The common factors of 20 and 45 are 1 and 5, since these are the only factors that both numbers share.
To find the common factors of two numbers, we need to find the factors of each number and then identify the ones that they have in common. For example, if we want to find the common factors of 20 and 45, we first find the factors of 20 and 45:
The factors of 20 are: 1, 2, 4, 5, 10, 20
The factors of 45 are: 1, 3, 5, 9, 15, 45
The factor 1 is always a common factor of any two numbers, since every number is divisible by 1. The factor 5 is a common factor of 20 and 45 because both 20 and 45 are divisible by 5. It is important to note that the other factors of 20 and 45 are not common factors, since they are not shared by both numbers.
Therefore, the common factors of 20 and 45 are 1 and 5, since these are the only factors that both numbers share.
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What is the simplified value of the expression
The simplified value of the expression is,
⇒ [tex]\frac{1}{\sqrt[5]{3} }[/tex]
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ [tex]\frac{(\sqrt[3]{3} )^{3/5} }{(\sqrt[3]{3} )^{6/5} }[/tex]
Now, We can simplify by the rule of exponent as;
⇒ [tex]\frac{(\sqrt[3]{3} )^{3/5} }{(\sqrt[3]{3} )^{6/5} }[/tex]
⇒ [tex](\sqrt[3]{3} )^{3/5} }{(\sqrt[3]{3} )^{- (6/5)} }[/tex]
⇒ [tex](\sqrt[3]{3} )^{3/5 - 6/5[/tex]
⇒ [tex](\sqrt[3]{3} )^{-3/5[/tex]
⇒ [tex]\frac{1}{\sqrt[3]{3} ^{ 3/5} }[/tex]
⇒ [tex]\frac{1}{\sqrt[5]{3} }[/tex]
Thus, The simplified value of the expression is,
⇒ [tex]\frac{1}{\sqrt[5]{3} }[/tex]
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The rectangular floor of a classroom is 22 feet in length and 24 feet in width. A scale drawing of the floor has a length of 11 inches. What is the perimeter, in inches, of the floor in the scale drawing?
The scale floor's perimeter is 34 inches.
What is meant by perimeter?The overall length of a form's boundary is referred to as the perimeter of that shape. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet. The perimeter is the space surrounding a shape's edge. Get the perimeter of various forms by multiplying their side lengths.The circumference of an object is known as its perimeter. For instance, your home has a yard that is enclosed. The length of the fence is the perimeter. The length of your fence is 200 feet if the yard is 50 feet by 50 feet.To solve, we can set up fractions:
21/7 = 30/x
Cross multiply and you get:
21x = 210
Divide each side by 21:
x = 10
You can apply the following equation since you're attempting to determine the floor's perimeter:
2w + 2l = p
Substitute to solve:
2 ( width = 10 )
2 ( length = 7 )
2 (7) + 2 (10) = p
14 + 20 = p
34 = p
The complete question is:
The rectangular floor of a classroom is 21 feet in length and 30 feet in width. A scale drawing of the floor has a length of 7 inches. What is the perimeter, in inches, of the floor in the scale drawing?
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Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2 l plus 2 w equals 62 to find the width of the run.
Which statements are true of the solution? Check all that apply.
The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w
Answer:
11 feet long
Step-by-step explanation:
20+20=40
62-40=22
22÷2=11
check
11+11+20+20=62
How many solutions does the system of liner equations represented in the graph
Answer:
Infinite solutions
Step-by-step explanation:
There are an infinite number of solutions. If you have a system of linear equations, the solution for the system is the value that makes all of the equations true. For two variables and two equations, this is the point where the two graphs intersect.
-12x3^2+36 please ty
Answer:
-72
Step-by-step explanation:
Answer:
-72
Step-by-step explanation:
multiply-12 x3^2 and then add 36
The population in a small town is increasing annually by 2.8%. What is the quarterly rate of population increase?
Answer:
To find the quarterly rate of population increase, we first need to find the annual rate of population increase in decimal form, which is 2.8% expressed as 0.028.
To find the quarterly rate, we need to divide the annual rate by 4, since there are 4 quarters in a year:
0.028 / 4 = 0.007
Therefore, the quarterly rate of population increase is 0.007 or 0.7%
find missing value
i rlly need help thanks
The missing value using concept of similar triangle ratio is; 35
How to find the length of similar triangles ?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Using the concept of similar triangles on the given diagram, we have;
p/(30 + 20) = 14/20
p = (14 * 50)/20
p = 35
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During the month of May, the sheriff's department issued 130 traffic tickets for speeding or failure to obey traffic signals. The fine for each speeding ticket
was $67.00, and each fine for failure to obey traffic signals was $67.00. The sheriff's department collected $8,710.00 in fines from these two offenses.
Which system of equations can be used to determine the number of speeding tickets given, x, and the number of tickets given for failure to obey traffic
signals, y?
Answer: The number of speeding tickets issued is represented by x and the number of tickets for failure to obey traffic signals is represented by y. The total number of tickets issued is 130, so we have:
x + y = 130
The total amount of money collected in fines is $8,710.00, so we have:
67x + 67y = 8710
These two equations form a system of linear equations that can be used to determine the number of speeding tickets, x, and the number of tickets for failure to obey traffic signals, y. To solve this system, we can use any of the methods for solving a system of linear equations, such as substitution, elimination, or matrices.
Step-by-step explanation:
to find the value of a numerical or algebraic expression is called?
The process of finding the value of a numerical or algebraic expression is called evaluation.
Evaluation involves substituting the given values of the variables in the expression and then simplifying the expression using the order of operations (PEMDAS).
For example, if we are asked to evaluate the expression 3x + 2y when x=4 and y=5, we would substitute these values to get 3(4) + 2(5), which simplifies to 12 + 10 = 22. Therefore, the value of the expression 3x + 2y when x=4 and y=5 is 22.
In algebra, evaluation is an important process because it allows us to find the value of an expression for specific values of the variables, which can help us to solve equations or inequalities, and to simplify expressions.
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Point value: 15
Please HELP!
Answer:
There are three terms in the given expression.
Step-by-step explanation:
First, a term is a single individual value on which mathematical operations occur in an algebraic expression. Essentially, terms are every part of an expression that is separated by any mathematical operation, such as PEMDAS. In the expression [tex]\frac{v}{3} -4*2[/tex], [tex]\frac{v}{3}[/tex], -4, and 2 are all terms. Therefore, there are three terms in the given equation.
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Triangle ABC is similar to triangle FGH. Given the following angle measures, find the missing angle measures.
m∠A = 22 degrees
m∠B = 75 degrees
Enter your answers as numbers only.
m∠F = _____ degrees
m∠G = _____ degrees
m∠H = _____ degrees
m∠C = _____ degrees
The missing angle measures are:
m∠F = 22 degrees
m∠G = 75 degrees
m∠H = m∠C = 83 degrees
m∠C = 83 degrees
The angle measuresSince triangles ABC and FGH are similar, their corresponding angles are equal. Therefore:m∠F = m∠A = 22 degrees
m∠G = m∠B = 75 degrees
m∠H = m∠C, since they are corresponding angles, but we still need to find the measure of m∠C.
To find m∠C, we can use the fact that the sum of the angles in a triangle is always 180 degrees. So:m∠A + m∠B + m∠C = 180 degrees
Substituting the given values, we get:22 degrees + 75 degrees + m∠C = 180 degrees
Simplifying, we get:m∠C = 180 degrees - 22 degrees - 75 degrees = 83 degrees
Therefore, the missing angle measures are:
m∠F = 22 degrees
m∠G = 75 degrees
m∠H = m∠C = 83 degrees
m∠C = 83 degrees
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Which shape has two pairs of parallel sides
The shape with two pairs of parallel sides is called a parallelogram.
What is a paralellogram?A parallelogram is a shape that has four sides, in which the two opposite lengths are:
Parallel to each other.Have the same measure.As there are four sides, divided two by two, the shape has two pairs of parallel sides, and is called a parallelogram.
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Solve for x
A. Solve using the change of base formula.
Logby= log y/log b
B. Solve using a different method.
C. verify your solutions by substituting your value back into the original equation.
A) By using the change of base formula, the solution of the expression is,
⇒ x = - 2/3
B) The solution of the expression is,
⇒ x = - 2/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
Now, We have the change of base formula,
⇒ [tex]log_{b} y = \frac{log y}{log b}[/tex]
Here, The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
Take log on both side,
⇒ log 5³ˣ⁻² = log 5⁶ˣ
⇒ (3x - 2) log 5 = 6x log 5
⇒ 3x - 2 = 6x
⇒ - 2 = 6x - 3x
⇒ 3x = - 2
⇒ x = - 2/3
B) By using another method as;
The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
By comparing we get;
⇒ 3x - 2 = 6x
⇒ - 2 = 6x - 3x
⇒ 3x = - 2
⇒ x = - 2/3
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What are the equations of the
asymptotes of the functions
f(x) =1/x-5 +3? What are the
domain and range?
Step-by-step explanation:
I am in class 7 If I know I tell you I am go to ask my teacher
Answer:
Domain:(−∞,5)∪(5,∞),{x|x≠5}
Range:(−∞,3)∪(3,∞),{y|y≠3}
Step-by-step explanation:
??????
While shopping after her birthday, Annie bought 2 pairs of jeans and 3 shirts and spent $127. Her twin sister Hallie bought the same items consisting of 1 pair of jeans and 4 shirts and spent $116 how much does one pair of jeans cost and how much does a shirt cost
Answer:
The shirt costs $21
Step-by-step explanation:
2x + 3y = 127 ....eq 1
Her twin sister Hallie bought 1 pair of jeans and 4 shirts for $116.
So, x + 4y = 116 ....eq 2
Multiplying eq 2 by 2, we get :
2x + 8y = 232 ....eq 3
Subtracting eq 1 by eq 3, we get :
(2x + 8y) - (2x + 3y) = 232 - 127
5y = 105
Thus, y = 21
Putting this value of y in eq 2, we get :
x + 4(21) = 116
x = 116 - 84 = 32
Therefore, the cost of a pair of jeans = x = $32
And the cost of a shirt = $21
Name at least two independent variables that could result in a change in a monthly electric bill
The two independent variables that could result in a change in a monthly electric bill will be Product physical dimensions and Machine operators' skill level.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
Independent variables are variables that do not depend on anything.
Dependent variables are variables that depend on the independent variables.
The independent variables in the electric bill are as follows:
Product physical dimensionsMachine operators' skill level.Non-production machines that use electricity, among other thingsThe two independent variables that could result in a change in a monthly electric bill will be Product physical dimensions and Machine operators' skill level.
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The measure of an angle is 71.6°. What is the measure of its complementary angle
Answer:
18.4 degrees
Step-by-step explanation:
a complementary angle is 90 degrees and 90 - 71.6 is 18.4. So, the answer is 18.4 degrees.
ASAP!!! How do I solve this
Complete the equation of the circle that includes the points (-5,4), (3,4), and (3,0)
The equation of circle is ( x + 1 )² + ( y - 2 )² = 20
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the points on the circle be A ( -5 , 4 ) , B ( 3 , 4 ) and C ( 3 , 0 )
Now , the equation of the circle is of the form
ax + by + c = x² + y²
Substituting the values in the equation , we get
-5a + 4b + c = 41 be equation (1)
3a + 4b + c = 25 be equation (2)
3a + c = 9 be equation (3)
Subtracting equation (2) from equation (1) , we get
-8a = 16 be equation (4)
Divide by -8 on both sides of the equation , we get
a = -2
Substitute the value of a in equation (3) , we get
3 ( -2 ) + c = 9
-6 + c = 9
c = 15
Substitute the value of a and c in equation (2) , we get
-6 + 4b + 15 = 25
4b + 9 = 25
4b = 16
b = 4
So , the value of a , b and c are -2 , 4 and 15 respectively
Now , the equation of circle will be
-2x + 4y + 15 = x² + y²
On simplifying the equation , we get
x² + y² + 2x - 4y - 15 = 0
( x² + 2x + 1 ) - 20 + ( y² - 4y + 4 ) = 0
So , the equation will be
( x + 1 )² + ( y - 2 )² = 20
Hence , the equation of circle is ( x + 1 )² + ( y - 2 )² = 20
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Ann borrowed $8000 at a rate of 15%, compounded annually. Assuming she makes no payments, how much will she owe after 6 years?
Answer:
Ann will owe $15,258.23 after 6 years, assuming she makes no payments.
What is Compound Interest ?
Compound interest is a method of calculating interest on a loan or investment, where interest is earned on both the initial principal amount and on any interest that has already been earned. In other words, interest is added to the principal, and then interest is calculated on the new total amount (the principal plus the previously earned interest). This results in the interest earned growing exponentially over time.
According t o given condition :
To calculate the amount Ann will owe after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
where:
A = the amount Ann will owe after 6 years
P = the initial principal amount borrowed, which is $8000 in this case
r = the annual interest rate as a decimal, which is 15% or 0.15
n = the number of times interest is compounded per year, which is once annually in this case
t = the number of years, which is 6 in this case
Plugging in these values, we get:
A =
A =
A = $15,258.23
Therefore, Ann will owe $15,258.23 after 6 years, assuming she makes no payments.
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How many solutions does the equation have?
4x + 3 = 4x + 3
Answer:
Infinitely Many
Step-by-step explanation:
Both answer are equal to each other
What is an equation of the line that passes through the point (5,-8) and is parallel to the line 5x-4y=16
Answer:
To find the equation of the line that passes through the point (5,-8) and is parallel to the line 5x-4y=16:
1. Identify the slope of the original line (m = 5/4).
2. Use the point-slope formula: y - (-8) = (5/4)(x - 5).
3. Simplify the equation.
4. The equation is y + 8 = 5/4(x - 5), or 5x - 4y = 16.
WILL MARK BRAINLIEST drag and drop the discriptions into the box to correctly classify each pair of number angles each may be used more then once
Answer: 1 and 2 = vertical
3 and 4 = adjacent
4. A line segment has two end-points M(3, 7) and N(11, -6). Find the coordinates of the point W that lies on the y-axis such that W is equidistant from M and from N.
would appreciate a step by step answer (quickly please)
The coordinates of point W which is equidistant from M and N ( 7, 1 / 2).
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the points are M(3, 7) and N(11, -6). The coordinates of the midpoints are,
W = ( x₁ + x₂ ) / 2, ( y₁ + y₂ ) / 2
W = ( 3 + 11 ) / 2, ( 7 - 6 ) / 2
W = 14 / 2, 1 / 2
W = 7, 1 / 2
Hence, the value of the coordinate of the midpoint is ( 7, 1 / 2 ).
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Which function has a range limited to only negative numbers?
Answer:
F (x)=-x^2
Step-by-step explanation:
I need some help with my homework
Answer:
c
Step-by-step explanation:
c
Answer:
A
Step-by-step explanation:
2/ac + 1/ab + 3/bc = ?
Answer:
Abc
Step-by-step explanation:
2b + c + 3a = Abc
Write the number
five million four thousand three hundred
in standard form.
The required five million four thousand three hundred in standard form is 5,004,300.
What is a number system?A number system is described as a technique of composing to represent digits. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
In the question, we are asked to write the word of the number five million four thousand three hundred in standard form.
So,
five million four thousand three hundred = 5,004,300
Since
1 million = 1000, 000
1 thousand = 1000
1 hundred = 100
Thus, the required five million four thousand three hundred in standard form is 5,004,300.
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I need some help please
Answer:
32
Step-by-step explanation:
Substitute values given into the expression :
3[2(1)+(3)]-4[((1)-(3)]+(3)²
3[5]-(-8)+9
15+8+9 =
32
Hope this helped and have a good day
What is an equivalent expression for 27+3x
The equivalent expression is 81 + 9x
What is an algebraic expression?An algebraic expression is simply defined as an expression that is composed of terms, variables, coefficients, factors and constants.
They are also made up of arithmetic operations like subtraction, division, addition, multiplication, bracket and parentheses.
Equivalent expressions are defined as expressions with the same solution but which differs in the mode of their arrangement.
From the information given, we have that;
27+3x
Multiply the values by 3 each, we get;
81 + 9x
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During a seven-year period, the average housing prices (in thousands of dollars) for a year in Miami $M$M and Gainesville cap g$G$G are modeled by the equations
cap m is equal to 1 point 7 t cubed minus 6 point 5 t squared plus 212$M=1.7t^3-6.5t^2+212$M=1.7t3−6.5t2+212 and
cap g is equal to 1 point 6 t squared minus 14 t plus 165$G=1.6t^2-14t+165$G=1.6t2−14t+165 ,
where t is equal to 1$t=1$t=1 represents the first year.
a. Write a polynomial that represents the difference in housing prices.
Polynomial:
Question 2
b. What is the difference in housing prices in the fifth year?
$
The difference in housing prices in the fifth year is $7,125.
What is price?Price is the amount of money one has to pay for goods or services. It is also the return on an investment or the cost of borrowing money. Price is determined by the supply and demand of a product or service. It is also influenced by market forces such as competition, production costs, and availability of resources. Price is a key factor in determining the success of a business, as it can affect consumers' buying decisions and profitability.
$M(5) - G(5) = (1.7(5)³- 6.5(5)²+ 212) - (1.6(5)²- 14(5) + 165) = $7,125
Therefore, the difference in housing prices in the fifth year is $7,125.
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