For a loan of $24,000 at 6% interest over 60 months, the monthly payment is $466.47.
What is Monthly Payment?A monthly payment is the sum of money that is made towards a debt or loan on a regular basis; it normally consists of both the main and interest. It is a set sum that the borrower must consistently pay until the debt is repaid in full. Mortgages, auto loans, student loans, and personal loans all frequently include monthly installments. The loan amount, the interest rate, and the term of the loan all affect how much will be paid each month.
We can use the following calculation to determine a loan's monthly payment:
M = P * (r * (1 + r)ⁿ) / ((1 + r)ⁿ⁻¹)
where:
M = payment each month
P = Principal (the loaned amount)
r = (Divide the annual interest rate by 12 to get the monthly interest rate)
n = total payments (12 divided by the number of years)
By entering the specified values, we obtain:
P = 24000
r = 6% / 12 = 0.005
n = 60
M = 24000 * (0.005 * (1 + 0.005)⁶⁰) / ((1 + 0.005)^60 - 1)
M = $466.47 (rounded to the nearest cent)
So, $466.47 is the monthly payment for a $24,000 loan with a 6% interest rate over 60 months.
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Maverick spins a spinner 15. The spinner has 5 equal parts numbered 1-5. Which is the best prediction of the number of times Maverick should spin a 4?
The best prediction of the number of times Maverick should spin a 4 is 3 times.
How to determine the best prediction of the number of times Maverick should spin a 4Assuming the spinner is fair and unbiased, the best guess for how many times Maverick should spin a 4 is three.
The expected number of times a 4 should appear can be calculated by calculating the probability of spinning a 4 (1/5, or 0.2) by the total number of spins (15):
Expected number of 4's = Probability of spinning a 4 x Total number of spins
Expected number of 4's = 0.2 x 15
Expected number of 4's = 3
Therefore, the best prediction of the number of times Maverick should spin a 4 is 3 times.
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PLEASEEE HELP I BEGGG
Answer:
B and then A
Step-by-step explanation:
volume is × so the . means times
so it's the only option
and then the second area is
6×3×4= 72cm³
Altogether the Blue Team jumped 11,485 times. The Red Team did 827 more jumps than the Blue Team. How many jumps did the Red Team do?
Answer:
12312
Step-by-step explanation:
add the 11485 to 827 to figure out how many times did the red team do
a certain drug has a half-life in the body of . what should the interval between doses be, if the concentration of drug in the body should not fall below of its initial concentration? round your answer to significant digits.
The interval between doses should be approximately 10.4 hours to maintain a minimum concentration of 30% of the initial concentration in the body.
The interval between doses of a drug depends on its half-life and the desired minimum concentration in the body. The half-life of a drug is the time it takes for half of the initial dose to be eliminated from the body.
To determine the interval between doses, we can use the following formula
t = (t1/2 × ln(Cmin/Cmax)) / ln(2)
Where:
t1/2 is the half-life of the drug
Cmin is the desired minimum concentration in the body (expressed as a fraction of the initial concentration)
Cmax is the initial concentration of the drug
ln represents the natural logarithm function.
Substituting the given values, we get
t = (6.0h × ln(0.3)) / ln(2)
t ≈ 10.4h
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The given question is incomplete, the complete question is:
A certain drug has a half-life in the body of 6.0h. What should the interval between doses be, if the concentration of drug in the body should not fall below 30.% of its initial concentration?
Cameron invests money in an account paying a simple interest of 7% per year. If no money will be added or removed from the investment, what should he multiply his current balance by to find his total balance in a year in one step?
The total balance in a year after the simple interest is A = P ( 1 + r )
Given data ,
Let the total balance in a year after the simple interest is A
Now , the multiply the initial balance by (1 + r), where r is the annual interest rate as a decimal.
In this case, the interest rate is 7%, or 0.07 as a decimal.
Therefore, Cameron should multiply his current balance by (1 + 0.07) = 1.07 to find his total balance in a year in one step.
For example, if Cameron's current balance is $10,000, his total balance after one year with simple interest would be:
Total balance = $10,000 x 1.07 = $10,700
Hence , the total balance is given by A = P ( 1 + r )
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Which is more, 7 yards or 19 feet?
According to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.
What is multiplication?Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product.
According to the given information:To compare 7 yards and 19 feet, we need to convert them to the same unit. Since 1 yard is equal to 3 feet, we can convert yards to feet by multiplying by 3, and we can convert feet to yards by dividing by 3.
In the first answer, we converted 7 yards to feet by multiplying by 3, which gave us 21 feet. Then we compared 21 feet to 19 feet, and found that 21 feet is greater than 19 feet. Therefore, we concluded that 7 yards is more than 19 feet.
In the second answer, we converted 19 feet to yards by dividing by 3, which gave us approximately 6.33 yards (rounded to two decimal places). Then we compared 7 yards to 6.33 yards, and found that 7 yards is greater than 6.33 yards. Therefore, we concluded that 7 yards is more than 19 feet.
Therefore, according to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.
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you have a cake that is 16 inches by 18 inches.you want each piece to be exactly the same size.how many people can u serve equal sized piece of cake
The number of people are 72.
What is HCF?Highest Common Factor is the full name for HCF in mathematics.
According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.
What is LCM?Least Common Multiple is the full name for LCM in mathematics.
LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.
We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.
Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.
We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:
288 / x² = (16*18) / x² = 288 / x²
Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.
As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.
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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.
What is area?A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.
To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.
The total area of the cake is:
16 inches x 18 inches = 288 square inches
To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:
√(288 square inches) ≈ 16.97 inches
Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:
Each piece of cake will be approximately 16 inches by 16 inches.
To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:
288 square inches ÷ (16 inches x 16 inches) = 18
Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.
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I NEED HELP ON THIS ASAP!!!
The exponential function f(x) = 2^x is given by the blue graph on the given graph.
What is an horizontal asymptote?The horizontal asymptote of a function is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
The function in this problem is defined as follows:
y = 2^x.
Two relevant numeric values are given as follows:
When x = -1, y = 2^(-1) = 1/2 = 0.5.When x = 0, y = 2^0 = 1.Hence the function is represented by the blue graph.
The horizontal asymptote is of y = 0, as when x goes to negative infinity, y goes to zero.
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WILL MARK AS BRAINLEIST!! ASAP PLEASE!!
Question in picture
I have more questions on my account if u can help me out!!
For the region above x + 3y = 9 and below x + 9 = y², we have:
a = 18, b = -9, f(x) = (y² - 9)/3, and g(x) = (9 - x)/3.
For single integration: α = -6, β = 3 and h(y) = [(9 - y²)/3 - (y² - 9)].
What is the area bounded by the curves?To solve this problem, we first need to find the intersection points of the two curves x + 3y = 9 and x + 9 = y². We can do this by solving the system of equations:
x + 3y = 9
x + 9 = y²
Rearranging the first equation, we get:
x = 9 - 3y
Substituting this expression for x into the second equation, we get:
9 - 3y + 9 = y²
Simplifying, we get:
y² - 3y - 18 = 0
Factorizing, we get:
(y - 6)(y + 3) = 0
So the solutions are:
y = 6 or y = -3
Substituting these values of y into the equation x + 3y = 9, we get:
When y = 6, x = -9
When y = -3, x = 18
So the intersection points of the two curves are (-9, 6) and (18, -3).
Now we can find the area between the two curves by splitting it into two regions: the region above the curve x + 3y = 9 and below the curve x + 9 = y², and the region below the curve x + 3y = 9 and above the curve x + 9 = y².
For the region above x + 3y = 9 and below x + 9 = y², we have:
a = 18
b = -9
f(x) = (y² - 9)/3
g(x) = (9 - x)/3
Alternatively, to compute the area between the two curves x + 3y = 9 and x + 9 = y² using a single integral, we need to express the area as a function of y instead of x.
We can rearrange the equations x + 3y = 9 and x + 9 = y² to get:
x = 9 - 3y
x = y² - 9
Setting these two expressions equal to each other, we get:
9 - 3y = y² - 9
Simplifying, we get:
y² + 3y - 18 = 0
Factorizing, we get:
(y + 6)(y - 3) = 0
So the solutions are:
y = -6 or y = 3
Substituting these values of y into the equation x + 3y = 9, we get:
When y = -6, x = 27
When y = 3, x = 0
So the intersection points of the two curves are (27, -6) and (0, 3).
The area between the curves can be expressed as the difference between the integrals of the curves' respective functions with respect to y, since the curves are better expressed in terms of y.
The function representing the curve x + 3y = 9 in terms of y is:
x = 9 - 3y
We can rearrange this equation to get:
y = (9 - x)/3
Substituting x = y² - 9, we get:
y = (9 - y² + 9)/3
Simplifying, we get:
y² + 3y - 18 = 0
This is the same equation we obtained before, so we know that the bounds of integration are -6 and 3.
The function representing the curve x + 9 = y² in terms of y is:
x = y² - 9
Substituting this expression into the formula for the area of a region between two curves, we get:
Area = ∫(y=α)^(y=β) [(9 - y²)/3 - (y² - 9)] dy
Where;
α = -6 and β = 3 are the bounds of integration, and
the integrand [(9 - y²)/3 - (y² - 9)] represents the difference between the y-values of the two curves at a given x-value.
Simplifying the integrand, we get:
Area = ∫(y=-6)^(y=3) (18 - 2y²)/3 dy
Integrating, we get:
Area = [(6y - (2/3)y³)/3] |(y=-6)^(y=3)
Plugging in the limits of integration, we get:
Area = [(18 - 216)/3] - [(-36 + 216)/3]
Simplifying, we get:
Area = 66
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1. ) Any measure representing the center of a set of data arranged in a decreasing or increasing order of magnitude.
2. ) Commonly referred to as the average of all values.
3. ) Middle value in the set of data arranged in increasing or decreasing order.
4. ) Contains two modes.
5. ) Most frequently occurring score.
pls answer my grade dropped to 75 last grading pls answer correctly
The match of the given defines are any measure representing the center of a set of data arranged in a decreasing or increasing order of magnitude is Measure of central tendency, Commonly referred to as the average of all values is Mean, Middle value in the set of data arranged in increasing or decreasing order is Median, Contains two modes is Bimodal, Most frequently occurring score is Mode.
The identified match from the box to the given defines are the mean is the sum of all values divided by the total number of values. The median is the middle value when data is arranged in order.
The mode is the value that appears most frequently in a set of data. Bimodal refers to a distribution that has two modes. Finally, measure of central tendency refers to any method used to represent the center of a set of data.
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--The given question is incomplete, the complete question is given
" identify the following defines. and choose from below box:
mean, mode, median, measure of central tendency, bimodal
1. ) Any measure representing the center of a set of data arranged in a decreasing or increasing order of magnitude.
2. ) Commonly referred to as the average of all values.
3. ) Middle value in the set of data arranged in increasing or decreasing order.
4. ) Contains two modes.
5. ) Most frequently occurring score.
pls answer my grade dropped to 75 last grading pls answer correctly"--
For which angle θ is cos θ = −1?
a. 270° b. 360° c. 450° d. 540°
Answer: Dude adove is WRONGGG
Step-by-step explanation:
ANSWER IS 540
Answer:
c. 540°
Step-by-step explanation:
You want to know which angle θ has cos(θ) = -1.
CosineThe cosine function is periodic with period 360°. The smallest positive angle θ for which cos(θ) is -1 is 180°. The next such angle is ...
180° +360° = 540° . . . . . choice D
__
Additional comment
A graph of the cosine function is attached. The horizontal axis is in degrees.
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Keep moving: find the perimeter of each figure
The perimeter of the figure is as follows
1. 93 cm
2. 42 cm
3. 45 cm
What is perimeterPerimeter is the total length of the boundary of a two-dimensional shape or figure. In other words, it is the sum of the lengths of all the sides or edges of the shape.
Perimeter is measured in units of length, such as centimeters, meters, or feet, depending on the system of measurement being used.
The perimeter of the figures is solved as follows
1.
= 12 + 15 + 20 + 11 + 7 + 10 + 6 + 12
= 93 cm
2.
= 8 + 12 + 5 + 5 + 12
= 42 cm
3.
= 15 + 15 + 15
= 45 cm
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(2x+15)
Find the value of a.
to
Answer: 7.5
Step-by-step explanation: 2 x 7.5 = 15
A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=t3−6t2+9t. Over the time interval 0
Therefore, the maximum displacement of the particle is 4 units, and it occurs at time t = 1.
To find the maximum displacement, we need to first determine the particle's velocity and acceleration.
The velocity of the particle is given by the derivative of its position function:
[tex]v(t) = y'(t) = 3t^2 - 12t + 9[/tex]
The acceleration of the particle is given by the derivative of its velocity function: a(t) = v'(t) = 6t - 12
Now, to find the maximum displacement, we need to find the time at which the particle comes to rest.
This occurs when its velocity is zero:
[tex]3t^2 - 12t + 9 = 0[/tex]
Simplifying this equation, we get:
[tex]t^2 - 4t + 3 = 0[/tex]
This quadratic equation factors as:
(t - 1)(t - 3) = 0
So the particle comes to rest at t = 1 or t = 3.
Next, we need to determine whether the particle is at a maximum or minimum at each of these times.
To do this, we look at the sign of the acceleration:
When t = 1, a(1) = 6(1) - 12 = -6, which is negative.
Therefore, the particle is at a maximum at t = 1.
When t = 3, a(3) = 6(3) - 12 = 6, which is positive.
Therefore, the particle is at a minimum at t = 3.
Finally, we need to find the displacement of the particle at each of these times:
[tex]y(1) = 1^3 - 6(1)^2 + 9(1) = 4[/tex]
[tex]y(3) = 3^3 - 6(3)^2 + 9(3) = 0.[/tex]
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Choose ALL answers that describe the quadrilateral
Answer:
All of the above.
Quadrilateral's must have at the maximum 4 equal sides, or the minimum 2 equal sides.
a square has 4 equal sides.
a rectangle has 2 equal side. (that add up to 4 because each side is a pair of 2)
a rhombus can be a quadrlaterial depending on the shape.
a parrellelogram mostly have atleast 2 equal sides.
and a trapezoid mostly has atleast 2 equal sides.
Hope this helps!
How many square feet are in 288 square inches
{1 inch = 12 square feet}
I need to turn this in, in and hour please help!!!!!
Going from top left to right then bottom left to right
Answers:
1st. answer: 94
2nd. answer: 82
3rd. answer: 142
4th answer: 88.2
5th. answer: 130
6th. answer: 178
(also I relearned how to do triangles)
(I'm going to follow you so if you have any more questions I can help)
Let m represent: Angle A is obtuse
Let n represent: Angle B is obtuse
Which is a symbolic representation of the following argument?
9340
mvn
MAN
omen
mvn
..MAN
O
m-n
MAN
mvn
man
man
mvn
Angle A is obtuse if and only if Angle B is obtuse.
Angle A is obtuse or Angle B is obtuse
Therefore, Angle A is obtuse and Angle B is obtuse.
The symbolic representation of the argument is option B:
(m ↔ n)m ∧ n∴m ∧ nWhat is a logical argument?An argument in logic can be described as any group of propositions of which one is claimed to follow from the others through deductively valid deductions that preserve truth from the premises to the conclusion. Arguments in logic are typically written in symbolic language.
Considering the given statements:
Angle A is obtuse if and only if Angle B is obtuse; (m ↔ n)Angle A is obtuse or Angle B is obtuse; m ∧ n,Therefore, Angle A is obtuse and Angle B is obtuse; ∴m ∧ nLearn more about logical arguments at: https://brainly.com/question/4692301
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x2=441 -1
what wouod it be
Answer:
The answer for x is 11
Step-by-step explanation:
x²=144-1
Square root of both sides
√x²=√144-1
x=12-1
x=11
The way an individual perceives stimuli and the general manner in which he or she responds to it is a __________-_______ style
Answer:
decision-making
Step-by-step explanation:
Select the correct answer.
What is the range of the function graphed below?
A. -∞
B.-2
C. -∞
D.-∞
The range of the function graphed above include the following: D. -∞ ≤ y ≤ 2.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:
Range = {-∞, 2} or -∞ ≤ y ≤ 2.
Domain = {-1, ∞} or -1 < x < ∞.
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What is the area of this tile?
And it isn’t 12 because I did that for the other one and got it wrong.
The area of this tile is 12 cm2.
What is area?Area is a two-dimensional measure of space, referring to the total surface area of a shape. It can be measured in terms of square units, such as square feet, meters, or kilometers. Area is an important concept in geometry and can be used to calculate the perimeter, circumference, and volume of a shape. Area calculations are also used in fields such as engineering, architecture, and construction.
Area is the size of a two-dimensional shape or the amount of space within a three-dimensional figure. It is a measure of how much space an object occupies.
The area of this tile can be calculated using the formula:
Area = Length x Width
In this case, the length of the tile is 6 cm and the width is 2 cm. Therefore, the area of the tile is 12 cm2.
To calculate the area, we multiplied the length and width of the tile. This formula is applicable to all rectangles, as the area of any rectangle is determined by multiplying the length and width.
It is important to note that the units used to measure the length and width must be the same in order to get an accurate area measurement. For example, if the length was measured in inches and the width in centimeters, then the area would be incorrect.
In conclusion, the area of this tile is 12 cm2.
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Pls Help with this question.
Step-by-step explanation:
16x²-1 = (4x-1)(4x+1)
4x²-9 = (2x+3)(2x-3)
16x²-4 = 4(2x+1)(2x-1)
4x²-1 = (2x+1)(2x-1)
16x²+1 = (4x+i)(4x-i)
What is the length of the diagonal from P to Q?
The length of the diagonal from the given shape above would be = 12
How to calculate the length of the diagonal?To calculate the length of the diagonal from P to Q, the Pythagorean theorem should be used such as;
C² = a² + b²
The Pythagorean theorem states that the the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
Therefore;
C = ?
a = 8
b = 9
C² = 8²+9²
C² = 64+81
C² = 145
C = √145
= 12.
Therefore, the length of the diagonal P to Q of the given shape above is 12.
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Marcus fills his tank with premium gasoline. The graph shows the relationship between the number of gallons he puts in the tank and the total cost for the gas.
The equation is given by y = 2.5x. It means that the cost of each gallon of gas is $2.5
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
Let y represent the cost in dollars for x gallons of gas she puts in the tank
The graph passes through point (0, 0) and (3, 7.5), hence:
y - 0 = [(7.5 - 0) / (3 - 0)](x - 0)
y = 2.5x
The equation is given by y = 2.5x
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3-4 If you know the rise and run of a fable roof, you can calculate the rake length and area using slope factors. (True or False)
Given statement "3-4 If you know the rise and run of a fable roof, you can calculate the rake length and area using slope factors." is true. Because the rise and run of a gable roof allows you to calculate the slope factor, which can then be used to calculate the rake length and area of the roof.
If you know the rise and run of a gable roof, you can calculate the rake length and area using slope factors. The slope factor is a ratio that relates the length of the roof to the height of the roof.
The slope factor is calculated by dividing the rise of the roof by the run of the roof. Once you have the slope factor, you can use it to calculate the rake length and area of the roof.
The rake length is the length of the diagonal edge of the roof, and it can be calculated by multiplying the slope factor by the run of the roof.
For example, if the run of the roof is 10 feet and the slope factor is 0.5 (which corresponds to a 6:12 pitch), then the rake length would be 5 feet (0.5 x 10).
The area of the roof can be calculated by multiplying the rake length by the width of the roof.
For example, if the width of the roof is 20 feet and the rake length is 5 feet, then the area of the roof would be 100 square feet.
Statment is true.
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What value of x makes this equation true?
A. x = −48
B. x = 1
C .x =1/2
D. x = 8
The value of x that makes the equation true is 8
What is linear equation?A linear equation is a type of equation that the highest power of it's variable is 1. Example of linear equation include, x+2 =y, x+7/2 =15.
The graph of a linear equation is a straight line and it is represented in form of y = mx+b. Where m is the slope and b is the y intercept.
Solving x-7 = (3/4)x -5
collecting like terms
x-(3/4)x = 7-5
x/4 = 2
x = 8
therefore the value of x that will make the equation x-7 = (3/4)x -5 true is 8.
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Rewrite 84 + 36 in the form
a(b+c)
where a is the greatest common factor of 84 and 36
The GCF of 84 and 36 is 12.
The GCF of two non-zero integers, x(36) and y(84), is the greatest positive integer m(12) that divides both x(36) and y(84) without any remainder.
GCF of 36 and 84 by Listing Common Factors
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
There are 6 common factors of 36 and 84, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 36 and 84 is 12.
Rewrite in the form of a(b + c), a is the greatest common factor of 84 and 36
84/ 12 = 7
36/12 = 3
So, 12(84 + 36)
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1. Triangles
B = 4in, H = 5in
B = 6ft, H= 10ft
B = 12m, H = 15m
Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?
2. Parallelogram (H = height) and (B = base)
H = 9in, B = 6in
H = 5 ft, B = 2ft
H = 7yds, B = 3yds
Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?
Hint: Use the formula. Substitute the given values and then solve as an equation.
3. Rectangle (L = length) and (w = width)
rect. DKIF with L = 8 ft and w = 6 ft
rect. AOPU with L = 13 ft and w = 5 ft
Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.
4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)
rhombus with d1 = 12 yds and d2 = 12 yds
rhombus with d1 = 10 ft and d2 = 25 ft
rhombus with d1 = 16 in and d2 = 22 in
Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?
5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)
b1 = 6 ft, b2 = 7 ft, H = 10 ft
b1 = 5 yds, b2 = 8 yds, H = 4 yds
c. b1 = 9 in, b2 = 11 in, H = 13 in
d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?
The answers are:
1) The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. For the given triangles:
Triangle 1: A = (1/2)(2ft)(4ft) = 4 sq ft (for one tablecloth), so for two tablecloths, the total area is 8 sq ft.
Triangle 2: A = (1/2)(6ft)(10ft) = 30 sq ft, so for two tablecloths, the total area is 60 sq ft.
Triangle 3: A = (1/2)(12m)(15m) = 90 sq m, so for two tablecloths, the total area is 180 sq m.
2) The area of a parallelogram is given by the formula A = Bh, where B is the base and h is the height. Rearranging this formula, we get h = A/B. For the given parallelogram:
A = 78 mm2 and B = 13 mm, so h = 78/13 = 6 mm.
3) The area of a rectangle is given by the formula A = LW, where L is the length and W is the width. For Charles' den:
The total wall space to be painted is (2 x 9 x 15) + (2 x 8 x 10) = 342 sq ft. One gallon of paint covers 440 sq ft, so Charles needs (342/440) = 0.7778 gallons of paint. Therefore, he does not have enough paint.
4) To calculate the total area of the walls to be painted, we can calculate the area of each wall and add them together.
The area of the two walls that are 9 ft high and 15 ft long is (9 x 15) = 135 sq ft each, for a total of 270 sq ft. The area of the other two walls that are 8 ft high and 10 ft long is (8 x 10) = 80 sq ft each, for a total of 160 sq ft. Adding them together, we get a total of 430 sq ft.
Since one gallon of paint covers 440 sq ft of wall space, Charles has enough paint to cover the den walls.
5) The area of a trapezoid is given by the formula A = (1/2)(b1 + b2)h, where b1 and b2 are the bases and h is the height. Rearranging this formula, we get h = 2A/(b1 + b2). For the given trapezoids:
A = (1/2)(6ft + 7ft)(10ft) = 65 sq ft and h = 2(65)/(6ft + 7ft) = 5 ft.
A = (1/2)(5yds + 8yds)(4yds) = 26 sq yds and h = 2(26)/(5yds + 8yds) = 2 sq yds.
A = (1/2)(9in + 11in)(13in) = 143.5 sq in and h = 2(143.5)/(9in + 11in) = 13.05 in.
For the application in part (d), we are given A = 32 km2 and (b1 + b2) = 16 km.
Rearranging the formula for A, we get h = 2A/(b1 + b2). Substituting the given values, we get h = 4
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Amelia is building a fence and wants it to be 40 feet long. Each panel is 8 feet long, and she will need a post at each end and between each panel. If she does NOT plan to buy any extra for waste, how many panels and posts will she need?
Answer:
5 panels6 postsStep-by-step explanation:
You want to know the number of panels and posts needed for a 40 ft fence comprised of 8 ft panels, with a post between panels and at each end of the fence.
PanelsThe number of panels needed is ...
(40 ft)/(8 ft/panel) = 40/8 panels = 5 panels
LayoutThe 5 panels will have 2 ends and 4 spaces, requiring 2 + 4 = 6 posts.
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