Classify each pair of labeled angles as complementary, supplementary, or neither.

Drag and drop the choices into the boxes to correctly complete the table. Each pair of angles may belong to more than one category.

The third number in the sequence is 46, found by adding 4 to the first number, which is 42, as the sum of three consecutive even numbers is 132.

Let's call the three consecutive even numbers x, x + 2, and x + 4.

According to the problem, the sum of these three numbers is 132:

x + (x + 2) + (x + 4) = 132

Now, let's solve for x:

x + x + 2 + x + 4 = 132

Combine like terms:

3x + 6 = 132

Subtract 6 from both sides:

3x = 126

Divide both sides by 3:

x = 42

Now we have the first number in the sequence: x = 42.

To find the third number, we add 4 to x:

[tex]\[ x + 4 = 42 + 4 = 46 \][/tex]

So, the third number in the sequence is [tex]\( \boxed{46} \).[/tex]

Answer:

division property of equality

Step-by-step explanation:

7q= 49

To solve this equation we  need to get 'q' alone

In order to get 'q' alone, we need to remove 7 from 'q'

Here 7 is multiplied with 'q'

To remove any number we always do opposite operation

Opposite operation of multiplication is division

So we divide both sides by 7

q= 7

Here we used division property of equality

Answer:

The equation of line is y = 2x.

Step-by-step explanation:

Consider the provided information.

A coordinate grid is shown. The x axis values are from negative 5 to positive 5 in increments of 1 for each grid line, and the y axis values are from negative 10 to positive 10 in increments of 2 for each grid line.

The slope intercept form of an equation of line is: y = mx + c

Where m is the slope and c is the y intercept.

[tex]Slope = m = \frac{Rise}{Run}[/tex]

Increments or decrements in x axis value represent the Run. Increments or decrements in y axis value represent the Rise.

It is given that "y axis values are from negative 10 to positive 10 in increments of 2 for each grid line."

Thus the Rise is 2 unit.

The x axis values are from negative 5 to positive 5 in increments of 1 for each grid line,

Thus the Run is 1 unit.

Hence the slope is: [tex] Slope=m=\frac{Rise}{Run}=2[/tex]

It is given that line passing through (0,0) it means the y intercept is 0.

Now substitute the value of m and y intercept in slope intercept form..

y = 2x + 0

y = 2x

Hence, the equation of line is y = 2x.

The area of the circle or area of one side of the flying disc is 113.04 square inches.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

A flying disc has a radius of 6 inches.

r = 6 inches

The disc has two circular circles.

The area of one circle = πr²

= (3.14)(6)²

= 113.04 square inches

Thus, the area of the circle or area of one side of the flying disc is 113.04 square inches.

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To calculate the probability of Dylan choosing a green apple sour worm, divide the number of green apple sour worms (3) by the total number of sour worms (15), resulting in a probability of 1/5 or 20%.

The probability that Dylan will choose a green apple sour worm is calculated by dividing the number of green apple sour worms by the total number of sour worms. Dylan has four strawberry, four lime, two black currant, two orange sour, and three green apple worms in his packet. This gives us a total of 15 sour worms.

To calculate the probability, we use the formula P(E) = Number of favorable outcomes / Total number of outcomes.

Therefore, the probability that Dylan picks a green apple sour worm is P(green apple) = Number of green apple worms / Total number of worms = 3 / 15 = 1 / 5.

So, the probability is 0.20 or 20%.

Yes, 3.6 repeating is equal to 11 /3 .

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Number is,

⇒ 11 /3

Now, We know that;

⇒ 11 / 3

After divide we get;

⇒ 3.666666...

Thus, 3.6 repeating is equal to 11 /3 .

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Answer:

We know that:

[tex]C_{(N)}=15000+8000N[/tex]

So first we need to substitute the next equation in the C(N) equation

[tex]N_{(t)} = 100t-5t^{2}[/tex]

And therefore we have:

[tex]C_{(t)}=15,000 + 8000*(100t-5t^{2})\\C_{(t)}=15,000 + 800000t-40000t^{2}[/tex]

Finally we replace at t = 5 in the equation above and we have:

[tex]C_{(5)}=15,000 + 800000*5-40000*5^{2}\\C_{(5)}= 3015000[/tex]

The interpretation is that after 5 hours of operation, we have wasted 3015000 dollars producing cars.  

To calculate the cost of production as a function of time, substitute the production function N(t) into the cost formula C(N). After simplifying, the cost function is C(t) = 15,000 + 800,000t - 40,000t². At 5 hours, the cost is 3,015,000 dollars.

To find the cost C as a function of the time t of operation of the factory, we first use the formula for the number of cars produced N(t) = 100t - 5t². Then we substitute the expression for N(t) into the cost function C(N) = 15,000 + 8000N.

Substituting N(t) into C(N), we get:

This is the cost C as a function of time t.

When t = 5 hours, the function becomes:

This result means that the cost of production after 5 hours of operation is 3,015,000 dollars.