help me with this please

The area of the largest equilateral triangle that can be inscribed in a square of side length 1 unit is (1/4) * √3 square units.

To find the area of the largest equilateral triangle that can be inscribed in a square of side length 1 unit, follow these steps:

1. Draw an equilateral triangle inside the square with one of its vertices touching the midpoint of the bottom side of the square, and the other two vertices touching the midpoints of the other two sides.

2. The height (h) of the equilateral triangle can be found using Pythagorean theorem. Since the triangle is equilateral, it can be split into two 30-60-90 right triangles. In this case, the shorter leg (a) is half the side length of the square (1/2), and the longer leg (b) is the height of the equilateral triangle (h).

3. In a 30-60-90 triangle, the ratio of the sides is a:b:h = 1:√3:2. Therefore, we can write the equation:

1/2 : h : 1

4. To find the value of h, we can set up the proportion:

(1/2) / h = 1 / √3

5. Cross-multiply to solve for h:

h = (1/2) * √3

6. Now we can find the area (A) of the equilateral triangle using the formula:

A = (1/2) * base * height

In this case, the base is the side length of the square (1 unit) and the height is h:

A = (1/2) * 1 * ((1/2) * √3)

7. Simplify the expression:

A = (1/4) * √3 square units

So, the area of the largest equilateral triangle that can be inscribed in a square of side length 1 unit is (1/4) * √3 square units.

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(a) Annually compounded interest:

In this case, n = 1 (compounded once a year)

Future Value (a) = $500 × (1 + 0.12 / 1)^(1 * 20)

(b) Quarterly compounded interest:

In this case, n = 4 (compounded four times a year)

Future Value (b) = $500 × (1 + 0.12 / 4)^(4 * 20)

(c) Monthly compounded interest:

In this case, n = 12 (compounded twelve times a year)

Future Value (c) = $500 × (1 + 0.12 / 12)^(12 * 20)

Let's calculate the values:

(a) Future Value (annually) = $500 × (1 + 0.12)^20

Future Value (annually) ≈ $500 × 6.1917364224

Future Value (annually) ≈ $3,095.87

(b) Future Value (quarterly) = $500 × (1 + 0.12 / 4)^(4 * 20)

Future Value (quarterly) ≈ $500 × 1.03^80

Future Value (quarterly) ≈ $500 × 10.0626534032

Future Value (quarterly) ≈ $5,031.33

(c) Future Value (monthly) = $500 × (1 + 0.12 / 12)^(12 * 20)

Future Value (monthly) ≈ $500 × 1.01^240

Future Value (monthly) ≈ $500 × 20.1814079986

Future Value (monthly) ≈ $10,090.70

Therefore, if Iona earns 12% interest compounded annually, her investment of $500 will grow to approximately $3,095.87 in 20 years. If compounded quarterly, it will grow to approximately $5,031.33, and if compounded monthly, it will grow to approximately $10,090.70.

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Answer:

1.3

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

There were 64 boys

Step-by-step explanation:

80/(4+1) is 16.

16*4 is 64

pls mark me brainliest if this helps :)

Answer:

15t+12r

Step-by-step explanation:

you have to do like term like -8t and-7t that is like term so the next like term is 3r and -9r

The giraffe is 15 feet tall based on the relation between the length of neck of giraffe and it's height.

Firstly convert the mixed fraction to fraction.

Length of neck of giraffe = (4×2)+1/2

Length of neck = 9/2 feet

Now, let us assume the height of giraffe be x. So, equation will be -

30% × x = 9/2

Rewriting the equation

30/100 × x = 9/2

Cancelling zero

3x/10 = 9/2

Again rewriting the equation

x = 90/6

Performing division on Right Hand Side of the equation

x = 15 feet

Thus, height of giraffe is 15 feet.

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Answer:

The answer is A

Step-by-step explanation:

The reason A is correct is because all of the other transformations change the size of the triangle, and A is the only answer that only reflects the image over the y axis without changing it, thus making it similar to the preimage

Steve spent 2/3 of $15, to find how much this 2/3 of $15 is, we have to multiply $15 by 2/3, as follows:

Therefore, we have found that Steve already spent $10 .

Answer: 23.1

Step-by-step explanation:

By the inscribed angle theorem, we know the measure of arc DC is 120 degrees. So, we can set 120=7x-42.

162 = 7x

x = 162/7, which is about 23.1

The most general solution to the original nonhomogeneous differential equation is y = y_h + yp = c1e^(-2x)cos(x) + c2e^(-2x)sin(x) + 2x - 3e^(-x), where c1 and c2 are arbitrary constants.

To find a particular solution to the nonhomogeneous differential equation y'' + 4y' + 5y = 10x + 3e^(-x), we can use the method of undetermined coefficients.

First, we find the complementary homogeneous equation by setting the right-hand side to zero: y'' + 4y' + 5y = 0. The characteristic equation is r^2 + 4r + 5 = 0, which has roots r = -2 ± i. Therefore, the general solution to the homogeneous equation is y_h = c1e^(-2x)cos(x) + c2e^(-2x)sin(x), where c1 and c2 are arbitrary constants.

To find a particular solution, we assume that yp has the same form as the nonhomogeneous terms, i.e., yp = Ax + Be^(-x), where A and B are constants to be determined. Substituting this into the nonhomogeneous equation, we get:

y'' + 4y' + 5y = 10x + 3e^(-x)
-Be^(-x) + 4A - 4Be^(-x) + 5Ax + 5Bx = 10x + 3e^(-x)

To satisfy this equation, we set the coefficients of the like terms on both sides equal to each other:

5A = 10, which gives A = 2
-4B + 5B = 3, which gives B = -3

Therefore, the particular solution is yp = 2x - 3e^(-x).

The most general solution to the original nonhomogeneous differential equation is y = y_h + yp = c1e^(-2x)cos(x) + c2e^(-2x)sin(x) + 2x - 3e^(-x), where c1 and c2 are arbitrary constants.

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The total surface area of the rectangle is 36.4583125cm squared.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The surface area of the rectangle can be calculated by multiplying the length of each side by itself. Since the diameter of the rectangle is 2.75cm, each side of the rectangle would be half of the diameter, or 1.375cm. To calculate the surface area, we must then multiply 1.375cm by 1.375cm, which equals 1.8983125cm squared. When combined with the original area of 34.56cm squared, the total surface area of the rectangle is 36.4583125cm squared.

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The numbers of large bowl sold at the fair is 20

Data;

To solve this problem, we need to write system of equations for this.

Let x represent the numbers of small ceramic bowl

let y represent the numbers of large ceramic bowl

\(x+y=32...eq (i)\\18x + 35y = 916 ...eq(ii)\)

From equation (i), let's make x the subject of formula

\(x + y = 32\\x = 32 - y...eq(iii)\)

Let's substitute equation (iii) into equation (ii)

\(18x+35y = 916\\x = 32 - y\\18(32 -y) + 35y = 916\\576- 18y + 35y = 916\\17y = 916 - 576\\17y = 340\\\frac{17y}{17} = \frac{340}{17}\\ y = 20\)

The numbers of large bowl sold at the fair is 20

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The capital includes :

Any financial contribution made to a business to assist in achieving and advancing its commercial goal is referred to as a capital investment. The phrase may also refer to a long-term purchase made by a company, such as one for land, equipment, businesses, etc.

When a corporation issues securities to equity investors and debt to bondholders, the total amount of debt and capital lease obligations are added to the amount of stock given to investors to determine the overall amount of money raised. This amount is referred to as invested capital. The balance sheet of the business does not include an item for invested capital because debt, capital leases, and stockholders' equity are all stated separately.

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Answer:

Multiply (3x - 5x) by 3

Step-by-step explanation:

First Step:

Multiply (3x - 5x) by 3

Answer:

3.25 pounds

Step-by-step explanation:

x + 4 (1/2) + 3 (1/2) = 11

x + 4.25 + 3.5 = 11

x + 7.75 = 11

x = 11 - 7.75

x = 3.25 pounds

Answer:

(-1, 0)

Step-by-step explanation:

bc big brain

Answer:

(-1, 0)

Step-by-step explanation:

-4 + 4 = 0

1 - 2 = -1

Answer:

12

Step-by-step explanation:

We know that 8x3=24, so we have to find what would equal 3 in the parenthesis.

12-9=3

The correct equation would be 8 (12-9) =24, or to be very simple, 8x3=24.

So y=12.

Alma ate 2 slices of pie.

Harris cut his pie into 8 slices and ate 3 slices, which means he consumed 3/8 of the pie. Alma cut her pie into 4 slices.

Harris cut his pie into 8 slices and ate 3 slices, which means he consumed 3/8 of the pie. Alma cut her pie into 4 slices. Together, they ate 5/8 of a pie. To determine how many slices Alma ate, we subtract the slices Harris ate from the total.

5/8 - 3/8 = 2/8

Simplifying the fraction, we have:

2/8 = 1/4

This means that Alma ate 1/4 of the pie, which corresponds to 2 slices. Therefore, the correct answer is option B: Alma ate 2 slices of pie.

Understanding fraction subtraction and the concept of proportion allows us to determine the number of slices Alma ate based on the information provided. By subtracting the slices Harris ate from the total, we find that Alma consumed 2 slices of pie.

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The equation that determines the total money spent on both machines in a day  = 2500b + 3000b

No. of batteries used by Machine Alpha in a day = 3000

No. of batteries used by Machine Delta in a day = 2500

Let the cost of the battery be b dollars

Money spent on batteries in Machine Alpha = No. of batteries used * Cost per battery

= 3000 * b = 3000b

Money spent on batteries in Machine Delta = No. of batteries used * Cost per battery

= 2500 * b = 2500b

The equation is used to determine the total cost of batteries used by both the machines in a day:

=2500b + 3000b

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Butt Koko, this is the solution:

Original price = 19.99

Sale price = 15.99

Discount = 19.99 - 15.99 = 4.00

We can use Direct Rule of Three to calculate the percent of discount, this way:

Price Percent

19.99 100

4.00 x

___________________

4 * 100 = 19.99 * x

400 = 19.99x

x = 400/19.99

x = 20.01

The approximate percent discount on the frisbee is 20%

After considering the given options we conclude that the evaluated best rated channel is Tel EVision, which is Option B under the condition that Tamela compared the rates of three cable companies.

The cable company that has the best rate per channel is evaluated by applying the principle of division
The rate per channel is found out by using  the proportions in the context of this problem, dividing the total price by the measure of channels.
Hence the rates for each company are given as by:
Then TV Watchers: 30.8/70 = $0.44 per channel.
Tel-EVision: 46.4/145-$0.32
Channels Galore: 40.8/120 = $0.34

Hence, the best rate is the lower rate, which is the causing factor for the answer given at the beginning of the problem.
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Given that the sheet metal has an average of 7 defects per 19 square feet, we can use the Poisson distribution formula to find the probability of 8 defects in a 34 square foot metal sheet.

The Poisson distribution formula is given by:P(X = x) = (λ^x * e^(-λ))/x!where λ is the average number of defects, x is the number of defects, and e is the base of the natural logarithm. For this problem, λ = (7/19) * 34 = 12.63 and x = 8. Plugging these values into the formula, we get:P(X = 8) = (12.63^8 * e^(-12.63))/8!P(X = 8) = (5428582.85 * 0.000281)/40320P(X = 8) = 0.0373Therefore, the probability that a 34 square foot metal sheet has 8 defects is 0.0373, or 3.73%, rounded to four decimal places.

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The probability that any two children will both like lima beans is 0.0016 or 0.16%.

Assuming that every child's choice for lima beans is independent of the other, we will use the binomial distribution to calculate the probability that two kids out of a group of will both like lima beans.

Let p be the chance that a child likes lima beans, which we realize is 0.04 primarily based on the survey. The probability that anyone infant does no longer like lima beans is then 1 - p = 0.96.

The possibility that each children will like lima beans is given through the binomial chance mass feature:

P(X = 2) = (2 choose 2) * \(p^2 * (1 - p)^{(2-2)} = p^2 = (0.04)^{2 }= 0.0016\)

So the chance that any two children will both like lima beans is 0.0016, or 0.16%. that is a very low probability, this means that that it is not likely that any two children selected at random will both like lima beans.

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Answer: $3.75 per rose

Step-by-step explanation:

45/12

3.75/1

where is the question

Answer:

hi

Step-by-step explanation:

hi

Answer:

200

Step-by-step explanation:

2*5=10

4*5=20

20*10=200