A 15-foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree. Approximately how high up the tree does the top of the pole reach? responses 1. 9 feet 1. 9 feet 7. 0 feet 7. 0 feet 12. 7 feet 12. 7 feet 17. 0 feet.

The probability that the teacher will choose two girls would be = 1/6

Probability is defined as the expression that shows the possibility of an outcome of an event which may or may not happen.

The total number of students in the class = 9

The total number of girls = 4

The total number of boys = 5

The formula for finding probability = No of favourable outcome/Total number of outcomes.

The probability that teacher choose first girl = 4/9

One girl is selected we must reduce the number of girls available for selection to 4 - 1 = 3.

We must also reduce the number of children available for selection 9 - 1 = 8.

The probability that teacher choose second girl = 3/8

Thus, the probability = 4/9 × 3/8 = 1/6

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Answer:

Step-by-step explanation:

We need to show that the path given by r(t) = (e^t sin t, e^(-t) cos t, e) intersects the sphere 2y^2 + 2z^2 = 4 once, traveling from outside the sphere to inside as t goes from -∞ to +∞.

The equation of the sphere is 2y^2 + 2z^2 = 4. To find the intersection points of the path and the sphere, we need to substitute the components of r(t) into the equation of the sphere:

2y^2 + 2z^2 = 4

2(e^(-t) cos t)^2 + 2e^2 = 4

2e^(-2t) cos^2(t) + 2e^2 = 4

e^(-2t) cos^2(t) + e^2 = 2

Multiplying both sides by e^(2t), we get:

cos^2(t) + e^(4t) = 2e^(2t)

We can rewrite this equation as:

e^(4t) - 2e^(2t)cos^2(t) + cos^2(t) - 1 = 0

This is a quadratic equation in e^(2t) with solutions:

e^(2t) = cos^2(t) ± sqrt(cos^4(t) - 4(cos^2(t) - 1))

We want to show that there is only one intersection point, which means we want to show that the discriminant of the quadratic is negative, i.e.:

cos^4(t) - 4(cos^2(t) - 1) < 0

Expanding the left-hand side, we get:

cos^4(t) - 4cos^2(t) + 4 < 0

Simplifying, we get:

(cos^2(t) - 2)^2 < 0

Since the square of a real number is always non-negative, this inequality has no real solutions. Therefore, the discriminant of the quadratic is negative, and there is only one intersection point.

To show that the path travels from outside the sphere to inside as t goes from -∞ to +∞, we can observe that as t goes from -∞ to +∞, the first component of r(t) goes from -∞ to +∞, while the second and third components oscillate between 0 and +∞. This means that the path starts outside the sphere (at the point (0, +∞, +∞)) and ends inside the sphere (at the point (+∞, 1, 1)). Therefore, the path must intersect the sphere once, traveling from outside to inside.

Answer:

Step-by-step explanation:

1st you solve the triangle by L x W then round it by x 10, hope this helps!

Answer:

there is an error in the question. if you compute ac - ab = 4 you get -2x+4 =4 that leads to x=0.

if so, ab = -6 and this is not allowed.

This equation demonstrates the distributive property of multiplication

What is distributive property ?

In mathematics, the distributive property is a property of binary operations that applies to numbers, sets, or other mathematical objects. It governs how to perform the operation of multiplication over addition or subtraction. The distributive property states that for any numbers a, b, and c:

a × (b + c) = a × b + a × c (multiplication distributes over addition)

or

a × (b - c) = a × b - a × c (multiplication distributes over subtraction)


The property demonstrated in this equation is the distributive property of multiplication over addition. This property states that the product of a number and the sum of two or more numbers is equal to the sum of the products of the number and each of the individual numbers. In other words, a(b + c) = ab + ac.

In this case, 15 is being multiplied by the sum of 5 and 7, which is equivalent to multiplying 15 by 5 and 15 by 7 separately and adding the results. So, we have:

15(5 + 7) = 15 x 5 + 15 x 7

This equation demonstrates the distributive property of multiplication over addition.

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Answer:

[tex]3p + 5p = 8p + 7[/tex]

Step-by-step explanation:

I don't know how to explain it, but

[tex]3p + 5p = 8p + 7[/tex]

Simplifying this

[tex]8p = 8p + 7[/tex]

It will never equal because no matter what number you put for P, one will always be 7 greater than the other

Answer:

102

Step-by-step explanation:

Angles in a quadrilateral is 360

120+85+53=258

360-258=102

Hope this helps!

The number of years for the interest amount to reach $ 1,500 at 4 % is given by b = 10.35 years

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount invested be P = $ 1,000

Let the number of years be = b

Let the number of times the interest is applied n = 1

Let the rate of interest be r = 4 %

Now , the compound interest + amount = $ 1,500

A = P ( 1 + r/n )ⁿᵇ

And , the number of years b = ln ( A / P ) / n [ ln ( 1 + r / n ) ]

On simplifying , we get

b = ln ( 1,500.00 / 1,000.00 ) / ( 1 × [ ln ( 1 + 0.04 ) ] )

b = 10.338 years

Hence , the number of years is 10.35 years

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Answer: it will be square or rhombus

Step-by-step explanation:

Answer:

40x + 17(468-x) = 11912

       23x = 11912 - 17*468     |Solve for x and then find (468-x) as well

The probability that a randomly selected teacher earns more than $525 a week is 0.1820. Therefore, the probability that a randomly selected teacher earns more than $525 a week is 0.2177.

This is calculated by using the standard normal distribution formula:

P(x > 525) = 1 - P(x ≤ 525) = 1 - 0.8413 = 0.1820

The probability that a randomly selected teacher earns more than $525 a week can be found by calculating the z-score for $525 and then using the standard normal table to find the probability.

The z-score is calculated as follows:

z = (x - μ)/σ

Where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

Plugging in the values from the question, we get:

z = (525 - 490)/45 = 0.78

Now, we can use the standard normal table to find the probability that a randomly selected teacher earns more than $525 a week. The table gives us the probability that a value is less than a given z-score, so we need to subtract the probability from 1 to find the probability that a value is greater than the z-score.

The probability that a value is less than 0.78 is 0.7823. So, the probability that a value is greater than 0.78 is 1 - 0.7823 = 0.2177.

Therefore, the probability that a randomly selected teacher earns more than $525 a week is 0.2177.

Answer: 0.2177

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Answer:

2x + h - 5

Step-by-step explanation:

To find f(x + h) we simply plug (x + h) into the function f(x), anywhere we see an x.

[tex]f(x) = x^{2} -5x+9\\f(x+h) = (x+h)^{2}-5(x+h)+9[/tex]

Now we can plug them into the fraction:

[tex]\frac{((x+h)^{2}-5(x+h)+9)-(x^{2} -5x+9)}{h}[/tex]

Expanding all of the terms, we get:

[tex]\frac{(x^{2} +2hx + h^{2} -5x-5h+9)-(x^{2} -5x+9)}{h}[/tex]

Distributing the negative we get:

[tex]\frac{x^{2} +2hx + h^{2} -5x-5h+9-x^{2} +5x-9}{h}[/tex]

Now we see that [tex]x^{2} -x^{2} ,-5x+5x,[/tex] and [tex]9-9[/tex] all cancel, leaving us with:

[tex]\frac{2hx + h^{2}-5h}{h}[/tex] (Notice the only terms left are those with h in them)

As every term contains an h, we can remove an h from every term, giving us:

2x + h - 5

Answer:

f-1(x)=x4+3 this is your answer

The solution of the system of equations is:

x = 12, y = 11, z = 2

We can rewrite our system of equations as:

x + y + z = 25

5x + y + 9z = 89

-7x + 6y + 6z = -6

First, if we subtract the first equation and the second one, we will get:

(5x + y + 9z) - (x + y + z) = 89 - 25

4x + 8z = 64

And if we subtract 6 times the first equation from the third one, we will get:

-7x + 6y + 6z - 6*(x + y + z) = -6 - 6*25

-13x = -156

We can solve this for x:

x = -156/-13 = 12

Now we know the value of x, replacing it in:

4x + 8z = 64

Will give:

4*12 + 8z = 64

8z = 64 - 4*12 = 16

z = 16/8 = 2

And the value of y will be given by:

x + y + z = 25

12 + y + 2 = 25

14 + y = 25

y = 25 - 14 = 11

Then the solution is:

x = 12, y = 11, z = 2

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Answer:

7:11

28:44

Step-by-step explanation:

Multiply both sides by 4.

Answer:

View Screenshot

Step-by-step explanation:

The linear equation for coordinate points (-2,8) and (5,-6) is option B: y = -2x + 4.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Since there are two points on the graph, use the slope-intercept form of a linear equation to find the equation that matches the graph.

The slope-intercept form is -

y = mx + b

Where m is the slope and b is the y-intercept.

To find the slope, we use the two given points -

m = (y2 - y1) / (x2 - x1)

m = (-6 - 8) / (5 - (-2))

m = -14 / 7 = -2

To find the y-intercept, we can use one of the points and the slope -

y = mx + b

8 = (-2) × (-2) + b

8 = 4 + b

b = 4

So the equation that matches the graph is -

y = -2x + 4

Therefore, the equation is -2x + 4.

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Answer:

              The x-intercept of Line A is (-3, 0), and the x-intercept of Line B is (-1, 0). Therefore, the x-intercept of Line A is less than the x-intercept of Line B.

Step-by-step explanation:

              The x-intercept of a graph or function is where the line hits the x-axis on a coordinate plane. In other words, the y-value of the x-intercept is 0. Since we are looking for the x-intercept of Line A, we can use the given equation to solve for it by inserting the value y = 0 (as mentioned above, the x-intercept of a function will have the y-value as 0). By solving the equation, you'll get that [tex]-2=\frac{1}{3} (x-3)[/tex] ⇒ [tex]-6=x-3[/tex] ⇒ [tex]x = -3[/tex]. Therefore, the x-intercept of Line A is (-3, 0).

              The x-intercept on a graph is easier to find, as it is where the line touches the x-axis. So the x-intercept of Line B would be (-1, 0). Now that we have both x-intercepts, we can compare them and come up with the final answer that is required. As -3 is less than -1, we can conclude that the x-intercept of Line A is (-3, 0), and the x-intercept of Line B is (-1, 0). Therefore the x-intercept of Line A is less than the x-intercept of Line B.

Have a great day! Feel free to let me know if you have any more questions :)

The most accurate calculation for the product of 2, 9, and 11, is 1, or 0 + 1.

Best estimate refers to the figure arrived at by an assessor using deterministic techniques that most accurately captures the anticipated result without optimism or conservatism.

To estimate a number is to round it up to the nearest full number.

We now have February 9 and November 11.

Hence, as 2/9 is closer to 0 than 0.5, we will estimate it to be 0.

Similarly, we will estimate 10/11 as 1 since it is closer to 1 than 0.5.

Hence, 0 + 1 = 1 is the result of adding up their estimates.

In conclusion, 0 + 1 = 1 is the best estimate for the product of the numbers 2/9 and 10/11.

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Answer:you did not give us anyting for us to answer

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

-5 x -12/ 3 x -5

60/-15

-4

The diagonal distance from the airplane to the runway is approximately 5230.8 ft.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to measurements of angles and distances.

The angle of depression of 18° is the angle between the airplane's line of sight and the horizontal line representing the runway. We can label the altitude of the airplane as 1560 ft:

Now we can use trigonometry to find the diagonal distance from the airplane to the runway. In particular, we can use the tangent function:

tan(18°) = opposite / adjacent

In this case, the opposite side is the altitude of the airplane (1560 ft), and the adjacent side is the diagonal distance we're trying to find (x). Therefore:

tan(18°) = 1560 / x

To solve for x, we can multiply both sides by x and then divide both sides by tan(18°):

x = 1560 / tan(18°)

Using a calculator, we find that:

x ≈ 5230.8 ft

Therefore, the diagonal distance from the airplane to the runway is approximately 5230.8 ft.

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Answer:   3

Step-by-step exp lanation:

divided

Answer:

3(x + 5y) - 2(x + y)

3x + 15y - 2x - 2y

x + 13y

(3x + 15y) + (-2x + -2y)

x + 13y

The key features of this rational function include the following:

Domain: (-∞, 2) ∪ (2, ∞)

Range: (-∞, 1) ∪ (1, ∞)

Y-intercept: 1.

X-intercept: 2.

Vertical asymptote: x = -2.

Horizontal asymptote​: y = -1.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

Additionally, the vertical extent of any graph of a rational function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

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Answer:

The answer is D.

Step-by-step explanation:

The image of the polygon after the rotation is added as an attachment

From the question, we have the following coordinates that can be used in our computation:

(1, 0), (2, 0), (0, 2) and (2, 2)

The location of point G is

G = (3, -1)

To rotate about point G, we start by subtracting the points from G

So, we have

[(1, 0), (2, 0), (0, 2) and (2, 2)] - (3, -1)

This gives

(-2, 1), (-1, 1), (-3, 3) and (-1, 3)

The rule is 90 degrees clockwise rotation

This is represented as

(x, y) ⇒ (y, -x)

So, we have

(-2, 1), (-1, 1), (-3, 3) and (-1, 3) ⇒ (1, 2), (1, 1), (3, 3) and (3, 1)

Next, we plot (1, 2), (1, 1), (3, 3) and (3, 1)

See attachment for the image of the transformation

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The solution of the equation are y=9 and x=4

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

WE are given that the system of equation;

5x+6y=26 and 10x-6y=-2

5x+6y=50

-1(-x+6y=26)

X-6y=-26

Then Eliminate the y and combine evrything

6x=24

Divide 6 both sides

X=4

Then, substitute the x

-(4)+6y=50

-4+6y=50

Add 4 both sides

6y=54

y=9 and x=4

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