- 3(x + 1) <6 solve the inequality

The arc length of arc AB is approximately 8.3076π units.

To find the arc length of arc AB, we need to know the angle subtended by the arc and the radius of the circle. In this case, we are given that angle AB is 115 degrees and the radius BC is 13 units.

The formula for the arc length (L) of a circle is given by L = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius of the circle.

Substituting the given values into the formula, we have:

L = (115/360) × 2π(13)

Simplifying this expression:

L = (0.3194) × 2π(13)

L ≈ 0.3194 × 26π

L ≈ 8.3076π

So, the arc length of arc AB is approximately 8.3076π units.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

3. 33.33, 4. 43, 5. 31

Step-by-step explanation:

3. 60+40=100/3= 33.33

4. 85+1/2=86/2= 43

5. 100+86=186/6= 31

PERIMETER

Answer:

Answer is 28 m

Step-by-step explanation:

Breadth= 2m

Length= 2X6m

= 12m

Perimeter of a rectangle = 2X (Length+ Breadth)

= 2X (2+12)

= 2X14

= 28m

AREA

Answer:

Answer is 24 m

Explanation:

Length= 12

Breadth= 2

Area of a rectangle= Length X Breadth

= 12X2

= 24 sq. m

Hope it helps ;)

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The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:

1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.

2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.

3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.

In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.

Answer:

7

Step-by-step explanation:

2.48>2.471>2.463

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Answer:

X = 10

Z = 67

Step-by-step explanation:

We see that the angles are formed by the intersection of two lines.

Angles z and  67° are vertically opposite angles and therefore they are equal to each other

z°= 67°

Angles z and (7x + 43) are supplementary angles. The sum of these angles add up to 180°

z + 7x + 43 = 180

67 + 7x + 43 = 180

7x + 110 = 180

7x = 180 -110 = 70

x = 70/7 = 10

Answer:

MDK and KMD is the valid name for the triangle ️

Answer:

FEA

Step-by-step explanation:

Answer:

Third option is the correct answer

Step-by-step explanation:

\(3 {x}^{5} \bigg( 2 {x}^{2} + 4x + 1 \bigg) \\ \\ = 3 {x}^{5} \times 2 {x}^{2} + 3 {x}^{5} \times 4x + 3 {x}^{5} \times 1 \\ \\ = 3 \times 2 {x}^{5 + 2} + 3 \times 4 {x}^{5 + 1} + (3 \times 1) {x}^{5} \\ \\ \red{ \bold{= 6{x}^{7} + 12{x}^{6} +3 {x}^{5} }}\)

\(f^{-1}(x) = \sqrt[3]{\frac{x +5}{3}}\\\)

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Let \(y = f(x)\) so that the inverse of \(y\) is equal to \(f^{-1}(x)\).

Solving for \(f^{-1}(x)\):

\(f(x) = 3x^3 -5 \\ y = 3x^3 -5 \\ x = 3y^3 -5 \\ 3y^3 -5 = x \\ 3y^3 = x +5 \\ y^3 = \frac{x +5}{3} \\ y = \sqrt[3]{\frac{x +5}{3}}\)

Since the inverse of \(y\) is equal to \(f^{-1}(x)\), \(f^{-1}(x) = \sqrt[3]{\frac{x +5}{3}}\\\).

To find the amount of wet food Luck mixed with the dry food, we can use the fact that he put 5/4 cups into each of the 4 bowls. Therefore, he used a total of 5/4 x 4 = 5 cups of wet food.

Thus, Luck mixed 3 cups of dry food and 5 cups of wet food to prepare the dog's meal.

Answer:

The total number of couples attending the banquet was 52.

Step-by-step explanation:

Given that a school reserved a banquet hall for the spring dance, and that, in addition to a $ 100 deposit, each couple must pay $ 20, to determine the total number of couples attending if the total cost of the banquet hall was $ 1,140 is due perform the following calculation:

100 + (20 x X) = 1140

20X = 1140 - 100

X = 1040/20

X = 52

Thus, the total number of couples attending the banquet was 52.

The bedroom of the apartment has 4 walls.

2 of them have the following dimensions: 16ft x 8ft.

2 of them have the following dimensions: 10ft x 8ft.

Find the area of each wall and then add them to find the total area:

It means that the total area to be covered is 416ft^2.

Now, divide this area by the area that can be covered by one roll of wallpaper to find the number of rolls needed:

It means that 8.32 rolls are needed to cover the bedroom. You will have to buy 9 rolls.

Answer:add $750.00 + $1000.00 + $375.00 = $2125.00

Step-by-step explanation:

add all together. Your monthly expense of fixed amount, living, annual monthly,

Answer:

If the segment is horizontal or vertical, you can find the midpoint by dividing the length of the segment by 2 and counting that value from either of the endpoints. Example 1: Given the graph at the right, find the midpoint of and of . AB = 4 units (by counting). The midpoint is 2 units from either endpoints.

Answer:

Step-by-step explanation:

The domain is the set of x values.

The range is the set of y values.

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Answer:

{3, 4}

Step-by-step explanation:

"M(x)=(2x-6)(x-4) true statements when M(x)=0 when x= ?" asks us to find the "roots" of M(x); that is, the x values at which M(x) = 0.  Thus, we set

(2x - 6)(x - 4) = 0, which is equivalent to 2(x - 3)(x - 4) = 0.

Thus, x - 3 = and x = 3; also x - 4 = 0, so that x = 4.  

The roots of M(x) are {3, 4}

Using the language of the original problem:  "true statements when M(x)=0 when x="              the correct results, inserted into the blanks, are x = 3 and x = 4.

Answer:

f(g(-3)) = -11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2x - 1

g(x) = 2x + 1

x = -3

Step 2: Evaluate

Answer:

\(y-2=3(x-4)\)

Step-by-step explanation:

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Substitute 3 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=3(x-x_1)\)

Now, substitute 4 as \(x_1\) and 2 as \(y_1\).

\(y-2=3(x-4)\)

Topic: parallel and perpendicular lines

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Answer:

The correct answer is A

Step-by-step explanation:

Hope this helps

Answer:

670,000

Step-by-step explanation:

because 10 to the 4 power is 10,000 just add the zero of the number and times 67 give you the answer 670,000

The probability that a ball selected at random from the jar is number 1, rounded to two decimal places, is 0.17.

To find the probability of selecting ball number 1 from a jar containing 6 balls numbered from 1 to 6, we need to determine the number of favorable outcomes (selecting ball number 1) and the total number of possible outcomes.

The total number of possible outcomes is 6 since there are 6 balls in the jar.

The number of favorable outcomes is 1 since we are interested in selecting ball number 1.

Therefore, the probability of selecting ball number 1 is given by:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

Probability = 1 / 6

To express this probability in decimal form, we divide 1 by 6:

Probability ≈ 0.1666667

Rounded to two decimal places, the probability of selecting ball number 1 is approximately 0.17.

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Answer:

7.60

Step-by-step explanation:

Answer:

i hop you will know the answer soon

Step-by-step explanation:

sorry i dont know

Answer:

11) 4/11

12) -0.2

Step-by-step explanation:

Answer:

x = 270 gallons

270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze

Step-by-step explanation:

Let x represent the number of gallons of the 50% antifreeze solution.

The volume of the 10% antifreeze is = 90 gallons

The volume of the mixture that is 40% antifreeze = 90+x

The amount of antifreeze in the two solutions must be equal to the amount of anti freeze in the mixture;

50% of x + 10% of 90 = 40% of (90+x)

0.50(x) + 0.10(90) = 0.40(90+x)

0.50x + 9 = 36 + 0.40x

Collecting the like terms;

0.50x - 0.40x = 36-9

0.10x = 27

x = 27/0.10

x = 270 gallons

270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze