For which set of lines is it reasonable to state that The two lines are ALMOST perpendicular to each other? A) y = 2.1x + 3, y = 2.1x + 5 B) y = 0.9x + 5, y = -1.26x + 8 C) y = 5x + 1.25, y = -5x + 1.25 D) y = 3 4 x + 0.28, y = 4 3 x + 0.29

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]

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

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

To convert the angle in degrees to radians, multiply the angle by π and divide by 180. The ship would travel approximately 3081.23 miles.

To find the measure in radians, we need to convert the given angle from degrees to radians. There are 2π radians in a full circle, which is equal to 360°. Therefore, to convert 140° to radians, we can use the formula: radians = (degrees × π) / 180. Substituting the given angle, we get: radians = (140 × π) / 180 = (7π / 9) radians.

Next, to find how far the ship would travel, we need to calculate the arc length. The formula for the arc length of a circle is: arc length = radius × angle in radians. Given that the radius of Earth is 3960 miles and the angle of rotation is (7π / 9) radians, we can calculate the arc length as follows: arc length = 3960 × (7π / 9) ≈ 3081.23 miles.

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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.

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.

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.

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.

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.

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Answer:

1.)No Triangle

2.)No Triangle

3.)More Than One Triangle

4.)Unique Triangle

5.)More Than One Triangle

6.)Unique Triangle

Answer:

74.02 square meters.

Step-by-step explanation:

We are asked to find the area of sector of circle, whose central angle is [tex]\frac{2\pi}{15}[/tex].

We will use area of sector formula to solve our given problem.

[tex]\text{Area of sector}=\frac{\theta}{2\pi}\times \pi r^2[/tex], where, r represents radius of circle.

Upon substituting our given values in above formula, we will get:

[tex]\text{Area of sector}=\frac{\frac{2\pi}{15}}{2\pi}\times \pi (18.8)^2[/tex]

Using fraction rule [tex]\frac{\frac{a}{b}}{c}=\frac{a}{bc}[/tex], we will get:

[tex]\text{Area of sector}=\frac{2\pi}{15\times 2\pi}\times \pi (18.8)^2[/tex]  

[tex]\text{Area of sector}=\frac{1}{15}\times \pi \times 353.44[/tex]  

[tex]\text{Area of sector}=23.5626666\times \pi[/tex]  

[tex]\text{Area of sector}=74.0243004\approx 74.02[/tex]  

Therefore, the area of given sector of circle is 74.02 square meters.

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

 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.