The measure of the smallest angle of a right triangle is 20° less than the measure of the next larger angle. Find the measures of all three angles.

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

Step-by-step explanation:

Year 1: $850 * 0.91 = $773.50

Year 2: $773.50 * 0.91 = $704.69

Year 3: $704.69 * 0.91 = $641.95

...

Year 34: (continue the pattern)

We can continue this calculation for each year, but to save time, we can use an exponential decay formula:

Remaining Amount = Initial Amount * (1 - rate)^years

Substituting the values:

Remaining Amount = $850 * (1 - 0.09)^34

Calculating this expression:

Remaining Amount ≈ $850 * (0.91)^34 ≈ $255.88

After 34 years, approximately $255.88 will be left with Sally.

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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Based on the description, the total area of the figure would be 45 square meters.

To find the total area of the figure, we need to divide it into two triangles and one rectangle.

The rectangle has a base of 9 meters and a height of 4 meters, so its area is 9 x 4 = 36 square meters.

The two triangles each have a base of 3 meters and a height of 3 meters, so each triangle has an area of 1/2 x 3 x 3 = 4.5 square meters.

Therefore, the total area of the figure is the sum of the area of the rectangle and the two triangles:

36 + 4.5 + 4.5 = 45 square meters

So the answer is 45 m2.

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Answer:

\(\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}\)

\( - 11 + (- 8) \\ = - 11 - 8 \\ = - 11 + - 8 \\ = - 19\)

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

\( \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}\)

Answer:

Step-by-step explanation:

1. Find the number of seats in 1 row.

There are 896 seats in one 1 row

2. Answer the question of what it is asking for!

There are total of 35 rows so:

896*35=

13860 in total of 35 rows

3. Answer!

13860 seats altogether

The approximate height difference between the birdhouse and the tree house is 3 ft.

It is less than the approximate difference in height between the swing set and the tree house.

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

We have:

height of birdhouse = 14\(\frac{9}{16}\) ft

height of tree house = 11\(\frac{13}{16}\) ft

Thus, the approximate height difference between the birdhouse and the tree house will be:

14\(\frac{9}{16}\) ft - 11\(\frac{13}{16}\)  = 2\(\frac{3}{4}\) ft

                   = 2.75 ft

                  = 3 ft

To determine if it is greater than or less than the approximate difference in height between the swing set and the tree house, we have to find the approximate difference in height between the swing set and the tree house. That is:

height of swing set = 8\(\frac{1}{4}\) ft

height of tree house = 11\(\frac{13}{16}\) ft

difference = 11\(\frac{13}{16}\) - 8\(\frac{1}{4}\)

                    = 3\(\frac{1}{2}\)

                    = 3.5

                    = 4 ft

Therefore, it is less than the approximate difference in height between the swing set and the tree house

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Answer:

\(A=8\ feet^2\)

Step-by-step explanation:

Given that,

The width of the rug is 2 feet.

The length of the rug is 4 feet.

We need to find the area of the rug. Fo a rectangle shape, the area of the rectangle is given by :

A = lb

So,

\(A=2\times 4\\\\A=8\ feet^2\)

So, the area of the rug is \(8\ feet^2\).

Answer:

Hello!

_____________________

Your answer would be ( 68% ).

Step-by-step explanation: To find percentage, we need to find an equivalent number with denominator 100. Multiply both numerator & denominator by 100

\(\frac{17}{25} . \frac{100}{100}\)

\(= ( \frac{17 . 100}{25} ) . \frac{1}{100} = \frac{68}{100}\)

Therefore, the answer is 68%

If you are using a calculator, simply enter 17÷25×100 which will give you 68 as the answer.

Hope this helped you!

The solution after change into percentage is, 68%

We have to change 17 out of 25 to a percentage.

Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We can change it as,

⇒ 17/25

⇒ (17/25) × 100%

⇒ 1700/25

⇒ 68%

Therefore, The solution after change into percentage is, 68%

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Answer:

The sequence is geometric

The common ratio is 0.5

Step-by-step explanation:

In the arithmetic sequence, there is a common difference between each two consecutive terms

In the geometric sequence, there is a common ratio between each two consecutive terms

Let us check the given sequence

∵ The first 3 terms are 12, 6, 3

∵ 6 - 12 = -6

∵ 3 - 6 = -3

∵ There is no common difference between the consecutive terms

∴ The sequence is not an arithmetic sequence

∵ 6 ÷ 12 = 0.5

∵ 3 ÷ 6 = 0.5

∴ There is a common ratio between each two consecutive terms

∴ The sequence is a geometric sequence

∴ The common ratio is 0.5

Given sequence is geometric sequence and common ratio between consecutive term is  \(\frac{1}{2}\) .

In Arithmetic sequence , common difference between consecutive terms should be equal.

In Geometric sequence, common ratio between consecutive terms should be equal.

Given sequence,     12, 6, 3, ...

  Since, common difference =  \(6-12\neq 3-6\) , this is not arithmetic sequence.

Common ratio =     \(\frac{6}{12}=\frac{3}{6}=\frac{1}{2}\)  Because common ratio is are equal. Thus, given sequence is geometric sequence.

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The binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

To determine which binomial is a factor of the trinomial x² - 13x + 30, we need to factorize the trinomial completely.

In this case, we need to find two binomials in the form (x - a)(x - b) that satisfy the equation:

(x - a)(x - b) = x² - 13x + 30

So, (x - 3)(x - 10) = x² - 13x + 30.

Therefore, the binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

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The amount is 4.8, base is 12 and the precent of the given condition is unknown.

Define base:

In mathematics, the term "base" refers to a fixed number or symbol used as a point of reference for counting, measuring or representing a quantity.

In the decimal system, for example, the base is 10, because there are 10 possible digits (0-9) that can be used to represent a number. In binary system, the base is 2, because there are only 2 possible digits (0 or 1) that can be used to represent a number.

What about precent?

In mathematics, percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred," so a number expressed as a percent represents a fraction of 100.

To convert a number to a percent, we multiply it by 100. For example, if we want to express the number 0.25 as a percent, we can multiply it by 100 to get:

⇒ 0.25 x 100 = 25%

According to the given information:

Percent: The precent is the number with the % symbol

Base: The base is the whole amount which in this case is 12.

Amount: The amount based on the precent is 4.8

So, from overall condition we have that option 'a' is correct.

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Answer:

a

Step-by-step explanation:

a measuring tape is more precise than measuring by whatever the second method is.

Answer:

there are 5 boys

Step-by-step explanation:

Answer:

waitttttttttttttttt- MY DAD IS A TEACHER!?!?!?!??!?!??!??!?!?!?!?

Step-by-step explanation:

I DIDNT KNOW MY DAD WAS A TEACHER-

The distance between Bloemfontein and Upington is a distance of 582 kilometers. The distance between two cities may vary depending on the route taken, traffic, and other factors. The distance between these two cities is measured in a straight line, which may not be the actual road distance.

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h = 0.5d + 35, shows the total amount of hours h, Julia exercised last year if she exercised d days the rest of the year.

Given,

Last year, Julia had already exercised 35 hours prior to May 1.

After that she exercised on some days during the rest of the year.

So,

Number of hours Julia has already exercised before may 1 = 35 hours.

For rest of the years Julia exercised on some days = 0.5 hours .

Hence,

The equation that satisfies the given condition of Julia for rest of the years will be,

h = 0.5d + 35

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Answer:

x=8

Step-by-step explanation:

the y-value in the first pair decreased by half, so the x-value must double due to inverse variation.

Answer:

D

Step-by-step explanation:

Each package has 18 granola bars.

This problem can be solved through a system of linear equations.

Let "x" be the total number of granola bars that each pack of granola has. Let "y" be the total amount of granola bars that each cafeteria has.

For cafeteria A: \(7x+12=y\)

For cafeteria B: \(3x+84=y\)

Since both equations are solved for y, we may take the argument at the left of the equal sign from both equations and equal them.

\(7x+12=3x+84\).

\(7x+12=3x+84\)

\(7x-3x=84-12\) --> Substract 3x and 12 from both sides.

\(4x=72\) --> Simplify by solving the substraction.

\(\frac{4x}{4} =\frac{72}{4}\)--> Divide both sides by 4.

\(x= 18\)

\(y=7(18)+12\\ \\y=138.\)

If a system of linear equations was created, where 2 equations that gave the number of granola bars that each cafeteria has, then the x value obtained when the system was solved, indicates the amount of granola bars that each cafeteria has in each package. Each package has 18 granola bars.

Answer:

89.38

Step-by-step explanation:

65 times 0.125 = 8.125

65 times 0.25 = 16.25

16.25 plus 8.125 plus 65 = 89.38 dollars

You would have four gallons :)

A mathematics topic that van be looked into is how linear algebra, graph theory and optimization can be used on the airline industry.

In this case, to solve the scheduling issues faced by airlines such as planning flights, assigning planes and crews to routes - mathematical techniques can be employed.

By leveraging Linear Algebra, operators can simulate the flow of aircrafts and passengers while Graph Theory can help model flight schedules and aircraft routes.

Simultaneously using Optimization techniques in the problem-solving process can work to streamline various operations resulting in reduced costs and improved efficiency which can increase profit margins.

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The equation of the line in point-slope form is y = 2x/7 + 8.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since the line is parallel to 2x - 7y-6=0, the slope is given by;

7y = 2x - 6

y = 2x/7 - 6/7

Slope, m = 2/7.

At data point (-7, 6) and a slope of 2/7, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = 2/7(x + 7)  

y = 2x/7 + 2 + 6

y = 2x/7 + 8

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Noah earned $160 last month, and his income tax rate is 10%. To calculate how much he earns after tax, we need to subtract the tax amount from his earnings.

The tax amount is equal to 10% of his earnings, which is:

0.1

×

160

=

16

0.1×160=16

Therefore, Noah's earnings after tax is:

160

−

16

=

144

160−16=144

Noah earns $144 after tax.

The requried answer is x>-6 shows 4th number line, x<-6 shows 2nd number line, x\(\leq\) -6 shows Ist number line and x< -8 shows 3rd number line.

In an equation, the two expression are deemed equal which nis shown by the symbol =. x=y. x is equal to y. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥. x>y.

To plot an inequality, such as x>3, on a number line, the first draw a circle over the number.Then if the sign inclide equal to \(\leq\) or \(\geq\) fill in the circle.We show the numbers by drawing a straight line and indicating the end points with circle or closed circle.  

\(\frac{7x}{9}\)>\(-\frac{14}{3}\)

x>-6

This solution shows the number line 4.

\(-\frac{75x}{4}\) >\(\frac{222}{5}\)

x<-6

This soloution show the number line 2.

\(\frac{x}{4} \leq -\frac{3}{2}\)

x\(\leq -6\)

This soloution show the number line 1.

\(2\frac{x}{3}\) > \(- \frac{16}{3}\)

x<-8

This solution show the number line 3.

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Answer:

(8-n=4)/4 click brainliest please and click thanks

Step-by-step explanation:

The mathematical expression which represents the phrase four equals the difference between eight and a number and the result is divided by four is (4 = 8 - x)/4.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given,

Difference of 8 and a number x = 8 - x

4 equal to 8 - x

4 = 8 - x

Now,

The result is divided by 4

Therefore,(4 = 8 - x)/4

Hence "The mathematical expression which represents the phrase four equals the difference between eight and a number and the result is divided by four is (4 = 8 - x)/4".

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