in right trapezoid abcd the area of one of the shaded triangles is 54 sq units more than the area of the other one. the length of the shorter leg is 12. find the length of the other leg.
rsm problem pls help

The statement means that the set X/== is a partition of X, where X is a set and == is an equivalence relation on X.

Intuitively, this means that every element of X belongs to exactly one equivalence class, and the union of all equivalence classes is X.

More formally, a partition of a set X is a set of subsets of X such that:

The union of all subsets is X.

No two subsets have any elements in common.

In this case, the set X/== is a partition of X because it satisfies both of these conditions. First, the union of all equivalence classes is X because every element of X belongs to exactly one equivalence class.

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For the given graph of f(x), find the following values-

a. lim_x→4⁺  f(x) = ∞      b. lim_ x→-3 f(x) = -2      c. lim_x→6 f(x) = DNE

d. lim_ x→4⁻ f(x) = ∞     e. lim_ x→2⁺ = 2         f. f(-3) = -2  g. lim_x→2⁻ = 1

h. lim_x→-6 = 0.5

i. The type of discontinuity at x = 4 is an infinite discontinuity

j. There is no discontinuity at x=2 because the function is defined at x=2

For the discontinuities;

a. The limit as x approaches 4 from the right side is infinity. Given that  as x approaches 4 from the right side, the y-values of the function continue to increase without bound, while the x-value remains constant at 4.

b. The limit as x approaches -3 is -2

c. The limit as x approaches 6 does not exist given that 6 has a whole and a defined spot.\

d. The limit as x approaches 4 from the left side is infinity. Similar explanation as a.

e. The limit as x approaches 2 from the right side is 2

f. The value of f(x) at x = -3 is -2

g. The limit as x approaches 2 from the left side is 1

h. the limit of the function as x approaches -6 is 0.5

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Answer:

45 tiles

Step-by-step explanation:

Nan has 30 tiles.

Sato has half the amount Nan does, so you would divide the amount Nan has by two.

30/2=15

Then, you add the two amounts up to find the total amount.

30+15=45 tiles

Answer:

AM=Dm=6

Step-by-step explanation:

this is a simple diameter....work on it by breaking it down

The right response is D) Because the matching sides of the triangles are not proportional, AABC and AFED are not similar.

We must compare the ratios of the respective sides of the triangles AABC and AFED in order to determine whether they are similar.

Given:

AABC: AC = 12, AB = 4, BC = 6

AFED: DF = 15, DE = 7.5, EF = 5

The respective side ratios must be the same for triangles to be considered comparable. We'll figure out the ratios for the appropriate sides as follows:

Ratio of AC to DF: AC/DF = 12/15 = 0.8

Ratio of AB to DE: AB/DE = 4/7.5 = 0.533

Ratio of BC to EF: BC/EF = 6/5 = 1.2

The triangles AABC and AFED are not comparable because the ratios of the corresponding sides are not equal.

Because the matching sides of the triangles are not proportional, the correct response is D) AABC and AFED are not similar. The ratios of the matching sides do not line up, proving that there is no similarity between the triangles.

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The quotient equation from the synthetic division table is (3x⁴ + 19x³ + 22x² - 6x + 4)/(x + 2) = 3x³ + 13x² - 4x + 2

From the question, we have the following parameters that can be used in our computation:

The synthetic division table

The synthetic division table has already been completed,

However, we have the following labels

Divisor  |   Dividend

             |  Some numbers

              |  Quotient  Remainder

using the above as a guide, we have the following:

Divisor = x + 2

Quotient = 3x³ + 13x² - 4x + 2

DIvidend = 3x⁴ + 19x³ + 22x² - 6x + 4

Remainder = 0

So, the quotient equation is

(3x⁴ + 19x³ + 22x² - 6x + 4)/(x + 2) = 3x³ + 13x² - 4x + 2

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Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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The length of the arc is approximately 61.68 cm, and the area of the sector is approximately 1509.16 cm^2.

To find the length of the arc and the area of the sector, we can use the formulas related to circles and angles.

Length of the arc:

The formula to find the length of an arc in a circle is given by:

Arc Length = (angle / 360°) × (2πr)

In this case, the angle is 72°, and the radius is 49 cm. Substituting these values into the formula, we get:

Arc Length = (72° / 360°) × (2π × 49 cm)

Arc Length = (1/5) × (2π × 49 cm)

Arc Length = (2/5) × (π × 49 cm)

Arc Length = (2/5) × (π × 49 cm)

Arc Length ≈ 61.68 cm (rounded to the nearest hundredth)

Therefore, the length of the arc is approximately 61.68 cm.

Area of the sector:

To calculate the area of the sector, we need to use the formula:

Sector Area = (θ / 360°) × (π × r^2)

where θ is the central angle in degrees and r is the radius of the sector.

In this case, the central angle is 72° and the radius is 49 cm. Plugging these values into the formula, we have:

Sector Area = (72° / 360°) × (π × (49 cm)^2)

= (1/5) × (π × 2401 cm^2)

≈ (1/5) × (3.14159 × 2401 cm^2)

≈ (1/5) × 7545.8 cm^2

≈ 1509.16 cm^2

Therefore, the area of the sector is approximately 1509.16 cm^2.

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The sentence can be completed thus: After 6 minutes, of cycling class, Tariq starts to burn more calories than Jim.

The sentence can be completed by stating that after 6 minutes of a cycling class, Tariq begins to burn more calories than Jim. In the tables, we see that Ji was burning 7 calories per minute while Tariq was burning calories at the rate of 5 per minute.

However, after the 6th minute, Triq burned 15 calories and continued at that rate while Jim maintained his rate. So, after 6 minutes Tariq exceeded Jim.

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Answer: Therefore, the price of a wrap is Rs 92.2 and the price of a milkshake is Rs (92.2 + 7) = 99.2.

Step-by-step explanation:

Let's assume the price of a wrap is x (in Rs).

According to the given information, a milkshake costs Rs 7 more than a wrap. So, the price of a milkshake would be x + 7 (in Rs).

The group buys 8 milkshakes and 2 wraps. Since they bought 8 milkshakes, the total cost of milkshakes would be 8 * (x + 7) = 8x + 56 (in Rs).

Similarly, the total cost of wraps would be 2x (in Rs).

The total cost for the lunch is given as Rs 978.

So, we can set up the equation:

Total cost of milkshakes + Total cost of wraps = Total cost of lunch

(8x + 56) + (2x) = 978

Combining like terms:

10x + 56 = 978

Subtracting 56 from both sides:

10x = 922

Dividing both sides by 10:

x = 92.2

Among the given options, the equation that matches this relationship is B. y = x + 5.

The table shows that as the value of x increases from 1 to 5, the corresponding values of y are 6, 7, 8, 9, and 10.

To determine the equation that represents the relationship between x and y, we can examine the patterns and relationships in the table.

Looking at the values, we can see that the y-values are always 5 more than the x-values.

Therefore, the equation that represents the relationship between x and y is:

y = x + 5

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The measure of the angle m∠BEC is equal to 77° using the Angles of Intersecting Chords Theorem

The Angles of Intersecting Chords Theorem states that the angle formed by the intersection of the chords is equal to half the sum of the intercepted arcs, and conversely, that the measure of an intercepted arc is half the sum of the two angles that intercept it.

m∠BEC = (arc AD + arc BC)/2

m∠BEC = (45 + 109)/2

m∠BEC = 154/2

m∠BEC = 77°

Therefore, the measure of angle m∠BEC is equal to 77° using the Angles of Intersecting Chords Theorem

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120.61 ft³ is the volume of the given cylinder.

Given that the diameter of the construction pipe is 3 ft, the radius (r) would be half of the diameter, which is 1.5 ft.

The length or height (h) of the pipe is given as 17 ft.

Plugging these values into the volume formula:

Volume = 3.14159 * (1.5 )² * 17

Calculating the expression:

Volume = 3.14159 * 2.25 * 17

Volume = 120.61 ft³

Therefore, the volume of the cylindrical construction pipe is approximately 120.645 cubic feet.

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Using substitution method, the solution to the simultaneous equations are;

1) x = 4, y = 2

2) x = 2, y = 4.

To solve the given simultaneous equations:

We can use substitution or elimination method. Let's use the substitution method:

From equation 2), we can express x in terms of y:

x = 6 - y

Substituting this value of x into equation 1):

[tex]2(6 - y)^2 - 5(6 - y)y + 2y^2 = 0[/tex]

Expanding and simplifying the equation:

[tex]2(36 - 12y + y^2) - 30y + 5y^2 + 2y^2 = 0\\72 - 24y + 2y^2 - 30y + 5y^2 + 2y^2 = 0\\9y^2 - 54y + 72 = 0[/tex]

Dividing the equation by 9 to simplify it further:

[tex]y^2 - 6y + 8 = 0[/tex]

Factoring the quadratic equation:

(y - 2)(y - 4) = 0

Setting each factor to zero:

y - 2 = 0 ;   y = 2

y - 4 = 0  ;   y = 4

Substituting these values of y back into equation 2) to find the corresponding values of x:

For y = 2:

x = 6 - y = 6 - 2 = 4

So, one solution is x = 4, y = 2.

For y = 4:

x = 6 - y = 6 - 4 = 2

So, another solution is x = 2, y = 4.

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To sketch the graph of the function f(x) = 2cos^2(x) - 3x + 4 for the values of x between 0 and 2, we can follow these steps:

1. Determine key points: Find the critical points and important features of the function within the given range. This includes the x-intercepts, local maxima, and minima.

2. Plot the x-intercepts: To find the x-intercepts, set f(x) = 0 and solve for x. In this case, cos^2(x) = (0 + 3x - 4)/2. Find the values of x where this equation holds true.

3. Identify local maxima and minima: Use calculus or other methods to find the local maximum and minimum points of the function within the given range.

4. Sketch the graph: Once you have the key points, plot them on a graph and connect them smoothly. Pay attention to the shape and behavior of the function.

Since the process of sketching a graph is best done visually, I'm unable to provide an image here. However, by following the steps outlined above, you can plot the graph of f(x) within the range of x between 0 and 2. Remember to label the axes and indicate any important points you have found.

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The absolute value function for this problem is given as follows:

y = |x - 4| - 6.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The coordinates of the vertex of the function are given as follows:

(4, -6).

The slope of 1 determines the leading coefficient a as follows:

a = 1.

Hence the function is given as follows:

y = |x - 4| - 6.

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The value of 7.682/0.072 using long division is 106 25/36

Division is a mathematical operation which involves the sharing of an amount into equal-sized groups.

By solving this, we need to make both the numerator and denominator a whole number by multiplying all by 1000

= (7.682×1000)/0.072 × 1000

= 7682/72

divide through by 2

= 3841/36

Now there is no common factor between the numerator and denominator,

We therefore find the number of 36 in 3841

= 106 remainder 25

therefore 7.682/0.072

= 106 25/36

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Answer:

15 is 7 more than 8.

Step-by-step explanation:

The only plausible answer.

A time that an inequality was needed was when I was recently planning a trip to the beach with some friends. We wanted to make sure we had enough money to cover our expenses, so I used an equation to calculate our total cost.

The equation I used was:

Total cost > (number of people) x (cost per person)

In this case, the number of people was 4 and the cost per person was $100. So, our total cost was $400. I was able to use this equation to help me plan our trip and make sure we had enough money to cover our expenses.

I believe that by following these steps, my friend would be able to successfully plan their trip and avoid overspending.

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Answer:

The nature of the image formed by a concave mirror depends on the magnification produced by the mirror.

(a) If the magnification produced by the mirror is +3, it indicates that the image formed is magnified and upright. The positive sign of the magnification indicates that the image is virtual. The size of the image will be larger than the size of the object.

(b) If the magnification produced by the mirror is -1, it indicates that the image formed is of the same size as the object but inverted. The negative sign of the magnification indicates that the image is real and formed on the opposite side of the object. The size of the image will be the same as the size of the object, but it will be inverted.

In both cases, the concave mirror is acting as a converging mirror, meaning it brings light rays together to form an image. The specific size of the image cannot be determined without additional information, such as the distance of the object from the mirror and the focal length of the mirror.

Answer: The nature of the image formed by a concave mirror can be determined based on the sign of the magnification produced.

(a) If the magnification is positive (+3), it indicates that the image is magnified and upright. In this case, the image is virtual and located on the same side as the object. The size of the image will be three times larger than the size of the object.

(b) If the magnification is negative (-1), it indicates that the image is diminished and inverted. In this case, the image is real and located on the opposite side of the object. The size of the image will be the same as the size of the object, but it will be inverted.

It's important to note that the actual size of the image cannot be determined solely based on the magnification. The magnification only gives information about the relative size of the image compared to the object. To determine the actual size, additional information, such as the size and distance of the object, is required.

The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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The surface area of Seung's block is approximately 3 times greater than Derek's block , option (B).

To compare the surface areas of Seung's and Derek's wooden blocks, we need to calculate the surface areas of both blocks and find the ratio between them.

Seung's block:

The surface area of a square pyramid can be calculated using the formula:

Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height

Given that the height of Seung's block is 6 cm and the base is 10 cm, we can calculate the slant height using the Pythagorean theorem:

Slant Height = sqrt((1/2 * base)^2 + height^2)

            = sqrt((1/2 * 10 cm)^2 + (6 cm)^2)

            = sqrt(25 cm^2 + 36 cm^2)

            = sqrt(61 cm^2)

            ≈ 7.81 cm

Now we can calculate the surface area of Seung's block:

Surface Area of Seung's Block = 10 cm^2 + (1/2 * 10 cm * 7.81 cm)

                            = 10 cm^2 + 39.05 cm^2

                            = 49.05 cm^2

Derek's block:

Since Derek's block has dimensions that are half of Seung's block, the base of Derek's block will be 10 cm / 2 = 5 cm, and the height will be 6 cm / 2 = 3 cm.

The surface area of Derek's block can be calculated using the same formula:

Surface Area of Derek's Block = 5 cm^2 + (1/2 * 5 cm * slant height of Derek's block)

To find the slant height of Derek's block, we can use a similar approach as before:

Slant Height of Derek's Block = sqrt((1/2 * 5 cm)^2 + (3 cm)^2)

                            = sqrt(6.25 cm^2 + 9 cm^2)

                            = sqrt(15.25 cm^2)

                            ≈ 3.90 cm

Now we can calculate the surface area of Derek's block:

Surface Area of Derek's Block = 5 cm^2 + (1/2 * 5 cm * 3.90 cm)

                            = 5 cm^2 + 9.75 cm^2

                            = 14.75 cm^2

Finally, we can find the ratio of the surface area of Seung's block to Derek's block:

Surface Area Ratio = Surface Area of Seung's Block / Surface Area of Derek's Block

                 = 49.05 cm^2 / 14.75 cm^2

                 ≈ 3.32

Rounded to the nearest whole number, the surface area of Seung's block is approximately 3 times greater than Derek's block. Therefore, the answer is option B: 3.

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Answer

a. The shape of the cross section is a rectangle.

b. To find the perimeter of the cross section, we need to determine the length of its sides.

In a cube with an edge length of 6 inches, when a plane intersects diagonally, it creates a rectangle with dimensions of the cube's diagonal and half of its edge length.

The diagonal of the cube can be found using the Pythagorean theorem:

diagonal = √(edge length^2 + edge length^2 + edge length^2) = √(6^2 + 6^2 + 6^2) = √(36 + 36 + 36) = √108 ≈ 10.39 inches

The length and width of the rectangle are half of the edge length, which is 6/2 = 3 inches.

Since the cross section is a rectangle, its perimeter is given by:

perimeter = 2 * (length + width) = 2 * (3 + 10.39) ≈ 26.78 inches

Therefore, the perimeter of the cross section, to the nearest hundredth, is approximately 26.78 inches.

c. To find the area of the cross section, we multiply the length and width of the rectangle:

area = length * width = 3 * 10.39 ≈ 31.17 square inches

Therefore, the area of the cross section, to the nearest hundredth, is approximately 31.17 square inches.

Step-by-step explanation:

The area of the Shaded region, when the frame is 1 unit wide, is 20 square units.

The area of the shaded region when one rectangle is framed within another and the frame has a width of 1 unit, we need to calculate the difference between the areas of the outer rectangle and the inner rectangle.

the dimensions of the outer rectangle as length and width, and the dimensions of the inner rectangle as length' and width'. Based on the information provided, the length and width of the outer rectangle are 5 and 7 units, respectively.

The dimensions of the inner rectangle can be found by subtracting twice the width of the frame (1 unit) from the dimensions of the outer rectangle:

Length' = length - 2 * frame width = 5 - 2 * 1 = 3 units

Width' = width - 2 * frame width = 7 - 2 * 1 = 5 units

Now we can calculate the areas of the outer and inner rectangles:

Area of the outer rectangle = length * width = 5 * 7 = 35 square units

Area of the inner rectangle = length' * width' = 3 * 5 = 15 square units

Finally, to find the area of the shaded region, we subtract the area of the inner rectangle from the area of the outer rectangle:

Area of shaded region = Area of outer rectangle - Area of inner rectangle = 35 - 15 = 20 square units

Therefore, the area of the shaded region, when the frame is 1 unit wide, is 20 square units.

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If Paul runs at the same pace, his rate will be 7 minutes per mile.

We know that, Paul runs 4miles in 28 minutes.

To find out his rate per mile, we need to divide 28 by 4.

Rate per mile,

27÷4

=7.

Therefore, Paul's rate is 7 minutes per mile.

Answer:

No

Step-by-step explanation:

To determine whether the given set of ordered pairs {(49,13),(61,36),(10,27),(76,52),(23,52)} represents a function, check if each x-value is associated with a unique y-value.

Check the x-values in the set: 49, 61, 10, 76, and 23. There are no repeated x-values.  Still need to check if each x-value has a unique corresponding y-value.

Check the y-values: 13, 36, 27, 52, and 52. There is one repeated y-value, 52, for the pairs (76, 52) and (23, 52).

Conclusion: the y-value 52 is associated with 2 different x-values, therefore the given set of ordered pairs does not represent a function.