Answer:
3w²+2w
Step-by-step explanation:
(9w² +3w)-(6w²+w)
=9w²+3w-6w²-w
collecting like terms
=9w²-6w²+3w-w
=3w²+2w
=w(2+3w)
The
perimeter of a rectangle is 75
ft and the length is 27 ft. What is
the area of the rectangle?
Michelle was instructed to write two equivalent expressions for 6x + 15.
Her work is shown.
6x + 15 = x + x + x + x + x + x + 15
6x + 15 = 6(x + 15)
Part A: Explain which one of Michelle’s equations is true for all values of x and which one of Michelle’s equations is false for all values of x. (2 pts.)
Part B: Write another equivalent expression for 6x + 15.
An equivalent expression for the expression 6x + 15 is 3(2x + 5)
Evaluating the expressionPart A:
The equation 6x + 15 = 6(x + 15) is false for all values of x because it does not follows the distributive property of multiplication over addition.
The equation 6x + 15 = x + x + x + x + x + x + 15 is true for all values of x because it is true when x has a specific value
Part B:
Another equivalent expression for 6x + 15 can be obtained by factoring out the greatest common factor (GCF) of the terms 6x and 15, which is 3:
6x + 15 = 3(2x + 5)
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Answer:
Part A: The equation 6x + 15 = 6(x + 15) is true for all values of x because it follows the distributive property of multiplication over addition. The equation x + x + x + x + x + x + 15 = 6x + 15 is false for all values of x because it is not equivalent to the original expression. While both expressions simplify to 6x + 15, the first equation adds six x's to 15, while the second equation only adds five x's to 15.
Part B: Another equivalent expression for 6x + 15 is 3(2x + 5). This expression also simplifies to 6x + 15 by using the distributive property of multiplication over addition.
Step-by-step explanation:
Find the value of x. If a segment looks like a tangent, it is a tangent.
Using laws of the outside angle theorem, we can find the value of the arc x to be = 130°.
Define outside angle theorem?The measure of an exterior angle is equal to the sum of the measures of the two distant interior angles of the triangle, according to the external angle theorem. According to the exterior angle inequality theorem, any triangle's outside angle has a measure bigger than either of its opposing interior angles.
Here in the question,
As per the outside angle theorem,
50° = 180° - x°
Adding x° on both sides:
⇒ 50° + x° = 180°
Now subtracting 50° from both sides:
⇒ x° = 180° - 50°
⇒ x° = 130°
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Probabilities always lie between _ and _ when in decimal form.
Answer:
0 and 1
Step-by-step explanation:
hope this helps ;)
A candle is in the shape of a cylinder. The candle has a diameter of 3. 5 inches and a height of h inches. Which equation can be used to find V, the volume of this candle in cubic inches?
The volume of the candle is,⇒ V = 31.4 in³.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;A candle in the shape of a cylinder has the dimensions shown, in inches.And, Diameter of candle = 5 in.Height of candle = 8 in.We know that;Volume of cylinder = πr²hHence, We get;The volume of the candle is,⇒ V = 3.14 × (5/2)² × 8⇒ V = 3.14 × 10⇒ V = 31.4 in³.Thus, The volume of the candle is,⇒ V = 31.4 in³.
Please solve number 7 I do not understand it at all. Please and thank you so much.
The equation of the largest circle is given as follows:
x² + y² = 9².
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The largest circle will have the largest radius, while the coefficients of x and y should be both of 1, hence the equation is given as follows:
x² + y² = 9².
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Sally uses a total of 1 cup of liquid for a recipe. She used 2/5 cup of vinegar. And the rest of the liquid was Malik
Sara used 3/5 cup of milk in the recipe. The answer corresponds to option (B) in the given answer choices.
The total amount of liquid used by Sara in the recipe is 1 cup. Out of this 1 cup, Sara used 2/5 cup of vinegar. Therefore, the amount of milk she used would be the difference between the total amount of liquid used and the amount of vinegar used.
Mathematically, we can represent this as:
Amount of milk = Total amount of liquid - Amount of vinegar
Amount of milk = 1 cup - 2/5 cup
Simplifying the expression on the right side, we get:
Amount of milk = 5/5 cup - 2/5 cup
Amount of milk = 3/5 cup
Therefore, Correct option is B.
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Complete question is:
Sara used a total of 1 cup of liquid for a recipe. She used 2/5 cup of vinegar, and the rest of the liquid she used was milk.
How much milk, in cups, did sara use for the recipe?
A) 2/5
B)3/5
C)5/5
D) 1 2/5
A man starts from his home and drives 169 km to the east and then 192 km to the west. How far is he from home finally and in which direction
The man is 23 km west of his home after driving 169 km to the east and 192 km to the west.
To determine how far the man is from his home after driving 169 km to the east and 192 km to the west, we can think of his movements as a displacement vector.
The vector representing the man's movement to the east has a magnitude of 169 km and is directed towards the east. Similarly, the vector representing his movement to the west has a magnitude of 192 km and is directed towards the west.
Since these two vectors are in opposite directions, we can subtract them to find the net displacement vector.
Net displacement = 169 km east - 192 km west
= -23 km west
The negative sign indicates that the net displacement vector is directed towards the west, which means that the man is 23 km west of his home.
To determine the distance between the man and his home, we can use the Pythagorean theorem. Since the man moved only in the east-west direction, the distance between him and his home is the absolute value of the net displacement, which is 23 km.
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2. Given: MNOP is a rectangle.
Show: The diagonals bisect each other, and the diagonals are congruent.
M
P
O
DA
We have shown that the diagonals of rectangle MNOP bisect each other and are congruent.
Describe Diagonal?In geometry, a diagonal is a line segment connecting two non-adjacent vertices of a polygon, such as a triangle, quadrilateral, or higher-order polygon. For example, in a rectangle, the diagonals are the line segments connecting opposite corners.
A diagonal can also refer to a line segment connecting two opposite corners of a three-dimensional solid, such as a cube or rectangular prism.
In many cases, diagonals have important properties and can be used to solve geometric problems. For example, in a rectangle, the diagonals are congruent and bisect each other. In a regular polygon with n sides, the number of diagonals can be calculated using the formula (n(n-3))/2. The length of a diagonal in a right triangle can be found using the Pythagorean theorem.
To show that the diagonals of rectangle MNOP bisect each other, we need to prove that the midpoint of diagonal MP is the same as the midpoint of diagonal NO.
Let's find the coordinates of the midpoints of MP and NO:
Midpoint of MP:
((x1 + x2)/2, (y1 + y2)/2)
= ((-7 + 5)/2, (1 - 7)/2)
= (-1, -3)
Midpoint of NO:
((x1 + x2)/2, (y1 + y2)/2)
= ((5 - 7)/2, (1 - 7)/2)
= (-1, -3)
As we can see, the midpoint of MP and NO are both (-1, -3), which means the diagonals bisect each other.
To show that the diagonals of rectangle MNOP are congruent, we need to find the length of both diagonals and prove that they are equal.
Let's find the length of diagonal MP:
MP = √((5 - (-7))² + ((-7) - 1)²)
= √(12² + (-8²)
= √(144 + 64)
= √(208)
Let's find the length of diagonal NO:
NO = √((5 - (-7))² + (1 - (-7)²)
= √(12² + 8²)
= √(144 + 64)
= √(208)
As we can see, the length of both diagonals is sqrt(208), which means the diagonals are congruent.
Therefore, we have shown that the diagonals of rectangle MNOP bisect each other and are congruent.
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The graph shows f(x). The absolute value function g(x) is described in the table.
The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 1, a point at negative 1 comma 2, and a point at 1 comma 2.
x g(x)
−4 0
−2 −2
0 −4
2 −2
4 0
If g(x) = f(x) + k, what is the value of k?
k = −5
k = −4
k = 4
k = 5
The value of k given the absolute value functions is (a) k = -5
Given that
graph = f(x)
table = g(x)
Since the vertex of the function f(x) is at (0,1), we have f(0) = 1.
Also, from the given table, we have g(0) = -4.
Therefore, if g(x) = f(x) + k, we must have g(0) = f(0) + k = 1 + k.
But we also know that g(0) = -4. Thus, we have:
1 + k = -4
Solving for k, we get:
k = -5
Therefore, the value of k is -5.
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pls give me an answer
The surface area for each package is given as follows:
Package A: 492 in².Package B: 404 in².Hence:
Package A has the greater surface area.
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
For Package A, the dimensions are given as follows:
l = 14 in, h = 12 in, w = 3 in.
Hence the surface area is given as follows:
S = 2 x (12 x 3 + 14 x 3 + 12 x 14)
S = 492 in².
For Package B, the dimensions are given as follows:
l = 11 in, h = 6 in, w = 8 in.
Hence the surface area is given as follows:
S = 2 x (11 x 6 + 11 x 8 + 6 x 8)
S = 404 in².
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Write a porportion that you can use to convert 60 inches to centimeters
Answer:
152.4 centimeters.
Step-by-step explanation:
1 inch = 2.54 centimeters
60 inches = x centimeters
Where x is the number of centimeters equivalent to 60 inches.
To solve for x, we can set up a proportion:
1 inch / 2.54 centimeters = 60 inches / x centimeters
Cross-multiplying, we get:
1 inch * x centimeters = 2.54 centimeters * 60 inches
Simplifying, we get:
x = (2.54 cm/in) * (60 in)
x = 152.4 cm
Therefore, 60 inches is equivalent to 152.4 centimeters.
Can you pls help? This is geometry
The equation of the circle centered at (4, -5) with radius 7 is (x - 4)²+ (y + 5)² = 49.
Define circleA circle is a two-dimensional form that may be described as a collection of points (locus) that are equally spaced apart from a central fixed point. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points at a certain radius from the centre.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)² + (y - k)²= r²
In this case, the center of the circle is (4, -5), and the radius is 7. So the equation of the circle is:
(x - 4)² + (y - (-5))² = 7²
(x - 4)² + (y + 5)² = 49
Therefore, the equation of the circle centered at (4, -5) with radius 7 is (x - 4)² + (y + 5)² = 49.
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 3 and DC = 9, what is the length of AC?
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 3 and DC = 9, the length of AC is: 4 units.
How to find the length?In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. Let's call the length of the hypotenuse AC as x, and the length of the segment containing point B as y. Then, the length of the other segment containing point C is x - y.
Using similar triangles, we can set up the following proportion:
BD/DC = y/(x - y)
Substituting the given values, we get:
3/9 = y/(x - y)
Simplifying this equation, we get:
x - y = 3y/9
x = 4y/3
We also know from the Pythagorean theorem that:
AC^2 = AB^2 + BC^2
Since triangle ABC is a right triangle, we have:
AB^2 + BC^2 = x^2
Substituting x = 4y/3, we get:
AB^2 + BC^2 = (4y/3)^2
But we also know that:
AB/BC = 3/4
So we can set up another proportion:
AB/BC = y/(x - y)
Substituting x = 4y/3, we get:
AB/BC = y/(4y/3 - y)
Simplifying this equation, we get:
AB/BC = y/((4/3)y - y)
AB/BC = y/((1/3)y)
AB/BC = 3
So we have:
AB = 3BC
Substituting this into AB^2 + BC^2 = (4y/3)^2, we get:
(3BC)^2 + BC^2 = (4y/3)^2
10BC^2 = 16y^2/9
But we also know that:
BC^2 + y^2 = x^2
Substituting x = 4y/3, we get:
BC^2 + y^2 = (4y/3)^2
5BC^2 = 7y^2/9
Combining this with 10BC^2 = 16y^2/9, we get:
15BC^2 = 21y^2/9
BC^2 = (7/3)y^2/3
Substituting this into BC^2 + y^2 = (4y/3)^2, we get:
(7/3)y^2/3 + y^2 = 16y^2/9
7y^2/9 + 9y^2/9 = 16y^2/9
16y^2/9 = 16y^2/9
So this equation is true for any value of y. Therefore, the length of AC is:
AC = x = 4y/3
Substituting y = BD = 3, we get:
AC = 4(3)/3 = 4
Therefore, the length of AC is 4 units.
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11. You have a bank account in which
your balance increases annually at a rate of 7.25%. If your initial
investment was $250, write an
equation that represents your
balance after x years.
Initial Value (a):
Rate (r):
Time (x):
Equation:
The equation that represents your balance after x years is: [tex]250 * (1.0725)^x[/tex]
what is interest ?
To calculate simple interest, multiply the principal by the rate of interest rates, the duration, and several other variables. The marketing formula is simple returns = capital + interests + hours.
Initial Value (a): $250
Rate (r): 7.25% per year (or 0.0725 as a decimal)
Time (x): x years
The formula for calculating the balance after x years is:
[tex]Balance = a * (1 + r)^x[/tex]
Plugging in the values, we get:
[tex]Balance = 250 * (1 + 0.0725)^x[/tex]
So the equation that represents your balance after x years is:
[tex]Balance = 250 * (1.0725)^x[/tex]
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Question 4
Davey is setting up a retirement account, planning to invest $5,000 per year. Assume the account earns 9.35%. He will keep these deposits up for the first 20 years, and then stop making deposits, leaving the account open for another 20 years. Based on these assumptions, how much will he have in the account at the end of 40 years?
Hence, after 40 years, Davey will have $1,476,289.64 in his retirement account as n = the number of cycles.
what is unitary method ?A problem-solving strategy known as the unitary technique is determining the worth of one unit of such a quantity and utilising that value to determine the value of an other number of units related to that quantity. For issues where the price of one unit is given and the value of some other quantity is needed, it is a proportionality strategy. The unitary method's fundamental principle is to establish a ratio between two numbers, where one of the numbers is represented in the form of one unit while the other quantity is defined in terms of a greater number of units.
given
If Davey doesn't add any more money to his retirement account for the next 20 years, it will increase to:
[tex]FV = P * (1 + r)^n[/tex]
where FV is the lump sum's future value
P is the lump sum's present value, which in this example is $214,111.26.
R is the annual interest rate, which in this case is 9.35%.
n = the number of cycles (in this case, 20 years)
The following equation can be used to determine Davey's retirement account's potential value after 40 years:
[tex]FV = 214,111.26 * (1 + 0.0935)^20 = $1,476,289.64[/tex]
Hence, after 40 years, Davey will have $1,476,289.64 in his retirement account as n = the number of cycles.
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using complete sentences, explain which function has the greatest y-intercept.
Answer:
Step-by-step explanation:
To determine which function has the greatest y-intercept, we need to look at the constant term, which represents the y-intercept, of each function. The function with the largest constant term will have the greatest y-intercept.
For example, consider the following three functions:
1. f(x) = 2x + 5
2. g(x) = 3x - 7
3. h(x) = -4x + 10
The constant term for each function is 5, -7, and 10 respectively. Therefore, h(x) has the greatest y-intercept of 10, since its constant term is larger than those of f(x) and g(x).
Suppose that water is poured into a tank at a rate of 2000t 1000 gallons per minute for t > 0. If the tank started with 5000 gallons of water how much water is in the tank after 4 minutes
There is a volume of 14,000 gallons of water in the tank after 4 minutes.
To answer your question, let's consider the given terms: the rate at which water is poured into the tank (2000t + 1000 gallons per minute) and the initial volume of water in the tank (5000 gallons).
Since the rate is given in terms of time t, we can find the volume of water poured in after 4 minutes by plugging t = 4 into the rate equation:
Volume poured in 4 minutes = 2000(4) + 1000
Volume poured = 8000 + 1000
Volume poured = 9000 gallons
Now, add this to the initial volume of water in the tank:
Total water in tank after 4 minutes = Initial volume + Volume poured
Total water = 5000 + 9000
Total water = 14,000 gallons
So, after 4 minutes, there are 14,000 gallons of water in the tank.
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How can I find the length of AB
To find line segment AB, you'd have to use the principle of proportions. Thus, Line AB is 10.5.
What is the explanation for the above response?To derive line segment AB,
6/4 = AB/7
To solve for AB, we can cross-multiply and simplify:
6/4 = AB/7
Multiply both sides by 7:
(6/4) * 7 = AB
Simplify:
10.5 = AB
Therefore, AB is equal to 10.5.
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a lot is in the shape of a right triangle. the shorter leg measures 150 m. the hypotenuse is 50 m longer than the length of the longer leg. how long is the longer leg?
Answer:
Starting with the 3-4-5 right triangle, multiply all lengths by 50, obtaining 150, 200, and 250. So the length of the longer leg is 200 meters.
Find the value of X.
Answer:
92.5°
Step-by-step explanation:
You want the angle where chords cross, given that they intercept arcs of 55° and 130°.
Chord angleThe angle x° is the average of the measures of the intercepted arcs:
x° = (55° +130°)/2
x° = 92.5°
What is 117 15% of what number, please give a step-by-step explaination!
Answer:
780
Step-by-step explanation:
To find out what number 117 is 15% of, you can use the following formula
(15/100) x n = 117
where n is the number you're trying to find.
To solve for n, you need to isolate it on one side of the equation. You can do this by dividing both sides by (15/100):
n = 117 / (15/100)
n = (117 x 100) / 15
n = 11700 / 15
n = 780
Therefore, 117 is 15% of 780.
Can someone help me find the area of this shaded shape?
sketch three solutions, with initial values y(0) > 0, y(0) = 0, and y(0) < 0.
To sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we'll need to use a differential equation or system of differential equations. So, to sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we would first draw a slope or direction field for our differential equation. Then, we would start at the point (0, y(0)) and follow the direction of the slope or arrow to sketch the solution for each initial value.
To sketch three solutions with the given initial values, follow these steps:
1. Determine the differential equation you're working with. For example, let's consider the equation y'(t) = y(t). This is just an example, and the process will be similar for other differential equations.
2. Solve the differential equation to obtain a general solution. In our example, the general solution is y(t) = C * e^t, where C is an arbitrary constant.
3. Apply the initial values to find specific solutions:
a. For y(0) > 0, choose a positive value for C, such as C = 1. The specific solution is y(t) = e^t.
b. For y(0) = 0, choose C = 0. The specific solution is y(t) = 0.
c. For y(0) < 0, choose a negative value for C, such as C = -1. The specific solution is y(t) = -e^t.
4. Sketch the three solutions on the same graph:
a. For y(t) = e^t, draw a curve that starts at (0,1) and increases exponentially as t increases.
b. For y(t) = 0, draw a horizontal line at y = 0.
c. For y(t) = -e^t, draw a curve that starts at (0,-1) and decreases exponentially (toward 0) as t increases.
These three curves represent the solutions with the specified initial values. Note that this process assumes you have a specific differential equation in mind. If you have a different equation, just follow the same steps to find and sketch the solutions.
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The chef at Pickin' Chicken Café bought 4 bunches of celery that each weighed 2 pounds. She cut up 3 pounds to serve with chicken wings. Then, she diced 8 ounces to put on garden salads. How many pounds of celery does she have left?
As per the unitary method, the chef has 9.14 pounds of celery left after cutting up 3 pounds to serve with chicken wings and dicing 8 ounces to put on garden salads.
To start, let's convert all of the weights to the same units. The chef bought 4 bunches of celery, each weighing 2 pounds, so in total she bought:
4 bunches * 2 pounds per bunch = 8 pounds
Next, we know that she used 3 pounds of celery for the chicken wings and 8 ounces (which is half a pound) for the garden salads. So in total she used:
3 pounds + 0.5 pounds = 3.5 pounds
To find the value of one pound of celery, we can subtract the amount of celery the chef used from the total amount of celery she bought, and then divide by the number of pounds she bought:
(8 pounds - 3.5 pounds) / 8 = 0.4375 pounds per pound
So one pound of celery is worth 0.4375 pounds. Now we can use this value to find out how many pounds of celery the chef has left. We know she started with 8 pounds of celery, and she used 3.5 pounds, so she must have:
(8 pounds - 3.5 pounds) / 0.4375 pounds per pound = 9.14 pounds left
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Angles X and Y are supplementary. Angle X measures 115. 75° and angle Y measures (m − 8)°. Find m∠Y
The measure of angle Y is m - 8 = 72.25 - 8 = 64.25 degrees.
What is the supplementary angle?
Two angles are said to be supplementary if their sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary, then:
A + B = 180.
Since angles X and Y are supplementary, their measures add up to 180 degrees. So we have:
X + Y = 180
Substituting the given values, we get:
115.75 + (m - 8) = 180
Simplifying, we get:
m - 8 = 180 - 115.75
m - 8 = 64.25
Adding 8 to both sides, we get:
m = 72.25
Therefore, the measure of angle Y is m - 8 = 72.25 - 8 = 64.25 degrees.
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A pizza with a diameter of 18 inches is cut into 10 equal slices. To the nearest square inch , what is the area of each slice of pizza
If a pizza with an 18-inch diameter is divided into 10 equal pieces, then each slice will have a surface area of roughly 25.45 square inches.
What is diameter?Diameter is defined as a straight line across the middle of a body or figure, particularly a circle or sphere. Pizza diameter is the length of a straight line that touches two locations on the edge of a pizza pie and passes through its center.
Each sector of the pizza, which is divided into 12 equal sections, has an arc measurement of 360/10= 36 degrees.
As = (360÷Ф) ×X r² where x is the measure of the intercepted wave, yields the area of a sector.
We know that x=36 and
d=18→r=9 in. Thus, r is the radius and A is the area of each intersecting arc of a sector.
A=1/10×81π
then each slice will have a surface area of roughly 25.45 square inches.
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URGENT - Will also give brainliest to simple answer
Find the length of the arc that outlines the sector
Answer:
4 or ≈ 12.6
Step-by-step explanation:
L = r * θ
r = 12
θ = 60 = (/3) when converted to radians by multiplying (/180)
then multiply
(/3)*12 = 4 or ≈ 12.6
Jackson takes a marker and draws an arrow at the top of his yo-yo, pointing it toward the string when it is all wound up. The location of the arrow on the yo-yo can be represented by a cosine function.
Answer:
Step-by-step explanation:
see it simple it's not asking quite much if I do my calculation right it would be 8[tex]\pi[/tex]
Find the area of an equilateral triangle with a perimeter of 45 inches.
The area of the equilateral triangle is approximately 58.78 square inches.
An equilateral triangle has all sides equal, so we can divide the perimeter by 3 :
45 inches ÷ 3 = 15 inches
Therefore, each side of the equilateral triangle measures 15 inches.
Area = (√3 / 4) x (side length)²
After putting the values,
Area = (√3 / 4) x 15 x 15 square inches
Area = (√3 / 4) x 225 square inches
Area = 58.78 square inches
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