if a 40-foot tree casts a 12-foot shadow, find the length of the shadow cast by a 28-foot tree

The x-coordinate in the solution of the given system of equations is -4.

The x-coordinate in the solution of the given system of equations can be found by substituting the value of y from one equation into the other equation and solving for x. Let's solve the system of equations:

Start with the equation y = -2/3x. Substitute this into the second equation:

4x - 9(-2/3x) = -40

Now simplify and solve for x:

4x + 6x = -40

10x = -40

x = -4

So, the x-coordinate in the solution of the system of equations is -4.

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To solve the operation 4/11 x 10/8, multiply the numerators and denominators separately. The result is 0.45454545454.

Perform the indicated operation: 4/11 x 10/8

Multiply the numerators: 4 x 10 = 40

Multiply the denominators: 11 x 8 = 88

The result is 40/88 = 0.45454545454

Nonlinear function (A)

The graph of a combination of line segments that passes the vertical line test is a Non Linear function.

The vertical line test states that a graph represents a function if and only if all vertical lines intersect the graph at most once.

The vertical line check is a graphical approach of determining whether or not a curve inside the aircraft represents the graph of a function by means of visually examining the variety of intersections of the curve with vertical lines.A vertical line intersects with them only once, making them features.Parabolas that face upward and downward are capabilities.They may be functions because a vertical line intersects the curve no extra than once.

If a vertical line intersects a curve on an xy-plane greater than once then for one price of x the curve has multiple value of y, and so, the curve does now not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.

The vertical line take a look at helps to find it a given curve represents a function or now not. If the vertical line cuts the graph of the equation at simplest one factor, then it's miles a characteristic, and if cuts the graph of the characteristic at a couple of point, then it does not constitute a characteristic. A vertical form is a shape with layers stacked on top of every other, with a fixed layer top, for instance a spherical tower where the radius corresponds to the datapoint.

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Answer:

By having or building a good credit history.

Step-by-step explanation:

When an item is to bought by you on credit , for you to have or build a good credit history , Buying something with credit means that you are buying something with money you don't have at that very time

Later on, you will have to give back this money borrowed to a person,an interest will be paid for lending it.

product means multiply

increased by means add

 so product of 4 and a number would be 4n

 than add 7

 so you have 4n+7

7/3 +3(2/3 -1/3)^2 =

2/3 -1/3 = 1/3 now you have

7/3 +3(1/3)^2

1/3^2 = 1/9

7/3 +3(1/9)

3*1/9 = 1/3

7/3 + 1/3 = 8/3, which can be changed to 2 2/3

To solve the system of equations xy = 6x + 12 and yy = x + 47, we can rearrange the equations, isolate one variable, and substitute it into the other equation. Then, solve for the variables. The solution is x = 282 / (270 - y) and y = (270 - xy) / 6.

To solve the given system of equations,

xy = 6x + 12
yy = x + 47

We can start by rearranging the equations:

xy - 6x = 12
yy - x = 47

Next, we can isolate one variable in terms of the other variable and substitute it into the other equation:

x = (yy - 47)
xy - 6(yy - 47) = 12

Simplifying the equation:

xy - 6yy + 282 = 12

Combining like terms:

-6yy + xy = -270

Now, we can solve this equation for y in terms of x:

y = (270 - xy) / 6

Re-substituting the value of y back into one of the original equations:

(270 - xy) / 6 * x = 47

Simplifying and solving for x:

270x - xy = 282

x(270 - y) = 282

x = 282 / (270 - y)

So, the solution to the system of equations is:

x = 282 / (270 - y)
y = (270 - xy) / 6

Answer:

170.202 years

Step-by-step explanation:

From the compound interest formula, that has interest rate in times per year but compounds monthly we have

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

A is the amount you want to save, P is the principal (what you put down, in this case 100), r is the anual interest rate, n is 12 i.e the times it compounds, and t is the amount of years it will take. So we have data for all variables but t.

Solving for t we have

[tex]\frac{A}{P}=(1+\frac{r}{n})^{nt}[/tex]

taking logs

[tex]log(\frac{A}{P})=nt \,log(1+\frac{r}{n})[/tex]

finally

[tex]t = \frac {log(\frac{A}{P}) }{ n[log(1 + \frac{r}{n})]}[/tex]

replacing and calculating we get t=170.202

The measure of an angle formed by the intersection of two angle bisectors in a triangle is the semisum of the two angles being bisected. So, in both situations, ∠ADB and ∠AMB will be (α + β)/2.

In a triangle, the angle formed by the intersection of two angle bisectors is always equal to the semisum of the two angles being bisected. Therefore, in ∆ABC, the measure of ∠ADB (∠ formed by the intersection of the bisectors from ∠A and ∠B) will be (α + β)/2.

For example, if angle A is 40° (let's represent it by α) and angle B is 60° (let's represent it by β), the ∠ADB will be (40 + 60) / 2, which equals 50°.

In the second problem, the measure of ∠AMB will also be equal to the average of ∠A and ∠B, so m∠AMB = (58° + 96°) / 2 = 77°. This rule applies to any triangle ABC, regardless of the type of triangle.

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Answer:

Hi, sorry, but my computer is glitching and I can't put in the answer for some reason.... I'm REALLY sorry...

Step-by-step explanation:

Line g is a line of symmetry of this regular polygon.

We have regular polygon as shown in the figure.

We have to determine which line is a line of symmetry for this regular polygon.

A plane figure is symmetric about a line if it is its own image when flipped across the line. The reflection line is the line of symmetry.

According to the question, we have a Regular Polygon.

According to the concept of Symmetry of any plane figure -

if we fold this polygon about the line g then both the sides will overlap.

The lines i and h do not fulfill this condition.

Hence, line g is a line of symmetry of this regular polygon.

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Final answer:

To convert the average height of a female giraffe from meters to centimeters, multiply 4.6 meters by 100, resulting in 460 centimeters.

Explanation:

To convert the average height of a female giraffe from meters to centimeters, we need to use the conversion factor where 1 meter is equivalent to 100 centimeters. If the average height is 4.6 meters, then we need to multiply this value by 100 to find the height in centimeters

Step-by-step calculation

This conversion process, from meters to centimeters, simplifies the representation of the average height of a female giraffe. Utilizing the conversion factor, where 1 meter equals 100 centimeters, the calculated result of 460 centimeters provides a more practical and commonly used metric. Such conversions are valuable for ensuring consistency in measurement units and facilitating communication across different contexts, enhancing our understanding of the physical dimensions of giraffes in a more accessible manner.

The probability of Mark hitting the bull's-eye on the fourth shot, assuming he misses the first three times, is 8.64%. This is calculated as the product of the probabilities of each event occurring independently.

This is indeed a problem related to probability, particularly, this pertains to the concept of an independent event in statistics. Mark's success in shooting an arrow accurately to the target is an independent event because the outcome of one shot doesn't affect the outcome of other shots.

In Mark's case, he hits the bull's-eye about 40% of the time, i.e. his success rate P(Success) is 0.40 and his failure rate P(Failure) is 0.60. Since the question asked about the probability of him hitting the bull's-eye on the fourth shot, we should look at the first three shots being failures and only the fourth being a success.

This leads us to the calculation: P(FFFH) = P(F) x P(F) x P(F) x P(H) = (0.60)*(0.60)*(0.60)*(0.40) = 0.0864 or 8.64% chance.

So, there's an 8.64% chance that Mark will hit the bull's-eye on the fourth shot given that he misses the first three.

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The probability that Mark hits the bull's-eye on his fourth shot, given he typically hits the bull's-eye 40% of the time, is 0.0864 or 8.64%

The problem is about the probability that Mark hits the bull's-eye on the fourth shot given that he hits the bull's-eye about 40% of the time. In these cases, for the first three shots, he should not hit the bull's-eye (probabilty of 60%) and on the fourth trial, he should hit the bull's-eye (probability of 40%). Therefore, we multiply the individual probabilities together to find the answer.

Step 1: Find the probability that he does not hit the bull's-eye in the first three trials. This is (0.6)*(0.6)*(0.6) = 0.216.

Step 2: Find the probability that he hits the bull's-eye on the fourth trial. This is simply 0.4.

Step 3: Multiply the two probabilities together to find the final answer. This gives us 0.216*0.4 = 0.0864.

So, the probability that Mark hits the bull's-eye on the fourth shot is 0.0864, or 8.64%.

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difference between -5 and 25 is

25 + 5 = 30 degrees

answer is C.

Each person would get 1/9 lb of pasta if 6 people were to share 2/3 lb of pasta equally.

In the given question, 6 people are sharing 2/3 lb of pasta equally. This implies that we are performing an operation of division. You would divide 2/3 by 6 to find out how much each person gets. Here's how you can do it:

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Dimensions are 50 feet by 50 feet.

Let the length = x

the width = y

So the perimeter = 2(x+y)=200

or, x+y=100

or, y=100-x

So the area is = A = xy = x(100-x).

For greatest area A' = 0 and A" < 0.

[tex]A= x(100-x)\\A=100x-x^2\\A'=100-2x\\A''=-2[/tex]

We set A'=0 to find x.

[tex]100-2x=0\\2x=100\\x=50[/tex]

For x=50, A"=2 < 0

It means for x=50, y=100-50=50 the rectangle will have the greatest area.

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We are given the incomplete expression:

x^2 + b x

Now to complete the square, we need to add the square of the half of b, that is:

(b / 2)^2

or

b^2 / 4

Therefore the complete expression is:

x^2 + b x + (b^2 / 4)

Final answer:

In the context of a folding chair, as angle 1 (between the backrest and the seat) increases, the distance between the back of the chair and the front leg correspondingly increases due to the lever-like movement of the backrest.

Explanation:

When considering the geometry of a folding chair and the angles formed by its parts, it's important to visualize the chair as a system of linked levers. As angle 1 increases, which is the angle between the backrest of the chair and the seat, the relationship between the back of the chair and the front leg changes. If we assume that the front leg stays still and the back of the chair moves backward to increase the angle, the distance between the back of the chair and the front leg increases. This movement can be seen as the backrest acting like a lever, where increasing the angle effectively moves the lever away from the pivot point at the front leg.

Therefore, the correct answer in the context of a folding chair is: A. As the measure of angle 1 increases, the distance between the back of the chair and the front leg of the chair increases.