The general steps to factor a composite number are dividing the composite number by the smallest prime number, if the division is exact, you have found one of the factors of the composite number.
After that then divide the quotient by the smallest prime number that is greater than the divisor used in step 1. Repeat this step with the quotient until the quotient is a prime number. The prime factors of the composite number are the divisors used in the previous steps and the quotient obtained in step 4.
Factoring is the process of finding the prime factors of a composite number.
For example, if you want to factor the composite number 60, you would begin by dividing 60 by 2. Since 60 is divisible by 2, we know that 2 is a factor of 60. The quotient is 30.
We will then divide 30 by 3 and got 10 as quotient.
Then we divide 10 by 2 and got 5 as quotient. 5 is a prime number, so we know that the prime factors of 60 are 2 x 3 x 5
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I need help please!!!
Evaluate f(3)
f(3) = 4(3)-2 = 12 - 2 = 10
f(3) = 10
f(x) = 6 = 4x- 2
4x=8
x = 2
Can you help me with this question pls
Answer: 3=5, 6=10
Step-by-step explanation:
Basic Logic)
Three times two equals six, therefore the correspondent must also double itself.
Five times two equals ten.
Alternate Logic)
Three plus two-thirds of itself is five(3+2=5)
Six plus two-thirds of itself is four(6+4=10)
Answer:
10
Step-by-step explanation:
3=5
3+2
3x2= 6
2x2=4
6+4=10
Which tri nominal is equivalent to 3(x-2)2 - 2(x - 1)
Answer:
4x - 10
Step-by-step explanation:
3(x-2)2 - 2(x - 1)
(3x - 6)2 -2(x -1)
6x - 12 - 2x + 2
4x - 10
What is 603/25 as a mixed number
Answer: 24 3/25
Step-by-step explanation:
Divide 600 by 25, giving you 24. The rest goes into the fraction part.
What mistake did the student make in the picture provided? How would you correct the error?
The mistake made is the error in finding the value of the slope, m, of the line.
The error can be corrected by plugging in m = 6/3 = 2 in the equation; y = m·x + b
What is the slope of a line?The slope of a line is the ratio of the rise to run of the points on the graph of the line.
The points on the graph of the line are; (0, -2), and (3, 4)
The slope of the line, m, can be found using the formula;
m = (y₂ - y₁)/(x₂ - x₁)
Where for the line in the question, we get;
(x₁, y₁) = (0, -2)(x₂, y₂) = (3, 4)Therefore;
Slope, m = (4 - (-2))/(3 - 0) = 6/3 = 2
The slope of the line = 2
The equation of the line in point-slope form is therefore;
(y - 4) = 2·(x - 3)
y = 2·x - 6 + 4 = 2·x - 2
y = 2·x - 2
The equation can also be found using the x-intercept as follows;
At the x-intercept, x = 0. The x-intercept is therefore, the point (0, -2)
The equation of the line in the slope-intercept form is, y = m·x + b, where b is the y-value at the x-intercept is therefore;
y = -2, when x = 0
-2 = 2×0 + b
b = -2
y = m·x + b, therefore; y = 2·x - 2
The mistake of the student is therefore;
The value of the slope of the graph of the line is 6/3 = 2The error can be corrected by plugging in m = 2 in the equation, y = m·x + b as follows;y = m·x + b
4 = 2·(3) + b
4 = 6 + b
-6 [tex]{}[/tex] -6
-2 = b
y = 2·x - 2
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Find the perimeter of
Triangle CBF
If
Triangle DEF ~ triangle CBE.
perimeter of
Triangle DEF = 32. EE = 8. EB = 16.
The scale factor is 2. Then the perimeter of the triangle ΔCBF will be 64 units.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
Triangle DEF ~ triangle CBE. Then the scale factor is given as,
Scale factor = 16 / 8
Scale factor = 2
The perimeter of the triangle ΔDEF is 32 units. Then the perimeter of the triangle ΔCBF will be given as,
P = (Scale factor) x (Perimeter of triangle ΔDEF)
P = 2 x 32
P = 64 units
The perimeter of the triangle ΔCBF will be 64 units.
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How many times can 400 go into 600?
Answer:
1.5
Step-by-step explanation:
Since, 400 is not half of 600 but past it, it would be:
1.0
Since it is half way to 600 it would equal:
1.5.
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6 x 6 x 6 x 6 × 6 written in exponential form
Answer:
[tex]6^{5}[/tex]
11. Three friends want to spend a day together during the holidays. One friend works three days with one day off, the second works five days with one day off and the third seven days with one day off. How many days will it take from the beginning of the holidays until they can all have a day off together?
The number of days until all of them will have a day off together is given as follows:
105 days.
How to obtain the period?Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.
The periods for each person are given as follows:
3 days.5 days.7 days.The least common factor of 3, 5 and 7 is given as follows:
3 x 5 x 7 = 105 days.
(as 3, 5 and 7 are prime numbers, hence we just multiply them).
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Algebra 2, Quadratics!
Siti opened her money box to find 50 pieces of
$5-notes and $2-notes. If the total value of all the
notes is more than $132, find the minimum number
of $5-notes she has
The minimum number of $5-notes she has 32/3
Now, According to the question:
Siti opened her money box to find 50 pieces of $5-notes and $2-notes.
If the total value of all the notes is more than $132.
To find the minimum number of $5-notes she has
Based on the given condition:
= 2 × (50 - x) + 5x = 132
Apply Multiplicative Distributive law:
100 - 2x + 5x = 132
Rearrange the unknown terms on left sides of the equation:
-2x + 5x = 132 - 100
Combine like terms:
3x = 132 - 100
Calculate the sum or difference:
3x = 32
Divide the both sides of the equation by the coefficient of the variable:
x = 32 ÷ 3
Rewrite as fraction :
x = 32/3
Hence, the minimum number of $5-notes she has 32/3
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There are forty students trying out for the school's trivia teams. If nineteen of them didn't get picked for the team and the rest were put into three groups, how many students would be in each group?
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y =f(2x)
b.
y = f(ç)
C.
2y = f (x)
d.
2 = f (x)
Enter
Therefore , the solution of the given problem of equation comes out to be option c is correct 2y = f(x) .
What is equation?The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation
y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.
Here,
Given :
Every point on the graph in red is 1/2 away from the x-axis as that of the equivalent position on the graph in black.
Therefore, the vertically scale factor is equal to 1/2:
=> y = (1/2)f(x)
This problem can be solved by multiplying it by two and yields the following solution:
=> 2y = f(x)
thus , option c is correct
Therefore , the solution of the given problem of equation comes out to be option c is correct 2y = f(x) .
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What is the nearest ten of 555?
The nearest ten of 555 is 550.
The number system or the numeral system is the system of naming or representing numbers. We know that a number is a mathematical value that helps to count or measure objects and it helps in performing various mathematical calculations.
In mathematics, there are various number systems such as the decimal number system, binary number system, octal number system, and hexadecimal number system.
Round the number to the nearest ten. 555 is between 550 and 560.
Looking at the 1 in the one's place. It's equal to 5, so round down to either 550 or 560. In this case, either one can be correct.
Thus, the nearest ten of 555 is 550.
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Almost 80% of the students in the class believe they are in the top 10% of the class on the midterm. What bias are these students subject to
Better-than-average illusion is the propensity to assume that one is superior to the majority within a certain group.
What is meant by bias ?The disparity between the parameter's actual value and its expected value is known as bias. Anything that causes a systematic discrepancy between the statistics used to estimate the parameters of a population and their true parameters is considered statistical bias.
Truth is warped by bias. It is a flaw in the system that we don't frequently notice since it is wrapped up in our humanity. The definition of bias is as basic as "unconscious preference," yet it can be benign or evil. Whatever form they take, though, the biases we have prevent us from seeing the world as it really is.
Better-than-average illusion is the propensity to think that one is superior to the majority in a specific group.
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5. Write a rational
expression that is
equal to the following
rational expression
whenx 1 or - 5.
4(x-1)/
(x-1)(x+5)
The rational expression that is equal to 4(x-1)/(x-1)(x+5) is 4/(x+5).
What are rational expressions ?
Rational expressions represent the relationship between two polynomials. It signifies that the numerator and denominator are both polynomials in it. It is an algebraic expression ratio with an unknown variable, similar to a fraction. We may, however, simplify this type of equation with the aid of a calculator.
Addition and subtraction: When adding or subtracting rational expressions with the same (or similar/common) denominator, keep the denominator alone. If possible, reduce the remaining expression.
If the rational expressions have different denominators, then LCM is applied first. Change each rational expression to its equivalent by changing the denominator exactly. Finally, combine or delete similar phrases. If feasible, reduce the remaining expression.
Multiplication: Factor the polynomial numerators and denominators (if any exist); then reduce wherever possible. Reduced form is obtained by multiplying the remaining numerators and denominators independently.
Division: Invert the denominator (or divisor) and multiply it with the first rational expression (i.e. dividend or numerator) since reduction can only be done simply after changing the division into multiplication, as with fractions. As previously demonstrated, further simplification is equivalent to multiplication.
Now ,
Given rational expression is =4(x-1)/(x-1)(x+5)
=4/(x+5) ( x-1 is same in numerator and denominator so cut it)
Final Rational expression = 4/(x+5)
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m∠ABC=(8x−48)°, m∠ABD=44°
Answer: m∠ABC and m∠ABD are the measures of angles in a triangle. The sum of the measures of the angles in a triangle is always 180°.
So if we know two of the angles, we can use this information to find the measure of the third angle.
Given that m∠ABC= (8x-48)°, m∠ABD=44°
we can find the measure of the third angle, m∠BCD by:
m∠ABC + m∠ABD + m∠BCD = 180
(8x-48) + 44 + m∠BCD = 180
m∠BCD = 180 - (8x-48) - 44
m∠BCD = 180 - 8x + 4
m∠BCD = (180 - 8x + 4)°
However, Since we don't know the value of x, the measure of angle BCD is not determined.
Step-by-step explanation:
△DSJ≅△RCW. If m∠D=114 m∠J=42 ∘ , find m∠C.
The measure of angle m ∠C is 24°.
What are congruent triangles?Congruent triangles have both the same shape and the same size.
Given is that △DSJ ≅ △RCW and m ∠D = 114 and m ∠J = 42.
Since △DSJ ≅ △RCW, we can write -
m ∠S = m ∠C
Now, in △DSJ, we can write -
m ∠D + m ∠S + m ∠J = 180
m ∠S = 180 - 156
m ∠S = 24 = m ∠C
Therefore, the measure of angle m ∠C is 24°.
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Genuinely don't even know how to do this lol
Rewrite the formula to solve for W
Answer:
Step-by-step explanation:
P = 2l = 2w
P - 2l = 2w
P - 2l / 2 = w
W = P - 2l /2
How do you do log and inverse log?
Logarithms can be calculated using the log function in a calculator or the formula loga(x) = y, where a is the base and x is the number you want to find the logarithm of.Inverse logarithms can be calculated using the 10x key on a calculator or the formula 10^y=x, where y is the logarithm and x is the number you want to find the inverse logarithm of.
Logarithms:
To calculate the logarithm of a number, use the log function in your calculator, or use the formula loga(x) = y, where a is the base and x is the number you want to find the logarithm of.
Inverse Logarithms:
To calculate the inverse logarithm of a number, use the 10x key on your calculator, or use the formula 10^y=x, where y is the logarithm and x is the number you want to find the inverse logarithm of.
Logarithms can be calculated using the log function in a calculator or the formula loga(x) = y, where a is the base and x is the number you want to find the logarithm of. Inverse logarithms can be calculated using the 10x key on a calculator or the formula 10^y=x, where y is the logarithm and x is the number you want to find the inverse logarithm of.
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Serving to estimate the height of a parking garage using a 50 yards-long rope.
sie oor while Sarah stands on the top level of the garage. Each holds an end of the rope. Joshua walks away until the rope is
completely dense, making a 30 angle with the floor and 60° with the garage wall.
Joshua says the height can be calculated using the function sin (30- and determines the height is 25 yards.
Sarah says the correct expression to be used is cos (60) and her calculation is that the height is 25 yards.
Which one is correct?
Sarah and Joshua both use correct trigonometry expressions to find out the height of garage wall.
Sarah and Joshua serving to estimate the height of a parking garage using a 50 yards-long rope.
Joshua is in the floor while Sarah stands on the top of garage. Each holds an end of the rope. Joshua walks away until the rope is completely tense,
making an angle of 30° with the floor and an angle 60° with the top.
Joshua determined the height of the wall is 25 yards with the help of trigonometry expression for Sin, and Sarah determined by Cos.
So, let us examine whose approach is correct,
We have length of rope is 50 yards and the angle with floor is 30 and angle with top is 60°
first examine the approach of Joshua,
according to trigonometry, we have
[tex]Sin\theta=\frac{perpendicular}{hypotenuse}[/tex]
[tex]Sin30=\frac{h}{50}[/tex]
[tex]\frac{1}{2} =\frac{h}{50}[/tex]
thus, h =25 yards,
now come on the approach of Sarah
[tex]cos\theta=\frac{base}{hypotenuse}[/tex]
[tex]cos60=\frac{h}{50}[/tex]
thus, h=25 yards.
According to our examination both Joshua and Sarah have corrected approaches.
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List the sample space for each chance experiment.
Flipping a coin
Selecting a random season of the year
Selecting a random day of the week
The required sample spaces for the given chance experiment, are as follows: flipping a coin: {heads, tails}, selecting a random season of the year: {spring, summer, fall, winter}, and selecting a random day of the week: {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The sample space for flipping a coin: {heads, tails}
The sample space for selecting a random season of the year: {spring, summer, fall, winter}
The sample space for selecting a random day of the week: {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
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Change each equation below into y = mx + b form. a. y - 4x = -3 b. 3y - 3x = 9 c. 3x + 2y = 12 d. 2(x - 3) + 3y = 0
Answer:
a. y=4x-3
b. y=x+3
c. y=3/2x+6
d. y=-2/3x+2
Step-by-step explanation:
a. y-4x=-3
+4x +4x
y=4x+3
b. 3y-3x=9
÷3 ÷3
y-x=3
y=x+3
c. 3x+2y=12
2y=3x+12
y=3/2x+6
d.
2(x-3)+3y=0
2x-6+3y=0
3y=-2x+6
y=-2/3x+2
How many solutions have following the pair of linear equations 3x 4y 5 0 and 12x 16y 15 0?
The pair of linear equations 3x + 4y + 5 = 0 and 12x + 16y + 15 = 0 has no solution.
To find the number of solutions that a pair of linear equations will have, we can use the concept of the ratio of coefficients.
For the pair of linear equations:
3x + 4y + 5 = 0
12x + 16y + 15 = 0
We can find the ratio of the coefficients of x in both equations.
In the first equation, the coefficient of x is 3 and in the second equation, the coefficient of x is 12. The ratio of these coefficients is
3/12 = 1/4
We can also find the ratio of the coefficients of y in both equations.
In the first equation, the coefficient of y is 4 and in the second equation, the coefficient of y is 16. The ratio of these coefficients is
4/16 = 1/4
As both ratio are equal, let us check ratio of constants.
5/15 = 1/3
So the ratio of constants is not equal, so there is no solution for this system of linear equations.
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Two way table Probability (100 points awarded)
If a student is selected at random find the probability the student is a freshman. P(Freshman) =
Round to the nearest whole percent.
Answer:
Out of the 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 total students, 4 + 3 = 7 are freshmen so the answer is 7 / 30 * 100 = 23%.
Step-by-step explanation:
Cuanto es -5-12 en álgebra
Match the inequality to its representation on a number line.
2. Write an inequality statement whose solution is an empty set.
6. Write an inequality statement to represent the graph shown.
en inequality statement to represent the graph shown.
4. Write an inequality statement whose solution is all real numbers. Graph the solution on a number line.
3. Write an inequality statement whose solution is some but not all real numbers. Graph the solution on a number line
9
Write an inequality statement whose solution is exactly one number. Graph the solution on a number line.
An inequality depicts the relationship between two values in an algebraic statement that are not equal.
What is an inequality statement ?Inequality, a declaration of the relation of greater, greater than or equal to, smaller, or less than or equal to between two numbers or algebraic expressions.
An inequality is a claim that demonstrates the connection between two (or more) expressions that have one of the following five signs:,, >,,. Similar to an equation, an inequality can be true or untrue. A true statement is: 34 - 12 > 5 + 2. An incorrect statement is 1 + 3 6 - 2.
When two values in an algebraic expression are not equal, an inequality illustrates their relationship. One of the two variables on the two sides of the inequality can be represented by an inequality sign as greater than, greater than or equal to, less than, or equal to another value.
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Zendaya invests money in an account paying a simple interest of 7.3% per year. If she invests $70 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?
Answer: If Zendaya invests $70 in an account paying a simple interest of 7.3% per year, and no money will be added or removed from the investment, she will have $75.11 in one year.
To calculate the amount of interest earned, you can use the formula:
Interest = Principal x Rate x Time
where
Principal = $70
Rate = 7.3/100 (expressed as a decimal)
Time = 1 year
So the interest earned is:
$70 x 0.073 x 1 = $5.11
To find the total amount at the end of the year, you add the interest to the original principal:
$70 + $5.11 = $75.11
Step-by-step explanation:
(TRIGONOMETRY) Please help me with 7-10 questions. Answer is to be rounded to the nearest tenth
Answer:
Step-by-step explanation:
1 7.3
2 33.3
3 21.3
4 31.9
5 25.6
6 11
7 41.8
8 64.2
9 12.8
10 51.3
11 24.4
12 35.1
couldn’t do 13 and 14 i’m doing same lesson with rizz but 15 is 44.6inches 16 78.8