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What is the solution to |x+ 2| <1?

Step-by-step explanation:

Dilation Geometry

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor. For example, a square of side 5 units can be dilated to a square of side 15 units, but the shape of the square remains the same.

Dilation Definition

The process of resizing or transforming an object is called dilation. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image. Dilation can be of two types:

Expansion - When the size of an object is increased.

Contraction - When the size of an object is decreased.

Observe the following figure which shows the dilation of a square. In this dilation, the size of the square is increased but the shape remains the same.

Pre-image and Image

Center of Dilation

Another important concept in dilation geometry is the 'center of dilation'. Dilation transforms the size of the figure which may either increase or decrease. The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted. In the figure shown below, the triangle is enlarged from the center of dilation which is marked as 'R'.

Center of Dilation

The Scale Factor

Scale factor is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. It is the ratio of the sizes of the original figure with the dilated figure.

The scale factor can be denoted by r or k.

The image is enlarged if the scale factor is more than 1 (k > 1).

The image is contracted if the scale factor is less than 1 (0< k <1).

The image remains the same if the scale factor is 1 (k = 1).

Note: The magnitude of the scale factor is considered and the scale factor cannot be zero.

Scale Factor Formula

The scale factor can either increase the size of an object or decrease the size of an object. The basic formula to find the scale factor of a dilated figure is:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

This formula can be written in another way which helps to find the dimension of the new shape: Dimensions of the original shape × Scale factor = Dimension of the new shape

Dilation in Geometry

In mathematics, dilation is a process of changing the size of an object or a shape without changing its shape. The shape can be a point, a line segment, a polygon, etc. It should be noted that the shape can be enlarged or shrunk but the proportion of each dimension of the shape and the angles remain the same.

Dilation in Geometry

In the above figure,

ΔPQR is dilated (enlarged) to ΔP'Q'R' and the angles are the same. The coordinates of the vertices of ΔPQR have been changed after dilation.

P(1,3) → P' (3,9)

Q(3,1) → Q' (9,3)

R(1,1) → R' (3,3)

How to Calculate the Scale Factor in Dilation?

The scale factor can be calculated when the original dimension and the changed dimension is given. Let us find the scale factor of a triangle with the original dimensions and scaled up dimensions. As seen above, after dilation, the coordinates of ΔPQR changed as follows:

P(1,3) → P' (3,9)

Q(3,1) → Q' (9,3)

R(1,1) → R' (3,3)

Let us consider each vertex one by one:

Vertex P:

The x-coordinate 1 changed to 3 and the y-coordinate 3 changed to 9. This shows that both the coordinates of P' became thrice the coordinates of P.

Vertex Q:

The x-coordinate 3 changed to 9 and the y-coordinate 1 changed to 3. This again shows that both the coordinates of Q' became thrice the coordinates of Q.

Vertex R:

The x-coordinate 1 changed to 3 and the y-coordinate 1 changed to 3. As we can see, both the coordinates of R' became thrice the coordinates of R

Therefore, the scale factor in this dilation is 3. Every coordinate of ΔPQR is multiplied by the scale factor of 3 to obtain the enlarged Δ P'Q'R'. In other words, if the scale factor is k, the coordinates (x,y) are transformed to (kx,ky).

(x,y) → (kx,ky).

The scale factor can also be calculated directly by using the formula: Scale factor = Dimension of the new shape ÷ Dimension of the original shape

In this case, if we divide the coordinates of the new vertices by the coordinates of the original vertices, we can get the scale factor. For example, let us take the dimensions of vertex P (1, 3) and P' (3, 9).

Take the x-coordinate of P' = 3 and the x-coordinate of P = 1.

Substitute the values in the formula: 3 ÷ 1 = 3.

Now, take the y-coordinate of P' = 9 and the y-coordinate of P = 3.

Apply the same formula: 9 ÷ 3 = 3. Thus, we get the scale factor of 3 from both the coordinates.

Answer:

(2, 10)

Step-by-step explanation:

(1, 5) dilated by a scale factor of 2:

(x * 3, y * 2) --> (1 *2, 5 *2) --> (2, 10)

Hope this helps!

Answer:

c I am pretty sure of deep nuts u am playin it c

Answer:

Step-by-step explanation:

I believe it should be 7, but 21 is out of the question. And 14 seems it would be too much,

Answer:

Step-by-step explanation:

Multiply 20 by 12:

Multiply 240 by 5:

Multiply the lengths:

Answer:

The missing side is 5 cm

Step-by-step explanation:

Step 1:  Determine the missing side

\(V=l*w*h\)

\(1200\ cm^3 = 20\ cm * w * 12\ cm\)

\(\frac{1200\ cm^3}{20\ cm * 12\ cm} = w\)

\(\frac{1200\ cm^3}{240\ cm^2} = w\)

\(5\ cm = w\)

Answer: The missing side is 5 cm

Answer:

figure d

Step-by-step explanation:

it is the smartes and most common answer

Answer:

5/1

Step-by-step explanation:

Example:

Decimal:

0.051

Fraction:

51/1000

Percentage:

5.1%

I think this is what you want

Solution

Step 1

To convert seconds to hours, divide the seconds by 3600.

Step 2

1 million seconds = 1000000 seconds

Step-by-step explanation:

one side.

as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.

the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.

so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.

The minimum number of moves required to solve the Tower of Hanoi puzzle with n disks is given by the formula n = 2(n -1) + 1.

The central limit theorem, a cornerstone of statistics, asserts that, regardless of the population's underlying distribution, the distribution of sample means tends towards normality as sample size grows. In other words, as sample size rises, the distribution of sample means will become more normal, even if the population is not normally distributed. This is a significant finding because, on the assumption that the sample is representative and randomly chosen, it enables us to draw conclusions about the population from a sample size that is rather small.

From the given table we observe the following pattern:

number of moves(n) = 2 * number of moves(n-1) + 1

Hence, the minimum number of moves required to solve the Tower of Hanoi puzzle with n disks is given by the formula n = 2(n -1) + 1.

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Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.

The leading term of a polynomial function is the term containing the highest power of the variable. Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.

The degree of a polynomial function is the highest degree of any of its terms.

If a polynomial has only one term, then the degree of that term is the degree of the polynomial and is also called a monomial.

For example, consider the given function:Now, observe the degree of the function, which is 14, as the highest exponent of the function is 14.

Thus, the term containing the highest power of the variable x is -18x¹⁴.

Therefore, among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.

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When it is required to minimize the effect of a few extreme scores, median is the measure of central tendency which is the most appropriate.

This is due to the fact that the median isn't influenced by extreme values, which means it is the middle value when the observations are ordered from least to greatest.There are several measures of central tendency, including the mode, median, and mean.

The most common measure is the mean, but it is greatly affected by the presence of a few very high or very low scores.To ensure that the mean isn't skewed too much by these scores, the median is a better choice. The median is the middle number in a data set when the observations are sorted from smallest to greatest.

In this way, if there are extremely high or low scores, they are not going to influence the median significantly as compared to the mean. Hence, we can say that the median is the most appropriate measure of central tendency when it is desired to minimize the effect of a few extreme scores.

The measure of central tendency that is most appropriate when it is desired to minimize the effect of a few extreme (very high or very low) scores is the median.

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After the boys from Barack Academy travel to Hillary High and then return with a combination of boys and girls, Hillary High will have more boys on campus compared to the number of girls at Barack Academy.

Based on the given information, we can determine that both schools initially have the same number of students. The boys from Barack Academy board the bus and travel to Hillary High for a dance. Afterward, the bus is filled with a combination of boys and girls and they travel back to Barack Academy for another dance.

Since all the boys from Barack Academy initially leave the school and then return with a combination of boys and girls, it can be inferred that the number of boys on campus at Barack Academy remains the same or increases (if some boys from Hillary High join them).

On the other hand, at Hillary High, the girls who stay at the school are joined by a combination of boys and girls from the other school. Therefore, it can be inferred that the number of boys on campus at Hillary High increases.

Based on this analysis, it can be concluded that after the events described, Hillary High would have more boys on campus than Barack Academy would have girls on campus.

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The true statements are:

a. The range for this function is the set {3}.

c. The domain for this function is all real numbers.

The given graph shows a horizontal line passing through the point (3, 3). Since the line is horizontal, the y-coordinate remains the same for all values of x, making statement b false.

The range of a function represents the set of all possible y-values, and in this case, it is only the value 3, making statement a true.

The domain of a function represents all possible x-values, and since there are no restrictions on x in the given graph, the domain is all real numbers, making statement c true.

The statements d and e are false because the domain is not restricted to just the value 3, and the range consists only of the value 3, not all real numbers.

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Answer:

42

Step-by-step explanation:

3x=180-54=126

X=42

hope this helps:))

Answer:

Slope = -2/3

Step-by-step explanation:

Slope = \(\frac{y_{2} -y_{1}}{x_{2}-x_{1}}\)

Slope = \(\frac{-1 -(-5)}{-4-2} = \frac{4}{-6} =-\frac{2}{3}\)

Answer:

9

Step-by-step explanation:

63 divided 7=9

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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The triangles that are right triangles are triangles A and E using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse(the longest side) is equal to the sum of the squares of the other two sides. 

For triangle A:

the long side (√5)² = 5

the sum of the other sides is

(√3)² + (√2)² = 5

For triangle B:

the long side (√5)² = 5

the sum of the other sides is

(√3)² + (√4)² = 7

For triangle C:

the long side 6² = 36

the sum of the other sides is

4² + 5² = 41

For triangle D:

the long side 7² = 49

the sum of the other sides is

5² + 5² = 50

For triangle E:

the long side 10² = 100

the sum of the other sides is

8² + 6² = 100

Therefore, the triangles that are right triangles are triangles A and E using the Pythagoras rule.

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The resulting probability distribution is:0.089

To convert the information on the number of hours parked to a probability distribution, we need to divide each frequency by the total sample size of 225. This will give us the probability of a car parking for each respective number of hours.

Number of Hours Frequency Probability

1 15 15/225 = 0.067

2 38 38/225 = 0.169

3 53 53/225 = 0.236

4 50 50/225 = 0.222

5 94 94/225 = 0.418

6 45 45/225 = 0.200

7 20 20/225 = 0.089

The resulting probability distribution is:

Number of Hours Probability

1 0.067

2 0.169

3 0.236

4 0.222

5 0.418

6 0.200

7 0.089

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Answer:

Step-by-step explanation:

Remark

This has nothing to do with parallel lines. All you need use is opposite angles (like k and 98 ) for example, and supplementary angles like h and 127.

h + 127

These 2 are supplementary.

h + 127 = 180              Subtract 127 from both sides.

h+127-127=180-127    Combine

h = 53

g and 127

g = 127. These two angles are opposite each other. (More correctly vertically opposite.

98 and k

These two are also vertically opposite

k = 98

m + 98                       are supplementary. They add to 180 degrees.

m + 98=180                Subtract 98 from both sides of the equation

m + 98-98 = 180-98  Combine

m = 82

And

Remember that opposite angles are equal

The integral needed to compute the total amount of water drained from the pool when the drain is left open indefinitely is: ∫(from 0 to ∞) 40e^(-0.05t) dt

To calculate how much water drains from the pool over an indefinite period of time, we need to set up an integral using the given rate function:
∫(0 to infinity) R(t) dt
= ∫(0 to infinity) 40 e^-0.05t dt
= 40 ∫(0 to infinity) e^-0.05t dt

We can solve this integral using integration by substitution. Let u = -0.05t, then du/dt = -0.05 and dt = du/-0.05. Substituting these into the integral, we get:
= 40 ∫(0 to infinity) e^u du/-0.05
= -800 ∫(0 to infinity) e^u du

Now we can evaluate the integral using the formula ∫e^x dx = e^x + C, where C is the constant of integration:
= -800 [e^u] (0 to infinity)
= -800 [e^-0.05t] (0 to infinity)

Since e^-0.05t approaches zero as t approaches infinity, we can simplify the expression to:
= -800 [e^0 - e^0]
= -800 [1 - 1]
= 0

Therefore, the amount of water that drains from the pool over an indefinite period of time is zero.

This makes sense because the drain rate function approaches zero as time goes on, indicating that the pool will eventually stop draining.

To find the total amount of water drained from the swimming pool when the drain is left open indefinitely, we need to integrate the rate function R(t) = 40e^(-0.05t) gal/hr over time. Since we want to find the total amount drained indefinitely, we'll integrate from t = 0 to t = ∞. Set up the integral as follows:
∫(from 0 to ∞) 40e^(-0.05t) dt
This will give us the total amount of water drained from the pool when the drain is left open indefinitely.

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Ginny should reorder when the inventory level reaches 116.515 pounds to maintain a 95% service level

To calculate the reorder point, we need to consider two factors: the lead time (time between ordering and receiving the delivery) and the safety stock (the extra amount of flour kept in case of unexpected demand or delay in delivery).

Using the formula: Reorder point = (Average daily usage x Lead time) + Safety stock, we can calculate the reorder point.

Here, the average daily flour consumption is 35 pounds with a standard deviation of 7 pounds, and the average delivery time from the supplier is 3 days with a standard deviation of 0.5 days. She decides to order 72 pounds at a time.

The lead time is 3 days, and the safety stock can be calculated using the service level and standard deviation of demand during lead time. Assuming a 95% service level, we can use the z-score of 1.645 (from the standard normal distribution table) to calculate the safety stock.

Safety stock = (z-score x Standard deviation of demand during lead time) = (1.645 x 7) = 11.515 pounds

Now, we can calculate the reorder point:

Reorder point = (Average daily usage x Lead time) + Safety stock = (35 x 3) + 11.515 = 116.515 pounds

Therefore, Ginny should reorder when the inventory level reaches 116.515 pounds to maintain a 95% service level. This ensures that she has enough flour to cover her daily usage and also account for any unexpected demand or delivery delays.

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Answer:

y= -5x+7

Step-by-step explanation:

since it is parallel, the gradient is the same

m=-5

y=mX+C

y=-5x + c

sub in the coordinate to get the y intercept

(2)= -5(1)+c

2+5 = C

C=7

therefore the ans is :

y= -5x + 7

(tell me if i got it correct)

The distance of the object from the helicopter based on the information about the height given will be 460 feet.

Your information is incomplete and the diagram wasn't found. This will be solved based on assumed figures.

From the information given, we are told that the helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post and we want to calculate the distance of the object from the helicopter.

Let's assume that the helicopter climbs 20 feet per seconds

Also, based on the information given, let us assume that the object is 10 seconds away.

Therefore, the distance will be calculated thus:

d = 250 + 21t

d = 250 + 21(10)

d = 250 + (21 × 10)

d = 250 + 210

d = 460 feet

Hence, based on the information, the distance of the object from the helicopter will be 460 feet.

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The probability is approximately 0.6915, or 69.15%..

Given that the mean (μ) of VO₂MAX scores for men aged 20 to 29 is 42 ml/min/kg and the standard deviation (σ) is 6 ml/min/kg, we can standardize the value of 45 ml/min/kg to calculate the probability using the z-score formula: z = (x - μ) / σ.

Substituting the values into the formula,

z = (45 - 42) / 6 = 0.5

Using a standard normal distribution table or calculator, we find the probability corresponding to a z-score of 0.5 is approximately 0.3085.

To find the probability of a score greater than 45 ml/min/kg, we subtract the obtained probability from 1:

1 - 0.3085 = 0.6915

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Answer:

Yes, point (2,4) satisfies the system of inequalities.

Step-by-step explanation:

The area of the graph that is the darkest contains all points that satisfy both inequalities. See the attached worksheet for further explanation of the graph and other colors.