cent.

Explanation:

To find the unit price, we need to divide the total price by the total quantity. In this case, Kaitlin paid $16.60 for 33.2 centimeters of wire. So, we need to divide 16.60 (in dollars) by 33.2 (in centimeters).

The calculation is:
16.60 ÷ 33.2 = 0.5

So, the unit price of the wire is approximately $0.50 per centimeter. Please note that we have rounded the final answer to the nearest cent, as requested.