A
The top of a signal tower is 135 meters above sea level. The angle of depression from the top of
the tower to a passing ship is 20°. How many meters from the foot of the tower is the ship? Round
to the nearest meter.

Answer:

Step-by-step explanation:523x2 1323

Step-by-step explanation:

Firstly you have to open brackets

4b(5a - 2) = 2c

20ab - 8b = 2c

20ab = 2c + 8b

Divide both sides by 20b(coefficient of a)

a = (2c + 8b)/20b

Answer:

[tex]a = \dfrac{2}{5} + \dfrac{c}{10b}[/tex]

Step-by-step explanation:

Expand 4b(5a-2) on the left side

4b(5a-2)  = 4b · 5a -4b · (-2)

= 20ab -8b

Therefore we get

20ab -8b = 2c

Add 8b on both sides to get rid of the -8b on the left

20ab - 8b + 8b = 2c + 8b

20ab = 8b + 2c

Divide by 20 both sides:
20ab/20 = 8b/20 + 2c/20

ab = (2/5)b + c/10

Divide by b both sides

==> ab/b = (2/5)b/b + c/10b

==> a = 2/5 + c/10b

Answer:

0.22  <  

1

4

 <  

26

100

 <  

272

10

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

As long as the odd numbers are not prime numbers, they can still be in a fraction that can be reduced. Not in all cases of course but in some, for instance 9/27 can be reduced to 1/3

62.5% fo boys plays cricket in the whole class.

A mathematical comparison of two or more values or quantities is called a ratio. It can be used to compare the relative sizes or amounts of various items since it expresses the relationship between the values in terms of a proportion or a fraction.

Let the number of boys who play cricket be x

and  the number of boys who play football be y

so total number of students is x+y

given the ratio that y/x=3/5

so y = 3k and x = 5k where k is a constant

so total number of student is x+y

=> 3k+5k

=> 8k

so percentage of boy who play cricket is given by

=> (5k/8k) * 100

=> 0.625 *100

=> 62.5

so 62.5 % of boys play cricket  and rest plays football.

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The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.

We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.

A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.

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Question correction:

Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0

The solution set for the system of equations is (x, y) = (-2.44, 10.11)

To find the solution set for the system of equations, we can use several methods such as substitution, elimination, or matrix method.

In the elimination method, we try to eliminate one of the variables by adding or subtracting the equations.

One method is to use elimination method:

9x + 5y = 28

5x + 9y = 56

We can eliminate one of the variables by multiplying the first equation by -5 and the second equation by 9:

-45x - 25y = -140

45x + 81y = 504

Adding these two equations together we get:

36y = 364

Solving for y, we get:

y = 364/36 = 10.11

We can then substitute this value back into one of the original equations, for example, the first equation:

9x + 5(10) = 28

9x + 50 = 28

9x = -22

x = -2.44

So, the solution set for the system of equations is (x, y) = (-2.44, 10.11)

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Answer:

Sample 1

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Sample 2

GATAGCTAGG

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The radius of the tank is 28.3 feet (rounded to one decimal place).

Radius is a term used to describe the distance from the center of a circle to any point on the circumference. It is a line segment that runs from the center of the circle outwards, perpendicular to the circumference. The radius of a circle is the same for all points on the circumference, and it is always half of the diameter.

The radius of the tank can be determined using the Pythagorean Theorem. Since we are given the distances from the center of the tank (O) to points A and B, we can use the following formula to calculate the radius:

R = √(OA² + OB²).

Plugging in the given values, we get:

R = √(21² + 19²) = √(441 + 361) = √802 = 28.29

Therefore, the radius of the tank is 28.3 feet (rounded to one decimal place).

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He ran 194 miles fewer he ran in 3 days than the 16 days run.

the statute mile, which is 5,280 feet long, is one example of a mile (1.609 km). The mille passus, or "thousand paces," was a unit of measurement used in ancient Rome and equaled 5,000 Roman feet.

The "old London" mile, which was eight furlongs, was first established around the year 1500. The mile at that time was equal to 5,000 feet, with the furlong being 625 feet at that time, using the larger northern (German) foot.

A statute from 1593 that confirmed the use of a shorter foot and made the length of the furlong 660 feet increased the mile by 280 feet during the reign of Queen Elizabeth I, bringing it to 5,280 feet.

The Fewer mile he ran = (16 × 14) - (3 × 10)

                                      = 194 miles

Thus, He ran 194 miles fewer he ran in 3 days than the 16 days run.

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A tudy how that the more exercie people had a day the more they lept at night which catter plot repreent the relationhip The overall pattern of the scatter plot would show that as the amount of exercise increases, the amount of sleep also increases.

A scatter plot would be used to represent the relationship between the amount of exercise people have per day and the hours of sleep they get at night. The scatter plot would show the number of hours of exercise on the x-axis and the number of hours of sleep on the y-axis. Each point on the scatter plot would represent an individual's exercise and sleep hours. The overall pattern of the scatter plot would show that as the amount of exercise increases, the amount of sleep also increases.

1. A scatter plot is used to represent the relationship between two variables.

2. In this case, the two variables are the amount of exercise people have per day and the hours of sleep they get at night.

3. The x-axis of the scatter plot would represent the amount of exercise, while the y-axis would represent the hours of sleep.

4. Each point on the scatter plot would represent an individual's exercise and sleep hours.

5. The overall pattern of the scatter plot should show that as the amount of exercise increases, the amount of sleep also increases.

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33ft wire is needed for 6 trees.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Each wire is attached to the trunk 3ft. above the ground,

and then anchored to the ground 2.5 ft. from the base of the tree.

So, for each tree total wire = 3+2.5

                                             =5.5 ft.

So, for 6 trees = 5.5*6

                       =33ft

Hence, 33ft wire is needed for 6 trees.

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So, your total bill including tip and tax is $11.37

First, calculate the subtotal of the food bill by adding the cost of the taco and burrito dinner:

$1.85 + $7.35 = $9.20

Next, calculate the sales tax by multiplying the subtotal by the tax rate (7.5%):

$9.20 x 0.075 = $0.69

Then add the sales tax to the subtotal to get the total before tip:

$9.20 + $0.69 = $9.89

Then calculate the tip by multiplying the total before tip by the tip rate (15%):

$9.89 x 0.15 = $1.48

Finally, add the tip to the total before tip to get the final total bill including tip and tax:

$9.89 + $1.48 = $11.37

So, your total bill including tip and tax is $11.37

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$1.85 + $7.35 = $9.20

$9.20 x 0.075 = $0.69

$9.20 + $0.69 = $9.89

$9.89 x 0.15 = $1.48

$9.89 + $1.48 = $11.37

So, your total bill including tip and tax is $11.37

Jamal and Lin will meet 3.21 miles from Jamal's house.

Meet is a gathering of two or more people for a specific purpose, such as to discuss an issue, make a decision, or socialize. It can take place in person or online, either in a formal or informal setting.

The time it takes for Jamal and Lin to meet is the time it takes for Jamal to travel 2 miles plus the time it takes for Lin to travel 2 miles.
Since Jamal is walking at 3 mi/h, it takes him (2 miles) / (3 mi/h) = 0.67 hours to travel 2 miles.
Since Lin is walking at 5 mi/h, it takes her (2 miles) / (5 mi/h) = 0.4 hours to travel 2 miles.
The total time it takes for Jamal and Lin to meet is 0.67 + 0.4 = 1.07 hours.
Jamal and Lin will meet 1.07 hours after they left their houses.
Since Jamal is walking at 3 mi/h, he will have traveled (1.07 hours) * (3 mi/h) = 3.21 miles when they meet.
Jamal and Lin will meet 3.21 miles from Jamal's house.

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Answer:

the answer is coefficient hope it helped you

Step-by-step explanation:

12 answer is option b

4 answer is option c

Answer:

m = [tex]\frac{1}{5}[/tex] , c = - 4

Step-by-step explanation:

m is the slope of the line and is calculated using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = (1, 1) ← 2 points on the line

m = [tex]\frac{1-0}{1-(-4)}[/tex] = [tex]\frac{1}{1+4}[/tex] = [tex]\frac{1}{5}[/tex]

c is the value of the y- intercept , where the line crosses the y- axis

the line crosses the y- axis at - 4, then c = - 4

Answer:

Step-by-step explanation:

A i think

The value of the variable for which the value of the expression –3(2x+1) is 20 is greater than the value of the expression 8x+5 is -2.

According to the question, 20 greater than 8x +5 = 8x +5 +20 = 8x +25.

We want this value to be -3(2x +1),

So, solving this equation we get: 8x +25 = -3(2x +1)

=> 8x +25 = -6x -3 (eliminating the parentheses)

Further solving this equation we get,

=> 14x = -28

=> x= -2

Thus, The value of the variable for which the value of the expression –3(2x+1) is 20 is greater than the value of the expression 8x+5 is -2.

Complete question: Find the value of the variable for which the value of the expression –3(2x+1) is 20 greater than the value of the expression 8x+5.

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The value of the variable for which the value of the expression –3(2x+1) is 20 is greater than the value of the expression 8x+5 is -2.

According to the question, 20 greater than 8x +5 = 8x +5 +20 = 8x +25.

We want this value to be -3(2x +1),

8x +25 = -3(2x +1)

8x +25 = -6x -3 (eliminating the parentheses)

14x = -28

x= -2

The scale factor was used to enlarge the picture is 31.5/7 or 4.5.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life

here, we have,

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

By simply taking the width after it was enlarged and dividing it by the width before it was enlarged we can find the scale factor that was used.

In this case it would be 31.5 (width after)/ 7 (width before)

which gives us a scale factor of 31.5/7.

Simplifying would yield a scale factor of 4.5 times.

hence, The scale factor was used to enlarge the picture is 31.5/7 or 4.5.

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The height that represents the 85th percentile is 66.8 inches.

The height that represents the first quartile is 62.4 inches.

Generally, To find the height that represents the 85th percentile, you would need to use a z-score table or calculator.

The z-score represents the number of standard deviations away from the mean of a particular value.

For the 85th percentile, the z-score would be 1.04. To find the height, you would use the formula:

(z-score) * (standard deviation) + mean

So, in this case:

1.04 * 2.8 + 63.7 = 66.612 inches

b) To find the height that represents the first quartile (25th percentile), you would use the same process but with a z-score of -0.67.

-0.67 * 2.8 + 63.7 = 61.824

This means that the height that represents the first quartile is 62.4 inches.

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The height of the statue is:

A. 276 inches

If Wally, who is 69 inches tall, catch a shadow that is 41 inch in length.

To determine the height of the statue, you can use the principle of similar triangles. Similar triangles have the same angles, but not necessarily the same side lengths. You can use the ratio of the height of Wally and the length of his shadow to the height of the statue and the length of its shadow to find the height of the statue.

Height of Wally: 69 inches

Length of Wally's shadow: 41 inches

Height of statue: x

Length of statue's shadow: 164 inches

You can set up the proportion as:

69/41 = x/164

Solving for x, you get:

x = (69 × 164)/41

x = 276 inches

Thus the answer is A. 276 inches.

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The diameter , radius and area of the circle is 126cm, 63cm, 12474cm² respectively.

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle.

The circumference of a circle is given as;

C = π d

where d is the diameter of the circle

therefore 396 = 22/7 × d

22d = 396× 7

22d = 2772

divide both sides by 22

d = 2772/22

d = 126 cm

the diameter of a circle is 2 times it's radius

d = 2r

126 = 2r

r = 126/2

r = 63cm

The area of the circle is

A = πr²

A = 22/7× 63× 63

A = 22×9× 63

A= 12474cm²

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Answer:

3, 7

Step-by-step explanation:

-5 - (-9) = 4

The common difference is 4.

Add 4 to a term to find the next term.

-1 + 4 = 3

3 + 4 = 7

Answer: 3, 7

Two lines that make right angles at their intersection are Perpendicular lines.

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Answer:

k = 75

Step-by-step explanation:

Let's write down the prime factors of 15 and 375

15 = 3 x 5

375 = 3 x 5 x 5 x 5

So 15 x 375 = 3 x 5 x 3 x 5 x 5 x 5

= (3 x 3) x   (5 x 5 x 5) x 5

This cannot be a perfect cube

However if we multiply this by 3 x 5 x 5 we will get

(3 x 3 x ) x (5 x 5 x 5) x(5 x 5 x 5) which is a perfect cube

Since we are asked to find k such that 15 x 375 x k is a perfect cube

k = 3 x 5 x 5 = 75

ans
k = 75

Answer: mean = 55

Step-by-step explanation:

Distance between 64 and 82 = 18

Each standard deviation is worth 9 units.

So 64 - 9 = 55(mean)

Or use m= x-zq

To find the equation of the axis of symmetry using factored form, we can use the multiply and conversion method which converts it into vertex form.

It can be multiplied and converted to vertex form.

Example: (x-3)(x+2) f(x)

f(x) = x^2 - x - 6

We can now combine the x terms to finish the square.

f(x) = (x^2 - x +1/4 ) - 6 - 1/4

f(x)= (x - 1/2)^2 -25/4

As a result, the vertex is (1/2, -25/4)

Any quadratic given in factored form can be solved this way.

If the parabola contains the equation y=f(x)=a(xr1)(xr2), the zeroes of f(x), i.e., r1 and r2, can be read off right away. The vertex then has coordinates (h,k), where k=f(h) is the result of inserting x=h through the function f(x), and h=(r1+r2)/2 is the average of the two zeroes.

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Answer: it's 5000 :)

Step-by-step explanation:

Answer: 5000

Step-by-step explanation:

4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).

[tex]p(x)=2x^3-7x^2+2x\\g(x)=2x-3\\dviding. p(x) by g(x),\\ we get2x-3)2x^3-7x^2+2x(x^2-2x2x^3-3x^2- +0 -4x^2+2x-4x^2+6x+ -0 -4xq(x)=x^2-2xand, r(x)=-4x\\Now,\\According to division algorithmp\\(x)=g(x)*q(x)+r(x)2x^3-7x^2+2x=(2x-3)(x^2-2x)+(-4x)\\adding 4x-2 on both side,\\ we get\\2x^3-7x^2+2x+4x-2=(2x-3)(x^2-2x)+(-4x)+4x-22x^3-7x^2+6x-2=(2x-3)(x^2-2x)+(-2)[/tex]

4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

what number must be added to[tex]2x^3-7x^2+2x[/tex] so that the resulting polynomial leaves the remainder -2 when divided by 2x-3​