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. If she stands 10 feet from the edge of the cliff, she can visually align the top of the cliff with the water at the back of her boat. Her eye level is 5½ feet above the ground. Approximately how far out from the cliff is Catarina’s boat? Round to the nearest foot.

a. Yes, it is possible for a line (y = mx + b) that passes through the origin (0, 0) to pass through no other rational points. An example of such a line is y = sqrt(2)x. This line passes through the origin (0,0), but the y-coordinate will only be a rational number if the x-coordinate is also a rational number and a perfect square.

b. Yes, it is possible for a line to pass through no rational points. An example of such a line is y = sqrt(2)x + sqrt(3). This line will never pass through any rational points because the y-coordinate will only be a rational number if both x and b are rational numbers and perfect squares, which is not possible in this case.

The numeric values for the piece-wise function in this problem are given as follows:

A piece-wise function is a function that has different definitions, depending on the intervals of the input x of the function.

From the image given at the end of the answer, the function has four definitions, depending on the range of x, hence for each numeric value, we have to first identify the range of x for which the input belongs, and then apply the rule.

Hence the numeric values are given as follows:

The problem is given by the image presented at the end of the answer.

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Answer:

I disagree

Step-by-step explanation:

[tex] \frac{ {2a}^{2} {b}^{2} \times ( - 3 {a}^{2} {b}^{2}) }{6ab \times {9a}^{2} {b}^{2} } \\ \frac{ {2a}^{2} {b}^{2} \times {9a}^{4} {b}^{4} }{6ab \times 9 {a}^{2} {b}^{2} } \\ \frac{18 {a}^{2 + 4} {b}^{2 + 4} }{54 {a}^{2 + 1} {b}^{2 + 1} } \\ \frac{18 {a}^{6} {b}^{6} }{54 {a}^{3} {b}^{3} } \\ \frac{1}{3} {a}^{6 - 3} {b}^{6 - 3} \\ \frac{1}{3} {a}^{3} {b}^{3} [/tex]

Hope this helps

Answer:

y = 5/6x - 1/12

Step-by-step explanation:

The slope-intercept form is y = mx + b

10x - 12y = 1

We subtracted 10x from both sides

-12y = -10x + 1

Divided by -12 both sides

y = -10/-12x - 1/12

To simplify we can get

y = 5/6x - 1/12

Answer:

m = 2 K.E / v^2

Step-by-step explanation:

K.E = 1/2 mv^2

K.E × 2/1 = mv^2

2 K.E = mv^2

2 K.E × 1/ v^2 = m

∴ m = 2 K.E / v^2

[tex]m=\frac{2KE}{v^{2}}[/tex].

Just for general knowledge. This is a formula from physics, specifically, classical mechanics. It is used to calculate the kinetic energy of bodies, that what the varaible "KE" stands for.

Now, let's rearrange the formula!

[tex]KE=\frac{1}{2} mv^{2}[/tex]

[tex]2KE=\frac{1}{2} mv^{2}*2\\ \\2KE=mv^{2}[/tex]

See that the 2 is used to cancel the 1/2 fraction.

[tex]\frac{2KE}{v^{2}} =\frac{mv^{2}}{v^{2} } \\ \\\frac{2KE}{v^{2}} =m\\ \\m=\frac{2KE}{v^{2}}[/tex]

[tex]m=\frac{2KE}{v^{2}}[/tex].

If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "m" by it's calculated value, [tex]\frac{2KE}{v^{2}}[/tex].

[tex]KE=\frac{1}{2} (\frac{2KE}{v^{2}})v^{2}[/tex]

Here, the 1/2 fraction is cancelled by the 2 inside the parenthesis. Also, the v² is cancelled out by the v² that's dividing inside the parenthesis, leaving us with this expression (check attached image to better understand this step):

[tex]KE=KE[/tex]

As you can tell, the same variable appears on both sides of the equal symbol, this means that the result is correct!

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A integer, a constant, or a mix of both, combined with specific operation symbols, make up an expression $3r+$37.5 is the equation.

A number, a constant, or a mix of both, combined with specific operation symbols, make up an expression. An expression can only be an exponential function if it contains both an operators and a variable. Any unknown term can be used as a factor, together with the operator + and -. Examples of such terms include x, y, and z. Since 5 isn't an exponential function, it can be claimed that it.

Here,

given:

It is reasonable to assume that r = n rides. Since each ride costs $3 ($3xr), the total cost is $3.

In addition, we know that FIVE people, including Tory and every one of her friends, will be at the fair. The entrance fee is $7.50, therefore we can increase it by five to reach $37.5.

That is $3r plus $37.5.

Therefore, the equation is $37.5 + $3r, where r seems to be the total of rides taken by Tory and his friends.

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Each member of the photography club got [tex]\frac{1}{8}[/tex] of the lasagna from the pan of lasagna.

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.

Given that the club was provided with half pan of lasagna. So the initial amount of lasagna is [tex]\frac{1}{2}[/tex].

The [tex]\frac{1}{2}[/tex] lasagna is further shared within 4 members. Hence each member will get:

[tex]\frac{\frac{1}{2} }{4} = \frac{1}{8}[/tex] lasagnas.

Hence, each member of the photography club got [tex]\frac{1}{8}[/tex] of the lasagna from the pan of lasagna.

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The measure of the tan of the angle T is 3.4286

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

Opposite = RS

Hypotenuse = 50

Adjacent = 14

The opposite of the angle T can be calculated as

Hypotenuse² = Opposite² + Adjacent²

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

50² = RS² + 14²

Evaluate the like terms

RS² = 2304

Take the square root of both sides

RS² = 48

The measure of the tan of the angle T is then calculated as

tan(T) = RS/Adjacent

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

tan(T) = 48/14

Evaluate

tan(T) = 3.4286

Hence, the value is 3.4286

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Therefore ,the solution of the given problem of triangle comes out to be

area is 84 inch square.

Since a triangle has number of sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker assigned to a triangle that has edges A, B, and C. So when three components are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and triple corners. The points where the three parts meet are known as the triangle's corners. The product of three triangle angles is 180 degrees.

Here,

Given : 7 inch , 25 inch and 24 inch.

To find the area of the triangle :

vertices are 7inch , 25inch and 24inch

Since from given vertices we can see it is an right angle triangle:

thus,

=> Area = 1/2 * base * height

=> Area = 1/2 * 24 * 7

=> Area = 12*7

=> Area = 84 inch square

Therefore ,the solution of the given problem of triangle comes out to be

area is 84 inch square.

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Answer: To solve 604 times 33, you can use the basic method of multiplication.

You can start by multiplying the ones digit of 604 (4) by the ones digit of 33 (3) to get 12.

Then, you can multiply the tens digit of 604 (0) by the ones digit of 33 (3) to get 0.

Finally, you can multiply the hundreds digit of 604 (6) by the ones digit of 33 (3) to get 18.

To get the final answer, you need to add these three intermediate values (0+12+18) and carry over if necessary:

604 * 33 = 20,012

You can also use long multiplication method, which is breaking down the multiplication problem into simpler problems.

Or use a calculator or computer.

Step-by-step explanation:

Answer: 12207032501220703250122070325012207032501220703250122070325012207032501220703250

Step-by-step explanation:

1220703250122070325012207032501220703250

The interpretation of the likelihood of choosing a green marble is; Likely

Theoretical probability is defined as the term that is used to describe what is expected to happen based on math theory. Meanwhile, experimental probability that is used to describe what actually happens when the actual situation is tried out as an experiment.

Now, we are told that the probability of selecting a green marble in a bag of marbles is 3/4. This expressed in percentage is 75%.

This experimental probability is more than half of the entire probability and as such we can say that it is very much likely to occur when we select a marble.

We conclude that the correct answer is Option A.

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Answer:

[tex]A = 125 \textrm{ yd}^2[/tex]

Step-by-step explanation:

The area of a triangle can be solved for using the formula:

[tex]A_\triangle = \dfrac{1}{2}b h[/tex]

where [tex]b[/tex] is the length of the triangle's base and [tex]h[/tex] is the length of its height (altitude).

Both [tex]b[/tex] and [tex]h[/tex] are given to us for the shown triangle, so all we have to do is plug the given values into the triangle area formula above.

[tex]A = \dfrac{1}{2} \cdot 10 \cdot 25[/tex]

[tex]A = 5 \cdot 25[/tex]

[tex]A = 125 \textrm{ yd}^2[/tex]

Note that the height of the triangle is given on the outline of an auxiliary (dotted) right triangle. This is just to show that the height is in fact an altitude, meaning it is perpendicular to the base, not at the angle of the triangle's other sides.

Yes, the statement is a tautology

Tautology is a compound proposition that is always true for all possible truth values of its variable. A tautology has only T in the last column of its truth table.

Truth table for p v ~p

p  ..... ~p  ..... p v ~p

T         F         T

T         F         T

F         T         T

F         T         T

Since the last column of the truth contains only T, the statement is a tautology

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The width of the flower bed is 3m.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangular lawn = 8m x 4m

The flower bed dimensions are:

Length = (8m + x)

Width = x

The combined area of lawn and flower bed area = 140 m²

(8 + 2x) x (4 + 2x) = 140

32 + 16x + 8x + 4x² = 140

4x² + 24x + 32 - 140 = 0

4x² + 24x - 108 = 0

4 (x² + 6x - 27) = 0

x² + 6x - 27 = 0

x² + (9 - 3) - 27 = 0

x² + 9x - 3x - 27 = 0

x(x + 9) - 3(x + 9) = 0

(x + 9) (x - 3) = 0

x + 9 = 0

x = -9 (rejected)

x - 3 = 0

x = 3

Thus,

The width of the flower is 3m.

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A polygon will map to itself after a rotation of a 60° would be a regular hexagon.

What is a polygon?

A polygon is a closed, two-dimensional geometric shape that is defined by a set of straight lines, called its sides, that are connected end-to-end. The number of sides in a polygon is referred to as its "order" or "degree"

A polygon that maps to itself after a rotation of 60 degrees is called a regular hexagon. A regular hexagon is a polygon with six sides of equal length and six angles of equal measure (120 degrees each).

To sketch a regular hexagon, you can start by drawing a dot in the middle of a piece of paper. From there, use a compass or a straightedge to draw a circle around the dot. Then, use the compass to draw six lines from the center of the circle to the edge of the circle, each line being 60 degrees apart from the other. Finally, connect the endpoints of each line to form a six-sided polygon.

Hence, a polygon will map to itself after a rotation of a 60° would be a regular hexagon.

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Part (a)

[tex](CG)(CE)=(CH)(CD)[/tex]

Part (b)

It is possible to find the length of [tex]\overline{DH}[/tex].

[tex](CG)(CG+GE)=(CH)(CH+DH) \\ \\ (3)(3+5)=(2)(2+DH) \\ \\ 24=2(2+DH) \\ \\ 12=2+DH \\ \\ DH=\boxed{10}[/tex]

Answer:

18 sattelites

Step-by-step explanation:

Let's make an equation

n is number of sattelites on Saturn

n-2 is number of sattelites on Jupiter

n-16 is number of sattelites on Mars

Equation would be like:

n+(n-2)+(n-16)=36

3n-18=36

3n=54

n=18

When your base wage is $20,000, your notch equals your basic salary times twelve, or $240000.

directly varying You have the function y = mx (commonly written y = kx), which is known as a direct variation, in the equation y = mx + b if m is a  Variation Theory is a general theory of learning that is mostly utilized in the pedagogy and teaching of mathematics. By emphasizing what remains the same and what changes, it draws attention to a concept's key components and provides the chance to draw connections that are significant.

given

basic salary = 20000

sello notch = basic salary * 12

20000 * 12 = $ 240000

When your base wage is $20,000, your notch equals your basic salary times twelve, or $240000.

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Answer: Roger should pick Printer B because it prints 2 more pages per minute.

Step-by-step explanation: We are given that printer A prints 33 pages per minute. We have to figure out how many pages printer B prints in a minute.

As shown in the table, in 2 minutes, printer B prints 70 pages, and in 3 minutes it prints 105 pages. We can create a function to model the rate at which printer A prints pages. This is a linear function since for each increase in x, there is a proportional increase in y. This means that if we were to back one minute the printer would print 35 pages since the common difference per minute is 35 pages. The function would therefore be p=35m where m=minutes and p=pages. This means that printer B produces 2 more pages than printer A per minute since 33+2=35.

Answer:

[tex]x=\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]x+\frac{21}{4}=6\\4x+21=24\\4x=3\\x=\frac{3}{4}[/tex]

linear operations When the function's degree is 1 and it depicts a straight line, the expression is f(x) is x .

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

The most basic form of an equation in a family of functions is a parent function. There are several types of parent functions, including: linear operations When the function's degree is 1 and it depicts a straight line, the expression is f(x)=x f (x) = x.

y(x) = x is the linear parent function to keep in mind. This is the function's simplest, most fundamental version.

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Answer:

the answer is 54 to the question 5 17 18 -2 23

Deductible: This is the amount that the insured is responsible for paying before insurance coverage begins. The higher the deductible, the lower the monthly premium will be.

Amount: This is the total amount that the insurance company will cover.

Number of Co-Payments: This is the number of times the insured will be responsible for paying a specific dollar amount (in this case, $10) for covered services.

Amount of Co-Payments: This is the total dollar amount that the insured will be responsible for paying in co-payments.

Amount Subject to Co-Insurance: This is the total dollar amount that the insured is responsible for paying after the deductible and co-payments have been met.

Insured Co-Insurance Rate: This is the percentage of the remaining amount that the insured is responsible for paying.

Amount of Co-Insurance: This is the dollar amount that the insured is responsible for paying according to their co-insurance rate.

Total Paid by Insured: This is the total dollar amount that the insured is responsible for paying, including the deductible, co-payments, and co-insurance.

For example, for the first row, the insured would be responsible for paying $500 for the deductible, $200 for co-payments (20 payments of $10 each), and $4,000 for co-insurance (20% of $20,000). The total paid by the insured would be $500 + $200 + $4,000 = $4,700

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Answer:

y = 3x - 6

y = -x+2

Step-by-step explanation:

Answer:

2 times the cost

Step-by-step explanation:

1 persona 1 costs

2 persons, double the cost

Answer:

a = 99

b = 51

Step-by-step explanation:

We can translate this problem into a linear equation. We know that:

2b - 3 = a

and

a + b = 150

We will start by minusing b from both sides in the second equation, giving us:

a = 150 - b

Then, we will substitute this into our second equation, giving us:

2b - 3 = 150 - b

We will add 3 and b to both sides, giving us:

3b = 153

Then we divide by 3:

b = 51

Now, we will substitute this into our second equation, giving us:

a + 51 = 150

Subtract 51 from both sides gives us:

a = 99

So, the a piece is 99 yards long, and the b piece is 51 yards long.

a = 99

b = 51

Hope this helped!

The statement that complete the proof that quadrilateral EFGH is a square is; A) Line EF, FG, GH, and EH are congruent

The four sides of a square are always congruent to each other which means that they are equal to each other.

Now, we see that;

EF = 3√2

GH = 3√2

FH =3√2

EH = 3√2

Thus, all four sides are equal.

We also see that the slopes that form 90 degrees with each other are perpendicular and as such that is also a requirement for the quadrilateral to be a square.

Thus, we can conclude that all four sides are congruent to each other from the evidence above.

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Answer:

Statement 4 of the proof should be:

segment EH is parallel to segment FG

Step-by-step explanation:

They have the same slope which is -1.

It is a scale factor of 2.

You could see that the JKL triangle has only 4 grids on one side and J'K'L' has 8. So 8/4=2, so, therefore, it is a scale factor of 2. Please correct me if I am wrong.