The sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?

In a  right angle triangle the three sides are represented by the letters a, b and c .

a represents the side adjacent with given angle .

b represents the side opposite to the given angle.

c represents the hypotenuse of the triangle .

Check the attached image for clear picture of the right angle triangle with angle 30 degrees .

Using the trigonometric ratio we can write the ratio as

[tex]\frac{b}{a} = tan(30^0)[/tex]

Multiplying both sides by a , we get

[tex]b =a * tan(30^0)[/tex]

since a=8 so

[tex]b = 8* tan(30^0)[/tex]

Answer:

1.)No Triangle

2.)No Triangle

3.)More Than One Triangle

4.)Unique Triangle

5.)More Than One Triangle

6.)Unique Triangle

Answer:

Option A , B , C And E are correct.

Step-by-step explanation:

We are given with a graph of a function.

We need to find numbers or values which belong to range of the function.

From graph of the function,

Value on x-axis or Horizontal line gives us the Domain of the Function .i.e., ( -∞ , -2 ] and [ 2 , ∞ )  = ( -∞ , -2 ] ∪ [ 2 , ∞ )

Value on y-axis or Vertical line gives us the Range of the Function .i.e.,

( -∞ , -1 ] and [ 1 , ∞ )  = ( -∞ , -1 ] ∪ [ 1 , ∞ )

So, From given values 2 , 1 -4 , -2 belong to range of the function.

Therefore, Option A , B , C And E are correct.

We are given Logarithmic equations.

We need to find the equation which illustrates the product rule.

We know, the product rule of Logarithms is:

[tex]log_b (mn) = log_b(m) + log_b(n)[/tex].

According to the product rule of Logarithms, we need to separate logs by plus sign.

In the given options only 4th option logs are separated by plus sign.

[tex]log_2(4x) = log_2\ 4+log_2\ x[/tex].

Answer:

Its D

Step-by-step explanation:

Took test

Jason found that each soda costs $1.29 by calculating (23.33 - 15.59) ÷ 6.

Jason spends $23.33 on the pizza and the sodas, and the total cost of the pizza is $15.59. Let's find out the total cost of the sodas by subtracting the cost of the pizza from the total amount spent. So, $23.33 - $15.59 = $7.74.

Now, to find the cost of each soda, we need to divide the total cost of the sodas by the number of sodas purchased. In this case, there were 6 sodas, so $7.74 ÷ 6 = $1.29.

Therefore, Jason found that each soda costs $1.29 by calculating (23.33 - 15.59) ÷ 6.

Cost of each soda (x) is approximately $1.29.

Jason buys a pizza for $15.59.

The cost of the pizza is $15.59.

He also buys 6 sodas:

The total cost of the pizza and sodas is $23.33.

Each soda costs the same amount:

Let's denote the cost of each soda as x.

He spends $23.33 on the pizza and the sodas.

The total cost can be expressed as the sum of the cost of the pizza and the cost of the sodas:

15.59+6x=23.33.

Now, Jason finds the cost of each soda by calculating (23.33 − 15.59) ÷ 6.

This expression represents the cost of each soda.

Let's calculate it:

[tex]\frac{7.74}{6} \approx 1.29[/tex]

So, Jason finds that each soda costs approximately $1.29.

The correct answer is gonna be B. Or x = -3√5 and x = -1

The lifetime cost of Jenny's refrigerator is A. $1,528.47.

Lifetime cost is the total expenses relating to the purchase of a good, like a car, a home, or a refrigerator from the purchase date to the end of the asset's lifespan.

We can calculate the lifetime cost by using an online finance calculator to determine the total payment, including interests, for the asset and then adding up other expenses like repairs and electricity costs.

Base cost of refrigerator = $824

Sales tax = 7.13%

Total cost of refrigerator, including sales tax (loan amount) = $882.75 ($824 x 1.0713)

Average daily electricity consumption = $0.09

Total electricity cost = $262.98 ($0.09 x 8 years x 365 days + $0.09 x 2 leap year days)

Payment period for credit purchase = 3 1/2 years

Total repairs cost = $206.25 ($68.75 x 3)

Period of possessing the refrigerator = 8 years

APR = 10.54% compounded monthly

From an online finance calculator:

Monthly Payment = $25.22

Total Payment = $1,059.24 ($25.22 x 12 x 3.5)

Total Interest for 3 1/2 years = $176.49 ($1,059.24 - $882.75)

Lifetime cost of Jenny's refrigerator = Total loan payment + Electricity cost + Repairs cost)

= $1,528.47 ($1,059.24 + $262.98 + $206.25)

Thus, the lifetime cost of Jenny's refrigerator is A. $1,528.47.

Learn more about lifetime cost at https://brainly.com/question/26892161

A linear pair of angles has a common side, and the vertex is on the line designated by the points denoting the non-common sides.

Consider the first choice:

... the common sided is RL, and the other two points are P and M. Point R (the vertex of the angles) is not on line PM. (In fact, line PM is not shown on the diagram.)

In the second choice, the given angles do not have a common side. (They are actually "vertical" angles.)

In the 3rd choice, the common side is RN, and vertex point R is found on line MO. These angles are a linear pair:

... - MRN and NRO

To establish congruence between figures in geometry, it is necessary to ensure their corresponding sides and angles match. The process involves utilizing the concept of congruent transformations to map one figure onto another without changing its dimensions.

Congruent figures have corresponding points, segments, and angles that are equal. To be convinced that two figures are congruent, you need to know that their corresponding sides and angles match.

Theorem 11 states that if one side and the two adjacent angles of two triangles are congruent, then the triangles are congruent.

In geometry, congruent transformations are used to show that two figures are congruent by mapping one onto the other without altering the size or shape.

 1) It can be used when considering the relationship between the price of a product and the quantities of the product that people want to buy at a certain price.

 2) It can be used to determine the speed, distance and time duration when traveling by car, and you want to know the values ​​of the unknown variables in your trips.

The equivalent expression to the given expression is:

                    [tex]-4.4c+1.1[/tex]

We are given an algebraic equation in terms of the variable c as follows:

                          [tex]-5.8c+4.2-3.1+1.4c[/tex]

Now, we will first combine the like term i.e. the terms with the same variable term and the constant terms are combined altogether i.e. the expression is given as follows:

        [tex]-5.8c+4.2-3.1+1.4c=-5.8c+1.4c+4.2-3.1[/tex]

On simplifying this expression we get :

                  [tex]-5.8c+4.2-3.1+1.4c=-4.4c+1.1[/tex]

Final answer:

To combine like terms in the expression -5.8c + 4.2 - 3.1 + 1.4c, we add the coefficients of the terms with 'c' and separately combine the constant terms. The simplified expression is -4.4c + 1.1.

Explanation:

To combine like terms and create an equivalent expression for -5.8c + 4.2 - 3.1 + 1.4c, we must identify and combine terms that have the same variable to the same power, which in this case are the terms with 'c' and the constant terms without variables.

Combining like terms with 'c':

-5.8c + 1.4c = -4.4c

Combining constant terms:

4.2 - 3.1 = 1.1

Equivalent Expression:

The equivalent expression by combining like terms is -4.4c + 1.1.

Answer:

[tex] \frac{1}{20}  [/tex]

Explanation:

Suppose there are x patron in the Joes restaurant.

[tex] \frac{1}{4} ^{th}  [/tex] patron are male

[tex] \frac{1}{5} ^{th}  [/tex] patron are outside of the town.

Now we need to find the proportion of male and out of town.

In order to find out the proportion, we will multiply both the fractions together.

[tex] \frac{1}{4}* \frac{1}{5}  [/tex]

In case of fraction multiplication, we will multiplying both numerator together and denominator together.

= [tex] \frac{1*1}{4*5}  [/tex]

=  [tex] \frac{1}{20}  [/tex]

Final answer is 1/20.

I hope its help you.

Answer:

The ratio is 7:8

We simply list the number of sixth graders (7 of them), then write a colon, and then write the number of fifth graders (8 of them). After writing all this down, we would reduce the ratio but it cannot be reduced any further. Why not? Because there are no common factors (other than 1) between 7 and 8.

So that's why the answer is 7:8

Final answer:

The shortest distance from the point (5, 0, -6) to the plane x + y + z = 6 is calculated using the distance of a point to a plane formula, resulting in 7 / √3 units.

Explanation:

To find the shortest distance, d, from the point (5, 0, -6) to the plane x + y + z = 6, we use the formula for the distance of a point to a plane in 3D space. The formula is given by:

d = |Ax1 + By1 + Cz1 + D| / √(A² + B² + C²)

For the plane x + y + z = 6, A = 1, B = 1, C = 1, and D = -6. Substituting the coordinates of the point (x1=5, y1=0, z1=-6) into the formula, we get:

d = |1(5) + 1(0) + 1(-6) - 6| / √(1² + 1² + 1²)

d = |-7| / √3

d = 7 / √3

Therefore, the shortest distance from the point to the plane is 7 / √3 units.