Answer:
The prime factorization of 21 is;
[tex]21=3\times7[/tex]Explanation:
We want to find the prime factorization of 21;
The number 21 is a product of 3 and 7;
[tex]21=3\times7[/tex]since 3 and 7 are both prime number, then the prime factorization of 21 is;
[tex]21=3\times7[/tex]зь
4
- 2 ≤ 2b + 8; b = -4
Answer:
true
Step-by-step explanation:
Which are the foci of the hyperbola represented by x2-3y2 + 12 = 0?
(0, -4) and (0,4)
(0, -2) and (0, 2)
(-2, 0) and (2, 0)
(-4, 0) and (4,0)
The foci of the hyperbola represented by x² - 3y² + 12 = 0 is; (0, -4) and (4, 0)
What is the Foci of the Hyperbola?The general form of equation of a vertical hyperbola is expressed as; (y²/a²) + (x²/b²) = 1
Some of the properties of a vertical hyperbola are;
Its center is at (0, 0)Its' foci is given by (0, -ae) and (ae, 0)Its' vertices is given by (0, -a) and (0, a)Its' eccentricity is given by e = [√(a² + b²)]/aWe are given the equation of the hyperbola as;
x² - 3y² + 12 = 0
Converting this equation to the general form of a vertical hyperbola, we have; x² - 3y² = -12
Divide through by -12 to get;
(y²/4) - (x²/12) = 1
From the general form, we can say that;
a² = 4
b² = 12
Thus;
Eccentricity; e = [√(a² + b²)]/a = e = [√(4 + 12)]/4
e = 1
Thus, the foci is;
(0, -(4 * 1)) and ((4*1), 0) = (0, -4) and (4, 0)
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Can you help me with this question Name the Domain.
Solution:
Given:
[tex]f(x)=\frac{x+1}{x^2-6x+8}[/tex]The domain is the set of all possible x-values (inputs) that will make the function (output) to be real and defined.
To get the domain of the function given, we need to get the undefined or singularity points.
[tex]\begin{gathered} f(x)\text{ will be defined only when the denominator is equal to 0.} \\ \text{Hence, singularity or undefined points will occur when,} \\ x^2-6x+8=0 \\ \text{Solving to get these points,} \\ x^2-4x-2x+8=0 \\ x(x-4)-2(x-4)=0 \\ (x-2)(x-4)=0 \\ x-2=0 \\ x=0+2 \\ x=2 \\ \\ OR \\ x-4=0 \\ x=0+4 \\ x=4 \\ \\ \text{Hence, singularity occurs at;} \\ x=2,x=4 \end{gathered}[/tex]
The domain of the function will exist when;
[tex]\begin{gathered} x\ne2,x\ne4 \\ \\ \text{Hence, the solution to the domain of the function is;} \\ x<2\text{ OR }24 \end{gathered}[/tex]Hence, the solution to the domain is;
[tex]x<2\text{ OR }24[/tex]In interval notation, the domain is;
[tex](-\infty,2)\cup(2,4)\cup(4,\infty)[/tex]Therefore, the final answer is;
All real numbers except 2 and 4.
pls help will mark brainliest
The equation of the line in slope intercept form is; y = 9x/4 - 37/4.
What is equation of line in slope intercept form?The slope intercept form of such a straight line is among the most common ways to represent a line's equation. When given the slope of a straight line and the y-intercept, the slope intercept equation can be used to find the equation of a line ( the y-coordinate of the point in which a line intersects the y-axis).For a straight line with a slope,'m,' and 'b' as the y-intercept, the slope intercept form equation is: y = mx + b.For the given question;
The equation of the parallel line is given as;
9x - 4y = 7
Find the slope of the equation by comparing the equation with the standard form.
4y = 9x - 7
y = 9x/4 -7/4
Slope = m = 9/4
As, the line is parallel to the line passing from the point (5, -2).
Thus, the slope of both lines will be equal.
The equation in slope intercept form is found using,
y - y1 = m(x - x1)
y + 2 = (9/4)(x - 5)
Solving,
y = 9x/4 - 37/4
Where, slope is 9/4 and y-intercept is -37/4.
Thus, the equation of the line in slope intercept form is; y = 9x/4 - 37/4.
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HELPP!!!! ASAP!! 35 POINTS!!!!
Answer:
$2
Step-by-step explanation:
The rate of change is equal to "rise over run"
the rise is: 20
the run is: 10
20/10=2
There are 221 students on a field trip 5 students ride in a van the rest of the students fill 6 buses enter an equation that can be solved to find the number of students
AJ, this is the solution to the exercise:
Applying one of the exponents property, we have:
(2^2t
Find the slope from the following graph....
Answer:
b is correct.
Step-by-step explanation:
Starting at (-2, -3), go 4 units up and then 5 units to the right. You will end up at (3, 1).
if maggie corrected her mistake, what would be the correct answer for x?
The correct value of x will be 9 as it is alternate angles which are equal so 4x+2=7x-25 for the given set of intersecting lines.
What is angle?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
What is alternate angles?When a transversal intersects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar.
Here,
4x+2=7x-25
3x=27
x=9
The value of x would be 9 and the value of angle is 38°.
Given that the alternate angles are equal, 4x+2=7x-25 for the given set of intersecting lines, the proper value of x will be 9.
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Graph the line with slope -3/4 and y-intercept 9.
The equation of the line with slope -3/4 and y intercept 9 is y=-3/4x+9.
Based on the conditions formulate:
m=-3/4
and b = 9
Write the equation of the linear function:
y=mx+b
substitute m=-3/4 and b=9 into y=mx+b:
y = -3/4x+9
A line's equation must be in the Slope-Intercept Form, y = mx + b, in order to be graphed using its slope and y-intercept.
This format makes it simple to read off the slope and y-intercept values. The y-intercept is the constant term b, whereas the slope is just the m coefficient of the variable x.
plot the y intercept (0,9) in the xy axis.
Use the slope to locate a different point beginning at the y-intercept. The direction you travel from one point to another is contained in the slope.
Hence the required graph is plotted.
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Can anyone show me how to find Arithmetic Sequences?
4.04 divided by 50.5
Answer:204.2
Step-by-step explanation:
Answer:
0.08
Step-by-step explanation:
1) Make the divisor a whole number by moving the decimal point.
[tex]505 \sqrt{4.04} [/tex]
2) Move the decimal point in the dividend the same number of places.
[tex] 505\sqrt{40.4} [/tex]
3) Divide
[tex]505 \sqrt{40.4} = 12.5[/tex]
4) Line up decimal point in the quotient with decimal point in the dividend.
[tex]4.04 \div 50.5 = 40.4 \div 505 = 0.08[/tex]
The cargo of the truck weighs no more than 2,400 pounds.
Answer:
give me the details then I might be able to actually answer it -_-
Step-by-step explanation:
arrange the following interest rates in a ending order: 3.4%, 3.039%, 3 3/16%, 3.499%, 3 1/2%
Answer:
3.039%, 3 3/16%, 3.4%, 3.499%, 3 1/2%.
Step-by-step explanation:
First convert to them all decimal fractions:
= 3.4, 3.039, 3.1875, 3.499, 3.5
so, the answer is
3.039, 3.1875, 3.4, 3.499, 3.5
Which expression is equivalent to 3x+4(3x+2) Responses
On simplifying the expression 4(3x + 2) it becomes equivalent to 12x + 8, that is, option D.
Here, we are given an expression- 4(3x + 2)
As we can see the expression has one variable, that is, x and rest all are constants.
Opening up the bracket and multiplying the constant term we get-
4*3x + 4*2
= 12x + 8
Since, only the like terms can be added together, we cannot simplify this expression further as they are not like terms, one is a constant and the other one is a variable.
Thus, we find that on simplifying the expression 4(3x + 2) it becomes equivalent to 12x + 8, that is, option D.
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Your question was incomplete. Check for full content below-
Which expression is equivalent to 4(3x + 2)?
A) 7x + 6
B) 7x + 6
C) 12x + 6
D) 12x + 8
8. How much of each ingrédient would you need to make an identical recipe that serves 24 people? Explain you reasoning.
each ingredient is multiplied by 24 will need to make an identical recipe that servers 24 people.
How to find How much of each ingredient would need for recipe?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of the two numbers, and the factors that are multiplied are referred to as the factors.
according the question
if 2 cups of flour is used for recipe prepared for 1 person.
if you want to prepare the recipe for 24 people it will need 2 X 24 = 48.
so 48 cups of flour is used for recipe prepared for 24 people.
Hence, each ingredient is multiplied by 24 will need to make an identical recipe that servers 24 people.
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A quadrilateral in the third quadrant is rotated 90° clockwise about the origin. Which quadrant will the transformed quadrilateral be in?
Answer: Quadrant 2
Step-by-step explanation: well quadrant 3 is the bottom right corner, and clockwise would put it up a quadrant, which is quadrant 2.
10 people always get on a bus in the same order and sit on the same places. what is the probability that, if the 1st person has randomly changed his/her seat, the 10th will be able to sit on his/her original seat?
The probability that the 10th will be able to sit on his/her original seat when the 1st person has randomly changed his/her seat is 7/9
Probability :
In Mathematics, Probability stands for the ratio of the number of favorable outcomes to the total number of outcomes in a random experiment. It is used to predict how likely an event can happen.
Probability of an event,
P(E) = No of favorable outcomes / total number of outcomes
Here we have,
10 people always get on a bus in the same order and sit in the same places.
The 1st person has randomly changed his/her seat
Except for 1 remaining number of seats is 9
If 1st person changes his/her place with the remaining 9 seats the number of ways that 1st person can be seated is 9
In 9 ways 10th will be able to sit on his/her original seat when the 1st person is seated in 2 to 9 seats i.e 7 seats
Therefore,
The number of favorable outcomes that the 10th person will be able to seat in his/her original seat = 7
From the above observations,
The probability that the 10th will be able to sit on his/her original seat
= 7 / 9
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La hipotenusa de un triángulo rectángulo mide 3 cm y uno de sus catetos mide 2 cm.
Encuentra la medida de la otra pierna.
The value of the missing length √5
What Pythagoras Theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given,
Hypotenuse = 3cm
One side = 2cm
Let the one side given be Base
Then, base = 2cm
Now, by Pythagoras Theorem we can find out the missing length or Perpendicular of the triangle
By Pythagoras Theorem:
H² = P² + B²
If we have to find perpendicular then,
P² = H² - B²
or,
P = √H² - B²
Putting the values we get,
P = √(3)² - (2)²
P = √(9 - 4)
P = √(5)
P = √5
Hence, The missing length of the triangle is √5
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Use De Morgans law to write a statement that is equivalent to the following statement
Note that the two De Morgan laws are:
[tex]\begin{gathered} (P\lor Q)^C=\text{ P}^C\wedge Q^C \\ (P\wedge Q)^C=P^C\lor Q^C \end{gathered}[/tex]For the statement
[tex]-(p\lor q)[/tex]The equivavent statement if De Morgan law is applied will be:
[tex]-p\wedge-q[/tex]in a systematic sampling study, if the sampling frame has 2,000 names and the desired sample size is 50, then the skip interval should be
The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.
Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.
To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;
skip interval = population / target sample size
Substituting the given values;
skip interval = 2000 / 50
skip interval = 40
Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.
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Eight less than four times a number is less than 56. What are the possible values of that number?
0 x>12
0 x<12
O
x<18
O x>16
The expression of the possible values of the number is x < 16
How to determine the possible values of the number?The statement is given as
Eight less than four times a number is less than 56.
Rewrite the statement as an expression
So, we have
4 * number - 8 is less than 56
Represent the number with x
So, we have
4 * x - 8 is less than 56
This gives
4 * x - 8 < 56
Add 8 to all sides
4 * x < 64
Divide both sides by 4
So, we have
x < 16
Hence, the number is all numbers less than 16
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solve this problem -2(w + 6) + 5w
plse answer this quickly:
150 adults complete a survey
80 are women
write the ration men:women in its simplest form
NEED HELP FAST!Use the drop-down menus to complete each equation so the statement about its solution is true.
The correct options that gives the required type of equation solution to the system of equations are;
No solution;
2•x + 9 + 3•x + x = 6•x + 5
One solution;
2•x + 9 + 3•x + x = 5•x + 9
Infinitely many solutions;
2•x + 9 + 3•x + x = 6•x + 9
What are the types of solutions to a system of equations?The types of solutions of a system of equations are; no solution, infinitely many solutions, one solution
The given expression is; 2•x + 9 + 3•x + x
The above expression when given as the right hand side of an equation gives;
2•x + 9 + 3•x + x = _x + _No solution;
A situation where the right and left hand side of an equation has no solution is where they form lines that do not meet or intersect.
Two lines do not meet when they are parallel, that is when their slopes are the same and however, their y–intercepts are different
Which gives;
Simplifying the expression on the right into the form, m•x + c, where m represents the slope, gives;
2•x + 9 + 3•x + x = 6•x + 9
An expression that can be written on the left that is parallel but does not intersect with the graph of the expression on the left is therefore; 6•x + 5
The first equation is therefore;
No solution;
2•x + 9 + 3•x + x = 6•x + 5One solution;
When the equation has one solution it means that the straight line graphs of the left and right sides intersect once.
Therefore, the lines are not parallel and therefore, the slopes are different, which gives the expression on the right as follows;
2•x + 9 + 3•x + x = 5•x + 9Infinitely many solutions;
When two equations have infinitely many solutions, we have that the equations meet at infinitely many points, such that the equations are essentially the same, which gives the correct option as follows;
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I need help please pronto! This is due today!
The function at x = -2 has a value of -1
How to evaluate the function?The graph represents the given parameter
From the question, we understand that:
The graph is a piecewise function
This means that there are breaks in the values represented on the graph
The x value is given as
x = -2
When this value is traced on the graph, we have
When x = -2, y = -1
When x = -2, y = 7
By considering the endpoint values of the domain, we have
When x = -2, y = -1 (inclusive)
When x = -2, y = 7 (not inclusive)
This means that
When x = -2, y = -1
Hence, the value of the function is -1
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The amount that a charter boat captain charges a group to go deep-sea fishing is shown. If the group tips the captain 17%, what is the total amount that the captain receives for the fishing trip?
The total amount that the captain receives for the fishing trip=850+17 percent $994.5
What is the percentage?
The Latin word "per centum," which means "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.Amount charged =$850
tip from the group=17 percent
The total amount that the captain receives for the fishing trip=850+17 percent 850
=850+(0.17X850)
=$994.5
The total amount that the captain receives for the fishing trip=850+17 percent $994.5
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the product of (6xy-5)(6xy+5)
Answer: 36x^2y^2 - 25
Step-by-step explanation:
(6xy-5)(6xy+5)=
(6xy*6xy)+(6xy*5)+(6xy*(-5))+(-5*5)=
36x^2y^2 + 30xy + (-30xy) + (-25)=
36x^2y^2 + (-25)=36x^2y^2 - 25
Answer:
[tex]\bf36x^2y^2-25[/tex]
Step-by-step explanation:
[tex]\boxed{\displaystyle\\(a-b)(a+b)=a^2-b^2}\\\\(6xy-5)(6xy+5)=(6xy)^2-5^2=36x^2y^2-25[/tex]
Indian cricket team won 4 more matches than it lost with NewZealand. If it won 3/5 of its matches
,how many matches did India play?
As per the unitary method, the number of matches did India play is 20.
Unitary method:
Unitary method is the method in which we first find the value of a unit quantity and then use it to find the value of any required quantity.
Given,
Indian cricket team won 4 more matches than it lost with New Zealand.
Consider If it won 3/5 of its matches, then we need to find the number of matches did it played.
Let us consider the number of matches lost = x
Number of matches won = x + 4
Therefore, the total matches played
=> x + x +4
=> 2x + 4
So, we know that, it won 3/5 th of the matches,
Then it can be written as,
=> x + 4 = 3/5 (2x +4)
Cross multiply it,
=> 5(x + 4) = 3(2x + 4)
=> 5x + 20 = 6x + 12
=> x - 8 =0
=> x = 8
Then the total number of matches played by India is,
=> 2(8) + 4
=> 16 + 4
=> 20.
Therefore, 20 matches are played by India.
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What is question 7......
The rule of the rotation to the right is a rotation by 90° clockwise about the origin.
We need to describe the rule of the rotation to the right.
A figure and its rotation keep the same shape and size but face in a new direction. A figure can be rotated in either a clockwise or counterclockwise direction. The angle of rotation is the measure of how far a figure is rotated about its centre of rotation. The angle of rotation is often expressed in degrees. We specify the rotation's degree measure and direction.
If the rotation is applied to the right, it means a rotation of 90° in a clockwise direction about the origin.
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based on previous data, an electronics manufacturer knows that 2\%2%2, percent of its computer processors are defective. suppose the manufacturer randomly selects these processors until one is found with a defect. let ddd represent the number of processors it takes to find the first one that is defective. assume that defective processors are independent. is ddd a binomial variable? why or why not?
X cannot be a binomial variable because it matches a geometric distribution having parameters of p = 0.02 and is instead a geometric variable.
What is a Binomial Distribution?
The number of successes and failures in a series of n (a finite value) independent trials or experiments is represented by a binomial distribution.
Given that the producer of electronics is aware that 2% of computer processors are faulty, and
The random variable X represents the number of processors it takes to find a bad processor.
X does not constitute a binomial variable in this situation.
In the example above, the amount of failures (processors) is being counted up until the initial success (a malfunctioning processor) is attained.
X cannot be a binomial variable because it matches a geometric distribution having parameters of p = 0.02 and is instead a geometric variable.
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