Need help questions 1-3

The cable is 805.4 ft long.

Draw a triangle to represent the situation.

Label the sides of the triangle.

Let x = length of cable
Let 1200 = height of mountain
Let 30 = angle of elevation

Use the Law of Cosines to solve for x.

x² = (1200)² + (1200)² - (2)(1200)(1200)cos(30)

x² = 288000 + 288000 - 1,728,000cos(30)

x² = 576000 - 1,728,000cos(30)

x = √576000 - 1,728,000cos(30)

x = √576000 - 1728000(0.866)

x = √576000 - 1511360

x = √646340

x = 805.4 ft

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Answer: 14

Step-by-step explanation: your correct

The equation of the line which passes through the point (0,-4) and has a gradient of 0. 5 is (x-8)/2.

A straight line can be represented by the "Point-Slope" form of the line.

In point-slope form, we can deduce an equation of any line on the Cartesian coordinate system with the help of its slope/gradient "m" and a point through which it passes (x1,y1).

the equation of Point Slope form is,

(y-y1)=m(x-x1),

where, x and y are any general point on the line.

in the given question the value of the slope/gradient (m) is given as 0.5

and it passes across the point (0,-4)

so according to the equation of the point-slope form,

the equation of line must be,

(y-(-4))=0.5(x-(0))

= y+4=0.5x

= 2y+8=x

= 2y = x-8

= y = (x-8)/2

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Answer: 476.7 feet

Step-by-step explanation:

65 miles = 343200 feet

1 hour = 3600 seconds

(343200/3600) = 476.7 feet in 5 seconds

Answer:

X Y

-1 8

0 3

1 -2

2 -7

Step-by-step explanation:

Using the x values of the table, simply plug in those x values, replacing the x in the equation. For example:

y = -5x + 3

y = -5 * 2 + 3

y = -10 + 3

y = -7

Answer: 2 1/4

Step-by-step explanation: Exact Form:

9/4

Decimal Form:

2.25

Mixed Number Form: 2 1/4

The y intercept has been moved down, and the g(x) graph is less steep than the f(x) graph.

the fundamental duty of a family. Y = x or f(x) = x is the parent function for linear functions. Transformation: Modification of a figure's size or position. Child Function: The parent function is f(x) = x for all linear functions. y = x.

The simplest function in a family of functions that yet preserves the definition (or shape) of the entire family is known as a parent function in mathematics.

When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear.

Therefore, the correct answer is option C. The graph of g(x) is less steep than the graph of f(x) and the y intercept has been shifted down.

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Answer:

10

Step-by-step explanation:

PEMDAS

The y intercept means that gallons of water in the base year is 10.

Y intercept is a coordinate of y which is the point where the line touches the Y axis.

The x coordinate corresponding to this point will be zero.

Given is a graph which relates the two variables year and the gallons of bottled water per person.

From the graph, it is clear that y intercept is at 10.

It is in the year 1990, which is the base value that we take.

All the other year values are based on the base value.

y intercept means in this context that in the year 1990, which is the initial year, gallons of water per person is 10.

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The interest rate on Malik's saving account is 4.62%. This was calculated by finding the total amount after 4 years, subtracting the original deposit, and then dividing the interest earned by the original deposit and multiplying by 100.

1. Calculate the total amount in the account after 4 years: 1050 + 241.50 = 1291.50

2. Calculate the interest earned: 1291.50 - 1050 = 241.50

3. Calculate the interest rate: 241.50 / 1050 x 100 = 4.62%

The interest rate on Malik's saving account is 4.62%. This was calculated by finding the total amount after 4 years, subtracting the original deposit, and then dividing the interest earned by the original deposit and multiplying by 100.

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Answer:

addition

Step-by-step explanation:

there's only one sign + so it means addition

Answer: addition

Step-by-step explanation:

The amount of gas used for 140 miles is 3.5 gallons and the inverse equation is g = m/40

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

m = 40g

The number of miles is given as

m = 140

substitute the known values in the above equation, so, we have the following representation

40g = 140

Divide by 40

g = 3.5

Hence, the amount of gas is 3.5 gallons

Recall that, we have

m = 40g

Divide by 40

g = m/40

Hence, the inverse is g = m/40

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The perimeter of five square and perimeter of rectangular cake is equal,

So, the perimeter of cakes is 600 cm.

The perimeter of a two-dimensional figure is the distance covered around it. It defines the length of shape, whether it is a triangle, square, rectangle or a circle. Area and perimeter are the two major properties of a 2D shape, which describes them.

We have five square cakes of side 30cm.

the perimeter of one cake is =4a

                                                 =4×30

                                                 =120 cm

So, the perimeter of five cake = 5(120)

                                                    =600 cm

The perimeter of five square and perimeter of rectangular cake is equal,

So, the perimeter of cakes is 600 cm.

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Answer:

15r-40

Step-by-step explanation:

By the Distributive Property, [tex]5(3r-8)=5(3r)+5(-8)=15r-40[/tex]

Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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a) A linear equation that describes the relationship between the number of buses and the number of vans needed for 120 students is 24x + 8y = 120.

b) If the teachers rent 4 buses, the number of vans they will need to transport all the students is 3.

c) If the teachers rent 6 vans, the number of buses they will need to transport all the students is 3.

d) If the teachers rent only vans, the number of vans needed will be 15.

e) Suppose the teachers rented only buses, the number of buses needed will be 5.

A linear equation is an algebraic equation of the form y = mx+b.

A linear equation involves a constant and a first-order (linear) term, with m as the slope and b as the y-intercept.

The total number of students on the field trip = 120

The number of students a bus can seat = 24

The number of students a van can seat = 8

Let the number of buses = x and the number of vans = y

24x + 8y = 120

b) Renting 4 buses, the number of vans needed:

24(4) + 8y = 120

96 + 8y = 120

8y = 24

y = 3

c) Renting 6 vans, the number of buses will be:

24x + 8(6) = 120

24x = 48 = 120

24x = 72

x = 3

d) Renting only vans, the number needed will be:

24(0) + 8y = 120

8y = 120

y = 15

e) Renting only buses, the number needed will be:

24x + 8(0) = 120

24x = 120

x = 5

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The equation of the line in slope intercept form is y = 8x -1.

What is slope intercept form?

The graph of the equation y = mx + b is a line with slope m and y-intercepts b. The form of the linear equation is called the slope-intercept form, and the values of m and b are real integers.

The slope, m, of a line indicates how steep it is. The gradient of a line is another name for the slope of a line. The y-intercept of a line is the y-coordinate of the location where the line's graph crosses the y-axis.

We are given two points which are (-1,-9) and (1,7).

First, we need to find the slope(m)

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

[tex]m=\frac{7 +9 }{1+1 }[/tex]

m = 16/2

m = 8

We know that b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)

So,

⇒b = (-9) + 1(7 + 9)/(1+1)

⇒b = -9 + 8

⇒b = -1

The equation comes out to be

⇒y = mx + b

⇒y = 8x -1

Hence, the equation of the line in slope intercept form is y = 8x -1.

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The equation of line with a gradient of 1 which runs through the point (0,4) is y = x + 4.

The slope-intercept form is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

The point-slope form is expressed as;

y - y₁ = m( x - x₁ )

Given that, the slope of the line m = 1 and it passes through (0,4)

Plug the slope m = 1 and point  ( 0,4 ) into the point-slope form above and simplify.

y - y₁ = m( x - x₁ )

y - 4 = 1( x - 0 )

y - 4 = x - 0

y - 4 = x

Add 4 to both sides

y = x + 4

Therefore, the equation of the line is y = x + 4.

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Answer:

The value equivalent to the expression 2^3 + 3^4 is 19

The Radius r changing with respect to time when volume v is  [tex]\frac{1}{9 \pi} \mathrm{cm} / \mathrm{s}\end{aligned}[/tex].

The volume here depends on the diameter of the radius of the sphere since if we take the cross-section of the sphere, it is a circle. The surface area of sphere is the area or region of its outer surface. To calculate the sphere volume, whose radius is ‘r’ we have the below formula:

Volume of sphere [tex]=\frac{4}{3} \pi r^{3}[/tex]

If you consider a circle and a sphere, both are round. The difference between the two shapes is that a circle is a two-dimensional shape and a sphere is a three-dimensional shape which is the reason that we can measure the Volume and area of a Sphere.

volume is,

[tex]$$\begin{aligned}& V=\frac{4}{3} \pi r^3 \\& \Rightarrow \frac{d V}{d t}=4 \pi r^2 \frac{d r}{d t}\end{aligned}$$[/tex]

given that,

[tex]\frac{dV}{d t}[/tex][tex]=4 \mathrm{~cm}^3 / \mathrm{s}, V=36 \pi \mathrm{cm}^3 \text {. }$$[/tex]

[tex]$$find $\frac{d r}{d t}$ :$$[/tex]

[tex]\begin{aligned}& V=36 \pi \\& \frac{4}{3} \pi r^3=36 \pi \\& r^3=27 \\& \Rightarrow r=3 .\end{aligned}[/tex]

substitute the above values,

[tex]$$\begin{aligned}& \frac{d V}{d t}=4 \pi r^2 \frac{d r}{d t} \\& 4=4 \pi(3)^2 \frac{d r}{d t} \\& \frac{d r}{d t}=\frac{1}{9 \pi} \mathrm{cm} / \mathrm{s}\end{aligned}$$[/tex]

Therefore, the radius r changing with respect to time when the volume v is [tex]\frac{1}{9\pi } cm/s[/tex].

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The profit when n = 101/2 hours is $1,842.50.

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According to one of Marvel's teachers, a typical learning-disabled student has an IQ of normal or above. Learning disabilities are not related to IQ, so a learning-disabled student could have an IQ of normal or above.

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Answer:

S = 25

Step-by-step explanation:

Since it's stated as a square, that means all sides equal each other

In other words;

s+50 = 3s

To get S alone, we will first subtract 50 on both sides

s = 3s-50

Let's now subtract 3s from both sides

s-3s = -50, aka -2s = -50

Changing those to positive, 2s = 50

Last step is to divide both sides by 2

s = 25

At the bicycle manufacturer, the average cost per bicycle is $77.

To find the average cost per bicycle, we need to find the total cost of making all three bicycles and divide that by the number of bicycles.

The total cost is of the bicycles is given by -

$72 (cost of first bicycle) + $83 (cost of second bicycle) + $77 (cost of third bicycle) = $232

Now to find the average cost per bicycle, we will divide the total cost by the number of bicycles.

Hence, $232 ÷ 3 = $77

Therefore, the average cost per bicycle is $77.

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If x is the point reached by F after t seconds, and y is the point reached by S after t seconds, then x = 3t, y = 2t. 30 seconds after leaving point 0, 30 units far apart are F and S. At 100 seconds, F and S will be 100 units apart.

The speed of F reached 12 units in 4 seconds or 3 units per second.

 x = 3t

The speed of S reached 8 units in 4 seconds or 2 units per second.

 y = 2t

x - y = 3t -2t = t

After 30 seconds, the bugs will be apart by (x -y) = 30 units

x - y = 100 = t

After 100 seconds, The bugs will be 100 units apart.

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Answer:

y=x^2

Step-by-step explanation:

There are 55 adults and 27 younglings attended the club.

let the number of adults attended the club be x

let the number of younglings  attended the club be y

total people attended the club = 82

so,

x + y = 82.....[1]

cost for the adult = $6

cost for the younglings = $4

so total amount collected = $438

so, equation formed is ,

6x + 4y = 438.......[2]

from equation [1]

x + y = 82

x = 82 - y

put this in equation [2]

6(82 - y) + 4y = 438

492 - 6y + 4y = 438

492 - 2y = 438

492 - 438 = 2y

2y = 54

y = 27

put this value in equation [1]

x + y = 82

x + 27 = 82

x = 82 - 27

x = 55

so, there are 55 adults and 27 younglings attended the club.

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