Two Buildings On Level Ground Are 120 M And 85 M Tall Respectively. Given That The Angle Of Elevation (2024)

Answer:

A.) (0,5)

B.) -3/2

C.) y= (-3/2)x + 5

Step-by-step explanation:

A.) The y-intercept of a graph is the point where the function crosses the y-intercept. For the function shown in the graph, the y-intercept would be (0,5) or y=5.

B.) Slope can be determined by using rise over run. To determine the rise and run, we will need to look at 2 points. Let's use the points (0,5) and (2,2). Instead of "rising" from (0,5) to (2,2), we must "sink" 3, giving us a rise of -3. Next, to get from (0,5) to (2,2), we must "run to the right 2. So, our "rise over run" or "rise/run" would be -3/2. This means our slope is -3/2.

C.) When writing an equation for the line, we are going to want to write it in slope-intercept form. Slope-intercept form is often shown as y=mx+b, when m is the slope and b is the y-intercept. Since we know both the slope and y-intercept, we can plug those values into the slope-intercept form equation. This then changes y=mx+b into y=(-3/2)x+5.

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Answer:

y= -3/2x+6

Point of intersection: (0,6)

Y Intercept: 6

Slope: -3/2

You can check slope by counting the number of units it goes down and to the side. it is rise/run so the amount of y values it goes down and x values goes to the side is the denominator.

Slope: rise/run= y1-y2/x2-x1

Step-by-step explanation:

An exponential function can be mixed with other exponential functions via addition, subtraction, multiplication, or division.

Which is an exponential function?

An exponential function is a mathematical function that has the following structure: f (x) = an x. where x is a variable and with an is a support to keep as the function's base. The most typical exponential-function base is the transcendent number e, or approximately 2.71828. Exponential functions are often used to model phenomena in the real world, including bacterial growth, population growth, and compound interest. Consider that you are investigating the effects of an antibiotic on a certain bacteria.

Given that (f + g) (x) equals (f (x) + g (x), (f + g) (x) equals (2x + 1) + (x2+ 2x - 1), which translates to 2x + 1 + x2 + 2x - 1 as 2x+ 4x.

(f + g) (2) = 22+ 4(2) = 4 + 8 = 12 since (f + g) (x) = x2 + 4x.

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Answer: One way to find the total number of handshakes is to use a table of values to track the number of handshakes as the number of people in the meeting increases.

Number of People | Number of Handshakes

1 | 0

2 | 1

3 | 3

4 | 6

5 | 10

6 | 15

7 | 21

8 | 28

9 | 36

10 | 45

11 | 55

12 | 66

13 | 78

14 | 91

We can use the formula for the triangular number (n*(n-1))/2 where n is the number of people in the meeting.

So, total handshakes (14*13)/2 = 91

Step-by-step explanation:

The number of integers N less than 1000 that can be written as the sum of j consecutive positive odd integers from exactly 5 values of j ≥ 1 is 15.

Arithmetic sequence is a sequence of numbers/terms that has a fixed pattern, based on the operation of subtraction or addition. Thus, each sequence of numbers will have a common difference.

Formula: aₙ = a₁ + (a - 1)d,

where aₙ is the nᵗʰ term and a₁ is the first term in the sequence, and d is the common difference between terms

Sum of n terms = n (a₁ + aₙ) / 2

We want to know the number of integers N less than 1000 that can be written as the sum of j consecutive positive odd integers from exactly 5 values of j ≥ 1

First, we determine:

- the first odd integer in the list: 2n + 1, where n ≥ 1

- the last odd integer in the list: 2n + 1 + 2(j - 1) = 2(n + j) - 1

These odd integers form a sequence with the following sum:

N = n (a₁ + aₙ) / 2

= j (2n + 1 + 2(n + j) - 1) / 2

= j (2n + 1 + 2n + 2j - 1) / 2

= j (4n + 2j) / 2

= j (2n + j)

We also know that there are exactly 5 values of j that satisfy the equation, there must be either 9 or 10 factors of N.

This means N = p₁².p₂² or N = p₁.p₂⁴

If N is odd, then j is also odd, which means that 2n+j is also odd. It is valid for all odd j. Given the boundary of 1000, the possibilities of odd N are (3².5²), (3².7²), (3⁴.5), (3⁴.7), and (3⁴.11) ---> 5 possibilities

If N is even, then j is also even. If we substitute j = 2k into the N, we get:

N = j (2n + j)

= 2k (2n + k)

= 4k (n + k)

N/4 = k (n + k)

This formula implies that the new upper bound is 250. So the possibilities of even N are (2².3²), (2².5²), (2².7²), (3².5²), (2⁴.3), (2⁴.5), (2⁴.7), (2⁴.11), (2⁴.13), and (3⁴.2) ---> 10 possibilities

Thus, the total number of integer N is 5 + 10 = 15

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After 6 months of birth the weight will become 6.95 kg.

A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.

from given condition, a baby weigh 3. 35 kilogram at birth and the baby weight constantly increase every two month by 1. 2 kilogram.

so, the weight after 2 months of birth is 3.35 kg + 1.2 kg = 4.55 kg

and the weight after 4 months of birth is 4.55 kg + 1.2 kg = 5.75 kg

and the weight after 6 months of birth is 5.75 kg + 1.2 kg = 6.95 kg

Therefore, after 6 months of birth the weight will become 6.95 kg.

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Answer:

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

On solving the provided question, we can say that the roasting approach, which represents sets as 3, 5, 7, and 8, is one way to write domains

what is domain?

The domain of a function is the set of possible values that it can accept. The x-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. This set is the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.

A set of ordered pairs (x, y), {(3,6),(5,7),(7,7),(8,9)}.

The collection of x values that make up the domain of the function f(x) include,

The roasting approach, which represents sets as 3, 5, 7, and 8, is one way to write domains. Another is the arrow diagram method.

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Answer:

5/12

Step-by-step explanation:

5/12

Answer:

x-intercept(s):

None

y-intercept(s):

(

,

5

√

2

)

Step-by-step explanation:

Answer:

f(2)=18

Step-by-step explanation:

f(2)=2(2)²+5√(2+2)

f(2)=2(4)+5√(4)

f(2)=8+5(2)

f(2)=8+10

f(2)=18

a) The probability of getting exactly 5 successes is 0.1029.

b)The probability of getting 6 or more successes is 0.8497510126.

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Here, p = 0.7, q = 0.3 and n = 10

a) The probability of getting exactly 5 successes

P (x= 5) = C(10, 5) (0.7)⁵ (0.3)⁵

= 10!/ 5! 5! x 0.16807 x 0.00243

= 0.1029

b)The probability of getting 6 or more successes

P(X≥6) = 1 - P(X<6)

= 1 - P(X = 0, 1,2, 3, 4, 5)

= 1 - [ P(0) + P(1) P(2) + P(3) + P(4) + P(5)]

= 1 - [C(10, 0) [tex](0.3)^{10[/tex] + C(10, 1) (0.7) [tex](0.3)^{9[/tex] + C(10, 2) (0.7)² [tex](0.3)^{8[/tex]

+ C(10, 3) (0.7)³ [tex](0.3)^{7[/tex] + C(10, 4) [tex](0.7)^4[/tex][tex](0.3)^{6[/tex] + C(10, 4) [tex](0.7)^5[/tex]

[tex](0.3)^{5[/tex] ]

= 1 - [ 0.0000059049 + 0.000137781 + 0.0014467005 +

0.009001692 + 0.036756909 + 0.1029]

= 1 - 0.1502489874

= 0.8497510126

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C. X=6 is a true solution and X=-6 is an extraneous solution

2log6(x) = 2

log6(x2) = 2

x2 = 6^2

x2 = 36

x = 6, -6

Since 6 and -6 are the only real solutions, 6 is a true solution and -6 is an extraneous solution.

2log6(x) = 2

log6(x)2 = 2

By taking the power of both sides with base 6,

x2 = 62

x2 = 36

By taking the square root of both sides,

x = ±6

x = 6, -6

Since 6 and -6 are the only real solutions, 6 is a true solution and -6 is an extraneous solution.

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Answer:

In this case, the mean is $1400, and the standard deviation is $200.

So, one standard deviation of the mean is 1400+200= $1600 and 1400-200 = $1200.

Therefore, according to the empirical rule, approximately 68% of the farms will have land and building values per acre between $1200 and $1600.

To estimate the number of farms that fall within this range, we can multiply the total number of farms (74) by 0.68.

(74)*(0.68) = 50.32 or about 50 farms

So, according to the empirical rule, approximately 50 farms will have land and building values per acre between $1000 and $1800.

Toni had 17 points, Effie had 25 points and Linda had 18 points.

The question is asking to find the number of points each girl had in a girl's basketball game. To find out how many points Effie had, you must multiply Toni's points by 3, subtract 8, and then multiply the difference by 2. To find out how many points Linda had, you must add 9 to Toni's points and divide the sum by 3. The given information is that Effie scored 9 more than Toni and Linda combined.

Formula and Calculation:

Toni's Points = x

Effie's Points = 3x-8

Linda's Points = (x+9)/3

Effie scored 9 more than Toni and Linda combined, so:

3x-8 = x+9/3 + 9

2x-8 = x+9

x = 17

Therefore, Toni had 17 points, Effie had 25 points and Linda had 18 points.

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Answer:

I can provide you with a description of the graph.

The graph would have the distance on the y-axis and the time on the x-axis.

The first 60 miles of the journey would be represented by a straight line with a slope of 60/1=60, since the car is traveling at a constant speed of 60 mph.

The point where the first 60 miles ends would be (1,60) which is the time of one hour from London, the distance of 60 miles from London.

After the 30-minute break at the motorway services, the car would continue its journey at a constant speed of 70 mph. This part of the journey would be represented by a straight line with a slope of 70/1=70.

The point where the whole journey ends would be (4,200) which is the time of 4 hours from London, the distance of 200 miles from London.

Please note that it is assumed that the car doesn't stop during the second part of the journey.

The midpoint of the given line segment can be determined by using the formula ( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ] .

As given in the question,

Let the two endpoints of the given line segment be A(x₁ , y₁) and B(x₂ ,y₂).

As per midpoint concept it divides the given line segment in the equal ratio.

let the given line segment AB divided in the equal ratio of n : n

Consider the coordinates of the required mid point be ( x , y ) :

using midpoint formula we have :

( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ]

If the point divides the given line segment in the ratio 2 : 2

The required midpoint is given by

(x ,y ) = [ (2x₁ + 2x₂ )/2(2) , (2y₁ + 2y₂ )/2(2)]

= [ (x₁ + x₂ )/2 ) , (y₁ + y₂ )/2 ]

Therefore, the required midpoint which divides the given line segment into equal parts is ( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ].

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The factorize expression of 25x²-4x²-9 is 3(7x²-3).

What is factorization?

Factorization is a process to simplify the expression by finding the factors of that expression.

And to find the same expression from factors, you have to reverse the process.

We have the quadratic function,

25x²-4x²-9.

To factorize the function:

First, combine similar terms,

25x²-4x²-9,

= 21x²-9.

Now, factor out the common factor.

That means,

3(7x²-3).

Therefore, the required function is 3(7x²-3).

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Answer:

1.) x=1; y=1

2.) x=1; y=5

3.) No solution

Step-by-step explanation:

1.) To start off with number one, we see that in both equations the x and y are positive, and the sums aren't equal to each other, this means we have to do something to make them equivalent. For example, we can multiply the top equation by 8 and the bottom equation by 7, so we get the equations 32x + 24y = 56 and the bottom equation to be 21x+35y=56. From here we can just make the equations equal each other to get 32x+ 24y = 21x +35y. From here we can just get a certain amount of x to equal certain amount of y by taking away the smaller amount of each and bringing it to the other side by subtracting. From that we get 11x = 11y. We can simplify this to be x=y. Now we can substitute either x or y in either equation to get 4x + 3(x) = 7. Then you solve algebraically and you get x=1. Now since we established that x was already equal to y, both x AND y are equal to 1.

2.) For this problem, we have an x that is negative in one equation and positive in the other. This means we can use the method of multiplying the bottom equation by 3 to get 3x +3y = 18. Now we are able to add both equations to each other crossing out the x's because they cancel out. From this we get 4y=20, Which means y=5. We can now plug this back into the equation to get x+(5) = 6. Which means y=5 and x=1.

3.) For this problem, we have both equations equal to y. However the x's are also equal to each other. Meaning if we were to solve them like in problem one, we would get the issue of cancelling the x's out and just getting 13/2=9/2 which is a problem because they do not equal each other. But, we can notice that both of the given systems are linear lines, meaning we could plot them off a graph. But to save time, we can notice that both equations have the exact same slope but different starting positions. Meaning that both lines would be parallel to each other. Since both lines are parallel to each other, There will never be an intersection, or answer between them. Making x and y null (no answer)

The length of line segment $BC$, which is the hypotenuse of a right triangle with legs of length 5.41 and 11, is 13.93.

Let AB = x.

Then, using the Pythagorean Theorem, we have:

[tex]$$x^2 + (3+8)^2 = (x+11)^2$$$$x^2 + 19^2 = (x+11)^2$$$$x^2 + 361 = x^2 + 242 + 22x$$$$22x = 119$$$$x = \frac{119}{22} = 5.41$$Therefore, $BC = x+11 = 5.41 + 11 = 16.41$.[/tex]

Let $AB = x$. We can use the Pythagorean Theorem to determine the length of $AB$. Since $A$ and $B$ are the endpoints of $AB$, the length of $AB$ is the hypotenuse of a right triangle with two legs of length 3 and 8. Therefore, we have:

[tex]$$x^2 = 3^2 + 8^2 = 9 + 64 = 73$$$$x = \sqrt{73} = 8.54$$[/tex]

Now that we know the length of AB, we can use it to calculate the length of BC. Since BC is the hypotenuse of a right triangle with legs of length x and 11, we have:

[tex]$$BC^2 = x^2 + 11^2$$$$BC^2 = 8.54^2 + 11^2$$$$BC^2 = 73.14 + 121$$$$BC^2 = 194.14$$$$BC = \sqrt{194.14} = 13.93$$[/tex]

Therefore, the length of BC is 13.93.

The complete question is: Circles with centers A and B have radii 3 and 8, respectively. A common internal tangent touches the circles at C and D, as shown. Lines AB and CD intersect at E, and AE is perpendicular to BC. Find the length of BC.

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On solving the provided question, we can say that integral so the value = (2/108) [429981697] = 7962624,02

what is integral?

In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas

∫C) y³ × ds = 7962624,02 surface units

F (r(t)) = y³ . = t³ . r ( t³ , t ) then . dr/dt = (3×t² , 1 )

|| dr/dt|| = √ ( 3×t²)² + (1)²

|| dr/dt|| = √9×t⁴ + 1

∫C) y³ × ds = ∫∫R) F(r(t) × dr . = ∫₀⁴ t³ ×√9×t⁴ + 1 ×dt

9×t⁴ + 1 = v . then . 36×t³ ×dt = dv

And when t = 4 . then . v = 9×(4)⁴ + 1 . = 2305

integral

∫₁²³⁰⁵ [ 1/36)× √v × dv . = (1/36) ×∫₁²³⁰⁵ (v)¹/² dv

= (1/36)×(2/3) × v³/² |₁²³⁰⁵ = (2/108)× √v³|₁²³⁰⁵ =

= (2/108) [ √( 9×t⁴ + 1 )³|₀⁴ = (2/108) [ √( 9⁴×4¹⁶ + 1 - √(9)⁴×0 + 1)

= (2/108) [√( (9⁴×4¹⁶ + 1 ) . + 1 ]

= (2/108) [429981697]

= 7962624,02

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The number of pages the book has is 2450.

How to find the number of pages in the book?

Mike has read 4/9 of a book; he has read 1,089 pages. The number of pages of book can be calculated as follows;

He has read 4 / 9 of the pages of book.

Therefore,

let

x = number of pages of book

Hence,

4 / 9 x = 1089

cross multiply

4x = 1089 × 9

4x = 9801

divide both sides by 4

4x / 4 = 9801 / 4

x = 2450.25

Therefore, the book has 2450 pages.

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I'm Saying 30C + 100

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

area of square CDE = 4 × 4 = 16

area of triangle BCA = 1/2 × 10 × 5 = 25

total area = 16 + 25 = 41

The function that gives the number of tickets bought by dragons fans after w consecutive wins is: t(w)= 200*(1.11)^w

Tickets bought by Dragon fans in one game = 200

For every consecutive win, the tickets increase by a factor of 1.11

Therefore, for the first win, the number of tickets were 200

For the second consecutive win, the number of tickets increased to 200*1.11= 200*(1.11)^1, since after each consecutive win the number of tickets increases by a factor of 1.11

For the third consecutive win, the number of tickets bought by fans increased to 200*1.11*1.11= 200*(1.11)^2

Hence, for w consecutive wins, the function will turn out to be;

t(w)= 200*(1.11)^w

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As per the Boolean algebra, the simplification law is M.(~M+N) = M.N

The term Boolean algebra is defined as the branch of mathematics that deals with operations on logical values with binary variables.

Here we have to find the simplification law from the given set of expression.

While we looking into the given option, we have identified that by Simplification Law we can have X.(~X+Y) = X.Y and X+(~X.Y) = X+Y.

According to De’ Morgan’s law ~(X+Y) = ~X.~Y.

And according to commutative law we can say that A.(B.C) = (A.B).C.

Therefore, option (a) is correct.

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The constant of proportionality 'k' is 247.

Since y = k/x

x= 13 y= 19

19=k/13

k=19*13

k=247

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional. If equivalent elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences are inversely proportional.

This definition is frequently expanded to include connected variable quantities, also known as variables. Variable has a distinct meaning in mathematics than it does in everyday language (see variable (mathematics)); these two ideas use the same name due to a shared etymology.

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According to the given information the line integral is [tex]=\frac{8}{15}(1+125.\sqrt{10})[/tex].

What distinguishes a line integral from a definite integral?

Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.

[tex]\int_C\hairsp xyds,C:x=t^2,y=2t,0\le t\le3\\x^\prime=2t\\y^\prime=2\\ds=\sqrt{\left(x^\prime\right)^2+\left(y^\prime\right)^2}\\\sqrt{{4\left(t\right)}^2+4}\\\int C\ xy\ ds\ =\int_0^3\hairspt^2\cdot2t\cdot2\cdot\sqrt{1+t^2}\mathrm{\ }dt\\t=\ \ tan\ \theta\\dt=(1+{tan}^2\theta)d\theta=({Sec}^2\theta)d\theta\ \\{=\int}_0^3\hairsp4t^3\sqrt{1+t^2}\mathrm{\ }dt\\=\frac{8}{15}(1+125.\sqrt{10})[/tex]

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Therefore ,performance task is indeed a learning project where students are required to perform in order to show their understanding, knowledge, and skill.

A performance task is what?

Your knowledge is lacking. Consequently, a summary will be provided. A function and variable performance task evaluates a student's ability to use their prior knowledge to interpret a novel phenomena.

Here,

It should be noted that performance tasks yield a tangible product and performance that serve as evidence of learning.

In those other words, the student must put what they have learned into practice.

These assignments often result in a physical output (such as a graphic display, blog post, or performance, such as an oral presentation or debate) that serves as proof of their knowledge and skill.

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The complete question is "What is Performance Task: Super Survey Simulator ?"

By using a trigonometric relation, we will see that the hypotenuse of the right triangle measures 160 units.

How to find the value of x?

On the image, we can see a right triangle where we know one of the angles and one of the cathetus.

We want to find the value of x, which is the hypotenuse of the right triangle, and the cathetus that we know is the adjacent cathetus to the known angle.

Then we can use the trigonometric relation:

cos(a) = (adjacent cathetus)/hypotenuse

cos(60°) = 80/x

Using that we can find the value of x, we will get:

x = 80/cos(60°) = 160

The value of x is 160 units.

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Answer:

Step-by-step explanation:

x / 12 = 3 / 8

x = 3 / 8 x 12

x = 3 / 94

x = 32

32 / 12 = 3 / 8