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Artyom0805 [142]

3 years ago

11

If the measurement of a central angle is 5 pie /6 , find the length of its intercepted arc in a circle with a radius of 15 inche

s.

1 answer:

Dahasolnce [82]3 years ago

8 0

The relationship between central angle lengtho of arc and radius is
L =R x teta, so L= (<span>5 pie /6) x15, L= 75Pi/6 inches</span>

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The difference between the areas of the figures is less than 4.

coldgirl [10]

Answer:

1. |40 – 4x| < 4

2. 9 < x < 11

Step-by-step explanation:

We'll begin by calculating the area of each figure. This can be obtained as follow:

For triangle:

Area = ½ × base × height

Base = 8

Height = 6

Area =?

Area = ½ × 8 × 6

Area = 4 × 6

Area = 24

For Rectangle:

Area = length × breadth

Length = x – 4

Breadth = 4

Area =?

Area = (x – 4) × 4

Area = 4x – 16

Summary:

Area of triangle (Aₜ) = 24

Area of rectangle (Aᵣ) = 4x – 16

1. Writing an absolute value for the inequality.

From the question given above, we were told that the difference between the areas of the figures is less than 4. This can be written as:

Aₜ – Aᵣ < 4

Area of triangle (Aₜ) = 24

Area of rectangle (Aᵣ) = 4x – 16

24 – (4x – 16) < 4

Simplify

24 – (4x – 16) < 4

Clear bracket

24 – 4x + 16 < 4

24 + 16 – 4x < 4

40 – 4x < 4

Thus, we can write the absolute value for the above inequality as:

|40 – 4x| < 4

2. Determination of the solution of the inequality.

This is illustrated below:

|40 – 4x| < 4

Thus the above equation can be written as

– 4 < 40 – 4x < 4

Subtract 40 from both side

– 4 – 40 < 40 – 4x – 40 < 4 –40

– 44 < – 4x < – 36

Divide through by –4

– 44/–4 < x < – 36/–4

11 > x > 9

Note: the inequality sign changed because we divided by a negative number

Thus, 11 > x > 9 becomes 9 < x < 11

Therefore, the solution to the inequality is 9 < x < 11

3 0

4 years ago

Question 3(Multiple Choice Worth 1 points)

Darya [45]

Answer:

1/4 ⋅ 12

Step-by-step explanation:

The oil company fills 1/12 of a tank in 1/4 hour (20 minutes) with gasoline.

1/4 ⋅ 12

(time) ⋅ (total tank size)

5 0

3 years ago

Read 2 more answers

Mrs. Merritt, has 75% of her $300 dollar goal, how much money does she have?

Triss [41]

Answer:

She has 225 dollars

Step-by-step explanation:

75% of her $300

Change the percent to decimal form

.75 * 300

225

She has 225 dollars

3 0

3 years ago

Plz help solve, <br>velocity units are ft/min<br>

Alex Ar [27]

Answer:

t = 11 min

and

t = 18 min

Step-by-step explanation:

When we have unidimensional motion, the sign of the velocity defines the direction.

So we could say that a positive velocity like:

v = 4ft/min

Means that you are moving to the right with a speed of 4 feet per minute.

And a negative velocity like:

v = -3 ft/min

means that you are moving to the left with a speed of 3 feet per minute.

Then the bug changes direction when the velocity changes of sign.

In the graph, we can see that the velocity changes of sing in two points, these points are:

t = 11 min

and

t = 18 min

8 0

3 years ago

The line that passes through (-2, 4) and is parallel to x - 2y= 6

lubasha [3.4K]

Answer:

The equation of other line parallel to given line is y = $\dfrac{x}{2}$ + 5 .

Step-by-step explanation:

Given as :

The equation of a line is

x - 2 y = 6

Or, 2 y = x - 6

Or, y = $\dfrac{1}{2}$ x - $\dfrac{6}{2}$

i.e y = $\dfrac{1}{2}$ x - 3

The standard equation of line is given as

y = m x + c

where m is the slope of line

Now, comparing given line with standard line equation

The slope of line x - 2 y = 6 is m = $\dfrac{1}{2}$

<u>Again</u>

Other line is passing through point (- 2 , 4) and is parallel to given line

For parallel line condition

slope of both lines are equal

Let The slope of other line = M

So, M = m = $\dfrac{1}{2}$

<u>Again</u>

Equation of line with slope $\dfrac{1}{2}$ and passing through point (-2 , 4)

y - $y_1$ = M ( x - $x_1$ )

i.e y - 4 = ( $\dfrac{1}{2}$ ) ( x + 2)

Or, y - 4 = $\dfrac{x}{2}$ + 1

Or, y = $\dfrac{x}{2}$ + 1 + 4

i.e y = $\dfrac{x}{2}$ + 5

Hence, The equation of other line parallel to given line is y = $\dfrac{x}{2}$ + 5 . Answer

6 0

3 years ago