Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589. You must show all of your work to receive credit.

Final answer:

Adam earned approximately a 28.03% interest rate on his $100 over 10 years to end up with $1649, as calculated using the formula A = Pert and taking the natural logarithm to solve for the interest rate.

Explanation:

To calculate the interest rate earned by Adam, we can use the given formula A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the original sum of money), r is the annual interest rate (in decimal), and t is the time the money is invested or borrowed for, in years. According to the question, Adam had a starting principal of $100 (P), which grew to $1649 (A) over 10 years (t).

Let's solve for the interest rate (r): A = Pert $1649 = $100e10r 16.49 = e10r To find r, we need to take the natural logarithm (ln) of both sides:

[tex]ln(16.49) = ln(e10r) ln(16.49) = 10r\\\\ Now divide both sides by 10 to isolate r:\\\(\dfrac{ln(16.49)}{10} = r\) \(r = \dfrac{ln(16.49)}{10}\)Now you just compute the value using a calculator:r ≈ \(\dfrac{2.803}{10}\) r ≈ 0.2803 or 28.03%\\[/tex]

Therefore, the interest rate that Adam earned was approximately 28.03%.

Since both pairs of opposite sides of quadrilateral ABCD are parallel and equal, by definition, ABCD is a parallelogram.

Given that in quadrilateral ABCD, side AD is equal to side BC (AD = BC) and side AD is parallel to side BC (AD || BC), we can use these properties to prove that ABCD is a parallelogram.

Here is a step-by-step proof:

1. Definition of a parallelogram: A quadrilateral is a parallelogram if both pairs of opposite sides are parallel.

2. Given: AD = BC (opposite sides are equal) and AD || BC (opposite sides are parallel).

3. To Prove: AB || CD and AB = CD (the other pair of opposite sides are also parallel and equal).

4. Proof:

   - Since AD = BC and AD || BC, we have one pair of opposite sides that are equal and parallel.

   - In a quadrilateral, if one pair of opposite sides is equal and parallel, the quadrilateral is a parallelogram (This is a theorem in Euclidean geometry).

   - Therefore, AB must be parallel to CD (AB || CD) because the opposite sides of a parallelogram are parallel by definition.

   - Also, in a parallelogram, opposite sides are equal (another property of parallelograms), so we can conclude that AB = CD.

5. **Conclusion**: Since both pairs of opposite sides of quadrilateral ABCD are parallel and equal, by definition, ABCD is a parallelogram.

This logical sequence uses the properties of parallelograms and the given information to prove that ABCD must be a parallelogram.

To find the area of a sector given a central angle and diameter, use the formula A = ([tex]\frac{\theta}{360}[/tex]) x π x r². In this case, with a central angle of 170° and a diameter of 9.1 cm, the area of the sector is approximately 30.7 cm².

The area of a sector with a central angle and a diameter can be calculated using the formula for the area of a sector:

A = [tex]\frac{\theta}{360}[/tex] x π x r². First, convert the diameter to radius (r = d/2), then substitute the values into the formula to find the area. In this case:

Central angle (θ) = 170°

Diameter (d) = 9.1 cm

Radius (r) = 4.55 cm

Area (A) = ([tex]\frac{170}{360}[/tex]) x π x (4.55)² ≈ 30.7 cm²

Therefore, the area of the sector is approximately 30.7 cm².

A.

Its correct i got 100% on a test

The function with the most x-intercepts in the image is g(x), which has four x-intercepts. The function f(x) has three x-intercepts, and the function h(x) has two x-intercepts.

The number of x-intercepts a function has is equal to the number of times the function crosses the x-axis. The x-axis is also known as the line y = 0, so any point where the function's graph touches the x-axis is a solution to the equation f(x) = 0.

g(x) crosses the x-axis four times, at approximately -10, 3/2, 2, and 15.

f(x) crosses the x-axis three times, at approximately -2, 1, and 12.

h(x) crosses the x-axis twice, at approximately -1 and 3.

Therefore, g(x) has the most x-intercepts because its graph intersects the x-axis the most times.

TRUE IVE GOT IT WRONG  ON MY ASSIGNMENT.

Answer:

True

Step-by-step explanation:

To find the geometric men you have to cross multiply the two given numbers and then find x squared for those numbers. So to find x squared you have to find the square root of the product from the two multiplied numbers.

8/x = x/2

8*2 = 16 = x squared

x= square root of 16 which equals 4

4(x-7)=12=


4x-28=12 

add 28 to both sides

4x=40

x =40/4 = 10

x = 10

The two numbers are 80 and 8.

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e. a and b respectively, are not equal to zero.

The substitution method can be defined as a way to solve a linear system algebraically. This method works by substituting one y-value with the other.

Let the two numbers be x and y.

According to the question.

x = 10y

And,

x - 10y = 72

Now, We have a linear equation in two variables. So, for finding the values of x and y we solve the above two equations by substitution method.

Substitute the value of x = 10y in x - y = 72

[tex]\implies 10y -y = 72 \\\implies 9y = 72\\\implies y = \frac{72}{9} \\\implies y = 8[/tex]

Therefore,

x = 10 × 8 = 80

Hence, the two numbers are 80 and 8.

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The ladder is 29.9 feet long.

For solving this problem we have to use trigonometric ratio  

We need to use the tangent function:

[tex]tan (\theta) = opposite/adjacent[/tex]

[tex]tan 75 = opposite/8[/tex]

multiply both side by 8 so we will get,

Here, the opposite side is the length of the ladder and angle [tex]\theta =75^0[/tex]

Therefore by using the tan ratio we have,

[tex]8 * tan 75 = opposite[/tex]

[tex]29.8564065 = opposite[/tex]

Therefore, the ladder is 29.9 feet.

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Answer:

Parallel: [tex]m = 0[/tex] (Horizontal), Perpendicular: [tex]m = -\frac{1}{0}[/tex] (Vertical)

Step-by-step explanation:

The equation y = 1 is an horizontal straight line ([tex]y = 0\cdot x + 1[/tex]). The slope of a line parallel to it is [tex]m = 0[/tex]. The slope of line perpendicular to it is [tex]m = -\frac{1}{0}[/tex], since slope is represented by tangent function, which is undefined at [tex]\theta = \pm 0.5\pi[/tex].

The number series 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46 has a pattern whereby each number doubles the previous number. However, 20 does not follow this pattern, and the correct number should be 32 (being double of 16). Therefore, 20 is the incorrect number in this series.

This question is a query regarding a number series, specifically asking for us to identify any number that does not fit the pattern of the series. The series given is: 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46. By examining the series closely, we can observe a clear pattern: each number is doubling the previous number. So, after 2 we have 4 (2x2), then 8 (4x2), then 16 (8x2) and so forth.

However, at the fifth place, we have the number 20, which doesn't follow this pattern. If we were to follow the established pattern, the fifth number should be 32 (16x2), not 20. Therefore, the incorrect number in this series is 20, and the correct series should be 2 - 4 - 8 - 16 - 32 - 22 - 44 - 46.

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The incorrect number in the series is 20, and it should be replaced with 32. The accurate sequence is 2, 4, 8, 16, 32, 64, 128, 256.

Let's examine the sequence: 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46.
At a glance, it appears each number is double its preceding number, except for a couple of deviations.

If we look at the pattern,

Here, we expect 32 instead of 20.
Therefore, 20 is the incorrect number in the series. When we continue correctly:

The correct sequence would be,
2 - 4 - 8 - 16 - 32 - 64 - 128 - 256.

So, the number that should be replaced is 20, and it should be 32.

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

so

[tex]k=r'/r[/tex]  and [tex]k=h'/h[/tex]

The volume of the original cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

If the cylinder is scaled proportionally by a factor of k

then

the new radius is ------> [tex]r'=kr[/tex]

the new height is ------> [tex]h'=kh[/tex]

The volume of the scaled cylinder is equal to

[tex]V'=\pi r'^{2}h'[/tex]

substitute the values

[tex]V'=\pi (kr)^{2}(kh)[/tex]

[tex]V'=(k^{3})\pi r^{2}h[/tex]

Remember that

[tex]V=\pi r^{2}h[/tex]

so

substitute

[tex]V'=V(k^{3})[/tex]

The volume of the scaled cylinder is equal to the scale factor elevated to the cube multiplied by the volume of the original cylinder

The rays VW and VZ don't necessarily have to go in opposite directions even though they have the same endpoint. Even though they are opposite arrays only if the angle is 180 degrees, they could still go in right angle directions or any angle of directions. Fi the points V, W, and Z and collinear and W and Z are on the side of point V, then they could also in fact be the same ray as well. Travelling is opposite directions yet starting at the same point is one of the characteristics of opposite rays. The first point in the name must be the endpoint and rays are always named with two points.