Michael drove to the mountains last weekend. There was heavy traffic on the way there at the trip took six hours. When Michael drove home there was no traffic and the trip only took four hours. If his average rate was 22 mph faster on the trip home how far away does Michael live from the mountains?

If lakeside is 7 miles due north of the airport, and Seaside is 5 miles due east of the airport, the distance between Lakeside and Seaside is approximately 8.6 miles.

To find the distance between Lakeside and Seaside, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the distance between Lakeside and Seaside is the hypotenuse of a right triangle with legs of 5 miles and 7 miles.

To apply the Pythagorean theorem, we can square the lengths of the legs and then take the square root of their sum:

distance = √(5² + 7²)

distance = √(25 + 49)

distance = √74

distance ≈ 8.6 miles (rounded to the nearest tenth)

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According to the given data we have the following equations:

a. 6-x-3= 10

b. 100x + 300=200

c. 1/3x + 4 = x - 2

d. 36 - 2x = -x +2

To solve the equations we would have to make the following calculations:

a. 6-x-3= 10

-x=10-6+3

-x=4+3

-x=7

x=-7

b. 100x + 300=200

100x=200-300

100x=-100

x=-1

c. 1/3x + 4 = x - 2

1/3x=x-2-4

0.3333x=x-6

x-6-0.3333x=0

0.66667x=6

x=6/0.66667

x=9

d. 36 - 2x = -x +2

-x+2-36+2x=0

x+34=0

x=-34

Answer:

Q1: no idea

Q2: 2 kids get 2 pieces of taffy and 1 piece of licorice and the other three get 2 pieces of licorice and 1 piece of taffy.

Step-by-step explanation:

question 2 is quite obvious but no one can get the same amount of everything so the answer that i gave makes the most sense.

Answer:

1= 75 2= 60 3=180 4=45 5= vertical angles 6=45

Step-by-step explanation:

All we have to do is use supplimentary angles

For example angle 1

105+angle 1=180

angle one = 75 degrees

120+angle 2=180

angle two= 60 degrees

There 180 degreees in a triagle.

So angle 1 + angle 2+ angle 7= 180

75+60+angle 7=180

angle 7= 45 degrees

And since 6 and 7 are vertical angles, angle 6 is also 45 degrees.

Answer:

it very simple actually, just do it what its saying from any point it wont really matter youll still get it right

Step-by-step explanation:

The table is

x | 4 | 8 | 12
y |  1 | 2 | 3

The question is not understandable. The well-formatted question is

Complete the table for the given rule

Rule:

\(y=\dfrac{1}{4}x\)

Table:

x | 4 | 8 | 12
y |  ? | ? | ?

Evaluation of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the provided number to replace the expression's variable before applying the sequence of operations to simplify the expression.

For instance

On evaluation of y= x+7  when x=3, and x=12

we get y(3) = 3 + 7 = 10 and y(12) = 12 + 7 = 19

The given equation is

\(y=\dfrac{1}{4}x\)

So, the table is

x | 4 | 8 | 12
y |  1 | 2 | 3

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Answer:

0

12/4

1.75

in that order

The given differential equation y x²y² = x² is a nonlinear and not separable differential equation, which corresponds to option (D).

A linear differential equation can be written in the form dy/dx + P(x)y = Q(x), where P(x) and Q(x) are functions of x. In this equation, the term x²y² makes it nonlinear.

A separable differential equation can be written in the form g(y)dy = f(x)dx, where g(y) and f(x) are functions of y and x, respectively. However, in the given equation, we cannot separate the variables y and x to obtain such a form.

To solve this particular differential equation, one approach is to rewrite it in a more manageable form. Let's rearrange the terms:

x² = y/(x²y²)

Now, we can multiply both sides by (x²y²) to eliminate the denominator:

x²(x²y²) = y

This equation is still nonlinear but can be used to find a particular solution for y given a specific initial condition.

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The possible value of x which the two triangles are similar is x=60°.

What do you mean by triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Method:

Given that two angles of the triangle are specified, the triangles can be

similar for only one value of x.

According to the given data in the question,

The two triangles are similar when we have;

x + 10° = 2x - 50°

Which gives;

2x - x = 50° + 10° = 60°

x = 60°

Checking gives;

x + 10° = 2·x - 50° = 70°

Two angles of the first triangle are 70° and 60°

Then, the third angle of the first triangle is (180° - (70° + 60°)) = 50°

The three angles of the first triangle are therefore; 70°, 60° and 50°.

Two angles of the second triangle are 70° and 70°.

The third angle of the second triangle is (180° - (70° + 70°)) = 40°

The three angles of the second triangle are therefore; 70°, 70° and 40°

Therefore, the two triangles are similar by AAA similarity.

The two triangles are similar when, x = 60°

When x = 50°, we have;

x + 10° gives;

50° + 10° = 60°

∴ ∠(x + 10°) = 60°

The two angles of the first triangle are; 60° and 50°

The third angle on the second triangle is 180° - (60° + 50°) = 70°

On the second triangle, we have;

2·x - 50° gives;

2 × 50° - 50° = 50°

∴∠(2·x - 50°) = 50°

Therefore, the two angles of the second triangle are 70° and 50°

The third angle on the second triangle is 180° - (70° + 50°) = 60°

Therefore, the two triangles are not similar when x = 50°

Similarly, the two triangles are not similar when x + 10° = 50°

Hence, the possible value of x which the two triangles are similar is x = 60°.

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Answer:

2r(d-2)

Step-by-step explanation:

Answer:

The answer is I don't know

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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We have two flower beds in this example, the first has a perimeter of 100 feet, and the second has a perimeter of 180 feet

The total is 280 feet

Given Data

Dimension of the first flower bed

Length = 17 feet

Width = 33 feet

Perimeter = 2L + 2W

Perimeter = 2*17 + 2*33

Perimeter =  34 + 66

Perimeter = 100 feet

Dimension of the second flower bed

Length = 40 feet

Width = 50 feet

Perimeter = 2L + 2W

Perimeter = 2*40 + 2*50

Perimeter = 80 + 100

Perimeter = 180 feet

The total length will be 100+180 = 280 feet

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Answer:

It's 50

Step-by-step explanation:

D on edge

Answer:

3⁴

Step-by-step explanation:

Expressing in the simplest radical form means simplifying a radical so that there are no more square roots, cube roots, fourth roots etc.

It further means removing radicals in the denominator of a fraction.

Given

\(27^{4/3}\)

this can be written as

\((\sqrt[3]{27} )^{4}\)

This is simplified as;

(3)⁴

Answer: 576

Step-by-step explanation:

Answer:

x = ± √20

or if you want an approximate solution correct to the nearest hundredth:

x = -4.47, 4.47.

Step-by-step explanation:

4x^2-80=0

This a quadratic equation and will have 2 solutions.

Add 80 to both sides of the equation:

4x^2 = 80

Divide both sides by 4:

x^2 = 20

Take the square root of both sides:

x = ± √20.

Since you need 100 buttons and the pack contains 12, then we must divide 100 by 12 to find out how many packs should you buy:

now, we have that 12x8=96, then you have to buy 9 packs to get at least the 100 buttons needed

Answer:

1

Step-by-step explanation:

The absolute value of -3 is just 3, because it has a distance of 3 away from 0. Therefore, \(\mid -3 \mid -2=3-2=1\). Hope this helps!

Once all layers are solved, the Rubik's cube is done.

The Rubik's cube is a classic puzzle that has been challenging people for decades. It consists of a 3x3x3 cube with each of the six faces covered in smaller colored cubes, or "cubies".

There are many different methods for solving the Rubik's cube, but the most popular method is called the "layer-by-layer" method.

The first step in solving the Rubik's cube is to solve the top layer. This is done by aligning the top layer cubies with the center cubies of the same color. Once the top layer is solved, the next step is to solve the middle layer.

Finally, the last step is to solve the bottom layer. This is done by aligning the bottom layer cubies with the center cubies of the same color.

It's important to memorize some basic algorithms and techniques to be able to solve the cube efficiently, these techniques can vary from simple moves to more complex ones. There are many resources available online to learn these techniques, such as video tutorials and written guides.

Solving the Rubik's cube can be a fun and rewarding challenge, and it can also help to improve your problem-solving skills and spatial reasoning.

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Answer:

3, 5, 7, 9

Step-by-step explanation:

Give Brainliest if I helped!

The four consecutive odd integers that Zach found are x, x + 2, x + 4, and x + 6 are -11, -9, -7, and -5.

To solve this problem,  set up equations based on the given information.

"5 times the sum of the first and the third":

\(5(x + x + 4)\)

"the product of 8 and the sum of the second and the fourth":

\(8((x + 2) + (x + 6))\)

According to the problem, the first equation should be 22 greater than the second equation:

\(5(x + x + 4) = 8((x + 2) + (x + 6)) + 22\)

Next,  simplify and solve the equation:

\(5(2x + 4) = 8(2x + 8) + 22\)

Remove the bracket by multiplying the terms:

\(10x + 20 = 16x + 64 + 22\)

Take the variables to LHS and constants to other side and solve it:

\(6x = -66\)

On dividing by 6 on both sides:

x = -11

Now that the value of x, and  find the four consecutive odd integers:

x = -11

On substituting x value in the following terms:

\(x + 2 = -11 + 2 \\= -9\\x + 4 = -11 + 4\\ = -7\\x + 6 = -11 + 6 \\= -5\)

Therefore, the four consecutive odd integers are -11, -9, -7, and -5.

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Answer: 5x + (x + 54) = 6x + 54

So now 6x + 54 = 90 because u are solving a right angle.

90 - 54 is 36. So 6x = 36 and 36 divided by 6 is 6. Your answer for X = 6 Hope this helps you please mark brainliest

Step-by-step explanation:

The solution is :

There are 240 students in the school.

Here, we have,

Givens

55% of the total number of students in a school are girls.

Equation

55/100 * x = 132

Solution

Multiply both sides of the equation  by 100

55/100x * 100  = 132 * 100

55x = 13200                        [  Divide by 55  ]

55x/55  = 13200/55

x = 240

Hence, The solution is :

There are 240 students in the school.

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complete question:

Of the students at milton middle school, 132 are girls. if 55% of the students are girls, how many total students are there at milton middle school?

Answer:

341.28

Step-by-step explanation:

56.88 x 6 neighbors = 342.28

To find the length of the curve r(t) = sqrt(2)ti, we need to use the arc length formula:L = ∫[a,b] ||r'(t)|| dt,where ||r'(t)|| is the magnitude of the derivative of the curve.

First, we need to find r'(t):

r'(t) = (d/dt) [sqrt(2)ti] = sqrt(2)i

The magnitude of r'(t) is ||r'(t)|| = sqrt(2).

So, the length of the curve is:

L = ∫[0,1] sqrt(2) dt = sqrt(2) * [t] [0,1] = sqrt(2)

Therefore, the length of the curve r(t) = sqrt(2)ti is sqrt(2).

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The volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells is 486π cubic units.

To find the volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells, we can follow these steps:

First, let's sketch the region bounded by the curve y = x. This is a straight line passing through the origin with a slope of 1. It forms a right triangle in the first quadrant, with the x-axis and y-axis as its legs.

Next, we need to determine the limits of integration. Since we are rotating about the y-axis, the integration limits will correspond to the y-values of the region. In this case, the region is bounded by y = 0 (the x-axis) and y = x.

The height of each cylindrical shell will be the difference between the upper and lower curves. Therefore, the height of each shell is given by h = x.

The radius of each cylindrical shell is the distance from the y-axis to the x-value on the curve. Since we are rotating about the y-axis, the radius is given by r = y.

The differential volume element of each cylindrical shell is given by dV = 2πrh dy, where r is the radius and h is the height.

Now we can express the volume of the solid of revolution as the integral of the differential volume element over the range of y-values:

V = ∫[a, b] 2πrh dy

Here, [a, b] represents the range of y-values that define the region. In this case, a = 0 and b = 9 (as y = x, so the curve intersects y-axis at y = 9).

Substituting t

he values of r and h into the integral, we have:

V = ∫[0, 9] 2πy(y) dy

Simplifying, we get:

V = 2π ∫[0, 9] y^2 dy

Evaluating the integral, we have:

V = 2π [y^3/3] from 0 to 9

V = 2π [(9^3/3) - (0^3/3)]

V = 2π [(729/3) - 0]

V = 2π (243)

V = 486π

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The scale of the drawing is in the ratio of 1 millimeter : 3 meter

In this, we need to find the ratio that is 1millimeter:x meter where x is the original scaling of the plot.

We have been given that

                   24 millimeters = 72 meters

Now we have to find how many meters is equal to 1 millimeter which will find out by the unitary method.

Thus,   24 millimeters = 72 meters

               1 millimeter = 72/24 meter

               1 millimeter = 3 meter

Hence the scale of the drawing is 1 millimeter : 3 meter

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Answer:

The height of the parallelogram is 12 cm.

Step-by-step explanation:

We are given that a triangle and a parallelogram have the same base and same area.

The sides of the triangle measure 26 cm, 28 cm, and 30 cm.

We are given that the base of the parallelogram is 28 cm, and we want to determine its height.

Find the area of the triangle. Since we are given the three sides, we can consider using Heron's Formula:

\(\displaystyle A = \sqrt{s(s-a)(s-b)(s-c)}\)

Where a, b, and c are the sides and s is half of the perimeter.

The perimeter is:

\(P = (26) + (28) + (30) = 84\)

Hence, s = 42.

Then the area of the triangle is:

\(\displaystyle \begin{aligned} A&= \sqrt{42(42-26)(42-28)(42-30)} \\ &= \sqrt{112896} \\ &= 336\text{ cm}^2 \end{aligned}\)

The area of a parallelogram is given by:

\(\displaystyle A = bh\)

We are given that the base is 28 cm:

\(\displaystyle A = 28 h\)

Its area is equivalent to the area of the given triangle. Hence:

\(\displaystyle 336 = 28h\)

Divide:

\(\displaystyle h = \frac{336}{28} = 12\text{ cm}\)

In conclusion, the height of the parallelogram is 12 cm.

To record interest at the effective interest rate on December 31, Agee Technology, Inc. would make a journal entry that includes an interest expense and an increase in the bond liability.

To record interest at the effective interest rate on December 31, Agee Technology, Inc. would make the following journal entry:

Interest Expense XXX

Bond Interest Payable XXX

The interest expense would be calculated using the effective interest rate based on the carrying value of the bonds. The carrying value can be determined by subtracting any discount or adding any premium to the face value of the bonds.

In the statement of cash flows using the direct method, Agee would report cash paid for interest as an operating activity. The amount would be the actual cash paid for interest during the year. Additionally, the issuance of bonds would be reported as a financing activity, representing the inflow of cash from the issuance of the bonds.

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Answer:

5  y = -x + 2, 8   y = 2x + 4

Step-by-step explanation:

Hope this Helps!

Answer:

nonrigid and segement lengths ar enot

Step-by-step explanation: