Kayla wants to find the width, AB, of a river. She walks along the edge of the river 100 ft and marks point C. Then she walks 22 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown

x = 4

Hi there !

2 - 5x = - 18

2 + 18 = 5x

20 = 5x

5x = 20

x = 20 : 5

x = 4

Good luck !

Answer:

knjiqjwefiro fejweiejf

Step-by-step explanation:

1000

Step-by-step explanation:

1000+(b-8l^3=12(;2(

The simplification of the given expression would be = 210

A fraction is defined as the expression of part of a whole value in the form of a denominator and a numerator.

The above statement can be expressed above mathematically as follows:

= 7/8 × 16 × 1/2× 30

= 3360/16

= 210

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Answer:(-(3x^(3)-x-1))/((x^(2)+1)^(2))

The intersection points are: (0, -3) and (10, 2)

The bounded area is -20.83 unit²

(a) The  intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:

(0, -3) and (10, 2)

(b) The integral terms of y which gives the area bound are:

a = -3, b = 2 (These are the y values of the intersection points)

Since we have x = y² + 3y and x = 2y + 6, we can say:

y² + 3y = 2y + 6

y² + 3y - 2y - 6 = 0

y² + y - 6 = 0

Thus, h(y) =

Using a = -3 and b = 2  with h(y) = y² + y - 6, we have the bounded area as:

\(Area = \int\limits^b_a {y} \, dy\)

\(Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy\)

Integrating the area:

Area = [y³/3 + y²/2 - 6y + C]²₋₃

Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]

Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]  

Area = [-22/3] - [27/2]

Area = -125/6

Area = -20.83 unit²

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Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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The required zeros of the given polynomial x³ + 2x² = 49x + 98 are x = 7, x = -7, and x = 2.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The polynomial is given in the question as:

x³ + 2x² = 49x + 98

To determine the factor of the polynomial.

If you rewrite the polynomial as x³ + 2x² - 49x - 98 = 0, you can factor it as follows:

(x - 7)(x + 7)(x - 2) = 0

(x - 7) = 0, (x + 7) = 0, and (x - 2) = 0

x = 7, x = -7, and x = 2

This means that the zeros of the polynomial are x = 7, x = -7, and x = 2.

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The question seems to be incomplete the correct question would be

Find zeros of this polynomial x³ + 2x² = 49x + 98.

Answer:

x=4/3

Step-by-step explanation:

0=3x-4

+4   +4

4=3x

/3 /3

4/3=x

(-3, 23/2)

the picture i linked shows the step by step

The answers are a- 36

b- 9

c-0.1111

In mathematics or the field of statistics, probability is defined as the extent or the likelihood of something happening.

(a)- We have two dice in this question,

A die is known to be make up of 6 faces.

Therefore, the number of faces for two dice = 6 x 6

= 36

(b)- Out of these two dice, one die has 3 odd numbers and three even numbers,

Therefore,

the number of even number outcomes for both dice = 3 x 3

= 9

(c)- The probability of having an even number,

This is 1/9, remember 9 is the total number of even numbers = 0.1111

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Answer:

A = 19

Step-by-step explanation:

A - 6 = 13

19 - 6 = 13

A = 19

I hope this helps!

Answer:

19

Step-by-step explanation:

13 + 6 = 19

19 - 6 = 13

Answer:

The change in temperature is -13°F.

Step-by-step explanation:

The change in temperature is,

→ -1 + x = -14

→ x = -14 + 1

→ [ x = -13 ]

Therefore, -13°F is the change.

Answer: domain: all real numbers; range: all real numbers greater than or equal to –4

Step-by-step explanation: The function f(x) = x^4 - 2x^2 - 4 is a polynomial function, which means its domain is all real numbers. To find the range of the function, we can complete the square for the quadratic term x^4 - 2x^2 to get f(x) = (x^2 - 1)^2 - 5. The minimum value of (x^2 - 1)^2 is 0, which occurs when x^2 = 1 or x = ±1. Therefore, the minimum value of f(x) is f(±1) = (±1)^4 - 2(±1)^2 - 4 = -5 + 1 = -4. Hence, the range of f(x) is all real numbers greater than or equal to -4.

Answer:

probability is one for the position of the fourth vertex

it's co ordinates will be (2,2)

Answer:

0.001687 = 0.1687% probability that no more than 1 vessel transporting nuclear weapons was destroyed.

Step-by-step explanation:

The vessels are destroyed and then not replaced, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

Fleet of 18 means that \(N = 18\)

9 are carrying nuclear weapons, which means that \(k = 9\)

9 are destroyed, which means that \(n = 9\)

What is the probability that no more than 1 vessel transporting nuclear weapons was destroyed?

This is:

\(P(X \leq 1) = P(X = 0) + P(X = 1)\)

In which

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,18,9,9) = \frac{C_{9,0}*C_{9,9}}{C_{18,9}} = 0.000021\)

\(P(X = 1) = h(1,18,9,9) = \frac{C_{9,1}*C_{9,8}}{C_{18,9}} = 0.001666\)

Then

\(P(X \leq 1) = P(X = 0) + P(X = 1) = 0.000021 + 0.001666 = 0.001687\)

0.001687 = 0.1687% probability that no more than 1 vessel transporting nuclear weapons was destroyed.

Answer: 6

Step-by-step explanation:

\(\displaystyle\\\frac{54}{72}=\\\\\frac{9(6)}{9(8)}=\\\\\frac{6}{8}=\\\\\frac{1(6)}{8} =\\\\\frac{1}{8}(6)\)

Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.

Answer:

(0,0)

Step-by-step explanation:

Do the opposite. (2-5+3,0) is (0,0)

Answer:

75

Step-by-step explanation:

f(x)=-x^2-10x

f(-5)=(-5)^2-10(-5)

f(-5)=(-5)(-5)+50

f(-5)=25+50

f(-5)=75

Let:

x = Number of correct answers

For Daylyn:

For Brennan:

how many answers each of the boys would need to get correct to raise the same amount of money? in another words:

Solve for x:

The value of x for the chord is:

x = 12

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.

Recall that: If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords.

Using the above principle, we can say:

3 * x = 4 * 9

3x = 36

x = 36/3

x = 12

Thus, the value of x for the chord is 12.

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Step-by-step explanation:

1/16 for Washington County.

5/76 for Webster County.

so, let's bring both to the same denominator (bottom part of the fractions).

this is usual the LCM of both denominators.

since 16 = 2×2×2×2

76 = 2×2×19

the least common multiple (LCM) is the combination of the longest sequence per prime factor involved :

2×2×2×2×19 = 16×19 = 304

1/16 = 19/304

5/76 = 5× 1/76 = 5× 4/304 = 20/304

so, now we know, 20/304 > 19/304, and therefore Webster County has the greater fraction of adults, who enjoy gardening.

Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

Meaning of probability :

Probability is calculation of how likely some event will happen. Whenever we are not sure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are going to happen.

The analysis of events governed by probability is called statistics.

According to the given information :

Red section = \(\frac{2}{5}\)

multiply numerator and denominator by \(2\) we get

Red section = \(\frac{4}{10}\)

 Blue section = \(\frac{1}{2}\)

 multiply numerator and denominator by \(5\) we get

 Blue section = \(\frac{5}{10}\)

 Green section = \(1\)- Red section - Blue section

 Green section =\(1-\frac{4}{10} -\frac{5}{10}\)

  Green section = \(\frac{1}{10}\)

Therefore Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

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Answer:a

Step-by-step explanation: