determine the smallest integer value of x in -2x+1< -9

The total volume of the sample is 0.0067 m³ and the density of the sample is 2753.73 kg/m³.

An ore sample weighs 18.5 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.8 N. When the ore sample is immersed in water, the tension in the cord is given as 11.8 N.

Thus, the buoyancy force experienced by the ore sample is given by the difference between the weight of the sample in the air and the tension in the cord.

Buoyancy force experienced by the ore sample = Weight of the sample in the air - Tension in the cord

Buoyancy force experienced by the ore sample = (18.5 N) - (11.8 N)

Buoyancy force experienced by the ore sample = 6.7 N

Also, we know that the weight of the ore sample in air is equal to the weight of the ore sample when immersed in water.

Weight of the ore sample = Weight of the displaced water

Weight of the ore sample = Buoyancy force experienced by the ore sample

Weight of the ore sample = 6.7 N

The density of the ore sample

Density is given by the formula Density = Mass/Volume

Where Density is measured in kg/m³

Mass is measured in kg

Volume is measured in m³

Also, the density of water is given as 1000 kg/m³.

The density of the ore sample = Mass/Volume

Mass = Density x Volume

Volume of the ore sample can be obtained from volume of the displaced water.

Volume of the displaced water = Weight of the ore sample/Density of water

Volume of the displaced water = (6.7 N)/(1000 kg/m³)

Volume of the displaced water = 0.0067 m³

Density of the ore sample = (18.5 N)/(0.0067 m³)

Density of the ore sample = 2753.73 kg/m³

Therefore, 0.0067 m³ is the sample's total volume and 2753.73 kg/m³ is the density of the sample.

To know more about density: https://brainly.com/question/952755

#SPJ11

The order of events from least likely to most likely are as follows:

The reason for this order is because of the chances of each event occurring. Event D has the least chance of occurring because no numbers in the set have a value less than or equal to 0. Event A is the next least likely because only one number in the set is greater than 0, which is the number 1. Event C is the next least likely because only two numbers in the set are at least 2 (2 and 3). Event B is the next least likely, as there are only five even numbers in the set (2, 4, 6, 8, and 10). Events E, F, G, and H are the most likely to occur, because of the number of numbers that are divisible by 3, and 5, and are prime numbers.

To learn more about "Least likely events": brainly.com/question/30311304

#SPJ11

Option C. 6,160 yards. To convert miles to yards, we multiply the number of miles by 1,760 (which is the number of yards in one mile). So, 3.5 miles x 1,760 yards/mile = 6,160 yards.

To convert miles to yards, we need to know that there are 1,760 yards in one mile. Therefore, to find out how many yards are in three and one-half miles, we need to multiply 1,760 by 3.5:

1,760 x 3.5 = 6,160

Therefore, there are 6,160 yards in three and one-half miles.

The other options provided are:

4,400 yards: This is equivalent to 2.5 miles, since 1 mile is 1,760 yards. Therefore, this is not the correct answer.

5,280 yards: This is equivalent to 3 miles, since 1 mile is 1,760 yards. Therefore, this is also not the correct answer.

7,040 yards: This is equivalent to 4 miles, since 1 mile is 1,760 yards. Therefore, this is not the correct answer.

So, the correct answer is 6,160 yards, which is the result of multiplying 1,760 yards by 3.5 miles.

Learn more about yards here: brainly.com/question/14516546

#SPJ4

The statement "Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment" is false.

A binomial experiment is an experiment that is repeated multiple times with each repetition having only two potential outcomes. In a binomial experiment, the probability of success remains constant from trial to trial.

The criteria for a binomial experiment are as follows:

P(x) = (ⁿCₓ)(pˣ)(q^(n-x))

Where p is the probability of success, q is the probability of failure (q = 1 - p), and ⁿCₓ is the combination formula.

Therefore, the statement "Ten cards are selected out of a 52-card deck without replacement and the number of Jacks is observed. This is an example of a "Binomial Experiment" being false. This is because the probability of drawing a jack changes with each trial, as the deck's composition changes after each card is drawn.

To know more about the "Binomial Experiment": https://brainly.com/question/9325204

#SPJ11

The probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.

Bayes' theorem is used to update probabilities of a hypothesis or an event in light of new data or evidence. It is used to calculate the conditional probability of an event based on prior knowledge of the conditions that might be relevant to the event.In the given problem, we have to find the probability that the response indicated that the dog is small-sized given that they enjoyed the treat.

The probability that the dog is small-sized given that they enjoyed the treat is the conditional probability P(S|T), where S is the event that the dog is small-sized and T is the event that they enjoyed the treat. To find the value of P(S|T), we will use Bayes' theorem. Bayes' theorem states that P(S|T) = P(T|S) * P(S) / P(T) where P(T|S) is the probability that they enjoyed the treat given that the dog is small-sized, P(S) is the prior probability that the dog is small-sized, and P(T) is the probability that they enjoyed the treat.

P(S) = 3/7P(T|S) = 2/3P(T) = (2/3 * 3/7) + (1/4 * 4/7) = 18/84 + 4/28 = 1/3

(adding the probabilities of T given S and T given L)Therefore, P(S|T) = (2/3 * 3/7) / (1/3) = 2/7 = 0.285714...Rounding off to the nearest millionth, the probability is 0.286. Therefore, the probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.

See more about Bayes' theorem at: https://brainly.com/question/17010130

#SPJ11

Answer: 72°

Step-by-step explanation:

To find the interior angle of this shape, use the formula 180(n-2)/n, where n is the amount of sides. Plugging 5 in for the interior angle of a pentagon, you get 180(3)/5, or 108°.

Using the statement that PR intersects QS, we can see that triangle QOR is isosceles (to get this, look at triangle PQR, and note that because it has 2 equal side lengths, and its last length is not equivalent to the other 2 sides, it is isosceles). Solving for angle PRQ, we know one angle is 108°, and the other two are equal. The total angle in a triangle is 180°, so (180°-108°)/2 = 36° (angles QPR and PRQ).

Since the angle of R = 108°, we can find angle PRS as 108° - 36°, or 72°. Since triangles PQR and QRS are similar (share the same angles and side lengths), we can see that angle RQS and RSQ are both 36°.

Since ORS is a triangle, its angle total is 180°. Since we know the angles ORS and OSR (respectively) already as 72° and 36°, we can subtract these angles to find angle ROS. 180°-72°-36° = 72°

Answer:

AB = 27

Step-by-step explanation:

AC = AB + BC

[tex]{ \rm{57 = 3x + (4x - 6)}} \\ \\ { \rm{57 = 7x - 6}} \\ \\ { \rm{7x = 57 + 6}} \\ \\ { \rm{7x = 63}} \\ \\ { \rm{x = 9}}[/tex]

Therefore;

[tex]{ \rm{AB = 3x = 3 \times 9}} \\ { \boxed{ \rm{AB = 27}}}[/tex]

Answer: 198 families live farther than 1 mile from the square.

Step-by-step explanation:

We know that there are 238 families that live within 1 mile of the village square. To find the number of families that live farther than 1 mile from the square, we can subtract 238 from the total number of families:

436 - 238 = 198

Therefore, 198 families live farther than 1 mile from the square. We can do this subtraction mentally without needing a calculator.

If the school has population of 2,462, then approximately 1,784 students at the school wore their school shirt on Friday.

If 19 out of 26 students wore their school shirt on Friday, then the fraction of students who wore their school shirt is:

[tex]\frac{19}{26}[/tex]

We can use this fraction to estimate the number of students who wore their school shirt on Friday. If there are approximately 2,462 students in the school, then the estimated number of students who wore their school shirt on Friday is:

[tex](\frac{19}{26}) * 2,462 = 1,783.69[/tex]

Rounding this to the nearest whole number, we get an estimate of 1,784 students who wore their school shirt on Friday.

Learn more about fraction

brainly.com/question/10354322

#SPJ4

The Variance Inflation Factor (VIF) measures the degree of correlation or the collinearity of the explanatory variables.

VIF quantifies how much each explanatory variable is correlated with a linear combination of the other variables in a multiple regression model. This can help identify variables that are redundant, irrelevant, or harmful to the model's accuracy. The VIF is calculated for each explanatory variable by dividing the variance of the regression coefficient estimates by the variance of the regression coefficient estimates when that variable is excluded from the model.

If the VIF is greater than 1, it indicates that the variance of the regression coefficient estimate for that variable is inflated by the presence of the other variables, which reduces the model's accuracy. Therefore, a VIF greater than 1 is considered to be an indication of collinearity or multicollinearity in the explanatory variables. The VIF measures the degree of correlation or the collinearity of the explanatory variables, and it can identify variables that are redundant, irrelevant, or harmful to the model's accuracy.

Learn more about Variance Inflation Factor (VIF) here: https://brainly.com/question/28941844

#SPJ11

The sum of the decimal fraction equation is:

seventy-six hundredths

The equation we are given is sixteen hundredths plus six-tenths

Now, when we talk about the decimal hundredths. Hundredths after decimal points shows 1/100th part of a whole. It represents the place value of the digit that occurs two places after the decimal.

Thus:

sixteen hundredths = 16/100

Similarly, six-tenths = 6/10

Thus:

The sum is:

16/100 + 6/10

= (16 + 60)/100

= 76/100 or seventy-six hundredths

Read more about decimal fractions at: https://brainly.com/question/13635105

#SPJ1

The integers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 have been written on a chalkboard by Dayna. She then erased the integers from 1 through 6, as well as their multiplicative inverse $\mod{13}$.

We can find the multiplicative inverse of an integer { a modulo 13 } by using the extended Euclidean algorithm.The integers from 1 to 6 are 1, 2, 3, 4, 5, and 6.The multiplicative inverse of : 1 modulo 13 is 1, 2 modulo 13 is 7,  3 modulo 13 is 9, 4 modulo 13 is 10, 5 modulo 13 is 8, and 6 modulo 13 is 11.The only integer that Dayna does not erase is 12.

To learn more about Modulus & Integer : https://brainly.com/question/31132117

#SPJ11

The weight becomes 1/4 of its original value when the distance is multiplied by 2.

According to the question, "the weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth." We need to determine the effect on the weight when the distance is multiplied by 2.

Let w be the weight of a body, d be the distance from the center of the earth, and k be the constant of variation. According to the question,

w = k / d²

When the distance is multiplied by 2, the new distance is 2d. Therefore, the new weight is given by:

w' = k / (2d)²

w' = k / 4d²

w' = w / 4

Therefore, the weight becomes 1/4 of its original value when the distance is multiplied by 2.

To learn more about weight refer :

https://brainly.com/question/30825684

#SPJ11

In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.

To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].

This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).

To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).

We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).

for such more questions on Venn diagram

https://brainly.com/question/30599101

#SPJ11

we can use the notation P(A) and apply the definition of probability: P(A) = P(B), P (A ∩ B), and P (A ∪ B) if we have the necessary information.

I believe you meant to say, "Venn diagram". A Venn diagram is a type of graphical representation used to illustrate relationships between sets or groups of objects, concepts, or ideas. It consists of a series of overlapping circles or other closed shapes, with each circle representing a set or group and the overlapping areas representing the relationships or intersections between them.

by the question.

Let A be the event that a student is a cast member of Seussical, and let B be the event that a student is a cast member of Wizard of Oz. Then, we can define the following:

A ∩ B: The event that a student is a cast member of both Seussical and Wizard of Oz.

A ∪ B: The event that a student is a cast member of either Seussical, Wizard of Oz, or both.

A': The event that a student is not a cast member of Seussical.

B': The event that a student is not a cast member of Wizard of Oz.

Based on the information given, we do not know how many students are in each of these events, but we can still make some general observations. For example:

If A and B have no students in common (i.e., A ∩ B = ∅), then the number of students in A ∪ B is equal to the sum of the number of students in A and the number of students in B.

If some students are in both A and B (i.e., A ∩ B is not empty), then the number of students in A ∪ B is equal to the sum of the number of students in A, the number of students in B, and the number of students in A ∩ B. In other words, some students are counted twice when we add up the number of students in A and the number of students in B, so we need to subtract the number of students in A ∩ B to avoid double-counting.

We do not know whether the events A and B are mutually exclusive (i.e., whether A ∩ B = ∅) or not. If they are mutually exclusive, then P(A ∩ B) = 0, and we can use the addition rule of probability to find P (A ∪ B) = P(A) + P(B). If they are not mutually exclusive, then we need to use the general addition rule of probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Finally, if we want to find the probability that a student chosen at random is a cast member of Seussical,

To learn more about probability:

https://brainly.com/question/30034780

#SPJ1

The Area of Bella's garden as required to be determined in the task content is the difference of the area of the rectangular backyard and the right triangular fish pond.

It follows from the task content that the area of Bella's trapezoidal garden is to be determined from the given information.

Since the garden and the fish pond are from the rectangular backyard; the sum of their areas is equal to the area of the backyard.

Ultimately, the area of the garden is the difference of the area of the rectangular backyard and the right triangular fish pond.

Read more on difference;

https://brainly.com/question/28368605

$SPJ1

The formula relating I and P is I = kP

a) When P= $800, then I = $48

b) When I = $72, then P = $1200

If the interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan, we can write:

I = kP

where k is a constant of proportionality. To find the value of k, we can use the given information that the interest rate is 6%, or 0.06 as a decimal. We know that when P = 100, the interest I = 0.06 × 100 = 6. Therefore:

I/P = 6/100 = 0.06 = k

Now we can use this value of k to answer the given questions,

a) When P = 800, the formula relating I and P is:

I = kP

I = 0.06 × 800

I = 48

Therefore, the interest on a loan of $800 for a year at a rate of 6% is $48.

b) When I = 72, the formula relating I and P is:

I = kP

72 = 0.06P

Solving for P:

P = 72/0.06

P = 1200

Therefore, a loan of $1200 for a year at a rate of 6% would have an interest of $72.

Learn more about interest rate here

brainly.com/question/29486301

#SPJ4

The concentration of hydrogen ions in a liter of the sports drink is approximately 3.98 x 10^(-3) moles per liter.

The pH of a substance is a measure of its acidity or basicity and is defined as the negative logarithm (base 10) of the hydrogen ion concentration [H+]. The formula for pH is given as pH = -log[H+].

To find the concentration of hydrogen ions in a liter of a sports drink that has a pH of 2.4, we can use the formula pH = -log[H+]. Rearranging this formula, we get [H+] = 10^(-pH).

Substituting the given value of pH into this expression, we get [H+] = 10^(-2.4).

It's worth noting that the hydrogen ion concentration is related to the acidity of a solution; the higher the hydrogen ion concentration, the more acidic the solution. The pH scale ranges from 0 (most acidic) to 14 (most basic), with a pH of 7 being neutral. The sports drink in question has a relatively low pH, indicating that it is quite acidic.

To learn more about hydrogen ions

https://brainly.com/question/8069088

#SPJ4

The number 2 is the first even counting number,4 is the second even number, 6 is the third even number, and so forth. the sum of the first 25th even counting numbers is 650.

Since we are given that the first even counting number is 2 and each subsequent even counting number can be obtained by adding 2 to the previous one. so  by using the formula for finding the 25th term of an arithmetic series  which :

an=a+(n-1)d, where the nth term d is a common difference and a is the first term so, the  25th term is 2 + (25-1)*2 = 2 + 48 = 50. Now for finding the sum of the first 25 even counting numbers, we use the formula which is Sn = n /2 * (a1 + an),  where Sn is the sum of the first n terms of the series, a1 is the first term, and an is the nth term. since in this  n=25, a1=2 and an=50, so  after substituting the  values we get  S25 = 25/2 * (2 + 50) = 25/2 * 52 = 650

To know more about arithmetic series refer to the link  brainly.com/question/16415816

#SPJ4

The value of x that makes the average between 3.15 and x equal to 40 is 76.85.

In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:

(3.15 + x) / 2 = 40

To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.

To solve for x, we can start by multiplying both sides of the equation by 2:

3.15 + x = 80

Next, we can subtract 3.15 from both sides of the equation:

x = 76.85

To know more about average here

https://brainly.com/question/16956746

#SPJ4

Answer:

1. first, add the amount of people who cannot swim. they need swim lessons.

2.  add up the people in 5th grade who can swim and the people who cannot. same with the 4th graders.

4.  the students that cannot swim, add up the 5th and 6ths graders that cannot swim.

5. add up all of the SOHO swimmers.

6. subtracts SOHO swimmers from swim academy.

set up an equation like this for #7

total number of students that can swim/ total amount of 5th graders = x/100

use the fraction on the left and multiply it by 100.

same with number 8

Step-by-step explanation:

A, C, and D. The angles that have a measure of 180-x are angles that have a measure of 180 minus the value of x. In this case, x is equal to mz1, so the angles that have a measure of 180-x are √3, √5, and √10.

Angle is a mathematical concept that is used to measure the amount of rotation of a line or a plane around a point. An angle is typically measured in degrees, which is the unit of angular measurement. Angles are used in many different fields of mathematics, such as geometry, trigonometry, and calculus. In geometry, angles are used to measure the size of a triangle, the size of a circle, or the angle between two lines. In trigonometry, angles are used to solve problems involving the length of sides and the measure of an arc. In calculus, angles are used to measure the rate of change of a function.

To learn more about angle
https://brainly.com/question/25716982
#SPJ1

Answer:153

Step-by-step explanation:

Answer:

not sure if this sign � was important did it the best way I could

Step-by-step explanation:

To solve this problem graphically, we will first set up a system of inequalities based on the given information:

x ≥ 8 (Fatoumata must work at least 8 hours lifeguarding)

y ≤ 12 - x (Fatoumata can work at most 12 total hours)

15x + 10y ≥ 140 (Fatoumata must earn a minimum of $140)

To graph these inequalities, we can plot the points (8,0), (12,0), and (0,14) on a coordinate plane and draw lines connecting them. The line between (8,0) and (12,0) represents the constraint on the number of hours Fatoumata can work, while the line between (8,0) and (0,14) represents the constraint on the amount of money she must earn. The shaded region that satisfies all three inequalities is the feasible region.

To find one possible solution, we can pick any point within the feasible region. One such point is (8,6), which represents working 8 hours lifeguarding and 6 hours tutoring. This point satisfies all three inequalities:

x ≥ 8 is true since x = 8

y ≤ 12 - x is true since y = 6 ≤ 12 - 8

15x + 10y ≥ 140 is true since 15(8) + 10(6) = 180 ≥ 140

Therefore, one possible solution is for Fatoumata to work 8 hours lifeguarding and 6 hours tutoring to earn at least $140 while not exceeding 12 total hours worked.

When evaluating a data set or statistics, the things to consider are sample size and data quality. It's important to consider these things because they provide insight into the validity of the data and the accuracy of the statistics that are being used.

When presented with a dataset or statistics, there are several things to consider.

Here are two examples of what you need to consider when evaluating a dataset or statistics:

1. Sample size: It's important to consider the sample size because small sample sizes are more likely to be biased. For example, a small sample size might be unrepresentative of a larger population. A sample size of 30 is commonly used to distinguish between small and large samples in statistics. Larger sample sizes are often more representative of the population and produce more reliable statistics.

2. Data quality: The quality of the data is also an important consideration. When evaluating statistics, you must ensure that the data is accurate, relevant, and up-to-date. This is important because using incorrect or outdated data can lead to incorrect conclusions. Additionally, if the data is missing or incomplete, you may not be able to get an accurate picture of the population that the dataset is supposed to represent. This can skew the results, making them less reliable or even completely useless. Therefore, data quality is an important consideration when evaluating statistics.

Learn more about Data set or statistics here:

https://brainly.com/question/15525560

#SPJ11

Answer:

1. n=6

2. n=19

3. n=15

4. n=20

5. n=40

6. n=16

7. n=19

8. n=6

9. n=2.4

10. n=30

Step-by-step explanation:

remember the priorities :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

inside every category you go usually from left to right, but you can use the commutative property where applicable.

4 + 5 - 3 = 4 + 5 - 3 = 4 + 5 - 3 = 4 - 3 + 5 = 6

8×3 - 5 = 24 - 5 = 19

15/3 + 10 = 5 + 10 = 15

8 + 3 - 1×2 = 8 + 3 - 2 = 9

14×3 - 2 = 42 - 2 = 40

(3 + 5)×2 = 8×2 = 16

10 + 7 + 2×1 = 10 + 7 + 2 = 19

16/8 + 4 = 2 + 4 = 6

7 + 5/5 = 7 + 1 = 8

20/4×6 = 5×6 = 30

The coordinate of centroid of the triangle is (2, 8/3), the coordinate of the circumcenter is (-7/32, 121/24) and the coordinate of orthocenter is (2, 9/2)

a. To find the centroid of a triangle, we take the average of the x-coordinates and the average of the y-coordinates of the vertices. Therefore, the x-coordinate of the centroid is:

(x₁ + x₂ + x₃) / 3 = (-4 + 2 + 8) / 3 = 2

Similarly, the y-coordinate of the centroid is:

(y₁ + y₂ + y₃) / 3 = (0 + 8 + 0) / 3 = 8/3

So the coordinate of the centroid is (2, 8/3).

b. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. To find the circumcenter, we can find the equations of the perpendicular bisectors of any two sides of the triangle and solve for their intersection point.

Let's take the sides formed by vertices (-4, 0) and (2, 8), and vertices (-4, 0) and (8, 0). The midpoint of the first side is ((-4+2)/2, (0+8)/2) = (-1, 4), and the slope of the line passing through the two points is (8-0)/(2-(-4)) = 8/6 = 4/3. Therefore, the equation of the perpendicular bisector passing through (-1, 4) is:

y - 4 = (4/3)(x + 1)

Simplifying this equation, we get:

y = (4/3)x + 13/4

Similarly, the midpoint of the second side is ((-4+8)/2, (0+0)/2) = (2, 0), and the slope of the line passing through the two points is (8-0)/(2-8) = -8/6 = -4/3. Therefore, the equation of the perpendicular bisector passing through (2, 0) is:

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

To find the intersection point of these two lines, we can set the equations equal to each other and solve for x:

(4/3)x + 13/4 = -(4/3)(x - 2)

x = -7/32

Substituting x = -7/32 into either of the equations, we get:

y = (4/3)(-7/32 + 1) + 4 = 121/24

So the coordinate of the circumcenter is (-7/32, 121/24).

c. The orthocenter of a triangle is the point where the altitudes of the triangle intersect. An altitude of a triangle is a line segment from a vertex of the triangle perpendicular to the opposite side.

Let's take vertex (-4, 0) and find the equation of the line passing through this vertex and perpendicular to the opposite side formed by vertices (2, 8) and (8, 0). The slope of the opposite side is (0-8)/(8-2) = -8/6 = -4/3, so the slope of the line we want is the negative reciprocal of this, which is 3/4. Therefore, the equation of the altitude passing through (-4, 0) is:

y - 0 = (3/4)(x + 4)

Simplifying this equation, we get:

y = (3/4)x + 3

Let's now take vertex (2, 8) and find the equation of the altitude passing through it. The slope of the opposite side formed by vertices (-4, 0) and (8, 0) is (0-0)/(8-(-4)) = 0, which means the altitude passing through (2, 8) is a vertical line passing through (2, 0). Therefore, the equation of this altitude is:

x = 2

Now we need to find the intersection point of these two altitudes. Substituting y = (3/4)x + 3 into the equation x = 2, we get:

y = 9/2

The coordinate of the orthocenter is (2, 9/2)

Learn more on centroid of triangle here;

https://brainly.com/question/7644338

#SPJ1

The equation of the circle is [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex].

Given:

Equation of the circle is [tex](x+3)^2+(y-9)^2=5^2[/tex]

Expand the equation

[tex](x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9[/tex]

[tex](y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81[/tex]

[tex]5^2 = 25[/tex]

Then, substitute the expanded expressions into the equation

[tex](x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\[/tex]

Simplify and combine like terms

[tex](x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25[/tex]

Rearrange the equation so that one side is 0

[tex]x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0[/tex]
Thus, the equation of a circle [tex](x+3)^2+(y-9)^2=5^2[/tex] can be rearranged using the distributive property to form [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex], with one side equaling 0.

Learn more about distributive property here: https://brainly.com/question/2807928

#SPJ11

Answer:

0% (0/40)

Step-by-step explanation:

I feel like this is a trick question. since chicken is not indicated on the graph, I believe chicken is nobodies favorite food

Answer:

To solve this equation, we will first simplify the left-hand side using the fact that the square root of a number squared is equal to the absolute value of that number.

So, we have:

| x - 4 | = 4 - x

We can now split this equation into two cases, depending on whether x - 4 is positive or negative:

Case 1: x - 4 ≥ 0

In this case, | x - 4 | = x - 4, so we have:

x - 4 = 4 - x

Simplifying this equation, we get:

2x = 8

x = 4

However, we must check this solution to make sure it satisfies the original equation. Plugging x = 4 back into the original equation, we get:

√(4 - 4)^2 = 4 - 4

√0 = 0

So, x = 4 is a valid solution.

Case 2: x - 4 < 0

In this case, | x - 4 | = -(x - 4), so we have:

-(x - 4) = 4 - x

Simplifying this equation, we get:

-2x + 8 = 4

-2x = -4

x = 2

Again, we must check this solution to make sure it satisfies the original equation. Plugging x = 2 back into the original equation, we get:

√(2 - 4)^2 = 4 - 2

√4 = 2

This is a valid solution.

Therefore, the equation has two solutions: x = 4 and x = 2.

Answer: Bro x = 4

Step-by-step explanation: