A wire is stretched from the ground to the top of an antenna tower. The wire is 15 feet long. The height of the tower is 3 feet greater than the distance d from the tower's base to the end of the wire. Find the distance d and the height of the tower.

The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].

Miller Indices of Direction Vector:

The Miller indices of direction are rationalized components of the direction vectors taken in all crystallographic directions. They are indicated by [[u v w ]]. They are always defined as the smallest integers, so if they occur in fractional or decimal form, we need to convert them into the smallest integral value by algebraic manipulation.

The indices of direction 1.

Let the length of direction 1 along the x-axis be X units. The length of the vectors along the y and z axes is 0.

[ X 0 0 ]

⇒ [tex]\left[\begin{array}{ccc}0&0&0\\X'&X'&X'\\\end{array}\right][/tex]

Divide each length by X to convert it into the smallest integer.

⇒ [1 0 0]

And, this is the Miller indices of the direction vector 1.

So, the Miller indices of the direction vector 1 are [ 1 0 0].

Direction 2

The indices of direction 2.

Let the length of direction 2 along the x-axis be X units. The length of the vector along the y and z axes are 0.

[ 0.2 0 0.3 ]

⇒[ 2 0 3 ]

Multiply each fractional length by 10 to convert it into the smallest integer.

So, the Miller indices of the direction vector 2 are [ 2 0 3].

Therefore, The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].

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The solution is

a) The motor boat traveled a displacement of

b) The velocity of the tugboat

c) The negative distances and velocities means the boat is traveling down a river

Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time. It is a vector quantity. Velocity is the change in displacement of an object with respect to time

Velocity = Displacement / Time

Given data ,

Some boats are traveling up and down a river

So , when the boat is traveling up a river , the velocity will be positive and when the boat is traveling down a river , the velocity will be negative

a)

The velocity of motor boat = - 3.4 mph

The time taken by the boat = 0.75 hours

Velocity = Displacement / Time

Substituting the values in the equation , we get

Displacement = Velocity x Time

Displacement D = - ( 3.4 ) x 0.75

On simplifying the equation , we get

Displacement D = -2.55 miles

Therefore , the boat traveled -2.55 miles down

b)

The displacement of the tugboat D = -1.5 miles

The time taken by the tugboat T = 0.3 hours

So , velocity of the tugboat V = ( -1.5 ) / 0.3

On simplifying the equation , we get

Velocity V = -5 mph

Therefore , the velocity of the tugboat is -5 miles per hour

c)

When the boat is traveling down a river , the velocity will be negative

Hence , the equations are solved

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The measure of the smaller complementary angles is 40°

When two angles add up to 90°, we say they complement each other in terms of mathematics. Hence in geometry, complementary angles are defined as two angles whose sum is 90 degrees.

The larger angle = 50°

we shall represent the smaller angle with the letter x so that;

x + 50° = 90°

subtract 50° from both sides of the equation

x + 50° - 50° = 90° - 50°

x = 40°

Therefore, the smaller complementary angle has a measure of 40°.

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The integral[tex]∫20(45t^3-34t^2+25t)dt[/tex] can be evaluated by using the power rule of integration, which states that the derivative of x^n is [tex]nx^(n-1)[/tex]. This rule can be applied to each term of the integral separately.

The first step is to integrate [tex]∫20(45t^3-34t^2+25t)dt[/tex] with respect to t. By using the power rule, we can find the antiderivative of each term inside the parentheses:

[tex]∫45t^3 dt = (45/4)t^4 + C[/tex]  (the antiderivative of 45t^3 is (45/4)t∧4)

[tex]∫34t^2 dt = (34/3)t^3 + C[/tex] (the antiderivative of 34t^2 is (34/3)t∧3)

[tex]∫25t dt = (25/2)t^2 + C[/tex] (the antiderivative of 25t is (25/2)t∧2)

Now, we can substitute these results back into the original integral:

[tex]20(∫45t^3 dt - ∫34t^2 dt + ∫25t dt) = 20((45/4)t^4 + (34/3)t^3 + (25/2)t^2) + C= 20(15t^4-11t^3+25t^2) + C[/tex]

So, the evaluated integral for [tex]∫20(45t^3-34t^2+25t)dt[/tex] is [tex]20(15t^4-11t^3+25t^2) + C.[/tex]

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Answer:

Out of all possible choices you've shown, I'd say the best answer would be C

Step-by-step explanation:

C = 12k, where C represents the cost on the electrical bill and k represents the electricity used is a relationship that varies directly. Option C is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,
A standard directly proportional relationship is given as,
y = kx

Now,
comparing the above equation with the equation among the option,
If the equation in options matches with the above equation, so that equation will be a relationship that varies directly.

Thus, C = 12k, where C represents the cost on the electrical bill and k represents the electricity used is a relationship that varies directly. Option C is correct.

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The value of an irrational numbers are,

⇒ √28

⇒ √11

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The numbers are,

⇒ √100

⇒ √28

⇒ √11

⇒ 2.78⁻⁻⁻

Now, We know that;

An irrational number is a number that cannot be expressed as a fraction for any integers.

Hence, We get;

The correct value of an irrational numbers are,

⇒ √28

⇒ √11

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The equation formed by the sentence is 9b - 7 = 8.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Let the variable be b

By the given sentence we get the equation

9b - 7 = 8

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The solution to the system of equations for this problem is given as follows:

(11.59, 479).

The system of equations for this problem is defined as follows:

The solution for x is obtained when the two equations are equal, hence:

14.3x + 318 = 3.6x + 442

10.7x = 124

x = 124/10.7

x = 11.59.

Applying the substitution in any of the equations, the solution for y is obtained as follows:

y = 3.2(11.59) + 442

y = 479.

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The shape that results from a plane passing through a cone that is perpendicular to the base is a B. Circle

A circle intersects a cone when a plane passes through it perpendicular to the base. This is due to the plane cutting through the cone's circular cross-section at a 90-degree angle to the base of the cone.

As a result, if the plane were to be slanted or angled, the intersection would have the shape of an ellipse, which is a circle that has been flattened.

This is due to the fact that an ellipse is the shape created when a plane crosses a cone at an angle other than perpendicular to the base.

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Answer: 1. 7a 2. 5r 3. 8y+4 4. 12m-7 5. 7u+5 6. 8q+6 7. 3w+5x 8. 4j + 4k 9. 5d+6

Step-by-step explanation: Add the coefficients of the terms with same variables. ex. 5a+4a+7... 5a and 4a have same variable which is a so add the 5 and 4 and you get 9a and the 7 doesn't match so leave it out and you get 9a + 7

Answer:

1) 7a

2) 5r

3) 8y +4

4) 12m-7

5) 7u+5

6) 8q+6

7) 3w+5x

8) 4j +4k

9) 5d+6

Step-by-step explanation:

you just add or subtract the number with the same letter after it (if there is no letter just leave it as is, unless there are two or more numbers with no letter after, then add or subtract as normal)

The area of the rectangle represented as the sum of cubes is x³ + 3³

An equation is an expression showing the relationship between numbers and variables.

The sum of cubes of a polynomial is in the form a³ + b³ while A the difference of cubes of a polynomial is a³ - b³

The area of rectangle = length * width

From the diagram, length = x² - 3x + 9; width = x + 3, hence:

The area of rectangle = length * width = (x² - 3x + 9)(x + 3)

Area = x³ - 3x² + 9x + 3x² - 9x + 27 = x³ + 27

Area = x³ + 3³

The area of the rectangle is x³ + 3³

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The triangles ∆AEC ≅ ∆AFC by Side-Angle-Side theorem

The complete question is added as an attachment

With the given information and the image attached below, we can state that the two triangles are congruent by SAS,

Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.

The proof is given as:

Statement Reason

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The exponential function that models this situation is given as follows:

y = 3(5)^x.

The y-intercept of the exponential function represents the number of people that were called by the administrators.

The graph of the exponential function is given by the image presented at the end of the answer.

The general format of an exponential function is given as follows:

y = a(b)^x.

In which:

First, the 3 school administrators decide when an announcement is needed, hence the parameter a, representing the y-intercept, is given as follows:

a = 3.

In each round, each person inserted into the conversion calls 5 more people, hence the parameter b is given as follows:

b = 5.

Meaning that the function is defined as follows:

y = 3(5)^x.

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a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

What is the z-score?

A z-score (also known as a standard score) is a measure of how many standard deviations an individual data point is from the mean of a distribution. A z-score is calculated by subtracting the population mean from an individual data point, and then dividing that number by the population standard deviation.

a) z score corresponding to top 5% area = 1.645

Hence,

Corresponding minimum UGPA = 3.40 + 1.645*0.18 = 3.70

b) z score corresponding to middle 50% area = -0.67, 0.67

Hence,

The range of middle 50% values will be:

(3.40 - 0.67*0.18, 3.40 + 0.67*0.18)

(3.28, 3.52)

Hence,

a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

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Answer:

it's a function

Step-by-step explanation:

to test if it's a function or not you do the vertical line test if it intersects the function at more than one point then it's not a function,, but here in the given function when you do the vertical test it'll only intersect it at one point so it's a function

Answer:

[tex]j = \dfrac{9}{2} = 4,5 \\\\\\k = 2[/tex]

Step-by-step explanation:

I am working on the assumption that the figure shown is a parallelogram, otherwise my answer will not be valid

The diagonals of a parallelogram bisect each other

In the above figure, the top left-bottom right diagonal is bisected by the top right  - bottom-left diagonal

This means

[tex]3j = 5j - 9[/tex]

Subtract 5j from both sides:

[tex]3j - 5j = -9[/tex]

[tex]-2j = -9[/tex]

[tex]j = \dfrac{-9}{-2} = \dfrac{9}{2} = 4,5 \\[/tex]
I am not sure if you want it in fraction or decimal

Similarly

[tex]k + 10 = 6k\\\\[/tex]

Subtract k from both sides:
[tex]10 = 6k-k\\\\\\10 = 5k\\\\\\\textrm{Switching sides,}\\5k = 10\\\\k = \dfrac{10}{5} = 2\\\\[/tex]

Answer:

22

Step-by-step explanation:

as you can see at the bottom, they have added up all of the tallies. so all you need to use addition to add 10 + 12 which is equal to 22.

Sawyer lives 12.7 km farther from the soccer field.

Jabar lives 5 miles from the soccer fields, Sawyer lives 12.7 km from the same soccer fields .

The person that lives farther form the soccer field can be calculated as follows;

Let's convert Jabar distance from the soccer field to km.

1 miles = 1.60934

5 miles = ?

cross multiply

distance of Jabar from the soccer field = 5 × 1.60934

distance of Jabar from the soccer field = 8.0467 km

Therefore, jabar lives 8.0467 km from the soccer field.

Hence, Sawyer lives 12.7 km farther from the soccer field.

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Answer:

Step-by-step explanation:

2n -3 =-21

2n-3+3=-21+3

2n=-19

n=-9.5

Answer:

Step-by-step explanation:

A typical geometric sequence can be represented as

c

0

a

,

c

0

a

2

,

⋯

,

c

0

a

k

and a typical arithmetic sequence as

c

0

a

,

c

0

a

+

Δ

,

c

0

a

+

2

Δ

,

⋯

,

c

0

a

+

k

Δ

Calling

c

0

a

as the first element for the geometric sequence we have

⎧

⎪

⎨

⎪

⎩

c

0

a

2

=

c

0

a

+

2

Δ

→

First and second of GS are  the first and third of a LS

c

0

a

+

3

Δ

=

10

→

The fourth term of the linear sequence is 10

5

c

0

a

+

10

Δ

=

60

→

The sum of its first five term is 60

Solving for

c

0

,

a

,

Δ

we obtain

c

0

=

64

3

,

a

=

3

4

,

Δ

=

−

2

and the first five elements for the arithmetic sequence are

{

16

,

14

,

12

,

10A typical geometric sequence can be represented as

c

0

a

,

c

0

a

2

,

⋯

,

c

0

a

k

and a typical arithmetic sequence as

c

0

a

,

c

0

a

+

Δ

,

c

0

a

+

2

Δ

,

⋯

,

c

0

a

+

k

Δ

Calling

c

0

a

as the first element for the geometric sequence we have

⎧

⎪

⎨

⎪

⎩

c

0

a

2

=

c

0

a

+

2

Δ

→

First and second of GS are  the first and third of a LS

c

0

a

+

3

Δ

=

10

→

The fourth term of the linear sequence is 10

5

c

0

a

+

10

Δ

=

60

→

The sum of its first five term is 60

Solving for

c

0

,

a

,

Δ

we obtain

c

0

=

64

3

,

a

=

3

4

,

Δ

=

−

2

and the first five elements for the arithmetic sequence are

{

16

,

14

,

12

,

10

If Catarina’s boat has come untied and floated away on the lake. She is standing atop a cliff that is 35 feet above the water in a lake. Approximately the distance from the cliff is Catarina’s boat is : 63.6ft.

Distance can be defined as how far an object is from another object.

Now let find the distance:

AE/CD = BC/DE

Hence,

5.5/3.5 = 10/DE

Cross multiply

AE = 350/5.5

AE = 63.6ft

Therefore we can conclude that the distance is 63.6ft.

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Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6

The study of numbers, their variations, mathematics and the regional tissue, structures, and both their actual and imagined locations, is known as mathematics. A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input. Each function is given a city, town, or scope, which is frequently referred to as a realm.

Here,

Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).

Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).

The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).

Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).

=> f(x) = (x-h)² + k

The outcome of translating a unit to the right with b unit up is

=>f'(x) = (x-h-a)² + k + b

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Answer:

Rectangle, parallelogram, trapezoid, quadrilateral

Step-by-step explanation:

because the properties of the rhomboid(that is what it is called) match with those different shapes listed above

The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).

given

slope = y2- y1 / x2 - x1

= -120/8  = -15

( 6 , 120 )

( 14 , 0 )

The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.

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Angles in parallel lines are formed when two parallel lines intersect with another line known as a transversal. So here ∠y is 40° and ∠z is 140°.

We know that sum of angles over a straight line is 180°

So here ∠x + 140° = 180°

So ∠x = 180 - 140

Therefore ∠x = 40°

So in this figure ∠x = ∠y , Since they are corresponding angles are equal.

Therefore ∠y = 40°

So ∠z will be 140° . Since ∠y = 40° its opposite angle will also be 40°.

So ∠z + 40° = 180°

Therefore ∠z = 140°

So the angles ∠y = 40° and ∠z = 140°.

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Answer:

the third one

Step-by-step explanation:

an open circle means it does not include that number. therefore, it needs to be x is less than -2. a closed circle means it includes that number. therefore, x is greater than or equal to 4

Answer: It will take 7 more years for George’s sister to be taller than him.

Step-by-step explanation:

Answer:

Step-by-step explanation:

7 years

Answer: x = -8/3

Step-by-step explanation:

7 = 3(5+x)

3(5+x)=7

apply the distributive property

15+3x=7

rearrange the variables to  the left side of the equation

3x=7-15

3x=-8

divide on both sides

x=-8/3

Answer:

x = -8/3

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 7 = 3(5 + x)

Then the value of x will be,

→ 7 = 3(5 + x)

→ 7 = 3(5) + 3(x)

→ 7 = 15 + 3x

→ 7 - 15 = 3x

→ -8 = 3x

→ 3x = -8

→ [ x = -8/3 ]

Hence, the value of x is -8/3.