Which of the following is a like radical to

The measure of a base angle in an isosceles triangle with a vertex angle of 38° is 71°, as isosceles triangles have two equal base angles and the total sum of angles in any triangle is 180°.

To calculate the measure of a base angle in an isosceles triangle, we need to remember that the sum of angles in a triangle is always 180°. Given that we have a vertex angle of 38°, we subtract that from 180° to find the sum of the two base angles. Since it's an isosceles triangle, these angles are equal:

Therefore, the measure of one base angle in this isosceles triangle is 71°.

The measure of each base angle of an isosceles triangle is 71°.

An isosceles triangle has two congruent sides and two congruent base angles. In this case, the vertex angle measures 38° and the congruent sides each measure 21 units. To find the measure of a base angle, we can use the fact that the sum of the angles in a triangle is 180°. Since the vertex angle is 38°, the sum of the base angles is 180° - 38° = 142°. Since the base angles are congruent, we can divide 142° by 2 to find the measure of each base angle.

142° / 2 = 71°

Therefore, the measure of each base angle is 71°.

The length of the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.

In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows:

- The length of the shorter leg is x.

- The length of the longer leg is x[tex]\sqrt{3}[/tex].

- The length of the hypotenuse is 2x.

Given that the hypotenuse of the larger triangle is 16 centimeters, we can set up the equation:

2x = 16

Solving for x:

x = [tex]\frac{16}{2}[/tex] = 8

Now, we know that the length of the longer leg of the larger triangle is x[tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex] centimeters.

Since the hypotenuse of the larger triangle becomes the longer leg of the smaller triangle, the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.

The question is:

There are two triangles. Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. What is the number of centimeters in the length of the longer leg of the smaller triangle?

To solve this problem, let us say that the number is called x and let us do this step by step.

1st step: 3 is added to the number, therefore:

x + 3

2nd step: the sum is tripled, therefore:

3 (x + 3)

3rd step: the result in the 2nd step is equal to 27 more than the original number, therefore:

3 (x + 3) = x + 27

4th step: find for the value of x using the equation

3 x + 9 = x + 27

3 x – x = 27 – 9

2 x = 18

x = 9

Answer:

The number is 9

To solve the equation 2x - 10 / 4 = 3x, multiply both sides by 4, simplify, and solve for x to find its value as -1.

Step 1: Multiply both sides of the equation by 4 to get rid of the fraction:
4 * (2x - 10) / 4 = 4 * 3x

Step 2: Simplify the equation:
2x - 10 = 12x

Step 3: Rearrange the equation to solve for x:
2x - 12x = 10
-10x = 10
x = -1

Final answer:

Sasha reads a total of 2775 minutes over 30 days, calculated using the formula for the sum of an arithmetic sequence.

Explanation:

To calculate the total number of minutes Sasha reads over 30 days, we note that she starts with 20 minutes on the first day and reads 5 minutes more each subsequent day. This is an arithmetic sequence where the first term (a1) is 20 minutes, the common difference (d) is 5 minutes, and the number of terms (n) is 30.

We can use the formula for the sum of an arithmetic sequence: Sn = n/2 (2a1 + (n - 1)d).

Plugging in the given values gives us S30 = 30/2 (2(20) + (30 - 1)(5)).

Now we calculate: S30 = 15(40 + 29(5)) = 15(40 + 145) = 15(185) = 2775 minutes.

Therefore, Sasha reads a total of 2775 minutes over the course of 30 days.

Answer:

2

Step-by-step explanation:

-6

Final answer:

To prove lines are parallel, their slopes must be equal, and to prove they are perpendicular, their slopes must be negative reciprocals. To write an equation for a parallel line, use the same slope as the original; for a perpendicular line, use the negative reciprocal of the original line's slope. Manipulating a line involves changing either its slope or intercept.

Explanation:

To use slope to prove that lines are parallel or perpendicular, you need to compare their slopes. Two lines are parallel if their slopes are equal. Conversely, two lines are perpendicular if their slopes are negative reciprocals of each other, meaning that one slope is the negative inverse of the other (e.g., the slope of one line is 2 and the other is -1/2).

To write an equation of a line so that it is parallel to a given line, you must use the same slope as the given line. If the equation of the given line is y = mx + b, then the equation of a parallel line will be y = mx + c, where c is a different y-intercept. To write an equation of a line so that it is perpendicular to a given line, you use the negative reciprocal of the slope of the given line. If the slope of the given line is m, then the slope of the perpendicular line will be -1/m.

For example, consider a line with the equation y = 3x + 9, which signifies a slope of 3 and a y-intercept of 9 based on Figure A1. A parallel line would have a slope of 3 but could have a different y-intercept, such as y = 3x + 4. A perpendicular line would have a slope of -1/3, so it could be something like y = -1/3x + 5.

Manipulating a line involves changing its slope (m) or intercept (b). Changing the slope will tilt the line, while changing the intercept will shift the line up or down on the graph. Understanding how to read and manipulate a graph is crucial for visualizing these changes.

Point C to Point B appears to have a slope of 2/3, 3 blocks apart (in width) and 2 blocks apart (in height). Using a^2 + b^2 = c^2 will help where ^2 means (squared).
(2 x 2) + (3 x 3) = 13
Line CB is (square root) of 13.

Point A and B are 2 blocks apart (width) and 3 blocks apart (height), so using what we did in the last step...
(3 x 3) + (2 x 2) = 13
Line AB is (square root) of 13.

So now... With Line AB and Line CB being the square root of 13, the line AC should be (square root) (13 + 13), so (square root) 26. If it does equal this, then it is a right-triangle.

Point C and A are 1 block apart (width) and 5 blocks apart (height) so...
(1 x 1) + (5 x 5) = 26
Square root of 26...

In conclusion, the Triangle IS a Right-angle and you should pick "D"

y=11x-5

x=11y-5

11y=5+x

divide each term by 11 to get:

y= 5/11 + x/11

 so f^-1(x) = 5/11 + x/11

The standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]

Further Explanation:

The random variable X follows binomial distribution.

[tex]\boxed{X \sim {\text{Bin}}\left( {n,p} \right)}[/tex]

Here, n represents the total number of experiments and p denotes the probability of the event.

Apply central limit theorem.

[tex]\boxed{X \sim {\text{Normal}}\left( {np,np\left( {1 - p} \right)} \right)}[/tex]

The mean of the binomial distribution can be calculated as follows,

[tex]\boxed{{\text{Mean}} = n \times p}[/tex]

The standard deviation of binomial distribution can be calculated as follows,

[tex]\boxed{{\text{Standard deviation}} = \sqrt {np\left( {1 - p} \right)} }[/tex]

Given:

Coin is tossed 72 times.

Explanation:

Consider X is the random variable that head will occur.

The probability of head occur is [tex]p = \dfrac{1}{2}.[/tex]

The mean can be calculated as follows,

[tex]\begin{aligned}{\text{Mean}}&= 72\times \frac{1}{2}\\&= 36\\\end{aligned}[/tex]

The standard deviation of the number of heads can be calculated as follows,

[tex]\begin{aligned}{\text{Standard deviation}}&= \sqrt {72 \times \frac{1}{2}\left( {1 - \frac{1}{2}} \right)} \\&= \sqrt {72 \times\frac{1}{2} \times \frac{1}{2}}\\&=\sqrt{\frac{{72}}{4}}\\&= \sqrt {18}\\&= 4.24\\\end{aligned}[/tex]

Hence, the standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]

Learn more:

1. Learn more about normal distribution https://brainly.com/question/12698949

2. Learn more about standard normal distribution https://brainly.com/question/13006989

3. Learn more about confidence interval of mean https://brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Binomial Distribution

Keywords: coin, tossed 72 times, number of heads, binomial distribution, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, proportion, empirical rule.

Final answer:

To find when the population of the city will reach 140 thousand, the formula a = 118e⁰.⁰²⁴t must be solved, resulting in approximately 3.52 years after 1998.

Explanation:

The formula a = 118e^0.024t models the population of a city, in thousands, t years after 1998. To find when the population reaches 140 thousand, set the formula equal to 140 and solve for t:
a = 118e⁰.⁰²⁴t
140 = 118e⁰.⁰²⁴t
t = (ln(140/118)) / 0.024 ≈ 3.52 years after 1998.

The distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10.

The distance between two points can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the two points are (3,8) and (-9,8). Plugging these values into the formula, we get:

d = √((-9 - 3)^2 + (8 - 8)^2)
d = √((-12)^2 + (0)^2)
d = √(144 + 0)
d = √144
d = 12

Therefore, the distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10

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The given expression gives x = 4.5.

If M is the midpoint of FG, this means that M divides FG into two equal segments. Therefore, FM = MG. We are given that MG = 7x - 15 and the total length of FG = 33. Hence, FM = MG = (1/2) * (FG).

Step-by-step solution:

Set up the equation for FM: FM = MG = (1/2) * 33.

This simplifies to FM = MG = 16.5.

Since MG = 7x - 15, we set 7x - 15 equal to 16.5.

Solve for x: 7x - 15 = 16.5.

First, add 15 to both sides: 7x = 31.5.

Finally, divide both sides by 7: x = 4.5.

Therefore, the value of x is 4.5.

Answer:

The answer is 440 pieces of checked luggage

Step-by-step explanation:

Mean = 380

Standard deviation = 20

No. of pieces of checked luggage for 1 standard deviation = 20 pieces

Therefore, Mean for 3 standard deviations above the mean = 3 × 20 = 60

Now, number of pieces of checked luggage 3 standard deviations above the mean = Mean for 1 standard deviation + Mean for 3 standard deviations above the mean

⇒ 380 + 60 = 440 pieces

The equation shown above is showing the Addition Property of Equation where the number “3” is added to both of its sides. This is shown below,

                                   4x - 3 = 7

                               4x - 3 + 3 = 7 + 3

                                   4x = 10