Solution to given logarithmic equations and inequalities are;
x = 1
x = 9
x = 261
x = 10/3
x = 4
3x² - 2x - 1 = 0
x = 1 or x = -1/3
x = 13
x = 0
x = 0 or x = 5
How to evaluate each part of the qustion?1. 3x = log6 216
Using the definition of logarithm, we have:
[tex]6^{3x} = 216[/tex]
[tex]6^{3x} = 6^3[/tex]
3x = 3
x = 1
2. x - 4 = log3 243
Using the definition of logarithm, we have:
[tex]3^{x - 4} = 243[/tex]
[tex]3^{x - 4} = 3^5[/tex]
x - 4 = 5
x = 9
3. log4 (4x - 20) = 5
Using the definition of logarithm, we have:
4⁵ = 4x - 20
1024 = 4x - 20
4x = 1044
x = 261
4. log9 (3 - x) = log9(5x – 15)
Using the property of logarithms that states that if log a b = log a c, then b = c, we have:
3 - x = 5x - 15
20 = 6x
x = 10/3
5. log81 (x + 20) = log81 (6x)
Using the property of logarithms that states that if log a b = log a c, then b = c, we have:
x + 20 = 6x
20 = 5x
x = 4
6. log9 (3x²) = log9 (2x + 1)
Using the property of logarithms that states that if log a b = log a c, then b = c, we have:
3x² = 2x + 1
3x² - 2x - 1 = 0
7. Using the quadratic formula, we have:
x = (-(-2) ± √((-2)² - 4(3)(-1))) / (2(3))
x = (2 ± √(16)) / 6
x = (2 ± 4) / 6
x = 1 or x = -1/3
8. log4(x - 1) = log4(12)
Using the property of logarithms that states that if log a b = log a c, then b = c, we have:
x - 1 = 12
x = 13
9. log7(5 - x) = log7 (5)
Using the property of logarithms that states that if log a b = log a c, then b = c, we have:
5 - x = 5
x = 0
10. logx (5x) = 2
Using the definition of logarithm, we have:
x² = 5x
x² - 5x = 0
x(x - 5) = 0
x = 0 or x = 5
Note that x = 0 is not a valid solution, since log 0 is undefined. Therefore, the only solution is x = 5.
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5+8x<3(2x+4) what’s the answer to that equation?
Answer:
Let us now solve the inequality:
5 + 8x < 3(2x + 4)
To begin, we will simplify the right side:
5 + 8x < 6x + 12
The variable on one side will then be isolated by subtracting 6x from both sides:
5 + 2x < 12
Then we'll take 5 off each sides:
2x < 7
Finally, split both sides by two:
x < 3.5
As a result, the solution to the inequality is x 3.5.
suppose that 36% of people own dogs. if you pick two people at random, what is the probability that they both own a dog? give your answer as a decimal (to at least 3 places) or fraction
Thus, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.
To solve this problem, we need to use the formula for calculating the probability of independent events: P(A and B) = P(A) x P(B).
In this case, let A be the event that the first person owns a dog and B be the event that the second person owns a dog.
We know that P(A) = 0.36, or 36% chance that the first person owns a dog. Since the events are independent, P(B) is also 0.36.
So, the probability of both events occurring (both people owning dogs) is:
P(A and B) = P(A) x P(B)
= 0.36 x 0.36
= 0.1296
This can also be expressed as a fraction:
P(A and B) = 36/100 x 36/100
= 1296/10000
Therefore, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.
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If patty had 120 clothing items in her closet and she chose to take 1/5 of her items to a donation center, how many clothing items did patty donate?
Answer: 24 clothing items
Step-by-step explanation:
The total is 120.
1/5 of 120 is the same as saying 120 divided by 5.
120 divided by 5 is 24.
Answer : 24
Hector has 3 shirts, 3 pairs of shorts, and 2 pairs of shoes in his locker for gym class. How many different outfits consisting of 1 shirt, 1 pair of shorts, and pair of shoes can he make?
Answer:
18 different outfits
Step-by-step explanation:
Hector can make 18 different outfits.
To see why, simply multiply the number of options for each item:
3 shirts x 3 shorts x 2 shoes = 18 possible outfits
Factorization x2-4x+24
Answer:
x^2 - 4x + 24 cannot be factored.
The temperature of a bowl of soup left out on the kitchen counter is modeled by the following table, where x is the time in minutes.
A table Time in minutes ranges as 5, 10, 20, 30, 45, 60, 80 and temperature in Fahrenheit ranges from 139.503, 109.047, 83.158, 75.361, 72.556, 72.092, 72.008 respectively.
Which statement is true about the temperature of the soup over time?
A.
As time increases, the temperature of the soup approaches 80 °F.
B.
As time increases, the temperature of the soup approaches 70 °F.
C.
As time increases, the temperature of the soup approaches 0 °F.
D.
As time increases, the temperature of the soup approaches 72 °F.
The statement which is true about the function of the temperature of the soup over time is D. As time increases, the temperature of the soup approaches 72 °F.
Given a table of values which shows the temperature of a bowl of soup left out on the kitchen counter with the time.
Here the time shown are ranged from 5, 10, 20, 30, 45, 60, 80.
Corresponding temperature of the soup left ranges from 139.503, 109.047, 83.158, 75.361, 72.556, 72.092, 72.008 respectively.
It is clear that as the time increases, the temperature of the soup is decreasing and at last approaches to 72 °F.
Hence the correct statement is D.
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which measure of variability should the charity use to accurately represent the data? explain your answer. the iqr of 10 is the most accurate to use, since the data is skewed. the range of 10 is the most accurate to use, since the data is skewed. the iqr of 45 is the most accurate to use to show that they need more money. the range of 45 is the most accurate to use to show that they have plenty of money.
The appropriate measure of variability depends on the characteristics of the data and the research question being addressed and the IQR is a more robust measure than the range if the data is skewed, and a large IQR indicates a wide range of expenses, requiring more funds. (option c)
Firstly, the IQR of 10 is the most accurate to use if the data is skewed. IQR is a measure of variability that measures the spread of the middle 50% of the data, thus, reducing the influence of outliers. Therefore, if the data is skewed, the IQR provides a more robust measure of variability than the range. The range is the difference between the largest and smallest value in a dataset and is sensitive to extreme values, which can distort the results.
Secondly, the IQR of 45 is the most accurate to use if the charity wants to show that they need more money. If the IQR is large, it means that there is a large variation in the data, and the spread is significant. Therefore, in this scenario, a large IQR indicates that the charity has a wide range of expenditures, and some expenses are significantly higher than others. Thus, the charity needs more funds to cover these expenses adequately.
Finally, the range of 45 is the most accurate to use if the charity wants to show that they have plenty of money. A large range indicates that the data points are spread out, and there is a significant variation in the expenses.
Therefore, in this scenario, a large range indicates that the charity has a wide range of expenses, and some expenses are higher than others, but overall, they have enough money to cover these expenses.
Hence the correct option is (c).
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The triangle above has the following measures.
q = 9 m
m∠Q = 42°
Find the length of side r.
Round to the nearest tenth and include correct units.
Show all your work.
Answer:
approximately 5.9 meters.
Step-by-step explanation:
sin(42°) = r/9
r = 9 * sin(42°)
r ≈ 5.9 m
Therefore, the length of side r is approximately 5.9 meters.
The triangle above has the following measures.
s = 29 m
r = 63 m
Find the m∠Q.
Round to the nearest tenth and include correct units.
Show all your work.
Answer:
Set your calculator to degree mode.
The measure of angle Q is
[tex] {cos}^{ - 1} \frac{29}{63} = 62.6 \: degrees[/tex]
Angle Q measures 62.6°.
For a certain milk shake recipe, the number of scoops of powder varies
directly with the number of cups of milk. 3 scoops of powder are
needed for 5 cups of milk. What is the formula for the number of
scoops of powder, p, as a function of the number of cups of milk, m?
Answer:
We know that the number of scoops of powder varies directly with the number of cups of milk. This means that there is a constant ratio between the two quantities.
Let's call this constant ratio k. Then, we can set up a proportion:
scoops of powder / cups of milk = k
We also know that 3 scoops of powder are needed for 5 cups of milk. We can use this information to find k:
3 / 5 = k
Simplifying this gives us:
k = 0.6
Now that we know k, we can use the proportion we set up earlier to find the formula for the number of scoops of powder, p, as a function of the number of cups of milk, m:
p / m = k
Multiplying both sides by m gives us:
p = km
Substituting the value of k we found earlier gives us:
p = 0.6m
Therefore, the formula for the number of scoops of powder, p, as a function of the number of cups of milk, m, is:
p = 0.6m
The clocks show when a movie starts and ends. How long is the movie?
2 analog clocks. The left clock is labeled start. The hour hand is between 11 and 12 and the minute hand is at 6. The right clock is labeled end. The hour hand is between 1 and 2 and the minute hand is at 2
As per the unitary method, the duration of the movie is 1 hour and 10 minutes.
To solve this problem, we can use a mathematical concept called the "unitary method."
Now, let's take a closer look at the information given in the problem. We have two analog clocks: one labeled "start" and the other labeled "end." The hour and minute hands on each clock provide information about the time.
Since the minute hand has moved halfway between the 6 and 7 marks, we can say that it has moved 30 minutes (since each mark represents 5 minutes). Therefore, the time on the start clock is 11:30 + 30 minutes = 12:00.
To determine the duration of the movie, we can subtract the start time from the end time.
End time - start time = 1:10 - 12:00
First, we need to convert the end time to 24-hour format for easier calculation. Since the hour hand is between 1 and 2, we know that the time is in the afternoon or evening. Therefore, we can add 12 to the hour value to convert it to 24-hour format.
1:10 + 12 hours = 13:10 (in 24-hour format)
Now, we can subtract the start time from the end time:
13:10 - 12:00 = 1 hour and 10 minutes
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Simplify (7/9a)(4/5a).
56/45
28/45a
28/45 -a²
56/45-a²
Answer:
28/45[tex]a^{2}[/tex]
Step-by-step explanation:
Helping in the name of Jesus.
Answer:
The simplified expression is 28/45a².
Step-by-step explanation:
To simplify (7/9a)(4/5a), we can multiply the numerators together and the denominators together, which gives:
(7/9a)(4/5a) = (7 x 4) / (9a x 5a) = 28 / 45a²
Therefore, the simplified expression is 28/45a².
the height of the rectangle and the triangle are the same. the base of the triangle is half the base of the rectangle. what is the area of the composite figure?
A. 225 cm
B. 300 cm
C. 375 cm
D. 450 cm
The area of the composite figure by adding the areas of the rectangle and the triangle is 375 cm, option (C) is correct.
Let the height of the rectangle and the triangle be 'h', and let the base of the triangle be 'b'. Then, the base of the rectangle is '2b' since it is twice the base of the triangle.
Area of the rectangle = base x height
A₁ = 2b x h
A₁ = 2bh
Area of the triangle = (1/2) x base x height
A₂ = (1/2) x b x h
A₂ = (b/2) x h
Total area of the composite figure = A₁ + A₂
Aₙ = 2bh + (b/2)h
Aₙ = (5/2)bh
Substituting the given values, we get:
A(total) = (5/2)(b x h)
A(total) = (5/2)(15 x 10) [given values: b=15, h=10]
A(total) = 375 cm
Hence, option (C) is correct.
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the first term of a geometric sequence is 2, and the common ratio is 3. what is the 8th term of the sequence? 4,374 8 1,458 13,122
The first term of a geometric sequence is 2, and the common ratio is 3.
Therefore, the 8th term of the sequence is 4,374.
To find the 8th term of a geometric sequence with the first term 2 and a common ratio of 3, you can use the formula:
T_ n = a * r^(n-1)
where T_ n is the nth term, a is the first term, r is the common ratio, and n is the position of the term you're looking for.
In this case, you want to find the 8th term (n = 8), the first term (a) is 2, and the common ratio (r) is 3. Plug these values into the formula:
T_8 = 2 * 3^(8-1)
T_8 = 2 * 3^7
T_8 = 2 * 2,187
T_8 = 4,374
So, the 8th term of the geometric sequence is 4,374.
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according to the federal trade commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. this year, a certain state kept track of how many of its 1245 complaints were for identity theft. they want to know if the data provide enough evidence to show that this state had a higher proportion of identity theft than 23%? state the random variable, population parameter, and hypotheses.
The proportion of identity theft complaints in the state is significantly higher than 23%.
The random variable for this scenario is the proportion of identity theft complaints out of the total number of complaints received by the state. The population parameter is the true proportion of identity theft complaints in the entire population of complaints in the state.
The null hypothesis (H0) is that the proportion of identity theft complaints in the state is equal to or less than 23%. The alternative hypothesis (Ha) is that the proportion of identity theft complaints in the state is greater than 23%.
To test this hypothesis, the state needs to conduct a one-tailed hypothesis test with a significance level (alpha) of 0.05. They can use the z-test statistic to compare the sample proportion with the population proportion. If the test statistic is greater than the critical value, they can reject the null hypothesis.
It is important to note that this test assumes that the sample of 1245 complaints is randomly selected and representative of the entire population of complaints in the state. If there is any bias or non-representativeness in the sample, the results of the test may not be accurate.
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The value of "y" varies directly with "x".
If y = 36, then x= 3.
Solve for k.
k=?]
Remember: y = kx
Enter
Answer:
[tex]3k = 36[/tex]
[tex]k = 12[/tex]
Answer:
12
Step-by-step explanation:
If y = 36 and X = 3 then K would = (y divided by x) so it would be 36 divide 3
that being 12 so, therefore, the answer is 12.
K= 12
For the function -3x^2+12
find the interval over which the function is increasing.
Answer:
The given function is:
f(x) = -3x^2 + 12
To find the interval over which the function is increasing, we need to find the critical points of the function.
f'(x) = -6x
The critical point is where f'(x) = 0
-6x = 0
x = 0
Now, we need to check the sign of f'(x) on either side of the critical point to determine whether the function is increasing or decreasing.
If x < 0, then f'(x) < 0, so the function is decreasing.
If x > 0, then f'(x) > 0, so the function is increasing.
Therefore, the interval over which the function is increasing is:
(0, infinity)
Step-by-step explanation:
gg
for the standard normal curve, find the z-score that corresponds to the 7th decile.
Using the Z-table, you can find the z-score that corresponds to a cumulative probability of 0.70, which is approximately 0.52. So, the z-score for the 7th decile on the standard normal curve is 0.52.
To find the z-score that corresponds to the 7th decile of the standard normal curve, we first need to determine the cumulative probability up to that point.
The 7th decile represents the point where 70% of the data lies below it and 30% lies above it. Using a standard normal distribution table or calculator, we can find the z-score that corresponds to a cumulative probability of 0.70.
The z-score that corresponds to a cumulative probability of 0.70 is approximately 0.524. Therefore, the z-score that corresponds to the 7th decile of the standard normal curve is 0.524.
To find the z-score corresponding to the 7th decile on the standard normal curve, you'll need to use the cumulative probability distribution function (also known as the Z-table or standard normal table). The 7th decile represents the point where 70% of the data is below it, so you'll be looking for a cumulative probability of 0.70.
Using the Z-table, you can find the z-score that corresponds to a cumulative probability of 0.70, which is approximately 0.52. So, the z-score for the 7th decile on the standard normal curve is 0.52.
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The following angles are supplementary to each other.
m∠A = (3x + 21)° and m∠B = (6x − 21)°
Determine x.
10
20
36
60
Question 2(Multiple Choice Worth 2 points)
(Polygon Angle Sums MC)
A regular polygon has 12 sides. If one of its angles measures (8h − 30)°, what is the value of h?
h = 10.75
h = 18.75
h = 20.25
h = 22.5
Question 3(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (6, −1), and Monique's desk is located at (−3, 1). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
square root of 98 feet
square root of 85 feet
square root of 6 feet
square root of 5 feet
Question 4(Multiple Choice Worth 2 points)
(Angle Relationships LC)
Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 115.2°.
244.8°
64.8°
25.2°
11.5°
Question 5(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 6 feet of fence for the shortest side and 10 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
8 feet
24 feet
26 feet
28 feet
Question 6(Multiple Choice Worth 2 points)
(Polygon Angle Sums LC)
Find the sum of the interior angles of a 17-sided polygon.
1,530°
2,017°
2,700°
3,060°
Question 7(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
One leg of a right triangle is 7 units long, and its hypotenuse is 16 units long. What is the length of the other leg? Round to the nearest whole number.
9 units
10 units
14 units
23 units
Question 8(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Determine which set of side measurements could be used to form a right triangle.
square root of 19 comma square root of 35 comma 54
square root of 15 comma 6 comma square root of 51
5, 8, 30
5, 6, 7
Question 9(Multiple Choice Worth 2 points)
(Angle Relationships MC)
Two angles are complementary to each other. One angle measures 26°, and the other angle measures (10x − 11)°. Determine the value of x.
2.6
5.6
7.5
24.5
Question 10(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the length of the line segment shown.
line segment from negative 3 comma 10 to 4 comma negative 1
13 units
12 units
7 units
3 units
Question 11(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Determine which set of side measurements could be used to form a triangle.
9, 13, 21
8, 9, 18
3, 18, 21
2, 5, 9
Question 12(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the distance between the points (−2, −3) and (2, 0).
2 units
4 units
5 units
10 units
Question 13(Multiple Choice Worth 2 points)
(Interior and Exterior Angles LC)
Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 32.55°. What is the measure of ∠Q?
147.45°
106.25°
73.725°
32.55°
Question 14(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In triangle EFG, m∠E = 84.3° and m∠F = 36.4°. Determine the measure of the exterior angle to ∠G.
47.9°
59.3°
121.1°
120.7°
Question 15(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
For triangle XYZ, m∠X = (5g + 18)° and the exterior angle to ∠X measures (8g + 32)°. Find the measure of ∠X and its exterior angle.
Interior angle = 68°; exterior angle = 112°
Interior angle = 112°; exterior angle = 68°
Interior angle = 73°; exterior angle = 105°
Interior angle = 105°; exterior angle = 73°
Using the definition of supplementary angles, we can see that x = 60
How to find the value of x?Im just answering the first question.
We know that two angles A and B are supplementary if the sum of their measures is equal to 180°.
Then:
A + B = 180°
In this case, we know taht:
m∠A = (3x + 21)° and m∠B = (6x − 21)°
We can replace that in the equation to get:
3x + 21 + 6x - 21 = 180
Now solve that for x:
9x =180
x = 180/9
x = 60
That is the value of x.
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If I get a haircut every two weeks for a year and my haircuts is 40 dollars how much money did I spend in all together?
Answer: $1040
Step-by-step explanation:
There are 52 weeks in a year so they will get 26 haircuts in the year at every 2 weeks.
26x$40 =$1040
Longwei, a new CEO, is excellent at setting and implementing goals, policies, and structure. Longwei is quite proud of the strategic successes he's had in his brief time as CEO. However, many of the employees seem unmotivated and are responding in ways he didn't expect. What should Longwei do? He should use the principles of OB to better understand the workers. He should take a personality assessment to become more self-aware, He should examine his perceptions to make judgments and decisions.
Longwei should first recognize that implementing goals, policies, and structure is only one aspect of effective leadership. A leader's ability to motivate and inspire their employees is just as important. Therefore, Longwei should use the principles of organizational behavior (OB) to better understand his employees and their motivations.
Additionally, Longwei should take a personality assessment to become more self-aware of his own leadership style and how it may be impacting the employees. He should examine his perceptions and biases to ensure that he is making fair and objective judgments and decisions. This may involve seeking feedback from other leaders or mentors, participating in leadership development programs, or engaging in self-reflection and mindfulness practices.
By taking these steps, Longwei can better understand and address the unmotivated employees in his company. He can then develop strategies to engage and inspire them, such as offering incentives, providing opportunities for professional development, or creating a more positive and inclusive work environment. Ultimately, Longwei's success as a leader will depend not only on his ability to set and implement goals but also on his ability to motivate and engage his employees.
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if the sum of zeros of polynomial p(x)=(a+1)x^2 + (2a+3)x + (3a+4) is -1. then find the product of its zeros
The product of the zeros in the given polynomial is 5.
Given is a polynomial p(x) = (a+1)x² + (2a+3)x + (3a+4), the sum of zeros is -1,
We need to find the product of its zeros,
So,
We know that in the polynomial ax²+bx+c = 0,
the sum of the roots = -b/a
Product of the roots = c/a
Therefore,
Here a = a+1, b = 2a+3 and c = 3a+4
So,
-(2a+3)/a+1 = -1
-2a-3 = -a-1
-a = 2
a = 2
Put a = 2 in value of c,
c = 3(2)+4 = 10
So, the product of the zeros is = 10/2 = 5
Hence the product of the zeros in the given polynomial is 5.
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3. Which expressions can be used to find
the product 6,300? Select all that apply.
A.7 X 900
B.(7× 9) + (10 × 10)
C.700 × 9
D.(63) + (100)
E.70 × 90
The expression uses to find the product 6300, are 7×900, 700×9, 70×90.
Given is a number 6300, we need to write it as a product of numbers,
So, the factors of 6300 = 2, 2, 3, 3, 7, 5, 5
We cannot write the, (7 × 9) + (10 × 10), (63) + (100) as a product of 6300,
(7× 9) + (10 × 10) = 63 + 100 = 163
(63) + (100) = 163
But,
7×900 = 6300
700×9 = 6300
70×90 = 6300
Hence, the expression uses to find the product 6300, are 7×900, 700×9, 70×90.
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I NEED HELP ASAP
(Please write the answer to this question)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The dashed triangle is a dilation
image of the solid triangle with the center at the origin. Is the dilation an
enlargement or a reduction? Find the scale factor of the dilation.
A solid triangle has vertices left parenthesis negative 6 comma 0 right parenthesis, left parenthesis 6
comma 3 right parenthesis, and left parenthesis 6 comma negative 6. A dashed triangle has vertices left
parenthesis negative 2 comma 0 right parenthesis, left parenthesis 2 comma 1 right parenthesis, and left
parenthesis 2 comma negative 2.
d
The scale factor of the dilation is 1/3.
What is scale factor?Scale factor is a numerical scale that represents the ratio of the dimensions of two similar geometric figures. It is used in geometry to compare the size of two similar figures.
According to given information:To determine whether the dilation is an enlargement or a reduction, we need to compare the size of the solid and dashed triangles.
We can calculate the lengths of the sides of the solid triangle using the distance formula:
[tex]Side 1: \sqrt{[(6 - (-6))^2 + (3 - 0)^2]} = \sqrt{(12^2 + 3^2)} = \sqrt{(144 + 9)} = \sqrt153\\\\Side 2: \sqrt{[(6 - (-6))^2 + ((-6) - 0)^2]} = \sqrt{(12^2 + 6^2)} = \sqrt{(144 + 36)} = \sqrt{180}\\\\Side 3: \sqrt{[(6 - 6)^2 + ((-6) - 3)^2]} = \sqrt{(0 + 81)} = \sqrt81 = 9[/tex]
So, the solid triangle has side lengths of √153, √180, and 9.
We can also calculate the lengths of the sides of the dashed triangle using the distance formula:
[tex]Side 1: \sqrt{[(2 - (-2))^2 + (1 - 0)^2]} = \sqrt{(4^2 + 1^2)} = \sqrt17\\\\Side 2: \sqrt{[(2 - (-2))^2 + ((-2) - 0)^2]} = \sqrt{(4^2 + 2^2)} = \sqrt20\\\\Side 3: \sqrt{[(2 - 2)^2 + ((-2) - 0)^2]} = \sqrt{(0 + 4)} = 2[/tex]
So, the dashed triangle has side lengths of √17, √20, and 2.
Comparing the side lengths, we can see that the dashed triangle is smaller than the solid triangle. Therefore, the dilation is a reduction.
To find the scale factor of the dilation, we can choose any corresponding side lengths from the solid and dashed triangles and divide them. For example, we can choose side 1:
Scale factor = (length of corresponding side in dashed triangle) / (length of corresponding side in solid triangle)
= √17 / √153
= √(17/153)
= (√17) / (3√17)
= 1/3
Therefore, the scale factor of the dilation is 1/3.
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I'm lost on how to work it out.
I'm using to w·x=z·y to solve it.
135 °·(7x-10)=(11x+10)·(7x)
To solve the equation 135°·(7x-10)=(11x+10)·(7x) is x ≈ -0.203 or x ≈ 1.567.
To solve the equation 135°·(7x-10)=(11x+10)·(7x), we can use the distributive property to expand the right side of the equation and then simplify.
First, convert the angle measure of 135 degrees to radians:
135° = 135/180π = 3π/4
Then substitute and simplify;
3π/4(7x - 10) = (11x + 10)(7x)
21πx/4 - 15π/4 = 77x² + 70x
Move all the terms to one side:
77x² + 70x - 21πx/4 + 15π/4 = 0
Next, we can solve for x using the quadratic formula;
x = (-b ± √(b² - 4ac))/2a
where a = 77, b = 70 - 21π/4, and c = 15π/4.
Plugging in these values, we get;
x = (-[70 - 21π/4] ± √[(70 - 21π/4)² - 4(77)(15π/4)])/(2(77))
Simplifying this expression gives two possible solutions for x;
x ≈ -0.203 or x ≈ 1.567
Therefore, the solution to the equation 135°·(7x-10)=(11x+10)·(7x) is x ≈ -0.203 or x ≈ 1.567.
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List all the 3 letter combinations of the word "APRIL"
Answer:
rail, lap, pal, pail
Step-by-step explanation:
Select the correct answer. What is the solution to this equation? (x+6)^1/3-5=-2
Answer:
x= 21
Step-by-step explanation:
(x+6)^1/3-5=-2
Solve for x
Add 5 to each side
(x+6)^1/3-5+5=-2+5
(x+6)^1/3=3
Cube each side.
((x+6)^1/3)^3=3^3
x+6 = 27
Subtract 6 from each side
x+6-6 = 27-6
x= 21
Answer:
x = 21
Step-by-step explanation:
[tex]\sf(x+6)^\frac{1}{3} -5=-2[/tex]
First, add 5 to both sides.
[tex]\sf(x+6)^\frac{1}{3} =-2+5\\\\\sf(x+6)^\frac{1}{3} =3\\\\\sqrt[3]{(x+6)} =3[/tex]
Cube both sides.
[tex]\sqrt[3]{(x+6)} =3\\\\x+6=3^3\\\\x+6=27[/tex]
Subtract 6 from both sides.
[tex]x+6=27\\\\x=27-6\\\\x=21[/tex]
Write an equation that model the linear relationship in the table below
What is the slope
What is the y intercept
What is the equation of the line
The equation of line passes through the points (-2, 1) and (0, 5). will be;
⇒ y = 2x + 5
And, Slope = 2
And, Y - intercept = 5
Given that;
Two points on the line are (-2, 1) and (0, 5).
Now,
Since, The equation of line passes through the points (-2, 1) and (0, 5).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - 1) / (0 - (-2))
m = 4 / 2
m = 2
Thus, The equation of line with slope 2 is,
⇒ y - 1 = 2 (x - (-2))
⇒ y - 1 = 2 (x + 2)
⇒ y - 1 = 2x + 4
⇒ y = 2x + 5
Therefore, The equation of line passes through the points (-2, 1) and (0, 5). will be;
⇒ y = 2x + 5
And, Slope = 2
And, Y - intercept = 5
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calculate n if mean 30n,12,40 and 10 is n
Answer:
To find n if the mean of 30n, 12, 40, and 10 is n, we can use the formula for the mean of a set of numbers:
mean
=
sumofnumbers
numberofnumbers
mean=
numberofnumbers
sumofnumbers
In this case, we have four numbers: 30n, 12, 40, and 10. The mean is n. So we can write:
�
=
30
�
+
12
+
40
+
10
4
n=
4
30n+12+40+10
Simplifying the right-hand side:
�
=
30
�
+
62
4
n=
4
30n+62
Multiplying both sides by 4:
4
�
=
30
�
+
62
4n=30n+62
Subtracting 30n from both sides:
−
26
�
=
62
−26n=62
Dividing both sides by -26:
�
=
−
31
13
n=−
13
31
Therefore, if the mean of 30n, 12, 40, and 10 is n, then n is approximately -2.381.
A skydiver jumps out of a plane from a certain height. The graph below shows their
height h in feet after t seconds. What is the skydiver's initial height?
Step-by-step explanation:
At t = 0 the graph shows the initial height to be 12 544 ft
