If the design is to have at least one foot of pavement over the drainage pipe what is the minimum depth of the ditch

The inverse equation of the equation is: A =T2/3

The equation is given as:

T = A3/2

To calculate the inverse equation, we start by multiplying both sides of the equation by 2

T2 = A3

Next, we divide both sides of the equation by 3

A =T2/3

The equation cannot be further simplified

Hence, the inverse of the equation is: A =T2/3

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The  value of A in terms of T is \(A=\frac{2}{3}T\)

The given equation is,

                       \(T=\frac{3}{2}A\)

We have to find value of A in terms of T.

                      \(T=\frac{3}{2}A\\\\A=T\div \frac{3}{2}\\ \\A=T*\frac{2}{3}\\ \\A=\frac{2}{3}T\)

Thus, the  value of A in terms of T is \(A=\frac{2}{3}T\)

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Since T(0) ≠ 0, we can conclude that the transformation T is not linear.

The correct answer is: T(0) ≠ 0

To determine if the transformation T is linear, we need to check if it satisfies two properties: T(0) = 0 and T(cu + dv) = cT(u) + dT(v) for all vectors u, v in the domain of T and all scalars c, d.

Let's evaluate T(0) to check if it satisfies the first property:

T(0, 0) = (3(0), -2(0), 0+5, 4(0)) = (0, 0, 5, 0)

Now, let's analyze what is true about T(0):

T(0) = (0, 0, 5, 0)

From this result, we can see that T(0) is not equal to the zero vector (0, 0, 0, 0). According to the first property, for a transformation to be linear, T(0) must be equal to the zero vector.

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Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

Answer:

w = 10

l = 50

Step-by-step explanation:

Formula of Perimeter: w + w + l + l or 2w + 2l

l = 5w

2l + 2w = 120

2(5w) + 2w = 120

10w + 2w = 120

12w = 120

w = 10

l = 5(10)

l = 50

Check:

2l + 2w = 120

2(50) + 2(10) = 120

100 + 20 = 120

120 = 120

Hope This Helps!

Lets denote our variables as:

The formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length of the rectangle and W is the width of the rectangle. We know that the perimeter of the rectangle is 120m, so we can write:

2(x) + 2(5x) = 120

2x + 10x = 120

12x = 120

 x = 120/12

 x = 10 m → Width of the rectangle

Substituting in the length:

5x = 5(10) = 50 m → Length of the rectangle

Answer:

the top one is 30 the second one is 60.22 the third one is 66.7 the forth one is 59.8

Answer:

19,17,15,13

Step-by-step explanation:

25-6=19

25-8=17

25-10=15

25-12=13

p = d(w)/dt ,  this equation is used to describe how the value of w changes over time.

Left side: p is the derivative of w

Right side: d(w)/dt, where d stands for derivative and dt stands for derivative with respect to time (t)

The mathematical translation of the sentence "p is the derivative of w with respect to time (t)" is expressed as p = d(w)/dt. This equation states that p is the rate at which w changes over time (t). The left side of the equation, p, is the derivative of w indicating that it is the rate of change of w with respect to time. The right side of the equation, d(w)/dt, is the derivative of w with respect to time. The d stands for derivative, and the dt stands for derivative with respect to time. Therefore, this equation is used to describe how the value of w changes over time.

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Answer:

−12 if simplfied .

Step-by-step explanation:

Answer:

328 is the total of 4*82 and -5 would be 323

Step-by-step explanation:

Brainliest pls

Answer:

55

Step-by-step explanation:

55 x 26 = 1430

55 x 8 = 440

1430 - 440 = 990

The store need to sell 55 sweater to earn $ 990 as profit.

Let us consider that, number of sweater needed to sell be x.

Since, cost price of one sweater is $8.

So that, cost price of x sweater\(=8x\)

Selling price of one sweater is $26.

So that, selling price of x sweater\(=26x\).

As we know that,

           \(S.P-C.P=Profit\\\\26x-8x=990\\\\18x=990\\\\x=990/18=55\)

Hence, the store need to sell 55 sweater to earn $ 990 as profit.

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The ratios of corresponding sides and corresponding angles are equal. The measurement of one side or angle in either triangle or additional information that allows us to set up proportions and solve for the unknowns.

To find the unknown measures in the similar triangles ▵XYZ ~ ▵PQR, we need to determine the corresponding sides and angles that are proportional.

Corresponding sides:

Corresponding side XY in ▵XYZ corresponds to side PQ in ▵PQR.

Corresponding side XZ in ▵XYZ corresponds to side PR in ▵PQR.

Corresponding side YZ in ▵XYZ corresponds to side QR in ▵PQR.

Corresponding angles:

Angle X in ▵XYZ corresponds to angle P in ▵PQR.

Angle Y in ▵XYZ corresponds to angle Q in ▵PQR.

Angle Z in ▵XYZ corresponds to angle R in ▵PQR.

Based on the similarity of the triangles, we can set up proportions using the corresponding sides or angles. Let's denote the measures of the corresponding sides as follows:

XY = x, PQ = y

XZ = a, PR = b

YZ = c, QR = d

Using the corresponding side lengths, we can write the following proportions:

XY / PQ = XZ / PR = YZ / QR

Substituting the values, we have:

x / y = a / b = c / d

Similarly, using the corresponding angles, we can write the following proportions:

Angle X / Angle P = Angle Y / Angle Q = Angle Z / Angle R

Now, without specific measurements or additional information about the triangle, we cannot determine the exact values of the unknown measures in ▵XYZ and ▵PQR. However, based on the given similarity, we know that the ratios of corresponding sides and corresponding angles are equal.

Therefore, to find the unknown measures, we need either the measurement of one side or angle in either triangle or additional information that allows us to set up proportions and solve for the unknowns.

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The value of X in the bottom question is 3.

The MidSegment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

To solve for X in the top and bottom questions using the MidSegment theorem, we need to first identify the midpoints of the two sides and the third side.

For the top question, we can see that the midpoints of AB and BC are D and E respectively. So, DE is parallel to AC and half its length. We know that AC = 12, so DE = 6. We also know that DE = X + 1, so we can set up an equation:

X + 1 = 6

Solving for X, we get:

X = 5

Therefore, the value of X in the top question is 5.

For the bottom question, we can see that the midpoints of AB and AC are D and F respectively. So, DF is parallel to BC and half its length. We know that BC = 14, so DF = 7. We also know that DF = X + 4, so we can set up an equation:

X + 4 = 7

Solving for X, we get:

X = 3

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Answer:

F' = (-6,3)

Distance = 12 units

Step-by-step explanation:

F is currently at (6,3).

Reflected over the y-axis, it would be at (-6,3).

That puts them 12 units apart.

Answer:

0

Step-by-step explanation:

Answer:

-30m^11n^5

Step-by-step explanation:

the length of a rectangle is width times length (or base times height).

5m^7n^3 times -6m^4n^2 = -30m^11n^5

I hope this helped, please give brainliest if this is correct! Thank you!

Answer:

A) gp+gq−gr+hp+hq−hr

Step-by-step explanation:

Original: (g+h)(p+q−r)

Multiply: (g)(p)+(g)(q)+(g)(−r)+(h)(p)+(h)(q)+(h)(−r)

Simplify: gp+gq−gr+hp+hq−hr

Hope this helped! :)

If  on Saturday he picks a shirt, a jumper and a hat. Show that there are 105 different combinations he can pick.

a.  There are 105 different combinations that Jamal can pick on Saturday.

b. Jamal is incorrect. If he picks just two of the three clothing items, there are only 71 possible combinations, which is less than the 105 possible combinations when he picks all three item

a) To find the total number of combinations, we need to multiply the number of options for each clothing item:

Number of combinations = (number of shirt options) x (number of jumper options) x (number of hat options)

Number of combinations = 7 x 5 x 3

Number of combinations = 105

Therefore, there are 105 different combinations that Jamal can pick on Saturday.

b) If Jamal picks just two of the three clothing items, there are two cases: he can either pick a shirt and a jumper, or he can pick a shirt and a hat, or he can pick a jumper and a hat. Let's calculate the number of combinations for each case:

Case 1: Jamal picks a shirt and a jumper

Number of combinations = (number of shirt options) x (number of jumper options)

Number of combinations = 7 x 5

Number of combinations = 35

Case 2: Jamal picks a shirt and a hat

Number of combinations = (number of shirt options) x (number of hat options)

Number of combinations = 7 x 3

Number of combinations = 21

Case 3: Jamal picks a jumper and a hat

Number of combinations = (number of jumper options) x (number of hat options)

Number of combinations = 5 x 3

Number of combinations = 15

To find the total number of combinations, we need to add up the number of combinations for each case:

Total number of combinations = 35 + 21 + 15

Total number of combinations = 71

Therefore, Jamal is incorrect. If he picks just two of the three clothing items, there are only 71 possible combinations, which is less than the 105 possible combinations when he picks all three items.

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9514 1404 393

Answer:

  D.  105 ft²

Step-by-step explanation:

The total surface area is the sum of the base area and the triangular face areas.

Area of base:

  A = s²

  A = (7 ft)² = 49 ft²

Area of 4 triangles:

  A = 4(1/2)bh

  A = 2(7 ft)(4 ft) = 56 ft²

Total surface area:

  base area + triangle area = 49 ft² +56 ft² = 105 ft²

The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.

In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.

The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.

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M<1 = 50°

Have a good night

In a circle, when two diameters intersect, the angles formed at the intersection point are always right angles (90°).

Therefore, none of the given angle measures (50°, 80°, 100°, 130°) can represent the angle formed by diameters AC and BD.

The correct answer would be 90° since the intersection of diameters always creates right angles in a circle.

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Answer: A. 50°

Asked the AI

Answer:

\(\frac{12}{13}\) miles

Step-by-step explanation:

The area of a rectangle is found by width multiplied by length. So, the width can be found by dividing the area by length.

12÷13=\(\frac{12}{13}\)

So, your answer is \(\frac{12}{13}\)

Answers:

============================================================

Explanation:

Let y be the measure of angle ABC.

We can see that y = 4x+17 because the two angles (y and 4x+17) are vertical angles. Vertical angles are always congruent.

-------------

From here, focus entirely on the interior angles of triangle ABC.

Recall that for any triangle, the interior angles always add to 180

A+B+C = 180

(x+23)+(y)+(80) = 180 ..... plug in the given angle measures

(x+23)+(4x+17)+(80) = 180 .... replace y with 4x+17

5x+120 = 180 ..... combine like terms

5x = 180-120 ..... subtract 120 from both sides

5x = 60

x = 60/5 ..... divide both sides by 5

x = 12

Now use that x value to find the following:

--------------------------

In short we have this summary of values we found:

Answer:

1. Dilation with a scale factor of 0.5 centered at the origin.

2. Translation of 4 units to the right.

3. Translation of 3 units up.

Answer:

m= -1

Step-by-step explanation:

You solve slope by using y2-y1/ x2-x1 so,

4-6/6-4

=-2/2

= -1

The random variation that occurs in any time series is called the irregular component.

The irregular component refers to the random fluctuations or unpredictable patterns that are observed in a time series. It represents the unexplained variability in the data that cannot be attributed to any identifiable pattern, such as seasonal patterns, cyclical effects, or trends. It is often characterized by short-term fluctuations that occur randomly and do not follow a specific pattern or trend.

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Answer:

M2=1

M1=8

Step-by-step explanation:

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

The measure of angle BCA is 81 degrees.                                            

The potential energy for the baby carriage is 308.7 Joules.

The potential energy for an object of mass M, that is at a height H, is given by the formula :

P = M*H*g

Where g is the gravitational acceleration, in this case, it is:

g = 9.8  m/s²

In this case we know that the mass is 1.5 kilograms and the height is 21 meters, then the potential energy is:

P = 1.5kg*21m*9.8  m/s²

P = 308.7 Joules.

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