solve the inequality x³-9x > 0

The longest piece of wood that could fit in your trunk to build a gate for the backyard is 60.65 inches.

The length of the diagonal of the cuboid is found out using the following formula.

\(D=\sqrt{l^2+b^2+h^2}\)

Here, (l) is the length of the cuboid, (w) is the width, and (h) is the height of the cuboid.

The wood has to buy to build a gate for backyard. The car trunk has the following dimensions (47 inches by 33 inches by 19.5 inches). Here, we have,

The longest piece of wood which fits is equal to the length of diagonal of cuboid. Put the values in the formula,

\(D=\sqrt{47^2+33^2+19.5^2}\\D=\sqrt{3678.25}\\D=60.65\rm\; in\)

Thus, the longest piece of wood that could fit in your trunk to build a gate for the backyard is 60.65 inches.

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Answer:

Step-by-step explanation:

-2x +38 = 2(3 + 3x)

-2x + 38 = 2*3 + 2*3x

-2x + 38 = 6 + 6x

Add 2x to both sides

38 = 6 + 6x + 2x  

Combine like terms

38 = 6 + 8x

Subtract 8  from both sides

38 - 6 = 8x

8x = 32

Divide both sides by 8

x = 32/8

x = 4

Answer:

x = 4

Step-by-step explanation:

Use distributive property to multiply 2 by 3 and 3x

subtract 6x from both side

combine -2x and -6x to get -8x

subtract 38 from both side

subtract 38 from 6 to get -32

divide both side by -8

\( \small \sf \frac{-8x}{ -8} = \frac{-32}{-8} \\ \\ \small \sf x = \frac{- 32}{-8}\)

divide -32 by -8 to get 4

Answer:

9

Step-by-step explanation:

The GCF between 54 and 27 is nine.

Answer:

v = -12

Step-by-step explanation:

29 = -8v - 7 + 5v

Combine the 'like terms':  

29 = (-8v + 5v) - 7

29 = -3v -7

Add 7 to both sides:

29 + 7 = -3v -7 +7

36     =    -3v + 0

36      =    -3v

Divide both sides by the coefficient in front of the variable 'v' because we want to get 'v' all by itself. So, divide by -3.

36/-3 = -3v/-3

   -12  =  v

And that is the answer, v is negative twelve

Answer:

v=

Step-by-step explanation:

29= -8v- 7 + 5v

-8v + 5v - 7 = 29

-3v - 7 = 29

-3v - 7 + 7 = 29 + 7

-3v = 36

-3v ÷ -3 = 36 ÷ -3

v = -12

Answer:

1/2

Step-by-step explanation:

42/84=1/2

Answer:

center (0, 3) and radius 2√2

Step-by-step explanation:

Equation of a circle

\((x-a)^2+(y-b)^2=r^2\)

where:

Given equation:

\(x^2+y^2-6y+1=0\)

Subtract 1 from both sides:

\(\implies x^2+y^2-6y=-1\)

To create a trinomial with variable y, add the square of half the coefficient of the y term to both sides:

\(\implies x^2+y^2-6y+\left(\dfrac{-6}{2}\right)^2=-1+\left(\dfrac{-6}{2}\right)^2\)

\(\implies x^2+y^2-6y+9=8\)

Factor the trinomial with variable y:

\(\implies x^2+(y^2-6y+9)=8\)

\(\implies x^2+(y-3)^2=8\)

Factor \(x^2\) to match the general form for the equation of a circle:

\(\implies (x-0)^2+(y-3)^2=8\)

Compare with the general form of the equation for a circle:

\(\implies a=0\)

\(\implies b=3\)

\(\implies r^2=8 \implies r=2\sqrt{2}{\)

Therefore, the center is (0, 3) and the radius is 2√2

x+11.95≤30

Then x≤30−11.95x≤30−11.95

x≤18.05x≤18.05Answer:

Step-by-step explanation:

Answer:

A: AB corresponds to FG

Step-by-step explanation:

The question is asking for which statement if not true/false.

Answer choice A is false because when you turn the rectangle, AB does not end up where FG is. Instead, AB ends up where EF is. Also,  the length of AB is 6 units, while the length of FG is 4 units. So, they cannot correspond to each other.

The graph shows that Connor traveled a total of seven blocks from his house to the store and then from the store to the bank.

Graph is a data structure used to represent data in a visual way. It is composed of a set of nodes and edges, where each node represents an object and each edge represents a connection between two objects. Graphs can be used to represent a variety of data structures, such as a network of roads, a family tree, or a list of friends. Graphs are powerful tools for understanding complex relationships in data.

It also shows that he stayed at the store and the bank for five and seven minutes respectively. After leaving the bank, he drove the remaining four blocks back home.

The graph also reveals that Connor was driving at a steady pace between the store and the bank and that the total journey time was twenty-two minutes. This time could have been reduced if he had driven faster. However, it is possible that he was being cautious due to the traffic or other conditions.

Overall, the graph provides a visual representation of Connor's journey and his decisions along the way. It also provides insight into his driving habits, as well as his ability to manage his time. Based on this data, it is clear that Connor was able to complete his errands in an efficient manner.

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A good practice to remember when adding transitions to a presentation is to ensure that they are purposeful, consistent, and enhance the overall flow of the presentation.

Purposeful: Use transitions to guide the audience through your key points and ideas, making sure they complement the content and contribute to the overall message.
Consistent: Maintain a consistent style of transitions throughout your presentation to maintain a cohesive look and feel. Avoid using too many different types of transitions, as this may be distracting.
Enhance flow: Transitions should help create a smooth flow between slides and ideas, making it easy for the audience to follow your presentation. Avoid using abrupt or overly flashy transitions that may interrupt the natural progression of your content.

finally, Test your presentation with the transitions to make sure they enhance the overall flow and comprehension of your message.

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The scale factor of figure B to figure A is 1/2.

To find the scale factor of figure B to figure A, we need to determine how much the corresponding sides of the two figures have been multiplied or divided by.

Looking at the figures, we can see that the corresponding sides of figure B are half the length of the corresponding sides of figure A. For example, the length of side AB in figure A is twice the length of side AB' in figure B, and the length of side BC in figure A is twice the length of side B'C' in figure B.

Since the corresponding sides of figure B are half the length of the corresponding sides of figure A, the scale factor of figure B to figure A is 1:2 or 1/2.

Therefore, the scale factor of figure B to figure A is 1/2.

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The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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The correct option is D, the parent quadratic function is:

f(x) = x²

First, we define the parent functions as the simplest function for each type.

For example, the parent linear function is.

y = x

The parent square root function is:

y = √x

The parent absolute value function is:

y = |x|

And so on.

So the parent quadratic function is a polynomial of degree 2 where we only have the quadratic term (and no coefficient).

Thus, the correct option is D; f(x) = x²

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The inverse statement is false.

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Answer:

6in 5in

you have to do 5×2 and 6×2 and add those together

Answer:

The 6 by 5 rectangle

Step-by-step explanation:

It is the 6 by 5 rectangle because the text says she used 22 inches to border the cover. this means we need to look at the rectangles perimeters to find the answer. to find the perimeter of  rectangles that only give you measurements for two sides you need to multiply each measurement by 2. So you need to do 6 times 2 and 5 times 2 to get 12 and 10. once you have your two numbers you add them together. 12+10=22. (remember we were looking for a recangle with a perimeter of 22 inches)

I hope this helps you out a little.

Answer:

the sale price of the one-terabyte external hard drive is $274.13.

Step-by-step explanation:

To find the sale price of the one-terabyte external hard drive, we can use the following formula:

Sale price = Original price - Discount amount

where the discount amount is the amount by which the original price is reduced. The discount amount is equal to the discount rate times the original price. The discount rate is 21%, or 0.21, because the hard drive is on sale at a 21% discount.

Substituting the given values into the formula, we get:

Discount amount = 0.21 * $347 = $72.87

To find the sale price, we subtract the discount amount from the original price:

Sale price = $347 - $72.87 = $274.13

Therefore, the sale price of the one-terabyte external hard drive is $274.13.

Answer:

look at the horizontal line in the picture. the degree measure of any line is 180° given there's a perpendicular ray through that horizontal line it's therfore split into two sides both with angle measure of 90°.

given f is 71° then g can be found knowing that both g and f must add to 90°. 71+g=90. g=19°

now look at f again. f and d are what's known as vertical angles and that means that they're angle measures are congruent. therfore the measure of d is 71° d=71°

Finally to find e we notice that angle d and e form a straight line which means both angles measures must add to 180°. therefore e can be found by computing d+e=180

aunaitituitmg our information we know 71+e=180 then e must equal 109° e=109°

Ss, variance and the standard deviation for the population of scores is 2.83 and 8 respectively

What is standard deviation and variance?

Standard deviation is a measure of the distribution of statistical data, whereas variance is a measure of how data points differ from the mean. The fundamental distinction between the two is that although the variance is expressed in squared units, the standard deviation is expressed in the same units as the data's mean.

Given,

SS = 40

Variance = 10

Standard Deviation = 3.16

Using Population Variance Formula :

= \(\frac{1}{n}\)∑( x-xbar)²  where i is 1

For the complete solution see the attachment of table

sum ( x - x bar)² = 40

so, variance = 40/5

= 8

standard deviation = \(\sqrt{8}\)

= 2.83

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Step-by-step explanation:

Understand

Gary owns a farm and he sent 35 of his cows to the market. He assumed he would have around 1100 cows left.

plan

we need to calculate the total amount of cows Gary owns and subtract the amount he sent to the market to find out the actual amount of cows left.

Carry out

total number of cattles = 305 + 530 + 320 + 130 = 1285

cattles left = 1250

Check

Gary assumed he had 1100 cattles left but he has 1250 left.

Q2

It was a good guess since the amount Gary guessed is close enough to the actual amount he has.

The actual amount left is greater than that Gary assumed.

The amount Gary guessed to have is reasonable since the amount is close to the actual amount.

Answer:

The answer is 3.

Step-by-step explanation:

The equation would be: x = 14.95 divided by 4.99, rounded to the nearest one:

14.95 divided by 4.99 = 2.99599...

Normally, I would not round the number to the nearest digit in problems like these, but 2.99599 is quite close to 3, so this might be an exception.

Anyways, that's how I got my answer.

Hope this helped.

The formula for the arc length is,

Substitute the values in the formula to determine the arc length.

So answer is 19.6 inches.

Answer:

At a package weight of 8 kilograms, the two couriers both cost $37

Step-by-step explanation:

Let's say the package weighs w kg.

First courier: 13 + 3 per kg = 13 + 3 for each w = 13 + 3w

Second courier: 5 + 4w

They are equal in cost, so

13 + 3w = 5 + 4w

subtract 3w from both sides to put all the variables on one isde

13 = 5 + w

subtract 8 from both sides to solve for w

w = 8

plug w=8 into one side of the original equation to solve for cost

13 + 3w = 5 + 4w = 37

Answer:

$43.74

Step-by-step explanation:

will pay= $45

10% of =$45×10/100=$4.5

so, $45-$4.5= $40.5

8% tax= $40.5×8/100 =$3.24

total= $43.74

Answer:

3

Step-by-step explanation:

This is the graph of y = tan(x) shifted 3 units up.

The graph shown is of tan function where the vertical shift is of 2 units.

The graph of a tan function is shown we have to determine the vertical shift to the graph. As we know that tanx function has its inflection point at the origin, as the graph is already translated we can see that the inflection point of the graph is at x = -π/12. The corresponding value of y is 2

Equation of the given function is given by:

f(x) = tan(x+π/12)+2

Where -π/12 shows the horizontal shift while +2 shows the vertical shift.

Therefore, the required vertical shift is +2 units.

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According to the information we can infer that to form a polygon, we need a set of coordinates that, when connected, create a closed shape with straight sides. Also, to find the perimeter of a polygon, we can use the distance formula to calculate the length of each side.

To create a polygon, we need a set of coordinates that define the vertices of the shape. These coordinates should be ordered in a way that when we connect them sequentially, we form a closed shape with straight sides.

Once we have the coordinates of the vertices, we can calculate the length of each side using the distance formula. The distance formula calculates the distance between two points in a Cartesian coordinate system. By applying this formula to consecutive pairs of vertices, we can find the length of each side.

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