Based on the given sets A and B, the following statements are true:
1. A B = {5,3,2,4}: This statement is true. When two sets are combined, they form a new set that includes all the elements from both sets. Therefore, when set A and set B are combined, the resulting set includes all the elements from both sets, which are {1,2,3,4,5}. However, the order of elements in a set does not matter, so A B = B A.
2. B-A = {4,5}: This statement is false. B-A represents the set of elements that are in set B but not in set A. In this case, B-A would include the elements {4,5}, since they are in set B but not in set A.
3. A-B = {1,3}: This statement is false. A-B represents the set of elements that are in set A but not in set B. In this case, A-B would include the elements {1}, since it is in set A but not in set B. Element 3 is in both sets, so it cannot be in A-B.
4. A n B = {2,3}: This statement is true. A n B represents the set of elements that are in both set A and set B. In this case, elements 2 and 3 are common to both sets, so they are in the intersection of the two sets, which is {2,3}.
In summary, the true statements are:
- A B = {5,3,2,4}
- A n B = {2,3}
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Find the factors of function f, and use them to complete this statement. From left to right, function f has zeros at , , , and .
The factorized form of the given function, f(x) = 2x⁴ - x³ - 18x² + 9x, is, f(x) = x(2x - 1)(x + 3)(x - 3), and the complete statement is, From left to right, function f has zeros at x = -3, x = 0, x = 1/2, and x = 3.
In the question, we are asked to find the factors of the function f, and complete the given statement.
The function f, given to us is:
f(x) = 2x⁴ - x³ - 18x² + 9x.
To factor the function, we first group the terms as follows:
f(x) = (2x⁴ - 18x²) - (x³ - 9x).
Now, we take common terms out of the group as follows:
f(x) = 2x²(x² - 9) - x(x² - 9).
Now, we again take common terms, as follows:
f(x) = (2x² - x)(x² - 9),
or, f(x) = x(2x - 1)(x + 3)(x - 3).
This is the factored form of the given function, f.
The statement given to us is:
From left to right, function f has zeros at x = _, x = _, x = _, and x = _.
To find the zeroes of the function, we equate the factorized form to 0.
x(2x - 1)(x + 3)(x - 3) = 0.
By zero-product rule, the zeroes are at:
x = 0,
2x - 1 = 0, or, x = 1/2,
x + 3 = 0, or, x = -3,
x - 3 = , or, x = 3.
Arranging these in ascending order, the zeroes are at: -3, 0, 1/2, and 3.
Thus, the factorized form of the given function, f(x) = 2x⁴ - x³ - 18x² + 9x, is, f(x) = x(2x - 1)(x + 3)(x - 3), and the complete statement is, From left to right, function f has zeros at x = -3, x = 0, x = 1/2, and x = 3.
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For the complete question, refer to the attachment.
Answer: Edmentum/plato
Step-by-step explanation:
A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by the x-axis and the base of the house is at the origin. There are two trees on the property. One tree is 8 feet from the base of the house and is 16 feet tall. The other tree is 11 feet from the base of the house and is 9 feet tall. What is the distance from the base of the house to the closest treetop? Round your answer to the nearest tenth. Need answer ASAP.
The distance from the base of the tree to the tallest would be 14.21 cm
We have the following data points in this questionX1 = 8 feet
y1 = 16 feet
x2 = 11 feet
y2 = 9 feet
To proceed with the solution we have to
We have to solve for the shorter tree
[tex]\sqrt{(y2 -y1)^2 + (x2-x1)^2} \\\\= \sqrt{9-0^2 + 11-0^2}[/tex]
= 9² + 11²
= √81 +121
= 14.21
For the taller tree we would have√8² + 16²
= √64 +256
= 17.89
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Given Circle G with radius r, what is the formula for the area of the segment (unshaded region)
Answer:
Option D
Step-by-step explanation:
The triangle ABJ is equitorial
So area
√3/4r²Then mBJ is a arc which is 1/6th of circle
Area.
π/6r²So area of unshaded region
πr²/6-√3/4r²r²(π/6-√3/4)Answer:
[tex]\textsf{d.} \quad r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)[/tex]
Step-by-step explanation:
To find the area of the unshaded region, subtract the area of ΔJGB from the area of sector JGB.
The measure of an arc is equal to its corresponding central angle measure. Therefore, the central angle of sector JGB is 60°.
As the two sides of ΔJGB adjacent the central angle are the radii of the circle (and therefore equal in length), ∠GJB = ∠GBJ.
Interior angles of a triangle sum to 180°. Therefore, all interior angles of ΔJGB are 60° which makes it an equilateral triangle.
Area of an equilateral triangle:
[tex]\sf A=\dfrac{\sqrt{3}}{4}a^2 \quad \textsf{(where a is the side length)}[/tex]
As the side length of the given equilateral triangle is the radius (r):
[tex]\implies \sf Area\:of\:triangle=\dfrac{\sqrt{3}}{4}r^2[/tex]
To find the area of the sector, first convert degrees to radians by multiplying the degrees by π/180 :
[tex]\implies 60^{\circ}=60 \times \dfrac{ \pi}{180}=\dfrac{\pi}{3}\:\:\sf radians[/tex]
Area of a sector of a circle
[tex]\textsf{A}=\dfrac12 r^2 \theta \quad \textsf{(where r is the radius and the angle }\theta \textsf{ is in radians)}[/tex]
Substituting the angle in radians, the area of the sector is:
[tex]\implies \sf A=\dfrac{1}{2}r^2\left(\dfrac{\pi}{3}\right)[/tex]
[tex]\implies \sf A=\dfrac{\pi}6}r^2[/tex]
Area of the unshaded region:
[tex]\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\\\& = \dfrac{\pi}{6}r^2 - \dfrac{\sqrt{3}}{4}r^2\\\\& = r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\end{aligned}[/tex]
Therefore, the solution is option D.
Select the correct answer from each drop-down menu.
Given: line AB ||line DC and DF_~BF
Prove: DFC _~BFA
Angles are formed when two or more lines intersect. Angles are majorly measured in degrees.
The required proof is as shown below:
Whenever a transversal passes through two parallel lines, angles are formed which have some similar properties.
STATEMENTS REASONS
1. AB ║DC Given.
2. < FDC ≅ < FBA Alternate angle theorem.
3. <AFB ≅ < DFC Vertical opposite angle rule.
4. DF ≅ BF Given
5. ΔDFC ≅ Δ BFA Angle-Angle-Side property
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What is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result?.
Answer:
factoring
Step-by-step explanation:
If a car travels 368.5 miles on 50 liters of gas, how many liters of gas will it take to go 691 miles if the car travels at the same rate? (Round to the nearest tenth)
how do u multiply 1x100000000000000000000000000000??
By using mind ig -,-
Hope Helpful ~
Alcohol is a major contributor to high percentages of academic problems and college dropouts. question: alcohol is a major contributor to high percentages of academic problems and college dropouts. true false not sure increasing alcohol consumption lowers gpas. question: increasing alcohol consumption lowers gpas. true false not sure students who drink more heavily miss classes at the same rate as other students. question: students who drink more heavily miss classes at the same rate as other students. true false not sure students who drink more study less. question: students who drink more study less. true false not sure students with a 2.0 gpa (c) consume twice as many drinks on average than students with a 4.0 gpa (a).
The correct decision for the statements are
True--->Alcohol is a major contributor to high percentages of academic problems and college dropouts. True--->Increasing alcohol consumption lower GPAs. False--->Students who drink more heavily miss classes at the same rate as other students.True----> Students who drink more study less. False----> Students with a 2.0 GPA (C) consume twice as many drinks on average than students with a 4.0 GPA (A).This is further explained below.
What is Alcohol?Generally, alcohol is a colorless liquid that is volatile and combustible. It is created during the natural fermentation of carbohydrates and is the component that gives wine, beer, spirits, and other beverages their intoxicating properties. Additionally, alcohol is utilized as an industrial solvent and as fuel.
In conclusion, The appropriate response for each of the statements is
Alcohol is a significant factor in the large percentage of students who struggle academically and drop out of college, which is true. It's true that drinking more alcohol brings a drop in GPA. Students who consume more alcohol miss the same number of courses as students who consume less alcohol. This statement is false. Students who drink more spend less time studying, which is true. Students with a grade point average of 2.0 (C) drink on average two times as much alcohol as students with a grade point average of 4.0 (A) (A).
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Pls help me
Here is a sequence of numbers
Answer:
a) Perfect square.
b) 9
Step-by-step explanation:
The given numbers are perfect squares.
64 = 8*8
49 = 7*7
36 = 6*6
25 = 5*5
16 = 4*4
So, the next number will be 3 *3 = 9
To model some data Gwyn ran an exponential regression and found the regression equation to be y = 6.72 x 0.996x
Answer:
y=6.72x^0.996x
Step-by-step explanation:
A store sells about 30 pants each week for Nu 800 each. The owner expects to lose one sale each week for every increase in price of Nu 40.
a) Write an expression to represent the
i) new price of a pant after n Nu 40 price increases.
ii) expected number of pants that will be sold weekly after n price increases. b) Write a function to represent the expected weekly sales as a function of the number of price increases of Nu 40. c) Use the function to determine the price that will maximize totally sales.
The new price after the price increase of Nu 40 will be Nu 840.
How to calculate the price?The price of a pant after n Nu 40 price increases will be:
= 800 + 40
= 840
The expected weekly sales as a function of the number of price increases will be:
= n - 1) × 800
= (30 - 1) × 800
= 29 × 800
= 23200
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A spherical ball of wax with a radius of 8 inches is melted and poured into a container shaped like a rectangular prism with a 14 inch x 16 inch base. What is the height of the melted wax in the new shape
It is expected the height of the melted wax in this shape is 9.57 inches, this height would make the volume remain constant.
What is the volume of the spherical ball?The volume of a sphere can be calculated using the formula V = 4/3 πr³. Let's use this formula to calculate the volume of the spherical ball of wax:
V = 4/3 π8³ V = 4/3 π 512V= 4/3 x 3.1416 x 512 V =2144.66 cubic inchesWhat is the height of the new shape?Considering the volume should be the same (2144.66 cubic inches) and the volume of this shape can be calculated by multiplying the sides, this would be the equation:
2144.66 = 14 x 16 x y ( unknown value)y= 2144.66 / 14 x 16y = 9.57This means the height would be 9.57 inches.
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Simplify the following expression. (2x-3)(5x^4-7x^3+6c^2-9)
The simplification of the expression (2x - 3)(5x⁴ - 7x³ + 6x² - 9) is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27
Simplification(2x - 3)(5x⁴ - 7x³ + 6x² - 9)
= 10x^5 - 14x⁴ + 12x³ - 18x - 15x⁴ + 21x³ - 18x² + 27
= 10x^5 - 14x⁴ - 15x⁴ + 12x³ + 21x³ - 18x² - 18x + 27
= 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27
The simplified expression is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27
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Which digit in 125 734 016 has a value of 20 000 000?
Step-by-step explanation:
in a number like 125,734,016
the right most position has the weight 10⁰ = 1
so, 6×1 = 6.
the second right most position has the weight 10¹ = 10.
so, 1×10 = 10
the third right most position has the weight 10² = 100.
so, 0×100 = 0
the 4th right most position has the weight 10³ = 1000.
so, 4×1000 = 4,000
the 5th right most position has the weight 10⁴ = 10000.
so, 3×10000 = 30,000
the 6th right most position has the weight 10⁵ = 100000.
so, 7×100000 = 700,000
the 7th right most position has the weight 10⁶ = 1000000.
so, 5×1000000 = 5,000,000
the 8th right most position has the weight 10⁷ = 10000000
so, 2×10000000 = 20,000,000
and so on.
as we can see, the 2 (the 8th most position from the right or the second position from the left) has the value of 20,000,000.
PLEASE HELP!!!
Review the table of values for function k(x).
x
k(x)
–19.1
37.5
–19.01
37.95
–19.001
37.995
–19.0001
37.9995
–19
undefined
–18.9999
43.9995
–18.999
43.995
–18.99
43.95
–18.9
43.5
What is Limit as x approaches negative 19 plusk(x)?
37.5
38
43.5
44
Can the sides of a triangle have lengths 2, 4, and 7?
Answer:
No, they can't
Step-by-step explanation:
According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides.
2+4= 6<7
As you can see from this Equation NOT any two side are greater than the third making this NOT possibly be a tringle.
2+7=9>4
4+7=11>2
An angle has turn through 15 one-degree angle. what is a measurement of this angle in degrees
The measurement of the angle is 15° (if initial angle is 0°).
Turning Through One-degree Angles
An angle is said to have an angle measure of n degrees if it rotates across n one-degree angles. Since turning through one degree means making an angle of one degree, every time you take a turn of one degree, you rotate through one degree more. Thus, turning through n one-degree angles give rise to an angle of n degrees.
Measurement of the Angle
It is given that the angle has turned through 15 one-degree angles. Thus, the angle will turn through 15°.
Let us assume the initial angle to be x°.
Then, the new angle after 15 one-degree turns would be (x+15)°
If initial angle, x = 0°, the measurement of the angle formed is 15°.
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a typist can type 495 words in 15 minutes. How many words can she type in 25 minutes?
Answer:
They can type 825 words in 25 minutes.
Step-by-step explanation:
First, we need to find how many words they can type per minute. To do that, we need to divide 495 by 15.
[tex]495 \div 15 = 33[/tex]
Now, we know how many words per minute, and the question is how many words they can type in 25 minutes. So to find our answer, we need to multiply 33 by 25, since 33 is how many words in one minute.
[tex]33 \times 25=825[/tex]
So now we know our answer: 825 words in 25 minutes.
The new video came console was priced at $400 when it was released last year. This year, the price decreased by 15% during the holiday sale period. The game manufacturer recently announced that the same console will be re-release with new updates and expanded functionality. The retail price will be 25%greater then the previous sale price . When the game concise is re-released whatcwill be the retail price?
A) 360
B)425
C)380
D415
Answer:
B
Step-by-step explanation:
15% off means 85 % of original price
400 * .85 now increase this price by 25%
400* .85 * 1.25 = $425
PLS HELP ITS DUE IN 9 MIN AND IM CONFUSED AND I DON’T WHAT TO DO ANSWER ASAP ILL GIVE BRAINIESTTTTT
A financial planner has three portfolios: A, B, and C. Because investors have different tolerances for risks, 20% of people are likely to invest in portfolio A, 30% are likely to invest in B, and 50% are likely to invest in C. Each portfolio has both stocks and bonds, and investors are equally likely to choose either.
This is a tree diagram that represents the probability of investors choosing the different financial products.
What is the probability of an investor choosing either stocks or bonds from portfolio C?
Considering the given tree diagram, there is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
At each node, the sum of the probabilities is of 1, hence:
0.2 + 0.3 + Z = 1.
Z = 0.5.
There is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.
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.
Which equation represents a circle with a center (-5, -6) and a radius of 5?
The equation of the circle with a center (-5, -6) and a radius of 5 is (x + 5)² + (y + 6)² = 25.
How to Write the Equation of a Circle?The standard equation for writing the equation of a circle is: (x - h)² + (y - k)² = r².
Given the following:
Center (-5, -6) = (h, k)
Radius = 5 = r
Plug in the values into the formula
(x + 5)² + (y + 6)² = 5²
(x + 5)² + (y + 6)² = 25
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Trigonometry. What's x? Dont know how to do it
Answer:
12.11069457
Step-by-step explanation:
You start by using sin(48) = 9/x
You then multiply both sides by x to give you
xsin(48) = 9
you then divide both sides by sin(48) to get x by itself
x = 9/sin(48)
this gets you
x=12.11069457
For the equation y = -2/5 x + 2, explain what x -values would be best to choose for making a table of ordered pairs. Be sure to explain why.
The x values to make a suitable ordered pair must be a multiple of 5
How to determine the best x values?The function is given as:
y = -2/5x + 2
The slope of the above equation is:
m = -2/5
The above is a fraction with a denominator of 5.
So, the x values to make a suitable ordered pair must also be a multiple of 5
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Which ordered pair is a solution to the equation 2x − 3y = 1?
The ordered pair that is a solution to the equation 2x − 3y = 1 is; (2, 1)
How to find the solution that is an ordered pair?
We are given the equation;
2x - 3y = 1
Now, the ordered pair that is a solution simply means the least whole numbers for x and y that will make the equation valid.
Now, since the coefficient before x is bigger than the coefficient before y which is negative, then it means x must be larger than y. Thus, let us try x = 2 and y = 1 to get;
2(2) - 3(1) = 1
This makes the equation valid.
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Find the measures of the numbered angles in each rhombus.
Answer:
Step-by-step explanation:
2=27
3=27
5=27
1=126
4=126
can someone please help mee (will give brainliest 20 points!!!)
Answer:
a.) C(x) = 10x + 8,000
Step-by-step explanation:
The fixed cost does not change regardless of the variable. Therefore, it should be attached to no variable. However, the variable cost does depend on the number of alarms and thus should be attached to the variable.
This makes the algebraic expression:
C(x) = 10x + 8,000
Your graph should look very similar to this. Keep in mind that our axis are slightly different. You can plot specific points on your graph by plugging random "x" values into your algebraic expression and finding the subsequent "y" values.
which of the answer choices could be the one missing data item for the following set, if the mode is 12? 7, 12, 9, 15, 12, 7, 9, 7, 12, 15 a. 15 b. 9 c. 7 d. 12
Answer: D. 12
Step-by-step explanation: The mode is the most popular number in a set of numbers. In this set, there are 3 sevens, 3 twelves, 2 nines, and 2 fifteens. If the mode is twelve, you need one more 12 because there are the same amounts of twelves and sevens. So that means the answer is 12!
A fishing trawler sails 30 km from port on a bearing of 120° until it reaches a submerged reef.
How far (to the nearest km) is the port north of the reef?
From rectangular component, the distance of the port north of the reef is 25.9808 km.
What is the distance of the given point by rectangular component analysis ?It is given that a fishing trawler sails 30 km from port on a bearing of 120° until it reaches a submerged reef.
Thus the direction of the fishing trawler is given to be 120° with respect to the movement of the trawler.
Resolving the direction by the horizontal and vertical components, we get
The horizontal component of distance is |30*cos(120°)| = 15 km
The vertical component of distance is |30*sin(120°)| = 25.9808 km
Thus as we have to find the north direction or the vertical component, the distance is 25.9808 km.
Therefore, from rectangular component, the distance of the port north of the reef is 25.9808 km.
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A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
Answer Options:
A.11.65
B.50.00
C.171.65
D.210.00
The time it took the rider to reach the ground level is 171.651seconds
Quadratic functionsQuadratic functions are functions that has a leading degree of 2.
Given the equation that represents roller coaster’s height as shown
h = –0.025t^2 + 4t + 50
The coaster will reach the ground when h = 0
Substitute
0 = –0.025t^2 + 4t + 50
Factorize
On factorizing, the time it took the rider to reach the ground level is 171.651seconds
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Answer:
171.65 seconds
Step-by-step explanation:
did the test and got it right
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactive substance. After 20 hours, 55 mg of the substance remains. How many milligrams will remain after 26 hours
Answer:
44.7 mg
Step-by-step explanation:
The equation for exponential decay can be written in the form ...
y = a·b^(t/p)
where 'a' is the initial value, 'b' is the decay factor, 'p' is the period over which the decay factor is applicable, and t is time in the same units as p.
SetupUsing the above equation, we have ...
a = initial value = 110 mg
b = decay factor = 55/110 = 1/2 over time period p=20 hours
Then the equation is ...
y = 110·(1/2)^(t/20) . . . . amount remaining after t hours
SolutionWe want the amount remaining after 26 hours. That will be ...
y = 110·(1/2)^(26/20) ≈ 44.67
About 44.7 milligrams will remain after 26 hours.