Explain the five properties of multiplication.

The families of solutions (variable x) for the square root of the trigonometric expression 2 · cos x - 1  equal to 0 are x₁ = π / 6 + i · 2π and x₂ = 11π / 6 + i · 2π, where i is an integer.

In this question we find the following trigonometric expression:

√(2 · cos x - 1) = 0

Where x is measured in radians.

By algebra properties and trigonometric formulas we must solve the trigonometric expression for x. First, use algebra properties until the trigonometric function is cleared:

√(2 · cos x - 1) = 0

2 · cos x - 1 = 0

2 · cos x = 1

cos x = 1 / 2

Second, find the family of solutions for the square root of the trigonometric function:

x₁ = π / 6 + i · 2π, where i is an integer.

x₂ = 11π / 6 + i · 2π, where i is an integer.

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The area of the triangle is 8 unit².

The amount of space a shape takes up is called the area of that space.

Here,

The given vertices are

A= (-4,1)

B= (-7,5)

C= (0,1)

Now, as we know the x and y coordinates of three vertices of triangle.

So, we will use the coordinate geometry formula.

The general formula of the area of triangle is

If the triangle have a vertices (Ax,Ay ),(Bx,By ) and (Cx,Cy ) then the area is

Area=1/2×|Ax (By-Cy )+Bx (Cy-Ay )+Cx (Ay-By )|

Now, we will put the given coordinates values in above equation

Then we will get

Area=(1/2)×|(-4)(5-1)+(-7)(1-1)+0(1-5)|

Area=(1/2)×|(-4)(4)+(-7)(0)+0(-4)|

Area=(1/2)×|-16|

Remove the mode bracket.

Area=1/2×16

Area=8

Thus, the area of the triangle is 8 unit².

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[tex]4\frac{1}{2}[/tex] as a percentage is 450% and [tex]4\frac{1}{2}[/tex] as a decimal is 4.5

So, your answer would be the last option!

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Have a great day and God bless! :D

Answer:

Step-by-step explanation:

280%, 2.8, 2 4/5

2 4/5 =2.8

The expression that can be used to represent this situation is 5p

Expression:

Expression refers the mathematical equation that consists of variables, numbers and mathematical operator.

Given,

Bre'Asia wanted to buy 5 pizzas. She used a coupon for $7 off the entire order. Let p represent the cost of 1 pizza.

Here we need to find the expression that represents the situation.

In the given question, let us consider p represent the cost of 1 pizza and the n refers the number of pizza.

So, the expression to calculate the price of the pizza based on the number of pizza is written as,

=> np

Here Bre'Asia brought 5 pizzas, then the expression is

=> 5p.

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After using the subtraction method 49 rose bushes the workers plant today.

What do mean by the subtraction method?
A method of estimating how long a psychological process will take by measuring how long it takes to react to an activity that involves the process in question and how long it takes to react to a task that doesn't, then subtracting the second from the first.

total rose bushes are 31

total bushes to be finished in the park, 80

rose bushes planted today =(80-31)

                                             =49

Hence, the rose bushes in the worker's plant today are 49

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Answer:

Determine whether the equation is half or double the given number, then solve for x.

Step-by-step explanation:

The hash marks on the sides of the triangles tell you that the pieces of the triangles are the same length. The piece with one mark is the same length as the other piece with one mark. The piece with two marks is the same length as the other piece with two marks.

This is important because it tells you that the place where the triangle is divided is at its halfway point — so, the triangles are cut right in half. The line that cuts the triangle in half will always be half the length of the line that is the bottom of the triangle. You can use this to solve for x in each of these problems.

12) We are trying to solve for x along the length of the longer line. The halfway-point line is seven.

Seven is half of fourteen (7*2=14). So, the longer line is 14.

Since the longer line has the equation 2x, we must determine what times two is fourteen. To find that, we would divide fourteen by two (division and multiplication are inverse operations). 14/2=7.

x=7.

15) We are trying to solve for x along the length of the shorter line. The longer line is 35.

The shorter line is half of the longer line, so in this case it is half of 35, which is 17.5.

However, in the equation, we subtract 8 from x. So, we have to find the number that becomes 17.5 only after you subtract 8. To do this, you simply add 8 to 17.5 (addition and subtraction are inverse operations). 25.5 - 8 = 17.5.

x = 25.5.

According to the population function, the population of mosquitoes in the area at any time is 400000 = 200000e⁷ⁿ

Population function:

The term population function refers the effective population served over the course of a time

Given,

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 200000 mosquitoes in the area initially , and predators (birds, bats, and so forth) eat 20000 mosquitoes/day.

Now, we need to determine the population of mosquitoes in the area at any time.

Here we have given that we have two time frames in the information given; weeks and days.

Now, we need the population after predation lets choose time in days.

And we also know that the population doubles every seven days (ignoring predation) so if P(a) is the population function we have IVP

For one week, the population function of the given situation is written as

=> dP/dt = rP

Then the value of P is P(0) = 200000

And through the given question we know that,

=> P(7) = 2P(0)

While we solving the function then we get

P = Ceⁿᵃ

When we apply the values of P(0) = 200,000 then we get the value of C = 200,000

Then, the function is rewritten as

P = 200000eⁿᵃ

Now, we have to apply the value of P(7) = 2P(0), then we get,

400000 = 200000e⁷ⁿ

When we simplify it then we get,

e⁷ⁿ = 1/2

When we apply the number of days on these function, then we can get the number of mosquitoes in the city.

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1) The yearly depreciation expense under the straight-line method is $2,000.

2) If the car was bought on April 3, the depreciation expense for the first year is approximately $1,500.

Under the straight-line depreciation method, the depreciation expense is the quotient of the depreciable amount (cost - residual value) divided by the estimated useful life of the asset.

The depreciation expense is prorated if it does not cover the full year.

Cost of car = $12,000

Estimated useful life = 5 years

Residual value = $2,000

Depreciable amount = $10,000 ($12,000 - $2,000)

Straight-line Depreciation (annual) = $2,000 ($10,000/5)

Depreciation for first year (April 3) = $1,496 ($2,000 x 273/365)

≈ $1,500

Thus, using the straight-line method, the depreciation expense for the car in each year is $2,000.

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The second graph represents that the function has two complex roots.

What are Complex Numbers?

Complex numbers are made up of two parts: a real number and an imaginary number. Complex numbers serve as the foundation for more complex arithmetic, such as algebra.

Solution:

Since, the graph in the second option is not making any contact with thew point on x-axis it can be very well said that the solutions/roots/zeros of the quadratic equation are complex numbers.

Which is not the case for option one and option two because, the curves are making intercepts on x-axis thus, giving real roots.

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Answer:

I'm doing the same exact test, it's B.

Answer:

Here we need to find the value of y

In the given figure, 2y and 110 are adjacent to each other.

Hence the value of y = 110.

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Answer: The credit after calling for 35 minutes will be 31.17 dollar

How do you determine a line's slope?

The slope is calculated by dividing the difference between the y-coordinates of two points on a line by the difference between their x-coordinates.

Step-by-step explanation:

Given that credit x = 32.86
and time for calling y = 22
slope is m = -0.13
c = ?

Equation of line
y = mx + c
32.86 = -0.13(22) + c

32.86 + 2.86 = c

c = 35.72
now we have c we can calculate credit at time 35 min
y = -0.13(35) + 35.72
y = 35.72 - 4.55
y = 31.17 dollar
Hence the credit at time 35 min is 31.17 dollar
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The value of x is 18.8m

Given:

θ = 48°

Y = 17m

The law of tangent which is also called as tangent formula or tangent rule is the ratio of the sine of the angle to the cos of the angle.

tan θ = Opposite / Adjacent.

Here,

Sum of triangle = 180°

90° + 48° + x° = 180°

x° = 42°

tan θ = opposite/ adjacent.

Substituting the values

tan 42° = 17/x  (∴tan 42° = 0.9004)

0.9004 = 17/x

So we get,

x = 17/0.9004

x = 18,8m

Therefore, the value of x is 18.8m.

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a. The Venn Diagram that represents the distribution of languages taken at the Kollar institute is given by the image at the end of the answer.

b. The percentage of students at the institute that take none of the three languages is of: 9%.

The Venn Diagram is built considering the proportions of students taking these three courses.

The most restricted proportion is one the students that speak three languages, given as follows:

0.13.

The proportions containing two of them are:

The proportions with only one language are:

The proportion who takes at least one is:

0.2 + 0.04 + 0.18 + 0.12 + 0.13 + 0.01 + 0.23 = 0.91.

The proportion who take none is:

1 - 0.91 = 0.09.

The percentage is:

9%.

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The value of s in the point (s,-3) after using slope formula is -4.

What is slope?

Slope is a term used to define how steep a line is. The rise of a line over the run of a line, or the change in the vertical direction (y) over the change in the horizontal direction, is the definition of slope (x). The slope is the angle at which one is moving forward or backward when skiing down a hill or climbing a mountain. Depending on what it is, the slope may occasionally be fairly flat or extremely steep. The slope of an object indicates how steep it is. Slope knowledge is crucial for daily decision-making. 

Using slope formula,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Now the given point  is ,

[tex](x_1,y_1)=(s,-3) \\(x_2,y_2)=(-8,-4)[/tex]

=> slope m= 1/4

=> [tex]\frac{1}{4}= \frac{-4+3}{-8-s}[/tex]

=> [tex]\frac{1}{4} = \frac{-1}{-8-s}[/tex]

=> -8-s=-4

=>-s=-4+8

=> -s=4

=> s =-4.

Hence the value of s is -4.

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Answer:the answer is 12x+12=7x+56 got it right on plato

Step-by-step explanation:

12 (x+1) = 7 (x+8)

12x+ 12 = 7x+ 56

Answer:

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1. The following transactions fully comply with the revenue recognition principle of generally accepted accounting principles and should be included in the 20X5 revenue of Revgression Corporation:

(3) Goods were delivered to customers during early 20X5, ...

(4) Customers purchased goods and services during late 20X5, ...

(6) Goods were purchased and paid for by customers during 20X5, ...

2. The following transactions do not comply with the revenue recognition principle of generally accepted accounting principles and should not be included in the 20X5 revenue of Revgression Corporation:

(1) Goods were sold and shipped in late 20X5 ...

(2) Goods were produced according to ...

(5) Advance payment from a customer in...

ASC 606 of generally accepted accounting principles or IFRS 15 states that companies should recognize revenue when the service or product is delivered to the customer, not when cash is received.

Ordinarily following the five-step revenue recognition process, the goods sold and shipped in late 20X5 may be recognized in 20x5, while the installation service is recognized when completed in 20X6.

However, the contract requires substantial installation and setup services, and Revgression Corporation needs to comply before recognizing revenue.

Thus, revenue items 3, 4, and 6 should be recognized in 20X5 while revenue items 1, 2, and 5 should be recognized in 20X6.

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Answer:

Step-by-step explanation:

You want to know the value of 1010 in binary.

We're not sure if you have the base ten number 1010 and you want its value in binary, or if the number 1010 is in binary, and you want its value in base ten.

Converting the base ten number to binary means looking at the remainders from division by 2, until the quotient is zero.

The binary value is the list of these remainders from the bottom up:

  1010₁₀ = 11 1111 0010₂

(It is often convenient for readability to group the digits by 3 or 4.)

The conversion from binary essentially uses the expanded form of the number. The arithmetic is done in the base you're converting to. Here, that's base ten.

  1010₂ = 1×2³ +0×2² +1×2¹ +0×2⁰ = 8 +2 = 10

  1010₂ = 10₁₀

The correct ascending order is 33000 cm, 0.34 km, 430 m.

to find the ascending order we firstly have to convert the  all values into a same unit system.

we will convert all the values into cm units.

so, 0.34 km = 0.34*100000 cm,

0.34 km = 34000 cm.

similarly 430 m = 430* 100 cm,

430 m = 43000 cm.

and lastly we have 33000 cm.

so in all the values 33000 cm is smallest and 43000 cm is largest and the correct ascending order will be 33000 cm, 0.34 km, 430 m.

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Answer:37

Step-by-step explanation:

Answer:

[tex]y > \frac{14}{3}[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

By using the concept of ratio, it is obtained that

AB : BC : CD = 4 : 3 : 13

What is ratio?

Ratio between two number signifies how much one number is larger than as compared to another. The first part of the ratio is called antecedant and the second part of the ratio is called consequent

Here, the concept of ratio has been used

Here, AB : BD = 1 : 4

AC : CD = 7 : 13

AC  + CD = 7 + 13 = 20

[tex]AB = \frac{1}{1 + 4} \times 20 = 4[/tex]

[tex]BD = \frac{4}{1+4} \times 20 = 16[/tex]

[tex]CD = 13[/tex]

BC = BD - CD = 16 - 13 = 3
AB : BC : CD = 4 : 3 : 13

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The quotient of the fraction illustrated as

0.64 / 3.8 is 16/95.

Here we have the following quotient to solve:0.64/3.8

First, we can write both numerator and denominator as fractions:

0.64 = 0.64*(100/100)

= 64/1003.8

= 3.8*(10/10)

= 38/10

Remember that the quotient between two fractions (a/b) and (c/d) can be rewritten as:(a/b)÷(c/d) = (a/b)*(c/d)

Our quotient here is:(64/100)÷(38/10)

= (64/100)*(10/38)

= (64/380)

= (32/190)

= (16/95)

That is the quotient.

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Answer:

Carmelita Jeter 10.64

Step-by-step explanation:

Because the first is Kerron Stewart,the second is Merlene Ottey and the third is Shelley-Ann Fraster

Answer:

21/2 or 10.5

Step-by-step explanation:

7 = 7/1

When dividing fractions we use KFC :

K - Keep the first fraction :

7/1

F - Flip the second fraction :

2/3 ⇒ 3/2

C - Change the sign :

÷ ⇒ ×

Now we have :

7/1 × 3/2 =

Now we multiply the first numerator with the second numerator and the first denominator with the second denominator :

7×3 = 21

1×2 = 2

So our final answer is 21/2 or 10.5

Hope this helped and have a good day

The triangle with sides length of  35 km , 83 km and 86 km cannot form a right triangle.

A right triangle is a triangle that has one angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The sides of a triangle can be found using Pythagoras's theorem. Right triangle obeys  Pythagoras's theorem.

The  Pythagoras's theorem can be represented as follows:

c² = a² + b²

where

The hypotenuse is the longest side of the right triangle.

Hence, let's check if the side length of 35 km 83 km 86 km is a right triangle.

35² + 83² = 86²

1225 + 6889  ≠ 7396

Therefore, it is not a right triangle.

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