In two similar polygons, the ratio of their areas is the square of the ratio of their sides. If the sides of any polygon are a and b then :
Ratio of area =[tex] a^{2} :b^{2} [/tex]
Given ratio of area =81:64
Or 81:64=[tex] a^{2} :b^{2} [/tex]
Taking root of both sides
9:8=a:b
The ratio of perimeter of any two similar polygon is equal to the ratio of sides.
Ratio of perimeter = a:b
Perimeter of first polygon is 32 cm.
Let the perimeter of second polygon be x.
32:x=a:b
Or, 32:x=9:8
[tex] \frac{32}{x} =\frac{9}{8}
[/tex]
Cross multiplying
9x= (32)(8)
9x=256
Dividing both sides by 9
x=28.4.
The perimeter of second polygon is 28.4cm.
the measure of two supplementary angles have a ratio of 5:4. What is the measure of the larger angles?
Two angles are supplementary. If one measures x and the other angle measures x+ 30, what is the value of x ?
Chris is twice as old as Don, and next year the sum of their ages will be four times as much as Don’s age last year. Find their present ages.
Answer:
Chris is 12 years old and Don is 6 years old.
Step-by-step explanation:
;)
The present age of Don is 6 years old and Chris age is 12 years.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's denote Don's current age as x.
As Chris is twice as old as Don, Then, Chris's current age is 2x.
Next year, their ages will be x+1 and 2x+1 respectively.
The sum of their ages will be four times as much as Don’s age last year.
(x+1) + (2x + 1) = 4(x-1).
Expanding and solving for x:
3x + 2 = 4x - 4
x = 6
So, Don is 6 years old and Chris is 2×6 = 12 years old.
Hence, the present age of Don is 6 years old and Chris age is 12 years.
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Why is it more difficult to use repeated addition when multiplying two mixed numbers than it is to use repeated addition when you are multiplying a mixed number by a whole number?
The reason why it is more difficult to use repeated addition when multiplying two mixed numbers than it is to use repeated addition when you are multiplying a mixed number by a whole number is:
There is a whole number of groups of the mixed number. Ex: 1 1/2 x 3 would be 3 groups of 1 1/2, so 1 1/2 + 1 1/2 + 1 1/2.What is Multiplication?This refers to the mathematical operation that involves to find the product of a set of numbers.
What is Mixed Number?This refers to the type of number that is made up of a whole number and a proper fraction, for example,2 [tex]1/4[/tex].
With this in mind, if we have mixed numbers like 1 1/2 x 2 1/2, and we were to use repeated addition to multiply them, we would have 2 whole groups of 1 1/2, but then we would need to represent 1/2 group which requires multiplying or dividing first.
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different varieties of field daisies have numbers of petals that follow a fibonacci sequence.Three varieties have 13,21, and 347 petals.
How many petals do the next two varieties of field daisy have?
a. 42, 55
b. 47,60
c. 42,50
d. 55,89
Answer: D
55,89
I just did it and I got it right
Step-by-step explanation:
if a=37 degrees and b=6, find a.
A. 3.4
B. 4.5
C. 6.1
D. 2.5
To find the value of 'a' when a = 37 degrees and b = 6, trigonometry principles are used to calculate 'a' as approximately 34.08 degrees.
Given: a = 37 degrees and b = 6. To find a.
Using trigonometry: We can use the trigonometric ratio tangent to find a. tan(a) = b/c, where c is the hypotenuse. So, tan(37) = 6/c. Therefore, c = 6/tan(37) = 8.37. Hence, a = tan-1(b/c) = tan-1(6/8.37) ≈ 34.08 degrees.
Answer: Therefore, a = 34.08 degrees.
This year Cornell’s class took one more than three times as many field trips as last years class. This year Cornell’s class took a total of 7 trips. How many trips did his class take last year
To find the number of field trips Cornell's class took last year, we set up the equation 3x + 1 = 7, where x represents the number of trips last year. Solving this, we find that Cornell's class took 2 field trips last year.
The question involves a basic mathematical equation to determine the number of field trips taken by Cornell's class last year. Since this year Cornell's class took 7 trips, and this number is one more than three times the amount of the previous year, we can set up the equation as x being the number of trips taken last year:
3x + 1 = 7
To find x, subtract 1 from both sides of the equation:
3x = 7 - 1
3x = 6
Now divide both sides by 3 to solve for x:
x = 6 / 3
x = 2
So, Cornell's class took 2 field trips last year.
Find the volume of the rectangular prism
23 in.3
297 in.3
318 in.3
159 in.3
Plz help!!
help please 40 points per question
Each edge of a cube measures 4.7 in. What is the surface area of the cube? Enter your answer, as a decimal, in the box.
The measure of an edge of a cube = 4.7 in
We have to determine the surface area of the cube.
The surface area of a cube is the area of the six squares that cover it. The area of one square is [tex] a^{2} [/tex]. Therefore, area of six squares = [tex] 6a^{2} [/tex].
Surface area of cube = [tex] 6a^{2} [/tex] , where a is the edge of a cube
Therefore, Surface area of this cube
= [tex] 6a^{2} [/tex]
= [tex] 6 \times (4.7)^{2} [/tex]
= 132.54 square inches.
Therefore, surface area of the cube is 132.54 square inches.
The value of the digit in the hundreds place in the number 653841 is 1/10 the value of the digit in the thousands place in which number?
A) 748917
B) 749817
C) 784917
D) 797481
Jeannie ate 1/4 of an apple.kelly ate 2/4 of the apple.how much did they eat together
Answer:
3/4
Step-by-step explanation:
if a triangle has side lengths of 22,32,and 55 units what type of triangle is it
acute,obtuse,right,no solution
A triangle with side lengths of 22, 32, and 55 units is an obtuse triangle.
Explanation:A triangle with side lengths of 22, 32, and 55 units is an obtuse triangle.
To determine the type of triangle, we can use the Pythagorean theorem. If the sum of the squares of the lengths of the two shorter sides is greater than the square of the length of the longest side, then the triangle is obtuse. In this case, 22^2 + 32^2 = 484 + 1024 = 1508, which is greater than 55^2 = 3025, so the triangle is obtuse.
An obtuse triangle is a triangle with one angle greater than 90 degrees. In this case, the angle opposite the longest side will be greater than 90 degrees.
What is the median of the numbers 8.7, 8.7 8.9, 9.0, 9.1, 9.2? I know I'm supposed to find the middle number, but there's an even amount of numbers here. So I'm supposed to find the average of the two middle numbers, which are 8.9 & 9.0. What does it mean when it says I'm supposed to "find the AVERAGE of the two middle values"?
simplify the expression 3 b 7 3b 21
a salesperson has averaged $120 in commissions for each of the past ten days. For how many days must her commissions average $160 in order to bring her overall average to %150?
Can someone please help me answer theses questions
Thank u so much
how do I do identify calculate the area and perimeter for quadrilaterals
To calculate the area and perimeter of a quadrilateral, you need to know the shape of the quadrilateral and the lengths of its sides. The area can be calculated using different formulas depending on the shape, such as trapezoid, rectangle, parallelogram, or square. The perimeter is calculated by adding the lengths of all the sides.
To calculate the area and perimeter of a quadrilateral, we need to know the shape of the quadrilateral and the lengths of its sides.
1. Area:
Trapezoid: The area of a trapezoid can be calculated using the formula A = (base1 + base2) × height / 2, where base1 and base2 are the lengths of the parallel sides, and height is the distance between the parallel sides.Rectangle: The area of a rectangle is calculated by multiplying its length by its width, so A = length × width.Parallelogram: The area of a parallelogram is calculated using the formula A = base × height, where base is the length of one side and height is the perpendicular distance between the base and the opposite side.Square: The area of a square is calculated by multiplying the length of any side by itself, so A = side × side.2. Perimeter:
Trapezoid: The perimeter of a trapezoid is calculated by adding the lengths of all its sides.Rectangle: The perimeter of a rectangle is calculated by adding the lengths of its four sides, so P = 2 × length + 2 × width.Parallelogram: The perimeter of a parallelogram is calculated by adding the lengths of its four sides.Square: The perimeter of a square is calculated by multiplying the length of one side by 4, so P = 4 × side.fill in the blank with a symbol that makes this statement true 5/12 and 1/3
Caitlin says that AC is the longest segment of fencing
Solve the equation
5m-10n=20
sos
thanks in advance
I need help on this one please
Please help and explain
Please help.
Frank is buying his first car and is stuck on what color it should be. He has to choose between three shades of green, two shades of blue or r two shades of purple. What is the probability he will choose a green car?
a used car lot has all vehicles on sale at a 15% discount. Which expression can be used to find the sale price of a vehicle with an original price of p dollars?
Answer:
a
Step-by-step explanation:
m,n
The required expression for the sales price is 0.85p.
Given that,
A used car lot has all vehicles on sale at a 15% discount. Which expression can be used to find the sale price of a vehicle with an original price of p dollars is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Cost price is the price the buyer pays to the seller for an object or product.
Here,
The original sales price of the card is p dollars,
There is a 15% discount on the sale of cars,
15 % discount,
= p 15/100
= 0.15p
Now, price after discount,
= p - 0.15p
= 0.85p
Thus, the required expression for the sales price is 0.85p.
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A group of children each rode a horse to the bottom of the canyon. They had 20 eyes and 30 legs between them, how many horses were there
You can calculate that, since all children and horses have two eyes, and that children have two legs and horses have four, and the total number of eyes is 20 and the total number of legs is 30, there were 5 children and 5 horses.
Explanation:This problem can be solved using basic algebra. We need to count the numberOfChildren and numberOfHorses in a manner where each child and each horse contribute two eyes and with each child having two legs while each horse has four legs.
Let's make two assumptions:
numberOfChildren = number of children numberOfHorses = number of horsesSo, we can write two equations according to the question:
The total number of eyes = 20 (which implies that numberOfChildren + numberOfHorses = 10, because each creature, whether child or horse, has two eyes)The total number of legs = 30 (which implies that 2*numberOfChildren + 4*numberOfHorses = 30, as each child has two legs and each horse has four)By solving these two equations, we find that the numberOfChildren = 5 and numberOfHorses = 5.
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The table shows summary statistics for the dollar amounts spent by customers at two store locations over a period of 2 weeks.
Location Mean amount spent ($) Range ($)
A 84 15
B 97 25
Which conclusion is true?
Answer:
A.
Step-by-step explanation:
A hot water heater measures 20" in diameter. What is the area of a metal base for the water heater, assuming a 2 inch overhang around the base of the water heater? (Round to the nearest tenth.) square inches.
If you add the extra 2 inches in each side and give the base a diameter of 24. The area comes out to 452.39. The answer is 452.39.
Area of the metal base of the water heater is equals to 452.6 square inches.
What is area of a circle?
"Area of a circle is the region enclosed by the circle in two dimensional plane."
Formula used
Area of a circle = πr²
Value of π = 22 /7
According to the question,
Given diameter = 20 inches
2 inches extended around the base of the water heater
New diameter = 24 inches
Therefore, radius = 12inches
Substitute the value of radius and π in the formula we get ,
Area of the base of the water heater = ( 22/ 7) ×(12)²
= 452.57 square inches
= 452.6 square inches (nearest tenth)
Hence, area of the metal base of the water heater is equals to 452.6 square inches.
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which one is it. please answer