1.3. The Dow Jones average (a stock market share index) dropped from 12 837 to 12 503 in one week in July 2012. 1.3.1. Calculate the drop in the share index. 1.3.2. If the price continued to drop at the same rate, calculate the Dow Jones average after 4 more weeks. ​

Answer:

The given equation is in vertex form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Comparing the given equation with the vertex form, we have a = -3, h = -3 and k = 4.

Since a = -3 < 0, the parabola opens downwards and has a maximum point.

To find the maximum value of y, we need to evaluate y at the x-coordinate of the vertex:

x = -3

y = -3(-3+3)^2 + 4 = 4

Therefore, the parabola y = -3(x+3)2 + 4 contains a maximum point and the maximum value of y is 4.

Hence, the answer is option C

Answer:

C)  Maximum point; 4

Step-by-step explanation:

Given parabola:

[tex]y=-3(x+3)^2+4[/tex]

The given parabola is in vertex form:

[tex]\boxed{y = a(x - h)^2 + k}[/tex]

where:

By comparing the given equation with the vertex form, we can see that:

As a < 0, the parabola opens downwards. Therefore, the vertex of the parabola is a maximum point.

The vertex of the parabola is (h, k) = (-3, 4).

Therefore, the maximum value of y is 4, which occurs at x = -3.

Therefore, the function that matches the mosquito counts is'(w) = 8([tex]1.5^{w}[/tex]).

by the question.

To determine which function matches the mosquito counts, we can plot the given data points on a graph and see which function fits the curve. Here are the counts for the first few weeks:

Week Mosquito Count

0 8

1 20

2 50

3 125

4 312

Plotting these points on a graph with weeks on the x-axis and mosquito count on the y-axis, we get:

mosquito graph

Looking at the graph, we can see that the curve increases rapidly and seems to be exponential. This rule out option A (which is linear), leaving us with options B, C, and D.

To determine which of these options matches the data, we can try plugging in the week numbers and seeing which one gives us values close to the actual counts. We can also use a calculator or graphing technology to help us with this.

Option B gives us the following mosquito counts for the first five weeks:

Week Mosquito Count

0            8

1         19.5

2        47.25

3       114.19

4       276.32

Option C   gives us:

Week Mosquito Count

0       8

1        12

2       18

3       27

4       40.5

Option D is not a function of mosquito counts with weeks as the input variable, so we can rule it out.

Comparing the values from options B and C to the actual counts, we can see that option C is the closest match.

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Answer:

6.25 minutes

Step-by-step explanation:

So, if there are 96 tests being graded in 2 minutes, the average per minute (using the equation 96/2 = average) would be 48 per minute. Next you would do 300/48 to get the number of minutes that it would take to grade that amount. The answer to that would be 6.25, So it would take approximately 6.25 minutes.

All monuments cast a shadow when the sun is shining, as they block the sunlight and create a shadow on the ground or nearby surfaces. T

The size and shape of the shadow will depend on the position of the sun in the sky, the orientation of the monument, and its size and shape.

Some famous monuments that cast impressive shadows include the Pyramids of Giza, the Eiffel Tower, the Washington Monument, and the Stonehenge.

We can use proportions to solve the problem.

Let x be the length of Kyle's shadow.

We know that the length of the monument's shadow is 16 feet, and its height is  [tex]64 f[/tex] Feet. So the ratio of the length of the monument's shadow to its height is:

[tex]16/64 = 1/4[/tex]

This ratio is equal to the ratio of Kyle's shadow length to his height:

[tex]x/6.25 = 1/4[/tex]

To solve for x, we can cross-multiply:

[tex]x = 6.25/4 = 1.5625[/tex]

Therefore, the length of Kyle's shadow is approximately [tex]1.56[/tex] feet (or  [tex]18.72 inches)[/tex] .

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Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.

Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.

The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.

As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.

using the formula no.

Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.

Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

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the complete question is

Write a positive or negative number to represent each change in the high temperature.

1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?

2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?

3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?

4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?

Answer:

0.33

Step-by-step explanation:

To solve this, you first write the problem as an algebra equation as follows: 3x + 4 = 5

Then you solve the equation by subtracting 4 from both sides, and then divide both sides by 3. Here is the math to illustrate better:

3x + 4 = 5

3x + 4 - 4 = 5 - 4

3x = 1

3x/3 = 1/3

x = 0.33

Answer = 0.33

Answer:

The answer is the standard error is a measure of the accuracy of the sample mean as an estimate of the population mean.

Step-by-step explanation:

The car sticker information indicates a highway average of 27 mpg, while the sample mean's standard deviation is around 1.455 mpg. The mean estimate's margin of error is roughly 3.06 mpg.

The simplest approach to figure out your gas mileage is to simply divide the distance driven by the quantity of petrol your car required to fill up. That amounts to kilometers traveled divided by petrol consumed.

a) The formula for the standard deviation of the sample mean, σx¯, is:

σx¯ = σ / sqrt(n)

where σ is the standard deviation of the population, and n is the sample size. In this case, σ = 6.5 mpg and n = 20. So,

σx¯ = 6.5 / sqrt(20) ≈ 1.455 mpg

b) To find the margin of error for the mean estimate at a 95% confidence level, we can use the following formula:

Margin of error = z* (σx¯)

where z* is the critical value for a 95% confidence interval, which is 1.96.

Therefore, the margin of error = 1.96 * 1.454 = 2.85 mpg.

c) To find the 95% confidence interval for the mean highway mpg for this vehicle, we can use the following formula:

Confidence interval = x¯ ± Margin of error

where x¯ is the sample mean, which can be calculated by adding up all the mpg readings and dividing by the sample size:

x¯ = (37.2+21.0+17.4+29.2+7.4+27.0+36.9+38.8+35.3+32.3+19.0+26.1+25.8+41.4+34.4+32.5+26.5+28.2+22.1) / 20

= 29.231 mpg

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Joe aura 35 pommes.

40-5=35

If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.

To do this, we can set the coefficients of x and y in the two equations equal to each other:

6 - 4m = 2k(2m - 1)

2n - 7 = 3k

Simplifying these equations, we get:

8m - 6 = 4km

2n - 7 = 3k

We can solve the first equation for k:

k = (8m - 6)/(4m)

Substituting this into the second equation and solving for n, we get:

n = (16m - 29)/(8m - 12)

Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.

We find that the expressions for k and n are the same for m = 3/2.

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Complete Question:

Determine the values of m and n so that the following system of linear equations have infinite number of solutions:

(2m−1)x+3y−5=0

3x+(n−1)y−2=0

Answer:

m<1=74

m<2=106

m<3=74

Step-by-step explanation:

m<1:

=180-106

=74

m<2:

=106

m<3;

if m<1 is 74, m<s will also be 74

The average number of beads that the girls have is 63

Let's start by using algebra to represent the given information:

Let b be the number of beads that Sally has.

Then, Kelly has 3/4 times as many beads as Sally, which can be expressed as (3/4)b.

Also, we know that Kelly has 18 more beads than Sally, which can be expressed as (b + 18).

Putting these together, we can write the equation:

(3/4)b = b + 18

Solving for b, we get:

b = 72

So, Sally has 72 beads, and Kelly has (3/4) × 72 = 54 beads.

The average number of beads that the girls have is (72 + 54)/2 = 63 beads

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The length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

so by Pythagoras rule we can evaluate for the length RV by considering the following right triangles:

For ∆TVU:

13² = 5² + TV²

TV = √(13² - 5²) {make TV the subject}

TV = √(169 - 25)

TV = √144

TV = 12

For ∆TVS:

15² = 12² + SV²

SV = √(15² - 12²) {make SV the subject}

SV = √(225 - 44)

SV = √81

SV = 9

For ∆RVS:

11² = 9² + RV²

RV = √(11² - 9²) {make RV the subject}

RV = √(121 - 81)

RV = √49

RV = 6.3246

Therefore, the length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.

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a)The probability that none of the restaurants are in violation of the health code is approximately 0.0482.

b)The probability that one of the restaurants is in violation of the health code is approximately 0.3729.

c)The probability that at least two of the restaurants are in violation of the health code is approximately 0.4681.

(a) Probability that none of the restaurants are in violation of the health code:

Let E be the event that a restaurant is in violation of the health code, and let F be the event that a restaurant is not in violation of the health code. Therefore, probability that a restaurant is in violation of the health code is:

P(E) = 0.30

,then the probability that a restaurant is not in violation of the health code is:

P(F) = 1 - P(E) = 1 - 0.30 = 0.70

The health inspector selects 9 restaurants. The probability that none of the restaurants are in violation of the health code is:

P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) = (0.70)^9 ≈ 0.0482.

Therefore, the probability that none of the restaurants are in violation of the health code is approximately 0.0482.

(b) Probability that one of the restaurants is in violation of the health code:

The health inspector selects 9 restaurants. We want to find the probability that one of the restaurants is in violation of the health code. We can use the product rule of probability for this. Let us assume that the health inspector selects the first restaurant and that it is in violation of the health code. The probability of that happening is:

P(E) = 0.30

Then the probability that the other eight restaurants are not in violation of the health code is:

P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) = (0.70)^8

Then, the health inspector could have selected the restaurant that is in violation of the health code from any of the 9 restaurants. So, we have to multiply by 9.

P(one restaurant in violation of health code) = 9 × P(E) × P(F)^8≈ 0.3729

Therefore, the probability that one of the restaurants is in violation of the health code is approximately 0.3729.

(c) Probability that at least two of the restaurants are in violation of the health code:

Let X be the random variable that denotes the number of restaurants that are in violation of the health code. Then, X can take on values 0, 1, 2, 3, ..., 9.The probability that at least two of the restaurants are in violation of the health code is the same as the probability that two or more are in violation of the health code:

P(X ≥ 2) = P(X = 2) + P(X = 3) + · · · + P(X = 9)

We can use the sum rule of probability for this.Let us calculate the probability that exactly k of the 9 restaurants are in violation of the health code:

P(X = k) = (9Ck) P(E)k P(F)9−k = (9Ck) (0.30)k (0.70)9−k

Then:P(X ≥ 2) = P(X = 2) + P(X = 3) + · · · + P(X = 9)= ∑ (9Ck) (0.30)k (0.70)9−k, where k = 2, 3, ..., 9

= 1 − [P(X = 0) + P(X = 1)]= 1 − [1 × (0.70)^9 + 9 × (0.30)(0.70)^8]≈ 0.4681

Therefore, the probability that at least two of the restaurants are in violation of the health code is approximately 0.4681.

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The resulting double-line graph should show the sales data for desktop and laptop computers over the five days, with a line for each type of computer.

A double-line graph is a graph that displays two sets of data on the same graph, using two lines to show how each set of data changes over time or some other variable.

To create a double-line graph of the sales data for desktop and laptop computers over five days, follow these steps:

Draw a graph with two perpendicular axes, the horizontal axis (x-axis) representing the days, and the vertical axis (y-axis) representing the number of computers sold.

Label the horizontal axis with the days from Day 1 to Day 5.

Label the vertical axis with the heading "Number of Computers Sold".

Plot the data points for desktop computer sales. For Day 1, plot a point at (1, 4), for Day 2 plot a point at (2, 1), for Day 3 plot a point at (3, 2), for Day 4 plot a point at (4, 5), and for Day 5 plot a point at (5, 1).

Connect the data points for desktop computer sales with a line.

Plot the data points for laptop computer sales. For Day 1, plot a point at (1, 5), for Day 2 plot a point at (2, 2), for Day 3 plot a point at (3, 3), for Day 4 plot a point at (4, 7), and for Day 5 plot a point at (5, 3).

Connect the data points for laptop computer sales with a line.

Use a different color or style for the line representing desktop sales and the line representing laptop sales.

Add a legend to the graph to indicate which line corresponds to desktop sales and which corresponds to laptop sales.

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The area of the region of overlap between the 8-inch by 10-inch paper and the 8(1/2)-inch by 11-inch paper measures 12 square inches.

The area of the region of overlap between an 8-inch by 10-inch paper and an 8(1/2)-inch by 11-inch paper can be found in the following steps:

Step 1: Calculate the area of each paper. The area of an 8-inch by 10-inch paper is:

[tex]$$\text{Area} = \text{length} \times \text{width} = 8 \text{ in.} \times 10 \text{ in.} = 80 \text{ sq. in.}$$[/tex]

The area of an 8 1/2-inch by 11-inch paper is:

[tex]$$\text{Area} = \text{length} \times \text{width} = \left( 8 \frac{1}{2} \right) \text{ in.} \times 11 \text{ in.} = 93.5 \text{ sq. in.}$$[/tex]

Step 2: Find the horizontal and vertical lengths of the region of overlap.

The horizontal length is the length that is common to both papers, which is 8 inches.

The vertical length is the amount by which the two papers overlap, which is 8(1/2) inches - 10 inches = -1(1/2) inches. However, since the region of overlap cannot have a negative length, we take the absolute value of this result, which is 1(1/2) inches.

Step 3: Calculate the area of the region of overlap.

The area of the region of overlap is the product of the horizontal and vertical lengths:

[tex]$$\text{Area of the region of overlap} = 8 \text{ in.} \times 1 \frac{1}{2} \text{ in.} = 12 \text{ sq. in.}$$[/tex]

Therefore, the area of the region of overlap in square inches is 12 square inches.

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Answer: So that means the answer is $112.5

Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.

YES THIS IS RIGHT!!!!

The original price of the baseball hat before 12% off in the sale was $14.20.

A number can be expressed as a fraction of 100 using a percentage. It frequently serves to indicate a portion of a total and is represented by the sign %. We may state that 25% of the class is made up of guys, for instance, if there are 100 pupils in the class and 25 of them are male.

The Roman term per centum, which meaning "by the hundred," is where the word "percent" originates.

Let us suppose the original price of the baseball hat = x.

Given that, baseball hats are on sale for 12% off the original price.

That is,

12.50 = x(1 - 12/100)

12.50 = x(100 - 12)/100

12.50 = x(0.88)

x = 14.2

Hence, the original price of the baseball hat was $14.20.

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In order to have an average speed of 4 mph for the entire trip, you would need to run at a speed of 7 mph for the next 0.5 hours after walking for 1.5 hours at 3 mph.

Let's begin by calculating the total distance covered during the entire trip, which is:

distance = (time walked) x (walking speed) + (time ran) x (running speed)

We know that the time walked is 1.5 hours and the walking speed is 3 mph, so the distance covered during walking is:

distance walked = (time walked) x (walking speed) = 1.5 x 3 = 4.5 miles

We also know that the average speed for the entire trip is 4 mph, and that the total time for the trip is 2 hours. Therefore, the distance covered during the entire trip is:

distance = (average speed) x (total time) = 4 x 2 = 8 miles

So the distance covered during running is:

distance ran = distance - distance walked = 8 - 4.5 = 3.5 miles

Now we can use the formula for average speed:

average speed = total distance / total time

To find the running speed, we need to solve for the running time, which is:

time ran = distance ran / running speed

Substituting this expression into the average speed formula, we get:

4 = (distance walked + distance ran) / (1.5 + time ran)

4 = (4.5 + 3.5) / (1.5 + distance ran / running speed)

Simplifying this expression, we get:

1.5 + distance ran / running speed = 2

distance ran / running speed = 0.5

Substituting the values we calculated, we get:

3.5 / running speed = 0.5

Solving for the running speed, we get:

running speed = 3.5 / 0.5 = 7 mph

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The family will use 3,600 fewer gallons of water with the new showerheads in a 30-day period.

A family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. Each member of the family averages 8 minutes in the shower per day. In a 30-day period, the family will use 3,600 fewer gallons of water with the new showerheads. How many fewer gallons of water will the family use with the new showerheads?

Calculate the number of gallons used per person per shower before:

5 gal/min x 8 min = 40 gallons per person per shower.

The number of gallons used per person per shower after:

2 gal/min x 8 min = 16 gallons per person per shower.

The number of gallons used per person per day before:

40 gallons x 1 shower = 40 gallons per person per day.

The number of gallons used per person per day after:

16 gallons x 1 shower = 16 gallons per person per day

The number of gallons used per family per day before:

40 gallons x 5 people = 200 gallons per day

The number of gallons used per family per day after:

16 gallons x 5 people = 80 gallons per day

The number of gallons used per month before:

40 gallons x 5 people x 30 days = 6,000 gallons per month

The number of gallons used per month after:

16 gallons x 5 people x 30 days = 2,400 gallons per month

The family will use 6,000 - 2,400 = 3,600 fewer gallons of water with the new showerheads in a 30-day period. Therefore, the answer is 3,600.

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Answer:

(a) Since there are 428 equally likely pages, the probability of randomly turning to page 45 is 1/428, which is approximately 0.00234 or 0.234%.

(b) There are two possible cases for an even numbered page: either the last digit is 0, 2, 4, 6, or 8, or the page number ends in 00.

For the first case, there are 5 possible digits for the units place, and each of these digits can be followed by any one of the 5 possible digits for the tens place. So there are 5x5 = 25 even numbered pages that end in a non-zero digit.

For the second case, there are 4 possible digits for the hundreds place, and each of these digits can be followed by 00. So there are 4 even numbered pages that end in 00.

Therefore, there are 25 + 4 = 29 even numbered pages in total. Since there are 428 pages in the book, the probability of randomly turning to an even numbered page is 29/428, which is approximately 0.06776 or 6.776%.

Step-by-step explanation:

(a) Оскільки існує 428 рівноймовірних сторінок, ймовірність випадкового переходу на сторінку 45 дорівнює 1/428, що становить приблизно 0,00234 або 0,234%.

(b) Існує два можливих випадки, коли сторінка має парний номер: або остання цифра 0, 2, 4, 6 або 8, або номер сторінки закінчується на 00.

У першому випадку є 5 можливих цифр для позначення одиниць, і за кожною з цих цифр може слідувати будь-яка з 5 можливих цифр для позначення десятків. Таким чином, існує 5x5 = 25 парних сторінок, які закінчуються на ненульову цифру.

У другому випадку є 4 можливі цифри для сотень, і за кожною з цих цифр може стояти 00. Отже, є 4 парні сторінки, які закінчуються на 00.

Таким чином, всього є 25 + 4 = 29 парних сторінок. Оскільки в книзі 428 сторінок, ймовірність випадкового переходу на парну сторінку дорівнює 29/428, що становить приблизно 0.06776 або 6.776%.

Answer:

the answer is c

Step-by-step explanation:

add 14 9 times and then whatever that number is double it and remove the negative sign

An Inequality is a relationship between two expressions or values that aren't equal. The relationship between n and 4 is given by the inequality n> 4.

We want to find a relation between n and 4 similar that

7 *( n/ 4)> 7

still, we get

If we now divide both sides of the former inequality by 7.

7 *( n/ 4)/ 7>7/7

n/ 4> 1

So n/ 4 must be lesser than 1.

A better way to show the relationship is to multiply both sides of the inequality by 4.

4 *( n/ 4)> 4 * 1

n> 4

So the relationship between n and 4 is that n must be lesser than 4.

In mathematics, an inequality is a relationship that results in an unstable comparison of two figures or other fine expressions. It's frequently used to compare two figures on a number line grounded on their size.

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Step-by-step explanation:

xy=6

x=6/y (1)

now,

XY=6

6/y-y=6

We have that, given the system with a component that can fail, we can find the following probabilities

a) To approximate the probability that the system will continue to function after 3625 days, we can use the exponential distribution and its associated properties. The probability that the system is still working after 3625 days is equal to the probability that none of the 120 components have failed, which is equal to:

Probability = e(-120*(3625-25)/25) = 0.091

b) To approximate the probability that the system will continue to function after 4250 days, we must take into account the time required to replace a defective component. Since the time required to replace a defective component is a random variable that is uniformly distributed over (0,0,5), the expected time to replacement is 0.25. Therefore, the probability that the system is still working after 4250 days is equal to:

Probability = e(-120*(4250-25)/25) * e(-120*(0.25)/25) = 0.018

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The force equation for the system is F = bV - bF, where F is the force of friction, V is the velocity of the object, and b is the coefficient of viscous friction.

Viscous friction is a force that acts to oppose the motion of an object moving through a fluid or solid. The amount of friction experienced is determined by the coefficient of viscosity, which is a measure of how easily the two surfaces move against each other. In this equation, bV is the force generated by the object's motion, and b

F is the opposing force of friction. Together, these two forces determine the net force acting on the object.

Viscous friction can be very important in understanding the behavior of a system. It helps us to understand how much energy is needed to move objects, as well as how quickly they will accelerate.

Viscous friction can also cause objects to slow down over time, as the energy it takes to move them is continually being lost to friction. Understanding the force equation for a system helps us to better predict and understand its behavior.

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16. The equatiοn οf the line in slοpe-intercept fοrm that passes thrοugh the pοint (-6, 5) and is parallel tο x + 2y = 14 is y = (-1/2)x + 2.

The equatiοn οf a straight line is y = mx + c, y = m x + c m is the gradient and c is the height at which the line crοsses the y -axis, alsο knοwn as the y -intercept.

16. Tο write the equatiοn οf a line in slοpe-intercept fοrm, we need tο find the slοpe and the y-intercept οf the line.

Tο find the slοpe οf the line, we can rewrite the equatiοn x + 2y = 14 in slοpe-intercept fοrm y = mx + b by sοlving fοr y:

x + 2y = 14

2y = -x + 14

y = (-1/2)x + 7

The slοpe οf the line is -1/2.

Since the line we want tο find is parallel tο this line, it will have the same slοpe οf -1/2.

Nοw we can use the pοint-slοpe fοrm οf the equatiοn οf a line tο find the equatiοn οf the line that passes thrοugh the pοint (-6, 5) with a slοpe οf -1/2:

y - y1 = m(x - x1)

where (x1, y1) is the pοint (-6, 5), and m is the slοpe, -1/2.

y - 5 = (-1/2)(x - (-6))

y - 5 = (-1/2)x - 3

y = (-1/2)x + 2

17. The equation perpendicular to y = -(2/3)x + 4, passing through (-4, 6)

perpendicular equations slope would be negative reciprocal to the current line.

The slope in y = -(2/3)x + 4, is m = -(2/3),

The negative reciprocal of -(2/3) is 3/2

Now, applying the x and y values in pοint-slοpe fοrm

y - 6 = 3/2(x - (-4))

y =  3/2(x+4) + 6

y =  (3/2)x + 6 + 6

y =  (3/2)x + 12

18. Since the line we want tο find is parallel tο this line, it will have the same slοpe.

Lets find the slope using slope formula

[tex]\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\rm m = \dfrac{0 - (-1)}{2 - (-1)}[/tex]

[tex]\rm m = \dfrac{1}{3}[/tex]

Now, using the point slope form

y - 1 = 1/3(x - 3)

y = 1/3(x - 3) + 1

y = (1/3)x - 1 + 1

y = (1/3)x

Learn more about equation of line on:

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Answer:

y = 12

Step-by-step explanation:

if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is

y² = 8(8 + 6 + 4) = 8 × 18 = 144 ( take square root of both sides )

y = [tex]\sqrt{144}[/tex] = 12