How do you solve a 45 45 90 and 30 60 90 triangle?

The Third side of the right triangle with two sides can be found by Pythagoras Theorem that means by adding the square of other two sides .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the , in a Right Triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.

The sides of this triangle are named as Perpendicular, Base and Hypotenuse. where , the hypotenuse is longest side of the triangle , because ,  it is opposite to the angle 90°.

Therefore , the third side (longest side) of a right triangle with two sides can be found by adding the square of the other two sides .

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The population of Cuba in 10 years will be 1.9243 million.

A process called exponential growth sees a rise in quantity over time. It happens when a quantity changes at an instantaneous rate that is proportionate to the quantity itself with respect to time.

Data patterns that exhibit exponential growth exhibit quicker rate of expansion over time. Compounding produces exponential returns in the financial world. Savings accounts with a compound interest rate have the potential to expand exponentially.

The population growth will be modeled using exponential growth:

f(x) = a(b[tex])^t[/tex]

where:

a be the initial value

b be the growth rate

Substitute the values in the above equation, we get

f(x) = 1.3(1.04[tex])^t[/tex]

The population after 10 years will be:

f(x) = 1.3(1.04[tex])^{10[/tex]

simplifying the equation, we get

f(x) = 1.9243

Therefore, the population in 10 years will be 1.9243 million.

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The population of Cuba in 10 years will be 1.9243 million, if the population is expected to grow at a rate of 4% each year.

Quantities increase over time through a process known as exponential growth. It occurs when a quantity shifts at a pace that is proportional to the quantity's own rate of change with regard to time.

Data patterns that show exponential growth expand more quickly over time. In the world of finance, compounding generates exponential profits. Compound interest savings accounts have the potential to grow tremendously.

The population growth will be modeled using exponential growth:

f(x) = a(b)[tex]^{t}[/tex]

where:

a be the initial value

b be the growth rate

Substitute the values in the above equation, we get

f(x) = 1.3(1.04

The population after 10 years will be:

f(x) = 1.3(1.04

simplifying the equation, we get

f(x) = 1.9243

Therefore, the population in 10 years will be 1.9243 million.

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Answer: 35

Step-by-step explanation:

So first you plug 5 into the equation which is:

10(5)-15

which is 50-15

50-15 is 35

Answer:

35

Step-by-step explanation:

plug 5 in for x and u will get 35

Answer:

1. A

2. 9

Step-by-step explanation:

Answer:

360.82

Step-by-step explanation:

Answer: A circle has a circumference C=1133.54 units. Substitute the value, Therefore, the diameter of the circle is 361 units.

Step-by-step explanation:

The equation which describes the nth term for the sequence 3/5,1/5,1/15,1/45,\cdots2 is  an = 3/5 (1/3)n-1 , which is option C.

We use the formula an=a1+(n−1)d an = a1 + (n−1)d , to calculate the nth term of a given sequence. The 'n' here  represents a number.

Using the nth term we can any number on the sequence which allows us to locate any term in a series.

By substituting different values for the term number, we can create a series utilizing the nth term (n).

To find the tenth term we use the sequence formula and substitute a random number in place of n.

Example if we need to find the first 50 term then we will substitute n as 50.

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Answer:

b 41cm, 40cm, 9cm form a right angle

Answer:

The answer is $4.50.

Step-by-step explanation:

To solve this problem, divide the result ($6.75) by the percentage (150%). This gives you the original number which was multiplied by the percentage. So,

$6.75 / 150% = $4.50.

Answer:

$4.50

Step-by-step explanation:

150% × □ = $6.75

First, we can rewrite 150% as the fraction 3/2.

[tex]\dfrac{3}{2} \times \square = \$ 6.75[/tex]

Then, we can also rewrite 6.75 as the fraction 27/4.

[tex]\dfrac{3}{2} \times \square = \$ \, \dfrac{27}{4}[/tex]

Next, we can isolate the unknown by multiplying both sides by 2/3 (the reciprocal of 3/2).

[tex]\left(\dfrac{2}{3} \right)\left(\dfrac{3}{2} \times \square \right) = \left(\$ \, \dfrac{27}{4}\right)\left(\dfrac{2}{3} \right)[/tex]

After that, simplify by multiplying out the numerators and denominators on the right side of the equation.

[tex]\square = \$ \, \dfrac{27 \times 2}{4 \times 3}[/tex]

[tex]\square = \$ \, \dfrac{54}{12}[/tex]

Finally, simplify the expression on the right side to a decimal form.

[tex]\square = \$ \, \dfrac{54 \div 2}{12 \div 2}[/tex]

[tex]\square = \$ \, \dfrac{27 \div 3}{6 \div 3}[/tex]

[tex]\square = \$ \, \dfrac{9}{2}[/tex]

[tex]\square = \$ 4.50[/tex]

Answer:

n(B U S) = 75

Step-by-step explanation:

P(E) =  

Let 'B' be the event of having twelve year old brother

Let 'S' be the event of having twelve year old sister

given data  P(BUS) = 0.25

given total survey  n(survey) = 300

we have to find the value is n(BUS) =?

we will use probability definition we get, P( BUS) =

substitute given values, we will get solution

after cross multiplication , we get

n(BUS) = 0.25 X 300

n(BUS) = 75

Answer:

75 twelve-year-olds will have a brother or sister

25% of 300 = 75

Step-by-step explanation:

Step 1: Our output value is 300.

Step 2: We represent the unknown value with x

Step 3: From step 1 above, 300=100%.

Step 4: Similarly, x=25%

Step 5: This results in a pair of simple equations:

300=100% (1).

x=25% (2).

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

300/x    100%/25%

Step 7: Again, the reciprocal of both sides gives

x/300     25/100

x=75

Therefore, $25% of 300 is 75

Answer:

a. 4^12

b. 6^7

c. 8^5

d. 7^2

Step-by-step explanation:

hope this helps :)

Answer:

[tex]L=3.999 \: dm[/tex]

[tex]A=183.4581\:dm^{2}[/tex]

Step-by-step explanation:

La relación del apotema y el lado de un dodecágono regular está dada por la siguiente ecuación:

[tex]a_{p}=L\frac{2+\sqrt{3}}{2}[/tex]

Sabiendo que la apotema es 7.464 el lado sera:

[tex]L=\frac{2*a_{p}}{2+\sqrt{3}}[/tex]

[tex]L=\frac{2*7.464}{2+\sqrt{3}}[/tex]

[tex]L=3.999 \: dm[/tex]

Por otro lado el area de un dodecágono regular esta dada por:

[tex]A=6a_{p}L[/tex]

[tex]A=6*7.646*3.999[/tex]

[tex]A=183.4581\:dm^{2}[/tex]

Espero te haya sido de ayuda!

The main unknown at this point is "the number of adult tickets." The "number of children's tickets" is another factor that is unknowable. In order to assign two variables, do as follows:

Let a = # of adult tickets

and c = # of children's tickets.

Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.

Setting up the equations using the unknowns that follow the word problem is the next step. Here are the details:

There are 460 tickets total because there are an adult ticket and a child ticket.

a + c = 460.

Now that we know we want to find the number of adult tickets, we can translate the basic equation a + c = 460 into terms of a:

a + c  = 460

-a       = -a        (For example, use -a to delete a from the left side of the equation on either side.)

c = 460 - a

We can now enter the equation c into the other equation, 8.75a + 3.50c = 3143, since we have the equation c expressed in terms of a.

Now, we need to find the value of c in the first equation so that we can plug it into the second equation:

292 + c = 460

-292     = -292

c =  168

(8.75 × 292) + (3.50 × 168) = 3143

2555 + 588 = 3143

3143 = 3143  

Therefore, We each have 3143

The  complete question is:

For a show adult tickets are $8.75 and children's tickets are $3.50. 460 tickets were sold for a total of 3143 how many adults tickets were sold?

Adult ticket = 8.75

child ticket = 3.50

460 tickets we're sold totaling 3143

how many adults tickets were sold

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Store Z charges $8 per movie.

An expression is the mathematical statement that is formed by numerical and variable terms along with operators. It represents the method of a mathematical operation in a symbolic form.

given, store A charges $8 per movie.

for each order shipping fee = $10

if store A is ordered x movie at a time than the total cost for one order

represented by the expression, $8 x + $10.

As per question, store Z cost always the same as store A for one order.

so, cost for one order in case of store Z = $8x + $10

if x denotes the number of movies that is ordered at a time, then the Z store charges $ 8 per movie.

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Answer:

B. Susan's location is cheaper for 10 people.

D. The charge for each additional person is greater for Charlie's location.

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.

Here,

Given : side = 12cm

Area of an equilateral triangle

=> √3/4 * side²

Side of triangle =12 cm

Area of an equilateral triangle

= >  √3/4 * 12²

=>√3/4 * 12*12

=> 62.28 cm²

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

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Answer:

D m =  [tex]-\frac{3}{8}[/tex]

Step-by-step explanation:

factor the expressions in the denominator and the numerator to simplify the expression:

=> [tex]\frac{2(-2m + 1)(2m - 1)}{2(2m - 1)(8m + 3)}[/tex]

=> [tex]-\frac{2m + 1}{8m + 3}[/tex]

to make a fraction undefined, the numerator should be 0, thus, we substitute the values of m from the options into the denominator to make the denominator equals to 0:

=> [tex]-\frac{2m + 1}{8(-\frac{3}{8} ) + 3}[/tex] = [tex]-\frac{2m + 1}{-3 + 3}[/tex] = [tex]-\frac{2m + 1}{0}[/tex]

in this case, the values of m from option D make the denominator of the fraction equals 0.

Answer: the answer is 1800

Step-by-step explanation:

18 percent of 10000 is 1800

Answer:

absolute deviation means distance between each data value and the mean of the data set.

Step-by-step explanation:

(MAD)

or

(Average)

Answer:

The height of the parallelogram is 6 cm.

Step-by-step explanation:

Given,

base=4.5 cm.

area=27 CM sq

Now,

height = area/base

.: height =27/4.5 cm

=6 cm

The graphic solution for each system of equations is given as follows:

20. (5/3, 28/3).

21. (0.205, 3.846).

22. (-1/2, -5/2).

23. (-4.615, 7.462).

The graphic solution of a system of equations is given by the point of intersection of all the equation that compose the system.

For this problem, the systems are composed by functions of the first degree, hence they are linear functions.

For each system, the graph is traced, and then the point of intersection is identified on the graph given at the end of the answer.

Each system is traced on a different color, as follows:

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For mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.

To compare the prices of the two companies, we need to determine the total cost for each company at different mileage.

For Company A, the total cost is the initial fee of $50. This is a fixed price, regardless of the mileage driven.

For Company B, the total cost is the initial fee of $30 plus the additional cost per mile driven. To calculate this, we can use the formula:

Total cost = initial fee + (mileage * additional cost per mile)

For Company B, this would be:

Total cost = $30 + (mileage * $0.50)

To find out when Company A charges less than Company B, we need to compare the total costs of the two companies at different mileage. We can set up the following inequality:

$50 <= $30 + (mileage * $0.50)

To solve for mileage, we need to isolate it on one side of the inequality. To do this, we can subtract $30 from both sides:

$20 <= (mileage * $0.50)

Then, we can divide both sides by $0.50:

40 <= mileage

So for mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.

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Answer:

Step-by-step explanation:

Without calculation, we should get:

Lets confirm

Area of the drawing:

Area of the wing:

Divide the area of the wing by the area of the drawing:

As we see the ratio is same, drawing to wing:

A customer purchased 1/4 pound of ham, 1 1/2 pounds of turkey, 1 pound of roast beef, and 3/4 pound of bologna. Therefore, the customer pay for the purchase before sales tax is $22.

Sales tax:

A sales tax is a tax paid to a governing body on the sale of certain goods and services. Laws generally allow sellers to collect taxes from consumers at the time of purchase. When a tax on goods or services is paid by consumers directly to the governing body, it is usually called a use tax. Laws often provide excise and use tax exemptions for certain goods or services, such as: food, education, medicine, etc. Value Added Tax (VAT) charged on goods and services is related to sales tax.

For Example:

I am shopping at The Clothing Boutique and would like to estimate the total after tax before checking out. After counting the total price of the items in the cart, the total is $100. Sales tax in this county is 9.5%, so you charge 9.5% (100 x 0.095) of $100.

According to the question:

The purchase before sales tax:

                   = 1/4 × $5.99 + 1 1/2 × $4.99 + 1 × $6.99 + 3/4 ×2.99

                   = $1.5 + $7.5 + $6.99 + $5.24

                   = $21.23 ≈ $22

Therefore,  the customer pay for the purchase before sales tax is $22.

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Answer:

3.201 x 10^9 and 4.85 10^3 = 3 201 004 850 = 3.20100485 × 10^9

Step-by-step explanation:

= 3.20100485 × 10^9

(scientific notation)

= 3.20100485e9

(scientific e notation)

= 3.20100485 × 10^9

(engineering notation)

(billion; prefix giga- (G))

= 3201004850

(real number)

To translate a triangle with vector (-5/2), you need to subtract 5/2 from the x-coordinate and add 2 to the y-coordinate of each vertex of the triangle. This will move the triangle 5 units to the right and 2 units up.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

To translate a triangle with a vector, you can use the vector to adjust the coordinates of the triangle's vertices.

For example, if the triangle has vertices at (x1, y1), (x2, y2), and (x3, y3), you can translate it by the vector (-5/2) by subtracting 5/2 to the x-coordinates of the vertices. The new coordinates of the translated triangle would be (x1-5/2, y1), (x2-5/2, y2), and (x3-5/2, y3).

This will move the triangle 5/2 units to the left along the x-axis.

It is important to note that the translation vector you provided only has one component, which is -5/2. Since the vector only has x component, the translation will only occur along the x-axis and the y-coordinate of the vertices will not change.

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Answer:

i do not not the answer of this question

Answer:

Hello There!!

Step-by-step explanation:

The answer is: 33/100.You time the numerator by the numerator and the denominator by the denominator and simplify it which is 33/100.

hope this helps,have a great day!!

~Pinky~

Step-by-step explanation:

I hope it helps you have a great weekend

Answer:

3,869.72

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

To find the equation of the line that goes through the points (5, 3) and (-1, 2), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

To find the slope of the line, we can use the following formula:

m = (y2 - y1)/(x2 - x1)

Plugging in the coordinates of the two points, we get:

m = (2 - 3)/(-1 - 5) = -1/6

Substituting this value of m and the coordinates of one of the points into the point-slope form, we get:

y - 3 = -1/6(x - 5)

This simplifies to:

6x + y - 13 = 0

Therefore, the equation of the line is:

6x + y - 13 = 0