Answer:
3 elements
Step-by-step explanation:
Let A = solution set of x²-4
B = solution set of x²-3x+2
First, find the solution of each sets:
[tex]\displaystyle{x^2-4=0}\\\\\displaystyle{(x+2)(x-2)=0}\\\\\displaystyle{x=2,-2}[/tex]
Set B:
[tex]\displaystyle{x^2-3x+2=0}\\\\\displaystyle{(x-2)(x-1)=0}\\\\\displaystyle{x=1,2}[/tex]
Now we can write new set as:
A = {2, -2}
B = {1, 2}
The union of A and B means combine both sets together:
A ∪ B = {2, -2, 1, 2}
However, in a set, we do not write duplicate elements, so the union set will be:
A ∪ B = {2, -2, 1}
Hence, there are 3 elements in A ∪ B.
A rectangle has a length of (3x - 1) and a width of (x + 1). part a determine the perimeter and area of the rectangle as polynomials. part b determine the perimeter and area of the rectangle if x equals 5. part c determine the perimeter and area of the rectangle if x equals 8.
Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..
Lets try to solve out the problem,
Length = 3x-1
Width = x+1
Perimeter = 2(l+b)
Area = l*b
Perimeter= 2 (3x-1 + x+1)
P= 8x
Area = (3x-1) (x+1)
=> 3x(x+1) -1 (x+1)
=> 3x^2 + 3x -x -1
=> 3x^2 + 2x -1.
Hence Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..
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Find the original price if the price was:
$520 after a 30% increase
(Please Help with explanation that makes sense...will mark brainliest)
Given that price was $520 after a 30% increase, the original price was $400.
What is the the original price?Given that;
Percentage increase = 30%Price after the increase = $520Original price = x
To determine the original price, we say;
x × ( 100% + 30% ) = $520
x × ( 130% ) = $520
x × (130/100) = $520
130x / 100 = $520
130x = $52000
x = $52000 / 130
x = $400
Given that price was $520 after a 30% increase, the original price was $400.
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Solve the equation 3x^2-2x-10=0
Show all your working and give your answers correct to 2 decimal place
Answer:
Step-by-step explanation:
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = -2
C = -10
B2 - 4AC =
4 - (-120) =
= 124
Applying the quadratic formula :
2 ± √ 124
x = —————
6
√ 124 simplified
The prime factorization of 124 is
2•2•31
To be able to remove something from under the radical, there have to be 2 instances of it
√ 124 = √ 2•2•31 =
± 2 • √ 31
√ 31, rounded to 4 decimal digits, is 5.5678
So now we are looking at:
x = ( 2 ± 2 • 5.568 ) / 6
Two real solutions:
x =(2+√124)/6=(1+√ 31 )/3= 2.189
or:
x =(2-√124)/6=(1-√ 31 )/3= -1.523
Answer:
Step-by-step explanation:
3x^2-2x-10=0
This is a quadratic equation that can be solved using the quadratic formula where
a = 3, b = -2, and c = -10
x=−b±(b^2−4ac)^(1/2)/2a
x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))
x=2±(124)^(1/2)/6
Simplify the Radical:
x=((2/6) ±2(31)^(1/2))/6
x=26±231−−√6
Simplify fractions and/or signs:
x=1/3±√31/3
which becomes
x=2.18925
See the attached image for a more clear display of solving using the quadratic equation.
x=−1.52259
Which statement can you use to conclude that quadrilateral xyzw is a parallelogram
Answer: Option (4)
Step-by-step explanation:
A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.
Find the common ratio for 0.1,0.01,0.001
The common ratio of the set of data is 0. 1
How to determine the common ratio
To determine the common ratio of a set of data, we have to
Divide the second term by the first term orDivide the third term by the second termFor the given set of data
0.1,0.01,0.001
Let's divide the second term by the first term
= 0. 01/ 0. 1
= 0. 1
Thus, the common ratio of the set of data is 0. 1
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A bookshelf is 4-3/4 feet wide. how many 3-inch-wide books will fit on the shelf?
19 books can fit into a bookshelf that has a width of 19/4 feet
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The bookshelf is 4 3/4 feet wide = 19/4 feet
1 ft = 12 in, hence:
19/4 feet = 19/4 feet * 12 in per feet = 57 inches
Number of books = 57 inches / 3 in = 19
19 books can fit into a bookshelf that has a width of 19/4 feet
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Mr.jake and me. sebastian are business partners. they divided the ratio of 3:2 the profit is 24,000. how much did mr.jake receive ?
Given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.
The ratio of the shares of business partners Mr. Jake to Mr. Sebastian given to us is 3:2.
So we assume Mr. Jake's share of profit to be 3x, and Mr. Sebastian's share of profit to be 2x.
Thus, the total profit between them is 3x + 2x = 5x.
The total profit given is 24,000.
Thus, we get an equation:
5x = 24000,
or, x = 24000/5 = 4800.
Thus, the share of profit Mr. Jake receives is 3x = 3*4800 = 14400.
Thus, given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.
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If the class sizes in a school from 18 to 24 what is the range?
Answer:
18 students
Step-by-step explanation:
Answer:
the range between 18 and 24 is 6
Step-by-step explanation:
24-18=6
What is the ratio of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution?
The ratio comes out to be 1:4.
What is ratio?
A ratio in mathematics shows how many times one number is contained in another. For instance, if a mixture of milk and water contains eight liters of water and six liters of milk, the ratio of water to milk is eight to six. Similarly, the ratio of water to the overall amount of mixture is 8:14, while the ratio of milk to water is 6:8.
Calculating the Ratio of the Solution:
Let us assume that x is the quantity of 30% of the solution and y be that of 5% solution, then,
30% of x + 5% of y = 10% of (x + y)
0.3x + 0.05y = 0.1 (x + y)
0.3x + 0.05y = 0.1x + 0.1y
0.3x - 0.1x = 0.1y - 0.05y
0.2x = 0.05y
Thus, the required ratio is,
0.2x / 0.05y = 1
x / y = 0.05 / 0.2
x / y = 5 / 20
x:y = 1 : 4
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10 points please help me
Answer:
(a)
A = 3
B = 17
C = 8
D = 15
(b)
surface area = 240
(using the formula)
There are 500 passengers on a train. 7/20 are men and 40% are women. the rest are children
On the train, there are a total of 125 children.
Calculating the number of childrenTotal number of passengers = 500
Out of 500 passengers, men =7/20
So, the number of men= 500* 7/20 = 175
Out of 500 passengers, women = 40%
So, the number of women passengers = 500*40/100 = 200
Therefore, the total number of men and women passengers= 175+200 = 375.
There are also children on the train. So, the rest number should be those children.
The rest number =children= 500- 375 = 125.
So, it is concluded from the above equation that there are 125 children on the train.
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Help! asap!
As shown in the figure below, a || b and c is the transversal, m∠1= 40°, m∠2= 70°.
Question: m∠3= ?
The measure of angle 3 from the figure is 110 degrees
Lines and anglesAn angle is the intersection between two lines. From the given figure, we have the following parameters
m∠1= 40°,
m∠2= 70°.
Required
Measure of angle 3
The sum of the interior angles of the triangle is equal to the exterior
Sum of interior = <1 + <2
Sum of interior = 40 + 70
Sum of interior =110 degrees
Hence the measure of angle 3 from the figure is 110 degrees
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In a binomial experiment, the probability of success is. 6. What is the probability of two successes in seven trials?.
The probability of two successes in seven trials is 0.0774144.
We can find the probability as shown below:The probability can be found using the binomial formula.
The probability of success is given as 0.6.
Therefore, the probability of failure is 0.4.
We have to find the probability of two successes in seven trials.
It is given by:
[tex]P = nC_x p^{n} q^{n-x}\\=7C_{2} (0.6)^{2} (0.4)^{7-2} \\=7C_{2} (0.6)^{2} (0.4)^{5} \\=\frac{(7)(6)}{(1)(2)} (0.36)(0.01024)\\=0.0774144[/tex]
The probability of two successes in seven trials is found to be 0.0774144.
Therefore, we have found that the probability of two successes in seven trials is 0.0774144.
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The pressure, p, with which water passes through a pipe varies inversely as the square of the pipe's radius, 2. If k is the constant of
variation, which equation represents this situation?
Opr²-k
Op=r²2²+k
Op+r²2²=k
Op=kr²
The variation equation is p = kr^2
How to determine the variation equation?The variables are give as:
Pressure = P
Radius= r
The direct variation from p to the square of r is represented as:
[tex]p\ \alpha\ r^2[/tex]
Express as an equation
p = kr^2
Where k represents the constant of variation
Hence, the variation equation is p = kr^2
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Answer:
The correct answer is the 3rd option
Find the lateral area of this pyramid whose
base is a regular hexagon with a side length of
3 cm and whose slant height is 12 cm.
12 cm
3 cm
[ ? ] cm2
The lateral area of the given pyramid is 108 cm².
Any three-dimensional figure's lateral surface area is its side surface area.
In the question, we are asked to find the lateral area of the given pyramid, whose base is a regular hexagon, with a side length of 3 cm, and the slant height of the pyramid is 12 cm.
To determine the lateral area, we determine the area of one lateral face, and then multiply it by the number of lateral faces in the pyramid.
The number of lateral faces = sides of the base = 6 {Since the base is a regular hexagon}.
Area of a lateral face = (1/2)*base*height {Since its a triangle},
or, area of a lateral face = (1/2)*3*12 {Since the base is the side length of the base, and the height is the slant height},
or, area of a lateral face = 18 cm².
Thus, the lateral area of the pyramid = 6 * 18 cm² = 108 cm².
Thus, the lateral area of the given pyramid is 108 cm².
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Can someone please tell me which one is correct??? The first screenshot is the question and the second screenshot is the options I have. I am in dire need of help
Answer:
43.5 unit^2.
Step-by-step explanation:
Area of the triangle
= 1/2 * base * height
= 1/2 * AB * AC.
AB = √ [(6-1)^2 + (6-8)^2] = √29
AC = √ [(8 - (-7))^2 + (1 - (-5)^2] = √261
So the area = 1/2 * √29 * √261
= 43.5
Finding a sunken submarine in the middle of the ocean using Bayes' theorem: the search for the Scorpion.
Finding a sunken submarine in the middle of the ocean using Bayes' theorem to the search for USS Scorpion.
In the event of a missing vessel or aircraft at sea, in this case a submarine, Bayes search theorem can be applied.
The ocean using Bayes' theorem: the search for the Scorpion.
In May 1968, the U.S. Navy's nuclear submarine USS Scorpion (SSN-589) failed to arrive as expected at her home port of Norfolk. The command officers of the U.S. Navy were nearly certain that the vessel had been lost off the Eastern Seaboard, but an extensive search there failed to discover the remains of Scorpion.Then John P. Craven, a Navy deep-water expert, proposed that Scorpion had sunk somewhere else. Based on a contentious approximation of hydrophone triangulation, Craven organized a search southwest of the Azores. He was only given one ship, Mizar, and to make the most of his resources, he sought help from a team of consulting mathematicians. A Bayesian search approach was used. To develop theories regarding what might have led to Scorpion's loss, veteran submarine commanders were questioned.What is Bayes' theorem?
Bayes' theorem is a theorem in probability theory. It is a trivial consequence of the definition of conditional probability.Bayesian search theory is the application of Bayesian statistics to the search for lost objects.Learn more about Bayes' theorem
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Which equation represents x, the side length of the greater square? x2 (x – 2)2 = 10 x2 2x2 = 10 x2 (x – 2)2 = 100 x2 2x2 = 100
Step-by-step explanation:
10x2(x-2)2=100x2x2 2x2
30men can do a piece of work in 40 days how long will it take to complete the work by 25 men
Step-by-step explanation:
men × days=men1×days1
30×40=40×x
x=30days
find the vertical asymptote(s) of f(x)=x2+3x+6/x2-4
Answer:
x=-2, 2
Step-by-step explanation:
Aighty check this out
[tex]f(x) = \frac{ {x}^{2} + 3x + 6 }{ {x}^{2} - 4 } = = = > \\(x + 2)(x - 2) \\ so \: x = - 2 \: and \: x = 2 \: are \: not \: defined \: \\ and \: are \: the \: candidates [/tex]
if non of the root give out 0/0 both can be the asymptotes:
[tex]f(2) = \frac{{2}^{2} + 3(2) + 6 }{ { - 2}^{2} + 4 } = = = > \\ f(2) = \frac{16}{0} [/tex]
this one is OK
[tex]f( - 2) = \frac{ { - 2}^{2} + 3( - 2) + 6}{ { - 2}^{2} + 4 } = = = > \\ f( - 2) = \frac{4}{0} [/tex]
so is this one
so the asymptotes are x=-2, 2
The graph below represents which type of power function of the form y = kx'?
Direct Variation with an odd r-value & a positive k-value
O Direct Variation with an even r-value & a positive k-value
Inverse Variation with an odd r-value & a negative k-value
O Inverse Variation with an even r-value & a positive k-value
The graph represents the type of power function of the form y = kx in the form of D. Inverse Variation with an even r-value & a positive k-value.
How to illustrate the graph?It should be noted that a graph simply means a diagrammatic representation of a particular thing.
Here, the function of the for y = kx is illustrated in the graph.
This is an inverse variation with an even r-value and a positive k-value.
In conclusion, the correct option is D.
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Solve for x in the equation: 8a = 2xy + b.
Step-by-step explanation:
Simplifying 8a = 2xy + b
Reorder the terms: 8a = b + 2xy
Solving 8a = b + 2xy
Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.
Divide each side by '8'. a = 0.125b + 0.25xy
Simplifying a = 0.125b + 0.25xy
Each side of a square is increasing at a rate of 5 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 9 cm2
The area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]
The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another
Let the side of a square be x.
So,
Area of square = [tex]x^{2}[/tex]
A =[tex]x^{2}[/tex]
Differentiating with respect to time we get,
dA/dt = 2x dx/dt
When area = 9 [tex]cm^{2}[/tex] the side becomes 3 cm
At x = 3cm and dx/dt = 5 cm/s (Given)
dA/dt = 2.3.5 = 30 [tex]\frac{cm^{2} }{sec}[/tex]
Thus the area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]
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HELP HELP HELP HELP
HELP HELP HELP HELP
Step-by-step explanation:
find the slope:
[tex]\frac{y2-y1}{x2-x1}=\frac{-4+2}{1+3} =\frac{-2}{4} =-\frac{1}{2}[/tex]
Now our equation looks like:
[tex]y=-\frac{1}{2} x+b[/tex]
To solve for b, plug in one of the coordinates
[tex]-4=-\frac{1}{2} (1)+b[/tex]
[tex]-4=-\frac{1}{2} +b[/tex]
[tex]b=-3.5[/tex]
Put our equation together to get y = -1/2x-3.5
Find the equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3
Answer: [tex]y=-\frac{5}{3}x-1[/tex]
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we want to find is -5/3.
Since the y-intercept is (0,-1), the equation is [tex]y=-\frac{5}{3}x-1[/tex]
The equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y + 3 = 0.
What is standard equation of the line?A line of the standard form y = mx + c , where m is the slope of the line and c is a y-intercept. Another way to express the equation for a line is in standard form.
Slope: A line's slope provides information on the steepness and direction of the line.
By figuring out the difference between both the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of such a straight line through them. The letter "m" denote the slope of the line.
Relation between slope of two perpendicular lines are-
Two perpendicular lines' slopes are the negative reciprocals of one another. This indicates that a line's slope is -1 / m if it's perpendicular to the a line with slope m.Calculation for the equation of the line.
Consider the given equation;
y=3/5x-3 (compare this with the standard equation)
The slope 'm' is 3/5
Use the relation of slopes of two perpendicular line.
The slope of orthogonal line will be -1/m
Slope = -5/3
Put the slope in the slope point equation of line.
(y - y1) = m(x - x1)
where (x1,y1) = (0,-1)
Substitute the coordinates in the equation
y - (-1) = (-5/3)×(x - 0)
y + 1 = -5x/3
Further simplifying the equation,
5x + 3y +3 = 0
Therefore, the equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y +3 = 0.
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Which of the following best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers?
A) the sum is a constant
B) the sum is a polynomial
C) the sum is an exponential expression
D) nothing can be determined about the sum without more information
The statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial
Sum of Polynomial expressionPolynomial expression are equation that has a leading degree of 2 and above. For instance the following expressions are polynomials.
ax^2+bx+c and;
mx^2+nx+p
Take the sum of the polynomials
P(x) =. ax^2+bx+c
f(x) = mx^2+nx+p
Since both expressions are quadratic in nature, hence the sum will result in a polynomial that is quadratic in nature.
Based on the explanation above, we can conclude that the statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial
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A survey was conducted in the class about their favorite subjects. 35% of the class voted for Math and Science. 45% of the class voted for Math. Find the percent of the class who voted for Math also voted for Science.
The percent of the class who voted for Math also voted for Science is 38.8%
How to find the percent who voted math and also voted for science?Therefore,
1 = p(m) + p(s) - p(m ∩ s)
Hence,
p(m) = 45% = 0.45
p(s) = ?
p(m ∩ s) = 35% = 0.35
Therefore,
1 = 0.45 + p(s) - 0.35
1 - 0.45 + 0.35 = p(s)
p(s) = 0.9
Therefore,
p(m | s) = 0.35 / 0.9 = 0.38888888888 = 38.8%
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what is x and y? i’m having trouble finding what x and y are
Answer:
y is 7, x is 14
Step-by-step explanation:
This is a 30-60-90 triangle,
The hypotenuse, the side opposite of the 90 degree angle, is twice the length of the side opposite of the 30° angle,
The side opposite of the 60° degree angle, is root 3 times the side opposite of the 30° degree angle
So y is
[tex] \frac{7 \sqrt{3} }{ \sqrt{3} } = 7 = y[/tex]
Then, that means x is
[tex]7 \times 2 = 14[/tex]
Find the value of cos F rounded to the nearest hundredth, if necessary. E 6 F 8 10 D
Answer:
cosF = 0.6
Step-by-step explanation:
cosF = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EF}{DF}[/tex] = [tex]\frac{6}{10}[/tex] = 0.6
Answer:
Cos F = 0.6
Step-by-step explanation:
Trigonometry ratios:[tex]\sf \boxed{\bf \ Cos \ F = \dfrac{adjacent \ side \ of \ \angle F}{hypotenuse}}[/tex]
[tex]\sf =\dfrac{EF}{DF}\\\\=\dfrac{6}{10}\\\\= 0.6[/tex]
HELP swiftly
Im not fully sure but does x measure 100?
x =x=x, equals
^\circ
∘
The value of X is 100 degree.
According to the statement
we have to find the value of x degree which represent the angle.
In this figure
we see that there are two angles which are vertically opposite angles and there is rule that the values of vertically opposite angles are always same.
So, due this reason Here the value of x is 100 degree
because in this figure the given angle which is 100 degree are vertical to the angle which we have to find and that angle which x, so, the value of x is same as the value of vertical angle.
so these angles are vertical angles. that's why x is 100 degree.
So, The value of X is 100 degree.
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