What is the formula for 30-60-90 triangle?

Answer:

Step-by-step explanation:

You have to rationalize the denominator by multiplying by a unit multiplier of the conjugate of it which is 1+5i:

[tex]\frac{-3+5i}{1-5i}*\frac{1+5i}{1+5i}[/tex] You will FOIL the top and the bottom to get

[tex]\frac{-3-15i+5i+25i^2}{1+5i-5i-25i^2}[/tex].  Combine like terms to get

[tex]\frac{-3-10i+25i^2}{1-25i^2}[/tex].  Remember that i-squared = -1, so this simplification then becomes:

[tex]\frac{-3-10i+25(-1)}{1-25(-1)}[/tex] which simplifies a bit more to

[tex]\frac{-3-10i-25}{1+25}=\frac{-28-10i}{26}[/tex]  but we need to make sure we can match our answer to one of the ones given, so we'll split up that numerator over the denominator to get:

[tex]-\frac{28}{26}-\frac{10i}{26}[/tex] which then goes down to

[tex]-1\frac{1}{13}-\frac{5i}{13}[/tex] which is choice a.

Answer:

5

Step-by-step explanation:

2,4,6,8,10

The ratio in which the point (2,-3) divides the line segment joining the points (-1,3) and (4,-7) is 3:2  .

If the line segment that have the end points as [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is divided by the point (x,y) in the ratio m:n , then the coordinate of the  point (x,y) is  [tex](\frac{mx_{2} +nx_{1} }{m+n} ,\frac{my_{2} +ny_{1}}{m+n} )[/tex] ;

the coordinate of the end points are given as : (-1,3) and (4,-7) ;

the point that divided the line segment is (2,-3) ;

On applying the above formula ,

we get ;

⇒ [tex]2 = (\frac{m\times 4 +n\times (-1) }{m+n} )[/tex] ;

⇒ 2(m+n) = 4m - n  ;

⇒ 2m [tex]+[/tex] 2n [tex]=[/tex] 4m - n ,

⇒ 4m - 2m = 2n + n ;

⇒ 2m = 3n ;

⇒ we get the ratio as m : n = 3 : 2  .

The given question is incomplete , the complete question is

What is the ratio in which the point (2,-3) divides the line segment joining the points (-1,3) and (4,-7) ?

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The right triangle shown in the figure is solved to get the dimensions as

c.

Angle B = 60 degrees, Side B C = 4 Start Root 3 End Root meters, Side A B = 8 Start Root 3 End Root meters

The dimension of the right triangle is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

Information from the question

opposite = a

adjacent = 12

hypotenuse = c

The opposite is calculated using tan, TOA

tan 30 = Opposite / Adjacent

tan 30 = a / 12

a = 12 * tan 30

a = BC = 4√3

The hypotenuse is calculated using cos, CAH

cos 30 = Adjacent / hypotenuse

cos 30 = 12 / c

c = 12 / cos 30

c = AB = 8√3

< A + < B + < C = 180 (sum of angles in a triangle)

30 + < B + 90 = 180

< B = 60

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Answer:

The last one(D)

Step-by-step explanation:

-1×-1=1

1*3=3

____

9*1=9

12-9=3

The value of a polynomial at a particular point is defined as the value that the provided function yielded at that moment.

As an illustration, consider the polynomial function (x) = x + 1.

When x = 1 for example, the polynomial at that point is given by P(1) = 1+1 = 2.

Consequently, the polynomial P(x) has a value of 2 when x equals 1.

'What are polynomials?'

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

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Answer: A conclusion drawn from a study is considered to be an observation or an inference based on the data collected. In this case, the dentist conducted a survey to determine whether a certain brand of mouthwash improves gum health more than others. The conclusion drawn from the survey results is that the brand of mouthwash in question does improve gum health more than other brands.

It is important to note that this conclusion is based on the sample of patients that were surveyed. A sample is a subset of a population that is used to represent the characteristics of the entire population. In this instance, the sample of patients surveyed may not be representative of the entire population of people who use mouthwash. Therefore, the conclusion drawn from the study is based on the sample and may not be generalizable to the entire population.

The study conducted by the dentist is a survey study. A survey study is a research method in which data is collected through questionnaires or interviews from a sample of individuals.

Step-by-step explanation:

If the computed upper deviation rate (sample deviation rate projected to the population and adjusted for sampling risk) exceeds the tolerable deviation rate during a compliance test that utilizes statistical sampling,

it means that the test results indicate, the population of items being tested is not in compliance with the standards or regulations.

There are several actions that the auditor could take in this situation, depending on the specific circumstances of the test and the nature of the non-compliance. These are:

Note that: the specific course of action will depend on the nature of the non-com pliance and the regulations or standards that apply. It is recommended that the debtor consults with legal or regulatory experts to ensure that they are taking the appropriate actions to address the non-compliance.

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Answer: 7 and -5 OR -35 and 1

Also could you mark my answer as brainliest? It helps and doesnt hurt

No. The corresponding pairs of sides must also be marked  congruent to determine that the triangles are congruent.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Explanation:

The arc markings tell us how the angles pair up, and which pairs are congruent. Eg: The double-arc angles are the same measure.

Despite knowing that all three pairs of angles are congruent, we don't have enough information to conclude the triangles are congruent overall. We can say they are similar triangles (due to the AA similarity theorem), but we can't say they are congruent or not. We would need to know if at least one pair of sides were congruent, so that we could prove the triangles congruent.

The list of congruent theorems is

SSS

ASA

AAS (or SAA)

SAS

HL

LL

Much of these involve an "S", to indicate "side" (more specifically "pair of sides). Both HL and LL involve sides as well. They are special theorems dealing with right triangles only.

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11. a. GH ≅ AX and b. ∠W ≅ ∠F  

12. a. ∠T ≅ ∠K  and b. THPA ≅ KEBI

13. a. The relation between ∠S and ∠H is ∠S ≅ ∠H and the measure of ∠S = 90  

Figures and shapes that may be reversed or rearranged such that they match up with other figures and shapes are said to be congruent. These forms can be mirrored to create these shapes.

Two triangles are considered to be congruent when all three corresponding sides and angles have the same size.

11. Given ΔFGH ≅ ΔWAX  

Here is the corresponding side to GH is AX and the corresponding angle to the angle ∠W is ∠F  

a. GH ≅ AX

b. ∠W ≅ ∠F  

12. Given that BIKE ≅ PATH      

Here the corresponding angle to the angle ∠T is ∠K

a. ∠T ≅ ∠K

b. THPA ≅ KEBI

13. In ΔHOT and ΔSUN

∠O ≅ ∠U and ∠T ≅ ∠N

Since two pairs of angles are congruent  

a. The relation between ∠S and ∠H is ∠S ≅ ∠H

b. Given that ∠O = 27 and  ∠T = 63  

As we know the sum of angles in a triangle = 180°

=> ∠H + ∠O + ∠T = 180

=> ∠S + 27 + 63 = 180   [ ∵ ∠S ≅ ∠H ]

=> ∠S = 180 - 90 = 90

=>  ∠S = 90  

Therefore,

11. a. GH ≅ AX and b. ∠W ≅ ∠F  

12. a. ∠T ≅ ∠K  and b. THPA ≅ KEBI

13. a. The relation between ∠S and ∠H is ∠S ≅ ∠H and the measure of ∠S = 90  

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The sample size for the Domestic cars should be around 129 and the sample size for the Foreign cars should be around 135.

To determine the sample size, one can use the formula n = (z^2 * p * (1-p)) / (E^2) where n is the sample size, z is the z-score for the desired level of confidence (in this case, 98% or 2.33), p is the estimated proportion of successes (assumed to be 0.5), and E is the margin of error.

Using the above formula, n = (2.33^2 * 0.5 * (1-0.5)) / (7^2) = 129. For the foreign cars, n = (2.33^2 * 0.5 * (1-0.5)) / (8^2) = 135. These sample sizes will allow the car expert to estimate the mean number of days to sell for each group of cars with a margin of error of seven days for domestic cars and eight days for foreign cars, at a 98% confidence level.

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Answer:

Step-by-step explanation:

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.

Standard form of polynomial  [g(x)-f(x)]  is   2[tex]x^{4}[/tex] -3/5[tex]x^{2}[/tex]+2x+7.

Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of the equation in this format is rather simple (x and y).

A polynomial example is 4 x 3 + 2 x 2 3 x + 1. There are four terms: 1, 4 x 3, 2 x 2, and 3 x. The coefficients are the numbers that are written in front of each variable in a phrase. Because those numbers appear in front of a variable, 4, 2, and -3 are coefficients.

polynomial [g(x)-f(x)] = 8+ 1/5[tex]x^{2}[/tex]+3x+2 -( -2[tex]x^{4}[/tex] -1 + 4/5[tex]x^{2}[/tex] -x )

                                   2[tex]x^{4}[/tex] -3/5[tex]x^{2}[/tex]+2x+7

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150 pounds of candy priced at 45 dollar should be coupled with 200 pounds of candy priced at 80 dollar .

As different sweets are not distributed evenly, a mixture of various candies in a container is an example of a heterogeneous mixture. In addition, since the particles of various sweets do not interact, different candies are visible with the eye.

Let "x" stand for the number of pounds of candy costing 45 Dollar per pound, and "(350-x)" for the number of pounds of candy costing 80 Dollar per pound. The decimal equivalents of 45, 80, and 65 Dollar are 0.45, 0.80, and 0.65.

350*0.65=0.45x+(350-x)0.80

Solve it for x

x=150

350-150=200

Thus, 150 pounds of candy priced at 45 cents should be coupled with 200 pounds of candy priced at 80 cents.

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So, the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3.

A can of soda can be modeled as a right cylinder, which is a three-dimensional geometric shape with two circular bases that are connected by a curved surface. The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where V is the volume, π is a constant (approximately equal to 3.14), r is the radius of the base and h is the height of the cylinder.

Given that the radius of the can is 2.6 cm and the height is 9.2 cm, we can substitute these values into the formula:

V = π (2.6 cm)^2 (9.2 cm)

To get the area of the base we need to square the radius and multiply by π, and then multiply it by the height to get the volume.

V = π * 6.76 * 9.2 = 61.99 cm^3

So the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3. This means that the can can hold 62 cubic centimeters of liquid.

It's worth noting that this is an approximation and the real value of π is not 3.14. Also, this answer is based on the assumption that the can is a perfect cylinder with no other gaps or spaces.

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Answer: hello person.

This is a system of equations problem that can be solved using substitution.

Let x be the number of pennies

Therefore the number of dimes is also x.

The number of quarters is 44 - 2x

The total value of the pennies is x * 0.01 = $0.01x

The total value of the dimes is x * 0.1 = $0.1x

The total value of the quarters is (44 - 2x) * 0.25 = $11 - 0.5x

Now we know that the total value is $0.01x + $0.1x + $11 - 0.5x = $3.59

So we can write the equation:

0.01x + 0.1x + 11 - 0.5x = 3.59

Now we can solve for x

0.6x + 11 = 3.59

0.6x = -7.41

x = -12.35

We know that x is the number of pennies and dimes. Since it is not a whole number, it is not possible.

We can think of another approach, assuming that x is the number of dimes and pennies, and y is the number of quarters.

x + y = 44

0.1x + 0.25y = 3.59

Now we can solve for x and y by substitution method.

x = 44 - y

0.1(44 - y) + 0.25y = 3.59

4.4 - 0.1y + 0.25y = 3.59

4.4 = 0.35y + 3.59

0.81 = 0.35y

y = 2.3

x = 44 - 2.3 = 41.7

We know that x and y must be whole numbers. Since x and y are not whole numbers it is not possible.

Hence, there is no possible number of coins for Carlos to have for the given scenario.

Step-by-step explanation:

The line crosses the Oy axis in A(0,  y), so x=0 and we have:

y + 4=11 ⇒ y = 7

Y is equal to 7 at the line's intersection with the y-axis.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

The point where the line crosses the y-axis is when x = 0. To find the value of y at this point,

we can substitute x = 0 into the equation and solve for y:

y + 4 = 6(0) + 11

y + 4 = 11

y = 11 - 4

y = 7

Therefore, the value of y at the point where the line crosses the y-axis is 7.

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The necessary information which is missing from this formula page is none of the above and is denoted as option D.

This is referred to as a sheet or page which helps a student recall formulas so that they can solve test items independently.

In the example given,  t-time V = d/t d-distance V = distance/time v-velocity and the meaning of their respective abbreviations were given for better explanation. We should note that a formula page lacks numerical values as only the formula for the parameter is given is contained which is why none of the above was chosen as the correct choice.

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To graph the transformation of a logarithmic function, you will need to start by plotting the parent function. To graph the transformation of a logarithmic function, you should start by plotting the parent function and then apply the transformation by shifting, stretching, shrinking, and reflecting the graph.

This can be done by plotting points on the graph for a few different values of x. Once the parent function is graphed, you can then apply the transformation to the parent function. This can be done by shifting the graph up or down, stretching or shrinking it, and reflecting it across the x-axis or y-axis.

To graph the transformation of a logarithmic function, you should start by plotting the parent function and then apply the transformation by shifting, stretching, shrinking, and reflecting the graph.

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We can find log without a calculator by using the some formula like:

log(a×b) = loga + logb

log(ab) = loga - logb

The power of 10 that must be raised in order to equal a given number is known as its logarithm. Simple illustrations:

[tex]10^2[/tex] = 100 , therefore log100 = 2

[tex]10^3[/tex] = 1000, therefore log1000 = 3

log200 = 2.301 (between log100 and log1000)

Mathematicians learn that the following are always true:

log(a×b) = loga + logb

log(ab) = loga - logb

Select a number that you can generate using factors whose logarithms you have learned, and that is very close to the original number.

Determine this estimated number's logarithm.

Determine the error percentage, multiply it by log1.01=0.00432 and then add or remove as necessary.

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Before the discount, the price of the table was $112.5.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the discount of 64% and the final sale price will be $72.

Assume the original price be {x}. Then, we can write -

72 = 64% of {x}.

72 = (64/100) x {x}

{x} = (72 x 100)/(64)

{x} = 7200/64

{x} = 112.5

Therefore, before the discount, the price of the table was $112.5.

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Answer:

Choice A and C

Step-by-step explanation:

If 1 magnet costs $5, then 3 magnets cost $15 because adding 3 magnets to your bag, would equal to 5+5+5, or 5x3. If 1 bookmark cost $2, then 9 bookmarks would cost $18 to your bag, which would equal 9+9, or 9x2.

So, C is correct because 5x3 is 15, and 2x9 is 18. A is also correct because it's just the other way around, 2x9=18 and 5x3=15.

There are 40320 ways the 8 horses can finish the race in terms of color combination.

The number of color combinations in which the horses can finish is determined by the number of ways the 8 horses can be arranged.

This is known as a permutation.

The formula for permutation is:

n! / (n-r)!

where:

n = total number of items

r = number of items being selected at a time

In this case, we want to know the number of ways the 8 horses can be arranged in a race, so we will use 8 for n and 8 for r.

8! / (8-8)! = 8! / 0! = 8! = 8x7x6x5x4x3x2x1 = 40,320

So, there are 40320 ways the 8 horses can finish the race in terms of color combination.

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Answer:

5 ft x 7 ft

Step-by-step explanation:

60/5 = 84/x

cross multiply to solve for x

60x = (84)(5)

60x = 420

x = 420/60 = 7

All of the equations that are equivalent to n − 9 = 12 include the following:

A. n - n - 9 = 12 - n

D. n - 9 - n = 12 - n

In this exercise, you are to determine the equations that are equivalent to the given equation (mathematical expression). This ultimately implies that, the left-hand side (LHS) of the given equation (mathematical expression) must be equal to the left-hand side (LHS) of the given equation (mathematical expression).

By substracting the variable n from both sides of the given equation (mathematical expression), we have the following:

n - 9 - n = 12 - n (equivalent)

By collecting terms and rearranging the equation (mathematical expression), we have the following:

n - n - 9 = 12 - n (equivalent).

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The composite figure has an area of 26 square units.

In this question we find a composite figure formed by the sum of the areas of two right triangles and rectangles, whose area formulas are shown below:

Right triangle

A = 0.5 · w · l

Rectangle

A = w · l

Where:

Now we proceed to determine the area of the composite figure:

A = 0.5 · 3 · 1 + 3 · 1 + 0.5 · 3 · 1 + √10 · √40

A = 1.5 + 3 + 1.5 + 20

A = 26

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A right angle is an angle that measures exactly 90 degrees.

A right angle is an angle that is exactly equal to 90 degrees (or π/2) in measure.

We can see many real-life examples of the right angles in our daily life. For example, the corner of a book, edges of the cardboard, etc.

Any shape that is a square or a rectangle, will have its corners equal to 90 degrees or right angle.

A right angle is hence called a 90-degree angle.

In geometry, the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle is known as an angle.

Angles created by two rays lie in the plane that contains the rays.

The intersection of two planes also forms angles.

The angle is also used to designate the measure of an angle or a rotation.

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The difference between a bar graph and a histogram is that of  b. a bar graph displays categorical data, while a histogram displays quantitative data.

A bar graph is majorly used to compare different categories or groups of data. It displays data in separate bars, each representing a different category. A histogram, on the other hand, is used to display the distribution of a continuous quantitative variable. It shows the frequency of different values within a range of values by using bars of different heights. The bars in a histogram are also adjacent to each other, with no space between them.

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