1. Given △PQR≅△STU, m∠R=80°, and m∠S=70°, what is the measure of ∠Q?


2. What is m∠AEB?
(image is for this question)

Answer:

A. [tex]8i\sqrt{2}[/tex]

Step-by-step explanation:

We have been given a radical expression [tex]2\sqrt{-32}[/tex]. We are asked to find equivalent expression to our given expression.

Using radical rule [tex]\sqrt{-a}=\sqrt{-1}\cdot \sqrt{a}[/tex], we can write [tex]\sqrt{-32}[/tex] as product of [tex]\sqrt{-1}\cdot\sqrt{32}[/tex].

[tex]2\sqrt{-32}=2\cdot \sqrt{-1}\cdot\sqrt{32}[/tex]

Substitute [tex]\sqrt{-1}=i[/tex]:

[tex]2\sqrt{-32}=2i\cdot\sqrt{32}[/tex]

[tex]2\sqrt{-32}=2i\cdot\sqrt{2\cdot 16}[/tex]

[tex]2\sqrt{-32}=2i\cdot\sqrt{2\cdot 4^2}[/tex]

[tex]2\sqrt{-32}=2*4i\cdot\sqrt{2}[/tex]

[tex]2\sqrt{-32}=8i\sqrt{2}[/tex]

Therefore, the equivalent expression would be [tex]8i\sqrt{2}[/tex].

The expression which is equal to 2√-32 is; 8i√2

According to the question, we have been given the radical expression; 2√-32

First, the expression can be evaluated as follows;

We must recall that, In complex numbers, √-1 = i.

Therefore, the expression which is equal to 2√- 32 is:. 8i√2

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In slope-intercept form, y = (1/3)x + 4 can be used to represent the equation of a line with a slope of 1/3 and a y-intercept of 4.

In mathematics particularly in algebra, the equation of a line is usually formulated in the slope-intercept form, which is y = mx + b. Where m is the slope of the line and b is the y-intercept. For a line with a slope of 1/3 and y-intercept of 4, you would substitute 1/3 for m and 4 for b. Therefore, the equation of the line would be y = (1/3)x + 4

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The temperature changes by 49.2F from day to night. You calculate this by subtracting the night temperature from the day temperature and remembering to treat subtraction of a negative as addition.

The subject of your question is the calculation of temperature change, which is a simple subtraction problem in mathematics. Given a temperature of 36.6F during the day and a temperature of -12.6F at night, you can find the temperature change by subtracting the night temperature from the day temperature.

So, it will be 36.6F - (-12.6F) equals 49.2F. It's important to note here that subtracting a negative number is the same as adding a positive number which is why we add 12.6F instead of subtracting it.

This means, the temperature changes by 49.2F from day to night.

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The measure of the smaller angle is 77 degrees, and the measure of the larger angle is 103 degrees.

Let's represent the measure of the smaller angle as x degrees. Since the measure of one angle is 26 degrees greater than the other angle, the measure of the larger angle can be represented as x + 26 degrees.

According to the definition of a linear pair, the sum of the measures of two angles forming a linear pair is always 180 degrees. So we can write the equation:

x + (x + 26) = 180

Solving this equation, we get: 2x + 26 = 180

2x = 180 - 26

2x = 154

x = 154/2

x = 77

Therefore, the smaller angle measures 77 degrees and the larger angle measures 77 + 26 = 103 degrees.

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Answer:

[tex]y=\dfrac{14-Ax}{2x}[/tex]

Step-by-step explanation:

The given expression is :

[tex]Ax+2xy=14[/tex].............(1)

We need to find the value of y. Subtracting "Ax" on both sides of equation (1) as :

[tex]Ax-Ax+2xy=14-ax[/tex]

[tex]2xy=14-Ax[/tex]

Dividing both sides of above equation by "2x" as :

[tex]\dfrac{2xy}{2x}=\dfrac{14-Ax}{2x}[/tex]

[tex]y=\dfrac{14-Ax}{2x}[/tex]

So, the value of y is, [tex]y=\dfrac{14-Ax}{2x}[/tex]. Hence, this is the required solution.

Final answer:

Betelgeuse will be either just above the horizon or at virtually the same position on the eastern horizon at 7:15 pm the next day, as stars like Betelgeuse rise in the east and set in the west, completing a rotation around the celestial sphere in about 24 hours.

Explanation:

The question pertains to the observation of the star Betelgeuse and its position relative to the horizon at a specific time from one day to the next. Since most stars rise in the east and set in the west, completing one full rotation around the celestial sphere in approximately 24 hours, we can infer that Betelgeuse will follow a similar path. However, due to Earth's rotation, any given star will appear to rise and set four minutes earlier each night, due to the Earth’s orbit around the Sun completing an extra degree each day. This might suggest that Betelgeuse would be slightly above the horizon at 7:15 pm the following night. Yet, the student should be aware that this four-minute difference can be negligible, and for practical observing purposes, Betelgeuse will be seen rising at virtually the same time, hence nearly at the same position on the horizon.

Explanation of the ratios of French decimal time to standard time after the French Revolution.

Ratio of French Decimal Week to Standard Week:

1 French decimal week = 10 days, whereas 1 standard week = 7 days. So, the ratio is 10/7.

Ratio of French Decimal Second to Standard Second:

1 French decimal second = 0.01 standard second since 1 hour = 100 French decimal minutes = 100 x 0.01 = 1 standard hour.

(a) The ratio of the French decimal week to the standard week is [tex]\( \frac{10}{7} \)[/tex].

(b) The ratio of the French decimal second to the standard second is [tex]\( \frac{5}{3} \)[/tex].

To find the ratios of the French decimal week to the standard week and the French decimal second to the standard second, we'll compare the durations of these units in the French decimal system to those in the standard system.

(a) Ratio of the French decimal week to the standard week:

In the French decimal system:

- One French decimal week consists of 10 days.

In the standard system:

- One standard week consists of 7 days.

So, the ratio of the French decimal week to the standard week is:

[tex]\[ \text{Ratio} = \frac{\text{French decimal week}}{\text{Standard week}} = \frac{10 \text{ days}}{7 \text{ days}} \][/tex]

(b) Ratio of the French decimal second to the standard second:

In the French decimal system:

- One minute consists of 100 seconds.

In the standard system:

- One minute consists of 60 seconds.

So, the ratio of the French decimal second to the standard second is:

[tex]\[ \text{Ratio} = \frac{\text{French decimal second}}{\text{Standard second}} = \frac{100 \text{ seconds}}{60 \text{ seconds}} \][/tex]

Now, let's simplify these ratios:

(a) Ratio of the French decimal week to the standard week:

[tex]\[ \frac{10}{7} \][/tex]

(b) Ratio of the French decimal second to the standard second:

[tex]\[ \frac{100}{60} = \frac{5}{3} \][/tex]

So, the ratios are:

(a)  for the French decimal week to the standard week.

(b) [tex]\( \frac{5}{3} \)[/tex] for the French decimal second to the standard second.

Answer: a) $17.31, b) $17.31.

Step-by-step explanation:

Since we have given that

Total bill for four pairs of shoes = $69.24

Number of pairs of shoes = 4

We need to find the average price for each pair of shoes .

So, Average price would be

[tex]\dfrac{\text{Total amount}}{\text{Number of pairs of shoes}}\\\\=\dfrac{69.24}{4}\\\\=\$17.31[/tex]

If he purchased only 1 pair of shoes, the amount he has to pay based on average price would be $17.31.

Hence, a) $17.31, b) $17.31.

Final answer:

The average price for each pair of shoes from the total bill of $69.24 is $17.31. If only one pair of shoes was purchased, it would also cost $17.31.

Explanation:

To find the average price for each pair of shoes in the first question, you divide the total bill by the number of pairs of shoes. In this case, the total bill is $69.24 for four pairs of shoes.

Step-by-step calculation:

Divide the total cost ($69.24) by the number of pairs (4).

The calculation will be $69.24 / 4 = $17.31.

The average price for each pair of shoes is $17.31.

For the second question, if you were to purchase only one pair of shoes, the cost would be equal to this average price, which is $17.31.

35 -21 = 14

14/35 reduces to 2/5

We know that:

1 mile = 5280 ft

1 minute = 60 sec

Therefore to convert this we simply use the conversion factors:

(30 ft / s) * (60 s / 1 min) * (1 mi / 5280 ft) = 0.34 mi / min

So we got 0.34 miles per minute.

Answer:

118.

Step-by-step explanation:

To find Jane's score on the national achievement test with a given mean of 100 and standard deviation of 15, we calculate it using her z-score of 1.20 to get her score of 118.

The question asks: A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test.

To find Jane score on the test, we use the formula for calculating scores from z-scores: Score = Mean + (Z-score × Standard Deviation).

Given that the mean is 100 and the standard deviation is 15, and Jane's z-score is 1.20, we can calculate her score as follows:

Therefore, Jane's score on the national achievement test was 118.