On the graph, two right triangles have the line as the hypotenuse. In this task, you will use these triangles to show that the slope
between points E and A is the same as the slope between points A and C.

Part A
Which angles of the triangles measure 90°?

Part B
To show that the other two angle measurements in each triangle are equal, you can use parallel lines cut by a transversal.
Which two pairs of line segments formed by triangle sides are parallel, and what is the transversal for each pair?

Part C
Which angle has the same measurement as angle DEA, and how do you know that the measurement is the same?

Part D
Which angle has the same measurement as angle DAE and why (vertical, corresponding, alternate interior, or alternate exterior
angles)?

Part E
Are the two triangles congruent? Why or why not?

Part F
Are the two triangles similar? Why or why not?

Part G
Write a fraction setting the vertical length of the larger triangle over its horizontal length. What does this fraction represent?

Part H
Write a fraction setting the vertical length of the smaller triangle over its horizontal length. What does this fraction represent?

Part I
To see if the slopes are the same, write an equation setting the two fractions equal to each other. Is this equation true? Why or
why not? What does that mean about the slope between points E and A and the slope between the points A and C?

To find the tangent to the curve y = x^2 - x - 1 at the point (2, 1) using the definition of the derivative, we need to follow these steps:

Step 1: Find the derivative of the function y = x^2 - x - 1.

Step 2: Evaluate the derivative at x = 2 to find the slope of the tangent line.

Step 3: Use the point-slope form of a linear equation to write the equation of the tangent line.

Let's go through each step:

Step 1: Find the derivative of the function y = x^2 - x - 1.

Using the power rule, the derivative of x^n is nx^(n-1), where n is the exponent, we differentiate term by term:

dy/dx = d/dx (x^2) - d/dx (x) - d/dx (1)

      = 2x - 1 - 0

      = 2x - 1

Step 2: Evaluate the derivative at x = 2.

Substitute x = 2 into the derivative equation:

dy/dx = 2(2) - 1

      = 4 - 1

      = 3

So, the slope of the tangent line at the point (2, 1) is 3.

Step 3: Write the equation of the tangent line using the point-slope form.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1),

where m is the slope and (x1, y1) is a point on the line.

Using the point (2, 1) and the slope 3, we have:

y - 1 = 3(x - 2)

Simplifying the equation:

y - 1 = 3x - 6

y = 3x - 5

Therefore, the equation of the tangent line to the curve y = x^2 - x - 1 at the point (2, 1) is y = 3x - 5.

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Answer:

7.6 miles

Step-by-step explanation:

Given the coordinate points :

A(−3, 1), B(2, 3), and C(4, −1)

Distance (d) between A and B:

x1 = - 3 ; x2 = 2 ; y1 = 1 ; y2 = 3

d = √(x2 - x1)² + (y2 - y1)²

d = √(2 - (-3))² + (3 - 1)²

d = √25 + 4

d = 5.385 miles

BC :

d = √(x2 - x1)² + (y2 - y1)²

d = √(4 - 2)² + (-1 - 3)²

d = √2² + (-4²)

d = √4 + 16

d2 = 4.4721359 miles

(1/2) of d2 = 1/2 * 4.4721359 = 2.236 miles

Total distance = (5.385 + 2.236) miles

Total distance driven before getting stuck in traffic = 7.6 miles

The strengths of this study design are:1. Randomization: It is the method of randomly assigning patients to either experimental or control groups. Randomization guarantees that groups would be equal in every respect except for the variable that is being studied.2. Placebo Control: A placebo control group makes it possible to identify the difference between the true effect of the treatment and the effect of other variables that are not being tested.3. Double-blind: When an experiment is double-blind, the experimenter and the patient do not know which group is which. This is important since experimenter bias and expectancy effects can be controlled in the study.

Jonas Salk conducted a large-scale controlled experiment involving over 400,000 children in 1954 to test the effectiveness of a polio vaccine. Children in the control group were injected with salt water (a placebo), while children in the experimental group were injected with the polio vaccine. Every test subject was followed for six months, and the experiment was double-blind, meaning that neither the participants nor the researchers knew to which group each child was assigned.Jonas Salk's primary goal in conducting the vaccine trial was to reduce the number of polio infections in the United States. Polio had become a major public health issue, with thousands of children being infected each year. The vaccine trial's outcomes confirmed the effectiveness of the vaccine, and it became one of the most important scientific breakthroughs in modern medicine.

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Answer:

the y intercept is (0,29)

Answer:

The Value of the reciprocal. The top one.

Step-by-step explanation:

As you notice the number Doubles everytime making it 2x more every time.

Answer:

20

Step-by-step explanation:

use ur head

DG, DM, DS, DT GD, GM, GS, GT MD, MG, MS, MT, SD, SG, SM, ST, TD, TG, TM, TS. Those are all the possible combinations using each letter only once in each set.

In short, you can make 20 sets.

The rate of change of the annual u.s. factory sales in 2000 is 7.7 billion dollars per year

From the question, we have the following parameters that can be used in our computation:

s(t) = 0.12t² − t + 5.7

In 2000, we have the value of t to be

t = 2000 - 1990

Evaluate

t = 10

So, we have

s(10) = 0.12 * 10² − 10 + 5.7

Evaluate

s(10) = 7.7

Hence, the rate in 2000 is 7.7 billion dollars per year

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Question

the rate of change of annual u.s. factory sales (in billions of dollars per year) of consumer electronic goods to dealers from 1990 through 2001 can be modeled as s(t) = 0.12t2 − t + 5.7 billion dollars per year

Calculate the rate of change in 2000

Based on the figure, the measure of the angle GPY is 118 degrees.

Alternate angles are a pair of angles that are formed by a transversal intersecting two parallel lines.

When a transversal intersects a parallel line, it creates four angles.

Alternate angles are the pairs of angles that are on opposite sides of the transversal and on opposite sides of the parallel lines.

The key property of alternate angles is that they are congruent, meaning they have the same measure.

Here angle GPY is alternate to angle RPK.

Thus;

8p + 94 = 5p + 103

8p - 5p = 103 - 94

3p = 9

Divide both sides by 3;

p = 3

The measure of angle GPY becomes ;

= 5(3) + 103= 15 + 103= 118 degrees.

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Let's denote the probability of obtaining heads on a toss of coin A as pA and the probability of obtaining heads on a toss of coin B as pB. The probability of selecting coin A is denoted as p(select A).

To calculate the expected number of tosses until the first heads, we can use the concept of conditional expectation. Let E be the expected number of tosses until the first heads.  If we select coin A, the expected number of tosses until the first heads is 1/pA, as the probability of obtaining heads on each toss is pA. If we select coin B, the expected number of tosses until the first heads is 1/pB, as the probability of obtaining heads on each toss is pB. Using the law of total expectation, we can calculate the overall expected number of tosses: E = p(select A) * (1/pA) + p(select B) * (1/pB) Simplifying further, we have: E = (p(select A)/pA) + (p(select B)/pB) Therefore, to find the expected number of tosses until the first heads, we need to know the probabilities pA, pB, and p(select A). Without these specific values, we cannot provide an exact numerical answer.

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The slope of given line is -3 and the y-intercept of the line is -2.

A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity.

Here, we know that slope intercept form of straight line;

            y = mx + c

Given equation;

          y = -3x - 2

compare this equation with general equation, we get

    m = -3 and c = -2

Thus, The slope of given line is -3 and the y-intercept of the line is -2.

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Answer:

Graph the linear function described by the equation

y=-3x-2

Step 1: Identify the slope and y-intercept.

slope =

Step-by-step explanation:

Answer:

Solution = (-8,-28)

Step-by-step explanation:

The modification to the system of sampling procedure will affect amount of dissolved oxygen in the water, leading to many consequences and finally resulting in rejection of collected data .



In short, the time of day when a sample is collected is regarded as crucial phase which can adversely  affect the results of a water quality test. The temperature of the water plays a important role which can change throughout the day, and also put lots of stress on  the amount of dissolved oxygen in the water.

Dissolved oxygen is an imperative measure for checking the water quality because it is a survival need for aquatic life. The total amount of sunlight that penetrates  the water seriously affects the amount of dissolved oxygen in the water. In the event  if a sample is acquired at a different time than usual, it may not be accurate to other samples that were taken at different times.

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The complete question is

A local citizen science group is monitoring the water quality of a nearby lake. They gather water samples once a week on Wednesday between the hours of 7 A.M. and 9 A.M. from the same location. One day in August they were unable to sample within that time frame and collected the sample at 3 P.M. How might this modification to the sampling procedure affect the results?                                                          

Step-by-step explanation:

the median = 140

the interquartile range = 141-138 = 3

Answer: The other guy is correct. You guys should give him 5 stars and Mark him brainliest.