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Answer:

173.21m^2

Step-by-step explanation:

So lets figure out how to find the formula for the area of a equilateral triangle.

We can immediatly notice that a equilaterial triangle is really just two right triangles merged together at their heights.

This means that the total area of the equilaterial triangle is equivelent to finding the area of 2 right triangles. this would make the formula:

\(width*height = area\)

This is a fairly simple formula, and works out nicely since our normal right triangle formula for area of  \(\frac{length*width}{2}\) must be multiplied by 2 since there are two right triangles.

The problem is, how we will actually find h, the height.

Each side length of a equilateral triangle equals 1/3 of the perimeter, meaning that each side length is 20.

W, the width of each right triangle is 1/2 of the side length of the equilateral triangle, meaning that the width equals 10.

\(width = 10\)

We also know that the hypotenuse of the triangle is equal to the side length of the equilateral triangle, which means that the hypotenuse equals 20.

\(hypotenuse = 20\)

We can use this to figure out our unknown height, which we can then use to find our area.

We can figure out this height using teh pythagreon theorm, since

\(Hypotenuse=\sqrt{width^2+height^2}\), which we can rewrite to get:

\(Height = \sqrt{hypotenuse^2-width^2}\)

Now we can plug in our hypotenuse and width to solve:

\(Height = \sqrt{20^2-10^2}\)

=

\(Height = \sqrt{400-100}\)

=

\(Height = \sqrt{300}\)

=

Height = 17.321

Now we can solve for the area using the formula from above, \(width*height = area\)

=

\(10*17.321 = 173.21\)

So our area equals 173.21!

Hope this helps! :3

Answer:

2³ · 7

Step-by-step explanation:

Answer:

2x2x2x7

Step-by-step explanation:

56

^  

2   28

   ^

2      14

     ^

2           7

Answer:

Step-by-step explanation:

The 2 angles with x in them are complementary. They add to 90. This is a right triangle.

3x - 14 + 2(3x - 6) = 90       Remove the brackets.

3x - 14 + 6x - 12 = 90          Combine

9x - 26 = 90                        Add 26 to both sides.

9x = 116                               Divide by 9

9x/9 = 116/9

x = 12.89

Answer:

1)Yes

2)No

Step-by-step explanation:

1) 3x^2 = -27

3 (-3)^2 = -27

Once you substitute your value in for x, you can follow the rule PEMDAS to solve the equation.

3 (-9) = -27

-27 =-27

2) 10 - 5x = y

In an ordered pair, the first number is x and the second number is y.

10 - 5 (-4) = 10

10 - 20 = 10

-10 = 10

-10 ≠ 10

PEMDAS: A rule that states solving an equation by the order of operations:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

The first two numbers in each row of the relative frequency table represent the percentage of cars and trucks of a particular color out of the total number of vehicles in the parking lot.

To create a relative frequency table, we need to divide the frequency of each color by the total number of vehicles (65) and then multiply by 100 to get a percentage.

Relative Frequency Table by Color:

The first two numbers in each row must add up to 100% because we are calculating the relative frequency of each color with respect to the total number of vehicles (65). Therefore, the percentage of cars and trucks of each color must add up to 100% of that color's total frequency. The total row must also add up to 100% because it represents the entire population of vehicles.

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The given question is incomplete, the complete question is:

There are 65 vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%. Frequency Table Type of Vehicle Color Car Truck Total Blue 22 14 36 Red 12 17 29 Total 34 31 65

Answer:

Step-by-step explanation:

36 hope it helps

Answer:

48

Step-by-step explanation:

Therefore, the correct answer is: The median of 20 is the most accurate to use, since the data is skewed.

A histogram is a graphical representation of the distribution of a dataset. It is a visual representation of the frequency distribution of continuous or discrete data. The x-axis represents the range of values of the data and is divided into equal intervals called bins or buckets. The y-axis represents the frequency or count of the data values that fall into each bin.

The data in the histogram is skewed to the right, meaning that there are some high values that are pulling the mean up towards them. In this case, the mean is not an accurate measure of center because it is being heavily influenced by the two values of 55.

Therefore, the best measure of center to use in this case is the median, which is less sensitive to extreme values and gives a better representation of the typical donation received by the charity. In this case, the median donation is $20, which is a more accurate representation of the center of the data than the mean.

Therefore, the correct answer is: The median of 20 is the most accurate to use, since the data is skewed.

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The integer number that represents the submarine's depth is given as follows:

-460.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

The concepts of height and depth are given as follows:

A submarine in the middle of the ocean at a depth of 115 feet, hence the integer that represents the initial depth is given as follows:

-115.

The submarine dived to a depth that is four times the initial depth, hence the integer that represents the final depth is given as follows:

4 x -115 = -460.

(meaning that the final depth of the submarine is of 460 feet).

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Answer:

Decrease by 3.9%

Step-by-step explanation:

54,500(1-x) = 52355

x=0.03935... = 3.935% or 3.9%

Answer:

first we subtract his new salary from the old salary to get the decrease.

Then percentage decrease ,we get the decrease over the new salary and multuply by 100. to get the percentage decrease

Answer:

Joel’s is the 28

Step-by-step explanation:

For the one is me cause Zyou KNOW ULTRA,,,!,,,,,,292

Answer:

The equation of the line  that passes through (1,3) and is perpendicular to y=1−2x is y=1/2x+5/2

Step-by-step explanation:

We can rewrite the original equation as y=-2x+1

To find an equation's perpendicular slope, you take the reciprocal of it and negate it, therefore the perpendicular slope is -2 -> 1/-2 -> 1/2

So far, we have y=1/2x+b, but to find the y-intercept, b, we would need to plug in (1,3) and solve for b:

y=1/2x+b

3=1/2(1)+b

3=1/2+b

5/2=b

Therefore, your final equation is y=1/2x+5/2

Answer:

D) a8 = 35 - (n - 1)(3)

Step-by-step explanation:

Answer:

Angle T

Step-by-step explanation:

Because it’s the closest to Angle R

if I'm right the small triangle is similar to the big one so it would be R&T just like Q&U and S&V go together

Answer: 9x+8x-6y

Step-by-step explanation:

Answer:

where r the equations?

Answer:

3(12-x)=6

Step-by-step explanation:

hope that helps !!!!!!!!!!!!!!!!!

Answer: there are 118 dimes in the jar.

Step-by-step explanation: Let's use a system of equations to solve the problem:

Let d be the number of dimes and n be the number of nickels.

We know that:

d + n = 250 (Equation 1) (The total number of coins is 250)

0.1d + 0.05n = 18.4 (Equation 2) (The total value of all coins is $18.4)

To solve for d, we need to eliminate n from the equations above. We can do this by multiplying Equation 1 by -0.05 and adding it to Equation 2:

-0.05d - 0.05n = -12.5

0.1d + 0.05n = 18.4

0.05d = 5.9

Dividing both sides by 0.05, we get:

d = 118

Therefore, there are 118 dimes in the jar.

Answer:

Step-by-step explanation:

5x-4+7x-8=180

12x-12=180

12x=192

x = 16

5(16)-4= 80-4= 76 degrees

7(16)-8= 112-8= 104 degrees

9y  +  5 = 104

9y = 99

y = 11

9(11) + 5 = 99 + 5 = 104

The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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At an angle of 270 degrees (or 3π/2 radians) on a circle with a radius of 2 and center at (0, 0), the x-coordinate is 0 and the y-coordinate is -2.

To find the x and y coordinates at an angle of 270 degrees (or 3π/2 in radian measure) on a circle of radius 2 with center (0, 0), we can use the trigonometric definitions of sine and cosine.

The x-coordinate (x-value) represents the horizontal position on the circle, while the y-coordinate (y-value) represents the vertical position.

For a point on the unit circle (circle with radius 1) at a given angle θ, the x-coordinate is given by cos(θ) and the y-coordinate is given by sin(θ).

In this case, the circle has a radius of 2, so we need to multiply the cosine and sine values by 2 to get the x and y coordinates, respectively.

Using the angle 270 degrees (or 3π/2 in radian measure):

x-coordinate = 2 * cos(3π/2)

y-coordinate = 2 * sin(3π/2)

Evaluating these expressions:

x-coordinate = 2 * cos(3π/2) = 2 * 0 = 0

y-coordinate = 2 * sin(3π/2) = 2 * (-1) = -2

Therefore, at an angle of 270 degrees (or 3π/2 radians) on the circle of radius 2 with center (0, 0), the x-coordinate is 0 and the y-coordinate is -2.

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The given statement is that 30 locusts consume 429 grams of grass in a week.It would take 10 days for 21 locusts to eat 429 grams of grass if they eat at the same rate as 30 locusts.

A direct proportionality exists between the number of locusts and the amount of grass they consume. Let "a" be the time required for 21 locusts to eat 429 grams of grass. Then according to the statement given, the time required for 30 locusts to eat 429 grams of grass is 7 days.

Let's first find the amount of grass consumed by 21 locusts in 7 days:Since the number of locusts is proportional to the amount of grass consumed, it can be expressed as:

21/30 = 7/a21

a = 30 × 7

a = 30 × 7/21

a = 10

Therefore, it would take 10 days for 21 locusts to eat 429 grams of grass if they eat at the same rate as 30 locusts.

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Answer:

i found this so srry if its wrong i saw no one answering this so i wanna help

Step-by-step explanation:

so,  x*(7/100) + (3500 - x)*(4/100) = 197

=> 3x + 14000 = 19700

=> 3x = 19700 - 14000

=> x = 5700/3 = 1900

Sergeant Carlton's monthly pay of $1856.40, using the conversion of the units of time measurement, indicates that his equivalent weekly rate of pay is $464.1

The factors of the units of time, to an accuracy of a day can be presented as follows;

12 months is equivalent to 1 year

4 weeks are equivalent to 1 month

7 days are equivalent to 1 week

However, there are;

52 weeks in a year

365 days in a year

366 days in a leap year.

The amount Sergeant Carlton's is paid per month = $1856.40

The number of weeks in a month, using the time units = 4 weeks

The equivalent weekly pay can be obtained by dividing the amount earned monthly by the number of weeks in a month as follows;

The equivalent weekly pay = $1856.4/4 = $464.1

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Answer:

The answer is,

\(x_3 = 3.31\)

Step-by-step explanation:

We are given the formula,

\(x_{n+1} = (1/x_{n}) + 3\)

Now,

\(x_1 = 5\\Then, finding \ x_2,\\using \ the \ formula,\\x_2 = 1/x_1 + 3\\x_2 = 1/5 + 3\\x_2 = 1/5 + 15/5\\x_2 = (1+15)/5\\x_2 = 16/5\\\)

Now, we find x_3,

Again, using the formula,

\(x_3 = 1/x_2 + 3\\since, x_2 = 16/5, we \ get,\\x_3 = 1/(16/5) + 3\\x_3 = 5/16 + 3\\x_3 = 5/16 + 48/16\\x_3 = (5+48)/16\\x_3 = 53/16\)

To 2 decimal points we get,

\(x_3 = 3.31\)

Answer:

D

Step-by-step explanation:

because Y has to be about 0.4 meters high and the X value has to be 1 meter wide

Answer:

(i) 1/2

(ii) 3/20

Step-by-step explanation:

(i) given total number of white counters = 10

total outcomes = 20 (3+10+5+2)

so it's 10/20

by simplifying it we get 1/2

(ii) given total number of red counters = 3

so it's 3/20

The equation for mass m is a term of d and V is m = dV. The correct answer is A.

The given density d of an object is found by dividing the object's mass m by the volume V.

Option A is correct. The density d of an object can be found by dividing the object's mass m  by its volume V.

Figuratively this is represented by the equation

d = m / V.

Solving this equation for m gives m = dV.

Choices other than A are B, C and D are imprecise and are likely the result of errors made when converting the definition of density into an algebraic equation and errors made when solving that equation for M. If the equations given in choices B, C, and D are all solved in terms of density d, then none of the equations obtained is equivalent to d = m/V.

Thus, the equation lets mass m be a function of d and V when the density d of an object is found by dividing the mass m of the object by its volume V which is m = dV.

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By starting with the assumption that r is a rational number, we showed that r^3 can be expressed as a quotient of integers with a non-zero denominator, which implies that r^3 is a rational number. Therefore, the statement holds true for every rational number.

(a) The statement can be written formally as: "For every rational number r, if r is a rational number, then r^3 is a rational number."

(b) Proof:

1. Suppose r is any rational number.

2. By substitution, r^3 = (a/b)^3, where a and b are integers and b ≠ 0.

3. Simplifying, r^3 = a^3 / b^3.

4. The cube of an integer is an integer, so a^3 is an integer.

5. The cube of a non-zero integer is also non-zero by the zero product property, so b^3 ≠ 0.

6. Therefore, a^3 / b^3 is a quotient of integers with a non-zero denominator.

7. Any quotient of integers with a non-zero denominator is a rational number.

8. Hence, r^3 is a rational number.

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Answer:

Yes it does exist

Step-by-step explanation:

You must be able to add any two sides and get a number greater than the third side in order to be considered a triangle.

In this case that is possible.

Hope this helps!

Answer:

Step-by-step explanation:

−23(3x−4)+3x=5619/6            Remove brackets on the left. Divide by 6 on the right.

-69x - 92 + 3x = 936.5         Combine like terms on the left.

-66x - 92 = 936.5                 Add 92 to both sides

-66x = 936.5 + 92

-66x = 1028.5                       Divide by -66

x = -15 7/12

Answer: 62.5%

Step-by-step explanation:

Given

Ms. Savage ate \(\frac{5}{8}\) of her lunch

i.e. she ate 5 parts of lunch out of 8

In percentage, it is expressed as

\(\Rightarrow \dfrac{5}{8}\times 100=62.5\%\)