2. Calculate the distance MI for the length of the zipline cable. 3. Calculate the angle at which our zipliners will be descending toward the island . Safety regulations state that the angle at which a zipline cable meets the launching point cannot be smaller than 68 degrees . Please determine if we are in compliance with these regulations

we get that the answer is

Answer:

=====================

Answer:

[tex](x,y)=\left(\; \boxed{-2,13} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{1,10} \; \right)\quad \textsf{(larger $x$-value)}[/tex]

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}\phantom{bbbb}y=x^2+9\\x+y=11\end{cases}[/tex]

To solve by the method of substitution, rearrange the second equation to make y the subject:

[tex]\implies y=11-x[/tex]

Substitute the found expression for y into the first equation and rearrange so that the equation equals zero:

[tex]\begin{aligned}y=11-x \implies 11-x&=x^2+9\\x^2+9&=11-x\\x^2+9+x&=11\\x^2+x-2&=0\end{aligned}[/tex]

Factor the quadratic:

[tex]\begin{aligned}x^2+x-2&=0\\x^2+2x-x-2&=0\\x(x+2)-1(x+2)&=0\\(x-1)(x+2)&=0\end{aligned}[/tex]

Apply the zero-product property and solve for x:

[tex]\implies x-1=0 \implies x=1[/tex]

[tex]\implies x+2=0 \implies x=-2[/tex]

Substitute the found values of x into the second equation and solve for y:

[tex]\begin{aligned}x=1 \implies 1+y&=11\\y&=11-1\\y&=10\end{aligned}[/tex]

[tex]\begin{aligned}x=-2 \implies -2+y&=11\\y&=11+2\\y&=13\end{aligned}[/tex]

Therefore, the solutions are:

[tex](x,y)=\left(\; \boxed{-2,13} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{1,10} \; \right)\quad \textsf{(larger $x$-value)}[/tex]

Given the function f(x) defined as:

We need to find the derivative first. Using the chain rule, we know that:

Then, taking the derivative if u = 2x:

Using this result, we can evaluate the derivative at x = π/2:

a. reflection over the y-axis and 4 units down

Note:

If f(x) is reflected over the x-axis, it becomes -f(x) because the y coordinate is negated.

If f(x) is reflected over the y-axis, it becomes f(-x) because the x coordinate is negated.

Therefore, for f(-x)-4, f(x) is reflected over the y-axis, and then translated 4 units down

Since a whole revolution has 360º, when we have an angle bigger than 360º the angles start to repeat.

We can subtract 360º to the given angle to find the coterminal angle. In this case:

And from an reference angle of 0º, this is exactly a half revolution. Thus, the angle is in the x axis, and it's coterminal angle is 180º

Solution

We are given that

Length (l) = 4ft

Width (w) = 2ft

Height (h) = 3ft

Note: Formula for Surface Area of the Locker

Substituting the parameters

Therefore, the surface area is

Given that a triangle has sides of the following dimensions

The diagram of the triangle can be seen below

To find the perimeter, P, of a triangle, the formula is

Where

Substitute the values to find the perimeter, P, of the triangle

Hence, the perimeter, P, of the triangle is

We have the following:

We must calculate the solution since that is the point of intersection.

we equalize the equations and we have:

for y:

The point is (1, -1)

Therefore, the answer is the graph A.

In order to calculate the percentage of surveyed people that liked red cars, we need to divide this amount of people by the total amount of people surveyed.

So we have:

Therefore the percent of the people surveyed that liked red cars is 4%.

We are given the following equation:

Where are asked to find the value of "u". To do that we need first to solve for "u", first by adding 4 on both sides:

Now, we will divide by 2 on both sides:

Therefore, the value of "u" is 5

Answer

The answer is 17.

Explanation

The absolute value of any number is taking the positive part of any number. For example, the absolute value of -2 = | -2 | = 2, the absolute value of -99 = | -99 | = 99.

So, the absolute value of -17 = | -17 | = 17.

Hope this Helps!!!

1) Let's plot those values on a number line. Since -5 1/2 and 8 1/2 can be written as -5.5 and 8.5

2) There we have:

Answer:

Nine rows X 8 in the row= 72

Step-by-step explanation:

Answer: For this question you would just multiply 8 and 9 and get 72.

Step-by-step explanation:

Because there are 9 rows of tomato plants and each row has 8 tomatos, you would be doing 9x8 and get your answer of 72. Hope this makes sense!

The value of 9.4 degrees in feet is 0.1884 feet and in inches is 2.26 inches.

To calculate feet from degrees, divide the angle by 360, multiply by 2 times pi, then finally, multiply by the radius.

And feet to inches we know 1 foot equals 12 inches.

Converting degrees to feet is commonly discussed while looking at a circle and converting an angle to the length of the arc of that angle. When discussing latitude and longitude, that circle is frequently the earth.

The following formula is used to convert an angle in degrees to length in feet.

L = (a/360) * 2 * pi * r

Where,

L is the length in the feet.

a is the angle in degrees.

r is the radius of the circle in feet.

We are given 9.4 degrees.

Let r = 1 feet

Put the given values in the above formula, we will get;

L = (9.4/360) * 2 * pi * 1

L = 0.03 * 2 * 3.14 * 1

L = 0.1884 feet

L = 0.1884 * 12 = 2.26 inches.

Thus, the value of 9.4 degrees in feet is 0.1884 feet and in inches is 2.26 inches.

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The tangential speed of a disk is  94.23.

Given:

radius (r) = 15meters

time t = 7 sec

tangential speed = 2[tex]\pi[/tex]r/t

                           = 2x 3.141x 15/7

                           = 94.23

Tangential speed is the linear component of its velocity as it moves in a circle. If an object moves along a circular path at a distance r from the centre of the circle, the velocity of the object is tangent to the circle at some point.

In mathematics, a tangent is a line that touches a curve at one point. A quantity is tangent to another if it touches the other quantity once and then moves in the other direction.

Therefore, the tangential speed is a measure of the speed at any point where the tangent curves in this circular motion. Tangential velocity is useful for circular motion because it allows angular motion to be transformed into linear motion.

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Part 1

we have

2(3m+7)

For m=1 ------> 2(3(1)+7)=2(10)=20

For m=2-----> 2(3(2)+7)=2(13)=26

we have

6m+14

For m=1 -----> 6(1)+14=20

For m=2----> 6(2)+14=26

Remember that

2(3m+7) is the same that 6m+14

Step 1:

Let the height below sea level before she descends = h feet

The length she descended after 10 minutes = 21.4 feet

The height of the submarine after descended below the sea level = 90.6 feet

Step 2:

Height of the submarine before descended below the sea level

x = 90.6 - 21.4

x = 69.2 feet

Final answer

69.2 feet

The vertex Y is triangle WXY is (7, -8)

The triangle will translate by the rule (x + 3, y - 4)

That means it will be moved right 3 units and down 4 units

So we will add the x-coordinate of point Y by 3 and subtract its y-coordinate by 4 to get its image Y'

The image of point Y is

Y' = (7 + 3, -8 - 4)

Y' = (10, -12)

The correct answer is C

the formula for the compound interest is given as follows,

here P = 2000 , R = 8 % , t = t.

so the value(V) is

so the answer is option C

Step 1:

Write the two equations

Step 2:

The amplitude of graph A = 2

The midline of the graph is D = 0

The graph is a sin graph.

y = 2sin[B(x - C)] + 0

y = 2sin[B(x - C)]

Final answer

y = 2sin[B(x - C)] + D

Given

To find the zeros of multiplicity one, multiplicity 2, multiplicity 3.

Now,

The zeros of multiplicity 1 are,

The zeros of multiplicity 2 are,

There are no zeros of multiplicity three since the polynomial has no factor to the power 3.

Step 1

Given;

Required; To find which answer shows two pairs of adjacent angles in the figure.

Step 2

Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.

Therefore, the pair of adjacent angles is;

Hence, the answer is: angles 4 and 5; angles 2 and 4

ANSWER

EXPLANATION

Parallel lines have the same slope. First we should rewrite the given line in the slope-intercept form by clearing y, so that we can see what is the slope:

The slope of the line is 2/3, so the slope of the parallel line must be 2/3 too. From this options, the equation with a slope of 2/3 is:

the given expression is,

so the correct answer is option B

the quotient is 321

SOLUTION:

Case: Triangles

Method:

First, It is an Isosceles triangle

When the base angles are equal, the opposite sides are equal too

Next, find y using Pythgoras theorem

Final answer:

we need to isolate x

first solve the parenthesis

now solve x

the value of x is -6

First, let's find the slope of the line that passes through the points (-4,3) and (6,2):

Now we can use the first point to get the equation of the line:

therefore, the equation of the line is y=-1/10x+13/5

How much did she spend?

She had 80 dollars, and after buying them she had 16 dollars. Then she spent

80 - 16 = 64

she spent $64 on 8 books.

How much did each book cost?

Since 8 books cost $64, each one should cost:

64 ÷ 8 = 8

each one cost $8.

Answer::

Explanation:

• The first year rent = $62,000

• The rate of increase, r = 3% = 0.03

Since the rent increases by a common factor each year, we can find the explicit rule by using the formula for the nth term of a geometric sequence.

The nth term of a geometric sequence is calculated using the formula:

In this case:

• a1 = 62,000

• r=1+0.03=1.03

Thus, an explicit rule that describes the rent after n years is:

The radical expression √108 is not equivalent to the expression √5√21 .

Given the radical expression as √108 .

Now the number 108 can be broken down into factors as

108 = 54 × 2 , 36 × 3 , 18×6

therefore we can see that the radical expression is equivalent to

√108 = √54 × √2

√108 = √36 × √3

√108 = √18 × √6

But 21 × 5 = 105 ≠ 108.

Therefore the radical expression √108 is not equivalent to √5√21 .

Expressions in mathematics are statements with variables, numbers, or both, and at least two terms joined by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

In mathematics, there are two types of expressions: numerical expressions, which only contain numbers, and algebraic expressions, which also contain variables.

A symbol with an unknown value is called a variable. A term can be made up of a single constant, a single variable, or a group of variables and constants multiplied or divided. A number that has been further multiplied by a variable serves as the coefficient in an equation.

Disclaimer: The complete question is :

Which of the following is not a radical expression that is equivalent to √108?

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