A tree that is 40 feet tall casts a 30 foot shadow. At the same time another tree casts a 20 foot shadow. How tall is the second tree?

Answer:

Let A(9, 9) & B(1, 4) are two point through which Line e passes.

Equation of e is given by

y - y1 = y2 - y1/ x2 - x1(x - x1)

or, y - 9 = 4-9/1-9 (x - 9)

or, -8y + 72 = -5x + 45

or, 5x - 8y + 27 = 0...........1.

Again,

consider C (1, 5) & D (9, 10) are other two points through with Line f pass through.

Also, eqn of f is,

y- 5 = 10-5/9-1 (x - 1)

or, 8y - 5 = 5x - 5

or, 5x - 8y =0 ...........2.

Let m1 and m2 are slopes between the lines.

Now, slope of 1. = - coef. of x/ coef. of y

= -5/-8 = 5/8 =m1

& slope of 2. = -5/-8 = 5/8 = m2

Since slopes of lines i. e. m1 = m2, so the lines are parallel to each other.

Answer:

16 subsets

Step-by-step explanation:

Set \(\displaystyle \{x/x\in \mathbb{W},0\leq x<4\}\) reads as \(x\) is a whole number greater or equal to zero but less than 4.

Therefore, the only values of \(x\) that satisfy this are \(\{0, 1, 2, 3\}\), a set with four elements. For a set of \(n\) elements, there exist \(2^n\) subsets. Therefore, there are \(2^4=\boxed{16}\) subsets of \(\displaystyle \{x/x\in \mathbb{W},0\leq x<4\}\)

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

The equivalent equation for the given algebraic expression would be Option A) \(\frac{1}{3x^\frac{5}{9} }\).

Hope this helps!

The absolute deviation of each of the data values are 4, 1 and 3 respectively.

The absolute deviatuon gives the distance of any given value in a dataset to the mean value. The absolute deviation is always positive as it does not consider the side to which the value belongs.

Absolute deviation = |value - mean|

Mean = 4

Absolute deviation of 0 = |0 - 4| = 4

Absolute deviation of 3 = |3 - 4| = 1

Absolute deviation of 7 = |7 - 4| = 3

Hence, The absolute deviation of each of the data values are 4, 1 and 3 respectively.

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Answer:

Is there more context? Like an image, describing what cars there are?

Step-by-step explanation:

You can sort cars by model type, brand, color, style, etc. So yes, unless there is only 2 types of car types/brands/colors/style etc

The biker needs to travel 45 km more to complete his journey.

Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,

Let the total distance of the road be x,
So,

2x/5 - 5 = 3x/8

2x/5 - 3x/8 = 5

Solving for x,

Multiply by 40 to both sides,

16x-15x = 200

x = 200

Therefore, the total distance of the road is 200 km.

Since, he travelled =

200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km

Therefore, he needs to travel 200-155 = 45 km more.

Hence, the biker needs to travel 45 km more to complete his journey.

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Answer:

315 newspapers in 6 hours

Step-by-step explanation:

The answer is 315 because 420 divided by 8 is 52.5 and 52.5 times 6 is 315.

Answer:answer 4

Step-by-step explanation: multiply each answer choose an dit leaves 6 time four is 24

Answer:

7/6 or 1 1/6

Step-by-step explanation:

2/3 = 4/6

1/2 = 3/6

3/6 + 4/6 = 7/6 = 1 1/6

The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

We have,

To write the equation 6y + y = 5 in slope-intercept form (y = mx + b), we need to simplify the equation and isolate the y variable on one side.

Starting with the equation 6y + y = 5:

Combining the like terms on the left side gives us:

7y = 5

To isolate the y variable, we divide both sides of the equation by 7:

y = 5/7

Now the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, since the equation only contains the variable y and no x, the slope (m) is not present, and the y-intercept (b) is 5/7.

Therefore,

The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

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In order to ensure that depositors would get their money back in the event of a bank run, the Federal Reserve can support the bank by lending money to the bank. Option C

When a bank faces a bank run and experiences a sudden and significant increase in withdrawals, it may face a liquidity crisis, meaning it may not have enough cash on hand to meet the withdrawal demands of depositors.

To address this, the Federal Reserve can step in and provide loans or emergency funding to the bank to help it meet its obligations to depositors. This lending can help stabilize the bank's liquidity position and ensure that depositors are able to access their funds.

It is important to note that this support from the Federal Reserve is typically done on a temporary basis and is intended to help address the immediate liquidity needs of the bank during a crisis

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Answer:

10z+20

Step-by-step explanation:

The perimeter is the sum of all the side lengths.  Starting at the top left corner and going clockwise:

2z+z+5+10+5+z+2z+4z

Combine like terms

2z+z+z+2z+4z+5+5+10

10z+20

Answer:

16z+10

Step-by-step explanation:

The explanation is in the attached file below

The pre-image of the point is A ( -1 , 9 )

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

Given data ,

To determine the coordinates of the pre-image point A, we need to reverse the translation by moving left 4 units and down 5 units from the image point B(3, 14).

Moving left 4 units from B(3, 14) means subtracting 4 from the x-coordinate:

x-coordinate of A = 3 - 4 = -1

Moving down 5 units from B(3, 14) means subtracting 5 from the y-coordinate:

y-coordinate of A = 14 - 5 = 9

Hence , the coordinates of the pre-image point A are (-1, 9)

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Answer:

10) m: 6

    b: 5

    y= 6x +5

12)  m: -2

     b: -1

     y= -2x-1

14)  m: 1

     b: 0

     y= x

Step-by-step explanation:

The slope-intercept form is the form y=mx+b

m is the slope. You can find it by finding two points that the line intersects, and counting the number of units between them.

Remember the slope is "rise over run", so, the difference in y over the difference in x.

b is the y-intercept. You can find it by looking at where the line crosses the y-axis.

Hope this helps you out!

Step 1. The angle that we have is:

And we need to find the reference angle and make a representation of it.

The reference angle is always between 0° and 90° and it represents the angle between the x-axis and the terminal point of the angle.

For example

Step 2. Since we have a large angle of more than 360°, this angle will turn around the plane many times. The first step is to divide 1,863 by 360 to find the number of times that the angle will turn around the plane:

The angle will complete 5 whole turns around the plane,

Step 3. Since

There will still be

63 degrees left, since this angle is already between 0° and 90°, this will be the reference angle.

Step 4. 63° is the leftover angle after 5 complete turns around the plane, this will be the reference angle:

Step 5. The drawing representation will look as follows:

Answer:

1. Reference angle: 63°

2. The diagram is shown in step 5.

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}\)

Answer:

3/4

Step-by-step explanation:

you do change in y over change in x which is 7-4 over 3+1

when you do the calculations you get 3/4

a. The table for the relation is given by the image shown at the end of the answer.

b. The domain and range of the relation are given as follows:

c. The relation is a function, as it value of the input is mapped to a single value of the output.

The ratio between the total cost and the number of vehicles is obtained as follows:

k = 3.75/5 = 3/4 = ... = 0.75/1 = 0.75.

Meaning that the situation is modeled by a proportional relationship with a constant of 0.75, and the function is given as follows:

y = 0.75x.

For which:

The domain and range are given as follows:

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i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).

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Answer:

jzb,vnnmn  v nvzJBCSKAJDSKCHJZXCGSIFNBVSAFVWLJFSD IZAUCDWKGASHUFUYHJJDHacvshvchvcaxnkccbhcc uwgdbd

Step-by-step explanation:

Answer:

The second one .

Step-by-step explanation:

They never included that.

Answer:

9.42

Step-by-step explanation:

Answer:

  C. RP = 4.5

Step-by-step explanation:

You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given  three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.

Similarity can be shown if all three sides are proportional, or if two angles are congruent.

The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.

  C. RP = 4.5

__

Additional comment

The side ratios in the two triangles are ...

  AB : BC : CA = 10 : 9 : 6

  QP : PR : RQ = 5 : PR : 3

For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.

The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

Here, we have,

we know that,

The sum of the angles in a triangle add to 180

x+2x+6x = 180

Combine like terms

9x= 180

Divide by 9

9x/9 = 180/9

x = 20.

Hence, The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

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complete question:

The sum of the angle measures in a triangle is 180°. The angles of a certain triangle measure x°, 2x°, and 6x°. Solve for x.

Answer:

Option 1

Step-by-step explanation:

The square of a real number is always non-negative.

Answer: D) 54 inches = 1 1/2 yards

explanation: 1 1/2 yards = 54 inches.

Responder:

1

Explicación paso a paso:

cuando una variable no tiene exponente, el grado siempre es uno. Ej: 8x es lo mismo que 8x elevado a 1

b) The inverse function of ƒ(x) is given by: ƒ⁻¹(x) = (1 - x) / x

c) The domain of ƒ⁻¹(x) is all real numbers except for 1.

d) The solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.

(a) To show that f(x) = 1 / (x + 1), we need to simplify the expression f(x) and demonstrate that it is equivalent to 1 / (x + 1):

f(x) = [2(x - 1) / (x² - 2x - 3)] - (1 / (x - 3))

f(x) = [2(x - 1) / (x - 3)(x + 1)] - (1 / (x - 3))

f(x) = [2(x - 1) - (x + 1)] / (x - 3)(x + 1)

f(x) = [2x - 2 - x - 1] / (x - 3)(x + 1)

f(x) = (x - 3) / (x - 3)(x + 1)

f(x) = 1 / (x + 1)

Therefore, we have shown that f(x) = 1 / (x + 1).

(b) To find the inverse function of ƒ(x), we interchange the roles of x and y and solve for y:

x = 1 / (y + 1)

xy + x = 1

xy = 1 - x

y = (1 - x) / x

Therefore, the inverse function of ƒ(x) is given by:

ƒ⁻¹(x) = (1 - x) / x

(c) The domain of ƒ⁻¹(x) can be determined by looking at the domain of the original function f(x), which is x > 3.

For ƒ(x), the range is all real numbers except for 1 (since f(x) = 1 / (x + 1)).

Therefore, the domain of ƒ⁻¹(x) is all real numbers except for 1.

(d) Given g(x) = 2x² - 3, we are asked to solve (ƒ o g)(x) = 1/8.

(ƒ o g)(x) means we need to substitute g(x) into ƒ(x):

ƒ(g(x)) = 1 / (g(x) + 1)

Substituting g(x) = 2x² - 3:

ƒ(2x² - 3) = 1 / (2x² - 3 + 1)

ƒ(2x² - 3) = 1 / (2x² - 2)

1 / (2x² - 2) = 1 / 8

8 = 2x² - 2

2x² = 10

x² = 5

x = ±√5

Therefore, the solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.

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