Answers
Where the function f(x) = x² + 2x - 3 is given, note that the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4. See the attached graph.
What is the explanation for the above response?
To find the minimum and maximum points of the function f(x), we can complete the square:
f(x) = x^2 + 2x - 3
= (x + 1)^2 - 4
We can see that the function is in the vertex form f(x) = a(x - h)^2 + k, where the vertex is (-1, -4).
Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the vertex is the minimum point. Therefore, the minimum value of the function f(x) is -4.
To find the x-intercepts, we can set f(x) = 0:
(x + 1)^2 - 4 = 0
(x + 1)^2 = 4
Taking the square root of both sides, we get:
x + 1 = ±2
x = -1 ± 2
Therefore, the x-intercepts of the function f(x) are x = -3 and x = 1.
In summary, the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4, which occurs at the vertex (-1, -4).
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Related Questions
Line x is parallel to line y. Line z intersect lines x and y. Determine whether each statement is Always True
Answers
Which of these could be the side lengths of a right triangle? list all possible answers and show your work for full marks.
a) 4-7-10
b) 36-48-60
c) 6-10-14
d) 14-48-50
Answers
The sets of side lengths that could form a right triangle are 36-48-60 (option b) and 14-48-50 (option d).
To determine which of these sets of side lengths could form a right triangle, we will use the Pythagorean theorem (a² + b² = c²), where a and b are the shorter sides and c is the hypotenuse. Let's evaluate each option:
a) 4-7-10
Applying the Pythagorean theorem: 4² + 7² = 16 + 49 = 65, which is not equal to 10² (100). So, this set does not form a right triangle.
b) 36-48-60
Applying the Pythagorean theorem: 36² + 48² = 1296 + 2304 = 3600, which is equal to 60² (3600). So, this set does form a right triangle.
c) 6-10-14
Applying the Pythagorean theorem: 6² + 10² = 36 + 100 = 136, which is not equal to 14² (196). So, this set does not form a right triangle.
d) 14-48-50
Applying the Pythagorean theorem: 14² + 48² = 196 + 2304 = 2500, which is equal to 50² (2500). So, this set does form a right triangle.
In conclusion, the sets of side lengths that could form a right triangle are 36-48-60 (option b) and 14-48-50 (option d).
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The box plot displays the number of push-ups completed by 9 students in a PE class.
A box plot uses a number line from 12 to 58 with tick marks every 2 units. The box extends from 27.5 to 42.5 on the number line. A line in the box is at 37. The lines outside the box end at 15 and 55. The graph is titled Push-Ups In PE and the line is labeled Number of Push-Ups.
Which of the following represents the value of the lower quartile of the data?
27.5
37
42.5
55
Answers
the answer is Q1 = 27.5
Terri is beginning a science experiment in the lab. The instructions call for 227 milligrams of potassium. Calculate the difference between this amount and 1 gram
Answers
The difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.
The amount of potassium called for in the experiment is 227 milligrams. To convert milligrams to grams, we divide by 1000: 227/1000 = 0.227 grams.
The amount of 1 gram is larger than 0.227 grams. To find the difference between the two amounts, we subtract the smaller amount from the larger amount:
1 gram - 0.227 grams = 0.773 grams
Therefore, the difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.
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The following graph shows a proportional relationship.
What is the constant of proportionality between
�
yy and
�
xx in the graph?
Answers
The constant of proportionality between y and x in the graph is 3
What is the constant of proportionality between y and x in the graph?From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings
(x, y) = (1, 3)
Using the above as a guide, we have the following:
The constant of proportionality between y and x in the graph is
k = y/x
substitute the known values in the above equation, so, we have the following representation
k = 3/1
Evaluate
k = 3
Hence, the constant of proportionality between y and x in the graph is 3
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A study reports that in 20102010 the population of the United States was 308,745,538308,745,538 people and the land area was approximately 3,531,9053,531,905 square miles. Based on the study, what was the population density, in people per square mile, of the United States in 20102010? Round your answer to the nearest tenth.
Answers
The population density is 87.4, under the condition that a study report shows that in 2010 the population of the United States was counted to be 308,745,538 people and the land area is approximately 3,531,905 square miles.
Now to evaluate the population density of the United States in 2010, here we have to use the principles of division
Population density = Population / Land area
Staging the values from the study
Population density = 308,745,538 / 3,531,905
The evaluated Population density = 87.4 people per square mile
Then, the United State's population density in 2010 was evaluated as 87.4 people per square mile.
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The complete question is
A study reports that in 2010 the population of the United States was 308,745,538 people and the land area was approximately 3,531,905 square miles. Based on the study, what was the population density, in people per square mile, of the United States in 2010? Round your answer to the nearest tenth.
what's the solution?
Answers
Answer:
(1, 1.5)
Step-by-step explanation:
If x = 1, plug it into the other equation, y = 1/2x + 1, and y = 1.5.
What is constant of proportionality if y=1. 75x
Answers
The constant of proportionality is 1.75.
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Given two variables x and y, y is directly proportional to x (x and y vary directly, or x and y are in direct variation) if there is a non-zero constant k such that
=> y=kx
The relation is often denoted, using the ∝ or ~ symbol, as
=> y ∝ x
and the constant ratio
=> k =y/x
In this equation y=1.75 x.
Hence the constant of proportionality is 1.75.
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A lawn sprinkler sprays water 2.5 meters in every direction as it rotates. What is the area of the sprinkled lawn?
Answers
The area of the sprinkled lawn is approximately 19.625 square meters.
What is the area of the sprinkled lawn?The formula for the area of a circle is:
A = πr²
Where A is the area and r is the radius and π is constant pi ( 3.14 ).
If the sprinkler as a circle with a radius of 2.5 meters. The area that the sprinkler can cover is the area of this circle.
Here, the radius is 2.5 meters, so we can substitute that into the formula:
A = πr²
A = 3.14 × 2.5²
Area = 3.14 × 6.25
Area = 19.625 m²
Therefore, the area is 19.625 m²
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To the nearest cubic centimeter, what is the volume of the regular hexagonal prism?
a hexagonal prism has a height of 7 centimeters and a base with a side length of 3 centimeters. a line segment of length 2.6 centimeters connects a point at the center of the base to the midpoint of one of its sides, forming a right angle.
the volume of the regular hexagonal prism is about ___ cm3
Answers
Rounded to the nearest cubic centimeter, the volume of the regular hexagonal prism is approximately 82 [tex]cm^3.[/tex]
To calculate the volume of the regular hexagonal prism, we need to find the area of the base and multiply it by the height.
The base of the prism is a regular hexagon with side length 3 centimeters. The formula for the area of a regular hexagon is:
[tex]Area = (3√3/2) * (side length)^2.[/tex]
Substituting the given side length of 3 centimeters:
[tex]Area = (3√3/2) * 3^2[/tex]
= (3√3/2) * 9
= (27√3/2).
Now, let's calculate the volume by multiplying the base area by the height:
Volume = Area * height
= (27√3/2) * 7
≈ 81.729[tex]cm^3[/tex].
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PLEASE HELP THIS AN FRESHMAN QUESTION
Answers
Answer:
Sure, I can help you with that.
To find the area of the gazebo floor, we can think of the decagon as being composed of ten congruent triangles. Each triangle has a base of 10 feet and a height of 192 feet. The area of a triangle is equal to (1/2)bh, so the area of each triangle is (1/2)(10)(192) = 960 square feet. The area of the decagon is equal to 10 times the area of each triangle, or 960*10 = 9600 square feet.
Therefore, the area of the gazebo floor is 9600 square feet.
Here is a diagram of the decagon, with the ten congruent triangles labeled:
[Image of a decagon with ten congruent triangles labeled]
I hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
I'm so grateful for your help. I would be honored if you would give me a Brainlyness award."
Please answer all three question
1. To the nearest tenth how many miles is alshleys house from Bridget house
2. To the nearest tenth how many miles is Ashley’s house from carlys house
3. Whose house does Ashley live the closet to and by how many miles
Please answer
Answers
The nearest tenth how many miles is alshleys house from Bridget house is AB = √[(xB-xA)² + (yB-yA)²]
The nearest tenth how many miles is Ashley’s house from carlys house is AC = √[(xC-xA)² + (yC-yA)²]
The distances from Ashley's house to both Bridget's house and Carly's house, we can compare them and see which one is shorter.
To find the distance between Ashley's house and Bridget's house, we need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Bridget's house is located at point B. We can use the distance formula to find the distance between A and B:
distance AB = √[(xB-xA)² + (yB-yA)²]
Here, xA and yA represent the coordinates of Ashley's house, and xB and yB represent the coordinates of Bridget's house. The formula calculates the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates of the two points.
To find the distance between Ashley's house and Carly's house, we again need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Carly's house is located at point C. We can use the same distance formula as before:
distance AC = √[(xC-xA)² + (yC-yA)²]
Here, xC and yC represent the coordinates of Carly's house. Plug in the values and calculate the distance to the nearest tenth of a mile.
To determine whose house Ashley lives closest to, we need to calculate the distances from Ashley's house to both Bridget's house and Carly's house. Whichever house has the shorter distance will be the closer one.
To find the difference between the two distances, we can subtract the smaller distance from the larger distance.
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3. The insurance company also offers safety glass coverage. There is a 50% chance of no repairs ($0), a 30% chance of minor repairs ($50), and a 20% chance of full replacement ($300). Which plan for optional safety glass coverage has the lower expected cost?
Enter your answer.
Answers
Plan C has the lower expected cost, so, this is best to minimize costs for safety glass coverage.
How can we compare the plans?In order to compare expected cost of Plan C and D, we must calculate expected payout for each plan and add to the premium.
For Plan C, expected payout is:
= 0.5*(0) + 0.3*(50) + 0.2*(300)
= 15 + 60
= 75
The total expected cost of Plan C is:
= 75 + 50 + 20
= 145
For Plan D, expected payout is:
= 0.5*(0) + 0.3*(50) + 0.2*(300)
= 15 + 60
= 75
The total expected cost of Plan D is:
= 75 + 100 + 0
= 175
Therefore, the Plan C has the lower expected cost.
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A, b & c form the vertices of a triangle.
∠cab = 90°,
∠abc = 65° and ac = 8.9.
calculate the length of bc rounded to 3 sf.
Answers
The length of BC rounded to 3 significant figures is 6.98.
Since ∠cab = 90°, we can use the Pythagorean Theorem to find the length of AB.
Let's call BC = x, then we have:
sin(65°) = AB/BC
AB = sin(65°) * BC
In right triangle ABC, we have:
AB^2 + BC^2 = AC^2
(sin(65°) * BC)^2 + BC^2 = 8.9^2
Solving for BC, we get:
BC = 8.9 / sqrt(sin^2(65°) + 1)
BC ≈ 6.98
Therefore, the length of BC rounded to 3 significant figures is 6.98.
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for each of the following situations identify the relation as linear quadratic or exponential. a. Larry is paid $10 per hour he receives a $1 per hour raise each year
Answers
The problem represents a linear equation.
What is linear equation?
A linear equation is a particular type of equation in which the highest power of the variable is always 1(linear). This type of equation is also known as a one-degree equation.
Larry is paid $10 per hour he receives a $1 per hour raise each year.
Let he works for x hours.
In 1 hour he receives $10 so for x hours he will receive $10x
$1 per hour raise.
So there will be a linear equation
The linear equation will be if we take total income as $y then,
y= 10x+1
which is of the linear equation form y=m x+ b where m is the slope.
Hence, the problem represents a linear equation.
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If Mikal uses all his money to buy one type of flour, he has exactly enough money to buy either 12 pounds of wheat flour, or 6 pounds of rice flour, or 4 pounds of almond flour. If Mikal uses all his money to buy an equal number of pounds of all three types of flour, what is the total number of pounds of flour that he can buy?
Answers
The total number of pounds of flour he can buy is 7 pounds of flour
Let's assume that Mikal has $1 to spend on flour. According to the problem, he can buy:
- 12 pounds of wheat flour for $1, which means that the price of wheat flour is 1/12 = $0.0833 per pound.
- 6 pounds of rice flour for $1, which means that the price of rice flour is 1/6 = $0.1667 per pound.
- 4 pounds of almond flour for $1, which means that the price of almond flour is 1/4 = $0.25 per pound.
If Mikal spends $1 on an equal amount of all three types of flour, he will spend $1/3 = $0.3333 on each type of flour. To determine how many pounds of each type of flour he can buy, we need to divide $0.3333 by the respective price per pound of each type of flour:
- Wheat flour: $0.3333 / $0.0833 per pound = 3.9996 pounds (rounded to 4 pounds)
- Rice flour: $0.3333 / $0.1667 per pound = 1.9998 pounds (rounded to 2 pounds)
- Almond flour: $0.3333 / $0.25 per pound = 1.3332 pounds (rounded to 1 pound)
Therefore, Mikal can buy 4 pounds of wheat flour, 2 pounds of rice flour, and 1 pound of almond flour with $1. The total number of pounds of flour he can buy is:
4 + 2 + 1 = 7 pounds of flour.
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What is the value of 200 + 3 (8 3/4) + 63.25
Answers
Answer:
289.5
Step-by-step explanation:
200+26.25+63.25
289.5
The radioactive substance uranium-240 has a half-life of 14 hours. The amount At) of a sample of uranium-240 remaining (in grams) after thours is given by
the following exponential.
A (t) = 5600
100(3)*
Find the amount of the sample remaining after 11 hours and after 50 hours.
Round your answers to the nearest gram as necessary.
Amount after 11 hours: grams
Amount after 50 hours: grams
Answers
Amount after 11 hours: 3,477,373 grams; Amount after 50 hours: 33,320 grams.
How to find the Radioactive decay ?The Radioactive decay formula provided in the question for the amount A(t) of a sample of uranium-240 remaining after t hours is:
A(t) = 5600100(3[tex])^(-11/14)[/tex]
To find the amount of the sample remaining after 11 hours, we substitute t = 11 in the formula and calculate:
A(11) = 5600100(3[tex])^(-11/14)[/tex] ≈ 3477373 grams
Therefore, the amount of the sample remaining after 11 hours is approximately 3,477,373 grams (rounded to the nearest gram).
Similarly, to find the amount of the sample remaining after 50 hours, we substitute t = 50 in the formula and calculate:
A(50) = 5600100(3[tex])^(-50/14)[/tex] ≈ 33320 grams
Therefore, the amount of the sample remaining after 50 hours is approximately 33,320 grams (rounded to the nearest gram).
The exponential formula for radioactive decay describes the behavior of a radioactive substance, where the amount of the substance decreases over time as it decays. In this case, uranium-240 has a half-life of 14 hours, which means that half of the initial amount of the substance will decay in 14 hours. After another 14 hours, half of the remaining amount will decay, and so on.
As time goes on, the amount of uranium-240 remaining decreases exponentially, and the rate of decay is determined by the half-life of the substance. The formula provided in the question allows us to calculate the amount of uranium-240 remaining after any given amount of time, based on its initial amount and half-life.
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The radioactive substance uranium-240 has a half-life of 14 hours. The amount of the sample remaining after 11 hours is approximately 2265 grams, and the amount of the sample remaining after 50 hours is approximately 95 grams.
The formula for the amount of uranium-240 remaining after t hours is given by: A(t) = 5600 * (1/2)^(t/14).
Find the amount of the sample remaining after 11 hours, we substitute t = 11 into the formula and evaluate:
A(11) = 5600 * (1/2)^(11/14)
A(11) ≈ 2265 grams (rounded to the nearest gram)
Find the amount of the sample remaining after 50 hours, we substitute t = 50 into the formula and evaluate:
A(50) = 5600 * (1/2)^(50/14)
A(50) ≈ 95 grams (rounded to the nearest gram)
Therefore, the amount of the sample remaining after 11 hours is approximately 2265 grams, and the amount of the sample remaining after 50 hours is approximately 95 grams.
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Can someone please help me ASAP? It’s due tomorrow.
Answers
The total number of outcomes for the compound event is m*n
option B.
What is the Counting Principle?The Fundamental Counting Principle states that if there are m ways to do one thing and n ways to do another thing, then there are m*n ways to do both things together.
This applies to compound events that consist of two or more independent events.
For example, suppose you have two dice and you want to know how many possible outcomes there are when you roll them. Each die has 6 possible outcomes, so by the Fundamental Counting Principle, the total number of outcomes for the compound event is 6*6 = 36.
So, for any two independent events with m and n outcomes, respectively, the total number of outcomes for the compound event is m*n.
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Morris shovels driveways during a big snowstorm. He charges $25 to shovel a drive way. He can shovel a drive way in a half hour assuming that he worked back to back how much could he make in 5 hours
Answers
Answer:
250
Step-by-step explanation:
5 x 2= 10
25 x 10= 250
A car drives down a road in such a way that its velocity ( in m/s) at time t (seconds) is v(t) =1t^(1/2) + 4 Find the car's average velocity in (m/s) between t=4 and t=10.Â
Answers
To find the car's average velocity between t=4 and t=10, we need to use the formula:
average velocity = (change in displacement) / (change in time)
Since we are only given the velocity function, we need to first find the displacement function by integrating the velocity function:
displacement = ∫(1t^(1/2) + 4) dt
displacement = (2/3)t^(3/2) + 4t + C
where C is the constant of integration.
Since we are only interested in the change in displacement between t=4 and t=10, we can ignore the constant of integration.
change in displacement = [(2/3)10^(3/2) + 4(10)] - [(2/3)4^(3/2) + 4(4)]
change in displacement = 28.147 - 14.265
change in displacement = 13.882
Now we can use the formula for average velocity:
average velocity = (change in displacement) / (change in time)
average velocity = 13.882 / (10 - 4)
average velocity = 1.98 m/s
Therefore, the car's average velocity between t=4 and t=10 is 1.98 m/s.
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In 1990, when the consumer price index (CPI) was 130.7, Deena purchased a
house for $98,700. Assuming that the price of houses increased at the same
rate as the CPI from 1980 to 1990, approximately how much would the house
have cost in 1980, when the CPI was 82.4?
OA. $72,650
OB. $67,600
O C. $62,200
OD. $84,600
Answers
Answer:
C is the right answer I think
To find the cost of the house in 1980, divide the cost of the house in 1990 by the rate of increase. The house would have cost approximately $62,200 in 1980 when the CPI was 82.4.
Explanation:To find the cost of the house in 1980, we need to use the concept of inflation. In this case, we can use the consumer price index (CPI) to compare the prices of the house in 1990 and 1980.
First, we need to determine the rate of increase from 1980 to 1990. The rate of increase is calculated by dividing the CPI in 1990 by the CPI in 1980:
Rate of increase = CPI in 1990 / CPI in 1980 = 130.7 / 82.4 = 1.585
Next, we can use the rate of increase to find the cost of the house in 1980. We divide the cost of the house in 1990 by the rate of increase:
Cost in 1980 = Cost in 1990 / Rate of increase = $98,700 / 1.585 = $62,200.
Therefore, the house would have cost approximately $62,200 in 1980 when the CPI was 82.4.
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Ed
8. A watering can holds 3 liters of water.
If Patricia waters her vegetable garden
5 times a day and uses one full can in
all, how many milliliters of water does
she use each time she waters?
~ 60 mL
B 3,000 mL
© 600 mL
D 300 ml
SNO
9. Find 4-5.
Answers
8. Patricia uses 600 milliliters of water each time she waters her vegetable garden. The correct option is A © 600 mL.
9. 4-5 =-1
For first question:
8. A watering can holds 3 liters of water, and Patricia waters her vegetable garden 5 times a day using one full can in total. To find out how many milliliters of water she uses each time, you need to first convert the 3 liters to milliliters (1 liter = 1,000 milliliters) and then divide by 5.
3 liters × 1,000 milliliters/liter = 3,000 milliliters
3,000 milliliters ÷ 5 = 600 milliliters
So, Patricia uses 600 milliliters of water each time she waters her vegetable garden. The correct answer is 600 mL.
9. For second question, the calculation is as follows:
4 - 5 = -1
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A person standing on the ground throws a rock upward with an initial velocity of 16 feet per second. The person’s hand is 12 feet above the ground when the rock is released. This is modeled by the equation h = -16^2 + 16t + 12. How long does it take for the rock to hit the ground?
Answers
It will take the rock 1.5 seconds to hit the ground
How to determine how long it take for the rock to hit the ground?Since the situation is modeled by the equation h = -16t² + 16t + 12
The rock will hit the ground when height is zero i.e. h = 0. Thus, we have:
-16t² + 16t + 12 = 0 and we can then solve for the time (t) .
-16t² + 16t + 12 = 0 (divide through by -16)
t² - t - 3/4 = 0
Using factorization method:
(t + 1/2) (t - 3/2) = 0
t = -1/2 or 3/2
Since t cannot be negative. Thus, t = 3/2 = 1.5.
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Write the product 5x2/3 as the product of a whole number and a unit fraction
Answers
The product 5x^(2/3) can be written as the product of the whole number 5 and the unit fraction 1/x^(-2/3), which simplifies to x^(2/3)/1 or just x^(2/3). So, we have:
5x^(2/3) = 5 * (1/x^(-2/3)) = 5x^(2/3) = 5 * (x^(2/3) / 1) = 5x^(2/3) = 5x^(2/3)
To write the product 5x^(2/3) as the product of a whole number and a unit fraction, we need to express x^(2/3) as a unit fraction.
Recall that a unit fraction is a fraction with a numerator of 1, so we need to find a fraction that has 1 as the numerator and x^(2/3) as the denominator. We can do this by using the reciprocal property of exponents:
x^(2/3) = 1 / x^(-2/3)
Now we can substitute this expression into the original product:
5x^(2/3) = 5 * (1 / x^(-2/3))
Simplifying the right-hand side of the equation, we can write it as:
5 / x^(-2/3) = 5x^(2/3)
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Rotate the vector (0,2) 270°
clockwise about the origin.
Answers
The rotated vector is (-2,0). To see why, imagine the original vector (0,2) plotted on the coordinate plane. To rotate it 270° clockwise about the origin, we can first rotate it 90° clockwise to get (2,0), then rotate that 180° clockwise to get (-2,0).
To understand this geometrically, think of the vector (0,2) as pointing straight up on the y-axis. Rotating it 90° clockwise means it now points to the right on the x-axis. Then, rotating it another 180° clockwise means it points straight down on the negative y-axis, which corresponds to the vector (-2,0).
In general, to rotate a vector (x,y) by an angle θ about the origin, we can use the following formulas: x' = x cos θ - y sin θ. y' = x sin θ + y cos θ In this case, θ = 270°, so cos θ = 0 and sin θ = -1.
Plugging in x=0, y=2, we get: x' = 0 - 2(-1) = 2 y' = 0(270) + 2(0) = 0. So the rotated vector is (2,0), which corresponds to (-2,0) because we rotated it clockwise instead of counterclockwise.
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Mathematical
PRACTICE
Use Algebra For Exercises 11-13,
2 x P
40
refer to the equation 5 x 9
100
2
11. What must be true about p and q if the equation show
equivalent fractions?
Answers
p and q both are equal and p=q=20.
Given are an equation show equivalent fractions 2p/5q = 40/100
We need to find the p and q,
So
2p/5q = 40/100
2p/5q = 2×20/2×20
p/q = 20/20
p/q = 1
p = q
Therefore p and q both are equal and p=q=20.
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Can someone please explain how to solve this question? Thanks!
Answers
The solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .
What is a polynomialA polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.
The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a)
For the polynomial; k²x³ - 6kx + 9 divided by x - 1, we shall evaluate for f(1) to solve k as follows:
k²(1)³ - 6k(1) + 9 = 1
k² - 6k + 9 - 1 = 0
k² - 6k + 8 = 0
by factorization;
(k - 4)(k - 2) = 0
k = 4 or k = 2
Therefore, solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .
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Calculate A. ∂z and ∂x
B. ∂z and ∂y
at the point
(5, 17, 1)
where z is defined implicitly by the equation
z4 + z2x2 − y − 9 = 0
Answers
At the point (5, 17, 1), the partial derivatives of z with respect to x and y are -12.5 and 0.25, respectively, as calculated using implicit differentiation. At the point (5, 17, 1), the partial derivatives of z with respect to z and y are 0.16 and -1.
To find the partial derivatives, we need to use the implicit differentiation.
To find ∂z/∂x, we differentiate the equation with respect to x, treating y and z as functions of x
4z^3(dz/dx) + 2z^2x^2 - 0 - 0 = 0
Simplifying, we get
4z^3(dz/dx) = -2z^2x^2
(dz/dx) = -1/2x^2z
At the point (5, 17, 1), we have
(dz/dx) = -1/2(5)^2(1) = -12.5
To find ∂z/∂y, we differentiate the equation with respect to y, treating x and z as functions of y
4z^3(dz/dy) - 1 - 0 + 0 = 0
Simplifying, we get
4z^3(dz/dy) = 1
(dz/dy) = 1/4z^3
At the point (5, 17, 1), we have
(dz/dy) = 1/4(1)^3 = 0.25
To find ∂z and ∂y at the point (5, 17, 1), we need to take partial derivatives with respect to z and y, respectively, of the implicit equation
z^4 + z^2x^2 - y - 9 = 0
Taking the partial derivative with respect to z, we get
4z^3 + 2z^2x^2(dz/dz) - dy/dz = 0
Simplifying and solving for ∂z, we get
∂z = dy/dz = 8z^3/(2z^2x^2) = 4z/x^2
At the point (5, 17, 1), we have
z = 1, x = 5
So, ∂z at the point (5, 17, 1) is
∂z = 4z/x^2 = 4(1)/(5^2) = 0.16
To find ∂y, we take the partial derivative with respect to y, keeping x and z constant
-1 = ∂y
Therefore, ∂y at the point (5, 17, 1) is -1.
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PLEASE HELP ME WITH THIS MATH PROBLEM!!! WILL GIVE BRAINLIEST!!! 25 POINTS!!!
Answers
Answer: In bold
Step-by-step explanation:
The formula they gave is a rate
Let's solve for the rate first.
This equation is done for 3 years 2018-2021 that's why ^3
3.55 = 2.90(1+x)³ >divide both sides by 2.90
1.224 = (1+x)³ > take cube root of both sides
1.0697 = 1+x
x= .0697
so let's make our generic formula
[tex]y = 2.90(1+.0697)^{t}[/tex] let t be years and let y= price
Let's calculate 2018, so this would be year 0
[tex]y = 2.90(1+.0697)^{0}[/tex]
y=$2.90 this is for 2018
They already gave you 2021 price
y=$3.55 this is for 2021
Rate of increase is .0697
In 2025
That's 7 years=t
[tex]y = 2.90(1+.0697)^{7}[/tex]
y=$4.65 for 2025
