If it takes bottling machine to fill 150 bottles per minute, how many minutes will it take the machine to bottle 4500 bottles

Answer:

1. None of these.

2. None of these (Supplementary angles ).

3. Corresponding angles.

4. Alternate exterior angles.

5. Corresponding angles.

Step-by-step explanation:

In figure 1, the two lines are not parallel to each other, therefore we can not establish any relation between both angles. The required option is none of these.

In figure 2, both angles 1 and 2 lie on a straight line, therefore both angles are  supplementary angles and the required option is none of these.

In figure 3, both angles have same relative position, therefore both angles are  corresponding angles.

In figure 4, both angles are on the exterior of and , but on opposite sides of the transversal line, therefore both angles are alternate exterior angle.

In figure 5, both angles have same relative position, therefore both angles are  corresponding angles.

Answer:

B. 2√10 + 2√29 units

After performing a 90 degree rotation about the origin on the points, the new coordinates for W, X, Y, and Z respectively are (5,3), (3,1), (5,-1), and (7,1).

In this problem, the task is to rotate a quadrilateral 90 degrees about the origin (0,0). The rule for rotation of points in the plane about the origin by 90 degrees is (x, y) -> (-y, x).

The new coordinates are,

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To find the length of the longest side of the triangle, use the Pythagorean theorem to solve for x and determine the side lengths of the triangle.

To find the length of the longest side of the triangle, we need to determine which side is the hypotenuse. In a right triangle, the hypotenuse is the side opposite the right angle. Using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can find the length of the hypotenuse.

Let's denote the three sides of the triangle as A, B, and C. The left side is 2x + 12, the bottom side is 6x - 2, and the right side is 5x - 9. Since we can't determine which side is which based on the given information, we can use the variables.

By applying the Pythagorean theorem, we can set up the equation (2x + 12)^2 + (6x - 2)^2 = (5x - 9)^2. Expanding and simplifying this equation will allow us to solve for x and find the lengths of the sides of the triangle. Once we have the side lengths, we can determine which side is the longest.

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Given that an angle is 34 degrees less than its supplementary angle and knowing that supplementary angles add up to 180 degrees, the two angles measure 73 degrees and 107 degrees respectively.

To solve this problem, let's assume that the measure of the supplementary angle is x degrees. Since the angle in question is 34° less than the measure of the supplementary angle, we can set up the equation: x - 34 = the angle in question. Now, since supplementary angles add up to 180°, we can set up another equation: x + (x - 34) = 180. Solving this equation, we find that x = 107°. Therefore, the measure of the supplementary angle is 107° and the angle in question is 107° - 34° = 73°.

An angle measures 34° less than the measure of a supplementary angle. By definition, supplementary angles add up to 180°. Let's call the first angle x. Then the supplementary angle would be x + 34° because it's 34 degrees more than x. Since they are supplementary, the sum of these two angles should be 180 degrees:

x + (x + 34°) = 180°
2x + 34° = 180°
2x = 180° - 34°
2x = 146°
x = 146° / 2
x = 73°

Therefore, the measure of the first angle is 73°, and the measure of its supplementary angle is 107° (73° + 34°).

Answer:

The lowest fraction equivalent to 0.6 is [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Given : The decimal number is 0.6

To find : An equivalent fraction for the decimal number in the lowest terms.

Solution : The decimal number 0.6 is written in fraction by removing decimal.

Step 1 - Write the decimal number

[tex]0.6[/tex]

Step 2- Remove the decimal

[tex]0.6 = \frac{6}{10}[/tex]

Step 3 - Reduced the fraction by dividing Nr. and Dr. by 2

[tex]0.6 = \frac{6}{10}=\frac{3}{5}[/tex]

Therefore, The lowest fraction equivalent to 0.6 is [tex]\frac{3}{5}[/tex]

Numerator is [tex]a_0=3[/tex] and Denominator is [tex]a_1=5[/tex]

Answer with explanation:

Take a thread of length x cm.Convert it into circle of radius r cm.

If you divide the Length of circle by value equal to 2 π, you will obtain radius of the circle.The value 2π is a constant Quantity is an Irrational number.

[tex]\rightarrow \frac{\text{Length of thread}}{2 \pi}=r\\\\ \rightarrow \frac{x}{2 \pi}=r\\\\ \rightarrow x=2 \pi r[/tex]

Diameter of Circle =8 cm

Circumference of a circle with a diameter of 8 cm has radius equal to 4 cm because radius is half of diameter

           =2 × 3.14 × 4 cm

          = 25.12 cm

⇒So, Actual Length of thread =25.12 cm

Irrational Quantity=2 π=2×3.14=6.28 cm

So Radius

       [tex]=\frac{25.12}{6.28}\\\\=4 cm[/tex]

Diameter =Radius × 2

            =4 cm × 2

          = 8 cm

Divide the given inequality 6x > -24 by 6 to isolate x, resulting in x > -4, which in interval notation is (-4, ∞). The correct choice is D. ( -4, ∞) ].

To solve the inequality 6x > -24, we will divide both sides of the inequality by 6 to isolate x, keeping in mind that since 6 is positive, the direction of the inequality will remain the same.

Step-by-step solution:

Start with the inequality 6x > -24.

Divide both sides by 6, which gives us x > -4.

In interval notation, this translates to (-4, ∞).

The correct choice is D. ( -4, ∞) ]

Answer:2x^3+2x

Step-by-step explanation: