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2 years ago

What is the value of x? 1/6 (3 - 2x) < 1/3 x

Mathematics

1 answer:

777dan777 [17]2 years ago

3 0

Step-by-step explanation:

1/6 (3 - 2x) < 1/3 x

let's multiply everything by 6

3 - 2x < 6/3 x

3 - 2x < 2x

3 < 4x

3/4 < x

so, x > 3/4

since 3/4 is never equal to x but is purely smaller than x, the interval of valid x values starts right after 3/4 and goes to infinity.

x = 3/4 is not valid, because 3/4 is not smaller than 3/4 (it is equal to) ...

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Patty bought a "P" poster to put on her wall, as shown below.

kolezko [41]

The area of the poster is B. 535.5 in².

Step-by-step explanation:

Step 1:

The poster consists of a rectangle and three-quarters of a circle.

The rectangle has a length of a and width of 3a. The circle has a radius of a.

We calculate the areas of the individual shapes and sum them up to calculate the entire area of the poster.

Step 2:

The area of a rectangle is the product of its length and its width.

If a = 10 inches, the length is 10 inches and the width is 30 inches.

The area of the rectangle $= (l)(w) = (10)(30)= 300.$

The area of the rectangle is 300 in².

Step 3:

The area of a circle $= \pi r^{2} .$ Here we only have three-quarters of a circle, so

The area of the given circle $=\frac{3}{4} ( \pi r^{2} ).$

Here r = a = 10 inches.

So the area of the circle $=\frac{3}{4} ((3.1415) (10^{2}) ) = 235.6125.$

The area of the circle is 235.6125 in².

Step 4:

The total area of the shape = The area of the rectangle + The area of the circle.

The total area of the shape $= 300 + 235.6125 = 535.6125.$

So the area of the poster is B. 535.5 in².

7 0

3 years ago

$8.50 with 6.5% markup

liraira [26]

Answer:

total would be $9.05

Step-by-step explanation:

$0.55 + $8.50

4 0

3 years ago

Indicate the equation of the given line in standard form. The line with slope and containing the midpoint of the segment whose e

Tems11 [23]

Answer:

x + y = -1

Step-by-step explanation:

To write the equation of a line, find the slope and use it with a point in the point slope form.

You can find the slope using the slope formula.

$m = \frac{y_2-y_1}{x_2-x_1} = \frac{5--3}{-6-2} = \frac{8}{-8}=-1$

Substitute m = -1 and the point (2,-3) into the point slope form.

$y - y_1 = m(x-x_1)\\y --3 = -1(x-2)\\y+3=-1(x-2)$

Convert to standard form by applying the distributive property and rearranging the terms.

y+3 = -1(x-2)

y + 3 = -x + 2

x + y + 3 = 2

x + y = -1

8 0

3 years ago

Joshua works in a coffee shop and makes $8.80 a day. If Joshua works 4 hours a day, how much does he get paid every hour?

viva [34]

Answer: Hi there! Joshua would make 2.20 an hour.

Step-by-step explanation:

The first step is to divide the amount he made in a day by the hour.

8.8 / 4 = 2.20

2.20 is the amount he makes an hour. If you want to make sure, you can multiply the 2.20 by the amount of hours he worked.

2.2 * 4 = 8.80

Have a lovely day!

5 0

2 years ago

Find the correct plugged in formula for each figure.

Mars2501 [29]

Answer:

$Area = 40 ( 84)+ 2 *(294)$

Step-by-step explanation:

There is only one figure in the attached image and the solution (surface area) is as follows:

The shape can be sub-divided into:

1. Rectangle

Dimension: 40 by 35

2. Rectangle

Dimension: 40 by 28

3. Rectangle

Dimension: 21 by 40

4. 2 triangles

Base: 21 and Height: 28

Calculate area of each and add them up to get the surface area of the figure.

1. Rectangle

Dimension: 40 by 35

$A_1 = 40 * 35$

2. Rectangle

Dimension: 40 by 28

$A_2 = 40 * 28$

3. Rectangle

Dimension: 21 by 40

$A_3 = 40 * 21$

4. 2 triangles

Base: 21 and Height: 28

$A_4 = 2 * \frac{1}{2} * 21 * 28$

So, the area is:

$Area = A_1 +...+A_4$

$Area = 40 * 35 + 40 * 28 +40 * 21 + 2 * \frac{1}{2} * 21 * 28$

Factor out 40

$Area = 40 ( 35 + 28 + 21 )+ 2 * \frac{1}{2} * 21 * 28$

$Area = 40 ( 84)+ 2 * \frac{1}{2} * 21 * 28$

$Area = 40 ( 84)+ 2 *(294)$

8 0

3 years ago