A zipline cable is attached to two platforms 1000 ft apart at an angle of depression from the taller platform of 12º. What is the length of the cable, rounded to the nearest foot?

Add a phrase to the shape's perimeter to get the side length that is missing.The total length of all of a shape's sides makes up the shape's perimeter.

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The missing side length of perimeter of the figure is 15 feet is 5.

To get the length of the missing side, subtract the perimeter from the total of the known sides. Advice: Consider it. The whole and one component are both known. You deduct the known portion from the total to determine the missing component.

Since there are two of each side length, it is easy to do this by simply adding the length and breadth and multiplying the result by two. The perimeter formula is defined as

perimeter=(length + width)2.

or

add all sides

4 + 3+ 3+ x = 15

10 +x = 15

x = 15 -10 = 5

x = 5

The missing side length of perimeter of the figure is 15 feet is

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The value of x is 9 and the measure of each side is 35 units.

A triangle is said to be equilateral if each of its three sides is the same length.

In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

Given, Triangle QRS is an equilateral triangle.  

QR is seventeen more than twice x ---> QR = 17 + 2x

RS is 19 less than six times x, ---> RS= 6x - 19

And QS is one less four times x, ---> QS = 4x -1

We have to find x and measure of each side.

Now, we know that, the sides of an equilateral triangle are equal,  

If we solve for RS and QS, we find they are both equals to 35.

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The Imaginary part is [tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]

[tex]& \frac{5+2 i}{-1+\sqrt{3} i} \times \frac{-1-\sqrt{3} i}{-1-\sqrt{3} i} \\[/tex]

[tex]& =\frac{-5-5 \sqrt{3} i-2 i+2 \sqrt{3}}{4} \\[/tex]

[tex]& =\frac{-5+2 \sqrt{3}}{4}+i\left(\frac{-5 \sqrt{3}-2}{4}\right) \\[/tex]

Imaginary part

[tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]

The complete question is,

Find the imaginary part of 5+2i/-1+√3i

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The complex number -i5 has -i5 as its imaginary component.

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If the student walks 3 miles north, south, east, or west,  the location at the end of the walk are respectively, (-10,-9). (-4,-9), (-7,-6). (-7, -12).

So Option A is correct

In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.

For example, if we take 4 pencils out of 10 then remaining pencils are 6

so this process is called subtraction.

And opposite operation of subtraction is known as addition, which means in addition, few portion provided to the whole part.

Given that,

A student starts a walk at (-7, -9)

If the student walks 3 miles north, south, east, or west,

The location at the end of the walk = ?

Plotting dotted diagram,

                  East

                      |

North --------- |-------------- South

                      |

                  West

Suppose, he goes to north  direction

Then, 3 will be subtracted from x coordinate,

It can be written as,

(-7-3, -9)

(-10, -9)

Similarly, for South, (-4, -9)

East, (-7, -6)

West, (-7, -12)

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Answer: I don't know what's in the drop down menu, but the relationship you displayed is indeed a proportonial relationship

Step-by-step explanation: For each change of x, an equal change of y occurs. If you double x, y doubles as well. That means that the relationship between x and y is dirctly proportional.

Answer:

Step-by-step explanation:

does not I think

The equivalent expression is 8x + 40.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(x + 5)² - (x - 3)(x + 5)

x² + 10x + 25 - (x² + 5x - 3x - 15)

x² + 10x + 25 - x² - 2x + 15

8x + 40

Thus,

8x + 40 is the equivalent expression.

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Answer: The answer is 12x-3

a) The double-declining-balance rate is 0.5 or 50%.

b) The double-declining-balance depreciation for the first year is $53800.

What is depreciation?

Depreciation is an accounting procedure that allows a business to distribute an asset's cost over the course of its useful life. In other words, it keeps track of how an asset's value decreases over time. In order to better align an asset's productivity in use to its operating costs over time, businesses depreciate assets on their financial statements and for tax purposes.

The formula of the double-declining-balance rate is 2 × (1/useful life)

Given that the building acquired at the beginning of the year at a cost of $107,600 has an estimated residual value of $4,300 and an estimated useful life of 4 years.

The double-declining-balance rate is

= 2 × (1/4)

= 0.5

= 50%

The double-declining-balance depreciation for the first year is

$107,600 ×  50%

= $107,600 × (1/2)

= $53800

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The transformation from the function f(x)=1/x to g(x)=1/5x can be achieved by multiplying the input value x by 5.

f(x)=1/x becomes g(x)=1/(5x) after the transformation

A mathematical transformation is a function that maps one set of values (input) to another set of values (output) based on a set of rules or operations. Transformations can be used to manipulate geometric figures, to change coordinate systems, to map one image to another, and more. Common examples of mathematical transformations include translation, rotation, scaling, and reflection.

It could then be concluded that the transformation is achieved by multiplying the input value x by 5.

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The complete question goes thus:

Describe the f(x)=1/x to g(x)=1/5x transformation

Answer:

Step-by-step explanation:

10

Ws

Answer: x = -2/3

Step-by-step explanation:

6x+8=3x+6

First, subtract 8 from each side. we now have 6x = 3x - 2. now we subtract 3x from each side and we get 3x = -2. we have to divide both by 3 now. The 3’s cancel each other out so now we have x = -2/3

The other equation in the form y = mx + b is y = x + 3

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

y = -3x + 5

y = mx + b has a slope of 1

So, we have

y = x + b

The point where the graphs of two equations intersect has y-coordinate 2.

So, we have

3x + 5 = 2

x + b = 2

Eliminate x

So, we have

3b - 5 = 6 - 2

Evaluate

3b = 9

So, we have

b = 3

hence, the equation is y = x + 3

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The area of the square pyramid with the height of the triangular faces of 10 inches and the side length of the square base of 4 inches is 96 square inches. The correct option is therefore;

B. 96 in²

The surface area is the area or extent covered by the outer faces or boundary enclosures of the figure.

The description of the shape in the figure = Square pyramid

Side length of the square base of the square pyramid = 4 inches

Base length of the triangular slant faces = Side length of the square base = 4 inches

Height of the triangular faces = 10 inches

The surface area of the square pyramid is therefore;

Sum of the area of the four triangular faces + Area of the square base

Area of one triangular face = (1/2) × 4 × 10 = 20

Area of the square base = 4 × 4 = 16

The total surface area of the square pyramid is therefore;

A = 4 × 20 in² + 16 in² = 96 in²

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The solution for the given equation is 15. Therefore, Nico, Raj and Sandra are correct.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 2/5 (5+x)=8

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Method 1:

Now, 2(5+x)=40

5+x=20

x=15

Method 2:

Multiply 5/2 on both the sides of an equation, we get

2/5 (5+x)×5/2 =8×5/2

5+x=20

x=15

Therefore, Nico, Raj and Sandra are correct.

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"Your question is incomplete, probably the complete question/missing part is:"

Nico, Aditi, Erick, Raj, and Sandra are solving the equation.

Two-fifths (5 + x) = 8

Each student begins to solve the problem as shown.

Nico

Aditi

Erick

Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves)

Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8

Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5

Raj

Sandra

Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half)

Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8

Which students are correct in their approach to solving the problem? Select three options.

Nico

Aditi

Erick

Raj

Sandra

The true statement is "viet's car can uses 13 gallons of gas for every miles it travels.

The correct answer choice is option B.

Julio's car:

m = k × g

Where,

m = miles traveled

g = gallons of gas used

m = k × g

300 = k × 12

300 = 12k

divide both sides by 12

k = 300/12

k = 12

So,

m = 12g

Viet's car:

m=13g

Therefore, the correct statement is viet's car uses 13 gallons of gas for every mile.

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Step-by-step explanation:

please make me brainalist and keep smiling

The solution of the system of equations is (8, 11).

We know that one of the equations of the system is:

y = x + 3

And the other line passes through the points (3, 1) and (4, 3), then the slope of that line is:

a = (3 - 1)/(4 - 3) = 2

So the line is something like:

y = 2*x + b

To find the value of b, the y-intercept, we can replace the values of one of the points.

I will use (3, 1)

1 = 2*3 + b

1 = 6 + b

1 - 6 = b

-5 = b

So the other line is y = 2x - 5

Then the system of equations is:

y = x + 3

y = 2x - 5

Now we can solve the system:

x + 3 =2x - 5

3 + 5 = 2x -x

8  =x

The x-value of the solution is 8, then the only option that can be correct is.

(8, 11)

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On December 31 of each year, the quick ratio is 1.6. According to the above computation, the quick ratio is improving.

A good fast ratio is often anything greater than 1 or 1:1. If the ratio is 1:1, the company's liquid assets and current liabilities are equal in amount. A greater ratio means the business could more than cover its current liabilities.

For the present year

Current liabilities minus Quick Assets is the Quick Ratio.

= ($1,000 + $1,200 + $800) ÷ $1,875

= $3,000 ÷ $1,875

= 1.6

Current liabilities minus Quick Assets is the Quick Ratio.

=($1,140 + $1,400 + $910) ÷ $2,300

= $3,450 ÷ $2,300

= 1.5

b. according to the above computation, the quick ratio is improving.

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The area of the napkin will be 162.5 inches².

The area of a square is -

{A} = Side x Side

Given is that a square piece of cloth with an area of 324 inches² is folded in half twice to form the napkin.

The area of the cloth is -

{A} = 324

Let the side of the square cloth be {a}. So, we can write -

a² = 324

a = √324

{a} = 18                                              ... Eq { 1 }

The diagonal of the square will be the base length of the napkin (in the form of triangle). So, we can write -

d² = a² + a²

d² = 2a²

d² = 648

d = √648

{d} = 25.5 inches                                       ... Eq { 2 }

The height would be -

h = d/2

h = 25.5/2

{h} = 12.75

The area of the napkin would be -

1/2 x d x h

1/2 x 25.5 x 12.75

162.5 inches²

Therefore, the area of the napkin will be 162.5 inches².

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On a coordinate plane, a vector has origin (0, 0) and terminal point (3, 2). The magnitude of the vector is 5

The magnitude of a vector can be calculated using the distance formula, which is the square root of the sum of the squares of the differences of the x and y components. In this case, the x component is 3 and the y component is 2, so the magnitude can be calculated as follows:

√(3^2 + 2^2) = √(9 + 4) = √(13) = 5

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Answer:

its D

Step-by-step explanation:

on edge

Answer:

70 parking spaces were full.

Step-by-step explanation:

To calculate this, multiply the total number of parking spaces (100) by the percentage of the lot being used (70%):

100 * 0.70 = 70

Answer: To find the product of two rational expressions, we multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator.

So, (2/x) * (3/2x-5) = (2 * 3) / (x * (2x-5)) = 6 / (2x^2 - 5x)

Step-by-step explanation:

Answer: $84

Step-by-step explanation:

The interest earned in 2 years would be $600 * 7% * 2 = $84.

The value of function for f'(2) is 0.22.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Given that, f(x)= √(x+3) at the specific point x=2.

f'(2)= [tex]\lim_{h \to \ 0}[/tex]((f(2+h)-f(2))/h)

Find the derivative using the chain and power rules.

[tex]f(x)=(x+3)^{\frac{1}{2} }[/tex]

f'(x) = [tex]\frac{1}{2(x+3)^{\frac{1}{2} }}[/tex]

f'(2)=  [tex]\frac{1}{2(2+3)^{\frac{1}{2} }}[/tex]

f'(2)=  [tex]\frac{1}{2(2+3)^{\frac{1}{2} }}[/tex]

f'(2)= 1/2√5

f'(2)= 1/4.47

f'(2)= 0.22

Therefore, the value of function for f'(2) is 0.22.

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The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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The ratio will remain constant. Then the value of the variable 'x' will be 2.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The ratio will remain constant. Then the equation is given as,

9/4 = 13.5 / (x + 4)

9(x + 4) = 13.5 (4)

9x + 36 = 54

9x = 18

x = 2

The ratio will remain constant. Then the value of the variable 'x' will be 2.

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Answer:

90

Step-by-step explanation:

[tex]\frac{1}{6}+\frac{5}{6}[/tex]

in here [tex]\frac{1}{6}= 15\\ \\so\\\\\frac{5}{6} =75\\\\\frac{1}{6} +\frac{5}{6}=\frac{6}{6} \\[/tex]

in this case it is 15+75=90

Answer:

D. The average rates of change of f and g cannot be determined from the given information.

Step-by-step explanation:

To determine the average rate of change of a function, we need the equation of the function. Since the equation of g is not given, we cannot determine the average rate of change of g and compare it with the average rate of change of f. Hence, option D is the correct answer.

Answer:

hi

Step-by-step explanation: