A point on the edge of a symmetrical canyon is 4500 feet above a river that cuts through the canyon floor. The angle of depression from each side of the canyon to the canyon floor is 60o.

a) Find the length of the canyon wall (from the edge to the river).
feet

b) Find the distance across the canyon.
feet

c) Is it more or less than a mile across the canyon? (5280 feet = 1 mile) more or less

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

Explanation:

Recall the discriminant formula is

d = b^2 - 4ac

which is the stuff found under the square root in the quadratic formula.

If d > 0, then the equation ax^2+bx+c = 0 will have two different real number roots.

So,

d > 0

b^2 - 4ac > 0

4^2 - 4(1)(k) > 0

16 - 4k > 0

16 > 4k

4k < 16

k < 16/4

k < 4 which points us to choice C

For example, if k = 0, then the equation x^2+4x+k = 0 becomes x^2+4x = 0. This has the two different roots of x = 0 and x = -4.

Answer:

q=3

Step-by-step explanation:

im very bad at explaining step by step.

Answer:

1.3

Step-by-step explanation:

(−2 3/5)(−0.5)

=(−13/5)(−0.5)

=−13/5(−0.5)

=1.3

=1.3

906/2so what is your name

If a ≤ b, then it is not true for all real numbers that a²≤ b² .

Consider a ≤ b.

Then squaring on both sides,

⇒ a²≤ b² .

But this is true only when both a and b are non-negative numbers.

For example, if we take a = 2 and b = 5, then clearly,

2² = 4 ≤ 5² = 25

Now we need to prove that this result is not true for all real numbers. So we find two real numbers a and b which does not follow this result.

Let a = -7 and b = 3

So here, a < b

Now a² = (-7)² = 49

and b² = 3² = 9

So here, a² > b².

Thus a = -7 and b = 3 is the required counter example to show that the given result is not true for all real numbers.

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The value of the fractional expression as a mixed numbers is: 2⅔ × 3¼ = 8⅔.

A mixed number is a combination of a whole number together with a fraction. It can also be referred to as mixed fractions.

Given the fractional expression, 2⅔ × 3¼, evaluate the fractions as explained below:

Convert the mixed numbers to improper fractions

2⅔ × 3¼ = 8/3 × 13/4

2⅔ × 3¼ = 2/3 × 13/1

Multiply the denominators together and the numerators together

2⅔ × 3¼ = 26/3

Divide

2⅔ × 3¼ = 8⅔

Therefore, the value of the fractional expression as a mixed numbers is: 2⅔ × 3¼ = 8⅔.

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Answer:

2x^2 + 6x - 2

Step-by-step explanation:

It's the second option using like terms

Answer:

The answer is 2x² + 6x - 2. which means it's B.

The unit rate for the turtle crawling is 1 mile per hour

An equation is an expression that shows the relationship between two or more numbers and variables.

Unit rate is the ratio of two different units, and also having a denominator of one.

For every of an hour that the turtle is crawling, he can travel of a mile. Hence:

Unit rate of crawling = 1 mile / 1 hour = 1 mile per hour

The unit rate for the turtle crawling is 1 mile per hour

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The number of students that are likely to be in the class will be 30 students.

From the information, it was stated that the classroom of students can be divided into two, three, and five groups, with no students left over.

Therefore, the number of students that are likely to be in the class will be:

= 2 × 3 × 5

= 30

Therefore, the number of students that are likely to be in the class will be 30 students.

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Answer:

7+5p+4r+6s

Step-by-step explanation:

the same thing cause their variables are different, you can't add if the variables are different

variables are those letters that are at the end of the coefficient

Answer:

y=-4x+9

Step-by-step explanation:

8x+2y=18

-8x       -8x

2y=-8x+18

Divide by 2.

2y/2=y

-8x/2=-4x

18/2=9

Put the pieces back together.

y=-4x+9

Hope this helps.

Answer:

x = 9-y / 4

Step-by-step explanation:

The expanded form of the number 34.576 is A: An expression that reads three times ten, plus four times one plus five times one-tenth, plus seven times one-hundredth, plus six times one-thousandth.

It should be noted that the correct form of the expression will be:

= (3 × 10) + (4 × 1) + (5 × 1/10) + (7 × 1/100) + (6 × 1/1000)

= 34.576

Therefore, the expanded form of the number 34.576 is an expression that reads three times ten, plus four times one plus five times one-tenth, plus seven times one-hundredth, plus six times one-thousandth.

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The more economical purchase is the 24-ounce box of cornflakes for $3.89.

The more economical purchase can be determined by calculating the unit rate for each box of cornflakes.

The unit rate can be calculated by the division of the total ounce of the box by the price of the box

Hence the unit rate for the 18-ounce box is calculated as,

unit rate of 18-ounce box = 18 / 3.49

unit rate of 18-ounce box = 5.16 ounce/$

The unit rate for the 24-ounce box is calculated as,

unit rate of 24-ounce box = 24 / 3.89

unit rate of 24-ounce box = 6.17 ounce/$

As the rate of 6.17 ounce/$ is more economical than 5.16 ounce/$, the more economical purchase is the 24-ounce box of corn flakes.

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A function is one-to-one if each horizontal line crosses the function's graph no more than once. The inverse function of F = 9/5C +32 is a one to one function.

A function is one-to-one if each horizontal line crosses the function's graph no more than once.

If the graph of a function f is known, determining whether the function is 1 -to-1 is simple. Make use of the Horizontal Line Test. If no horizontal line intersects the graph of the function f more than once, the function is one-to-one.

If f(x) = f(y)

⇒ x = y, then f is one to one.

Let the Fahrenheit temperatures be F = 9/5C +32

Subtract 32 from both sides of the above equation

F-32 = 9/5C

Multiply both sides by 5:

5(F-32) = 9C

Divide both sides by 9:

C = 5/9 (F-32)

For 27°

C = 5/9 (27-32)

simplifying the above equation, we get

⇒ C = 5/9 (-5)

⇒ C = -25/9

The value of C = -25/9.

= -2.78C°

⇒ 2dp

Yes, the inverse is a one to one function.

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The function has an inverse that is also a function would be {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} so correct option will be (A).

A certain kind of relationship called a function binds inputs to essentially one output. In other words, the function is a relationship between variables and the nature of the relationship.

We have been given that a function is only a function such that there is a unique value of y corresponding to x.

An inverse function is only be a function if the function which is going to be inverse is a function.

The inverse of a function: (x, y) → (y, x)

1. {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}

It has unique y- values, the inverse won't repeat x-values, so the inverse is also a function.

Hence, The function has an inverse that is also a function would be {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} so correct option will be (A).

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Answer:

so simple do it yourself and use the formula when is given in the text book to solve

[tex]\huge\boxed{\sqrt5}[/tex]

To find the value of [tex]x[/tex], we'll use the Pythagorean theorem.

The following formula applies, with the lengths of the sides with the right angle being [tex]a[/tex] and [tex]b[/tex], and the hypotenuse being [tex]c[/tex]:

[tex]a^2+b^2=c^2[/tex]

Substitute the values in.

[tex]x^2+(\sqrt{11})^2=4^2[/tex]

Square the numbers as possible.

[tex]x^2+11=16[/tex]

Subtract 11 from both sides of the equation.

[tex]x^2=5[/tex]

Take the square root of both sides of the equation to solve for [tex]x[/tex].

[tex]x=\sqrt5[/tex]

To have an inverse function, a function must be one-to-one.

[tex]$$f^{-1[/tex](x) = x³ is the inverse of f(x) = x³

An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by [tex]$$f^{-1[/tex] or F-1 if the function is denoted by ' f ' or ' F '.

To find the inverse, interchange the variables and solve for y.

f−1(x)=3√x

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

Replace y with [tex]$$f^{-1[/tex](x) then we get

[tex]$$f^{-1[/tex](x) = 3√x

[tex]$$f^{-1[/tex](x) = x³ is the inverse of f(x) = x³

The result of a mathematical operation, such as addition and subtraction, multiplication and division, is reversed. These are referred to as inverse operations. Typically, the inverse of a number is its reciprocal, or x - 1 = 1/x. A number and its reciprocal (inverse) product yield one.

To have an inverse function, a function must be one-to-one.

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The solution for the given Logarithms equation  2 log₃x=54 is x = 3²⁷ in the nearest ten-thousandth =  7625597484987.

Exponential functions have logarithmic inverses. A log is thus an exponent! y=logbx if and only when by=x for all x greater than zero and 0b1.

Logarithms depict changes in terms of multiplication: each step in the preceding instances is 10x larger. Each step is "e" (2.71828...) times longer using the natural log. When dealing with such a sequence of multiplications, logarithms assist in "counting" them in the same way as addition assists us in counting when effects are added.

Given  2 log₃x=54

Divide both side by 2:

(2 log₃x)2 = 54/2

simplify.

log₃(x)  = 27

apply log rule:

x = 3²⁷

Decimal value of x = 3²⁷ = 7625597484987

The solution for the given Logarithms 2 log₃x=54 is x = 3²⁷ in the nearest ten-thousandth =  7625597484987

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Answer: Use Structure multiply by a power of 10 when writing a repeating decimal as a rational number is 1/5.

Step-by-step explanation:

Define Decimal number :

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

Example: the numbers we use in everyday life are decimal numbers, because they are based on 10 digits (0,1,2,3,4,5,6,7,8 and 9). "Decimal number" is often used to mean a number that uses a decimal point followed by digits that show a value smaller than one. Example: 45.6 (forty-five point six) is a decimal number.

Define Rational numbers :

Rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.

Example : a rational number is a type of real number, which is in the form of p/q where q is not equal to zero. Any fraction with non-zero denominators is a rational number. Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on.

So, Given data,

Use Structure Why do you multiply by a power of 10 when writing a repeating decimal as a rational number?

Then we can write,

Let us assume to multiply by some number (10, 100, 1000, etc.)

so that,

when we subtract the original number from the multiple, the repeating part cancels out.

If we multiply by 10.

we get 10x = 2

              x = 2/10

              x = 1/5

Therefore ,

x = 1/5 is Rational number.

So,

Use Structure multiply by a power of 10 when writing a repeating decimal as a rational number is 1/5.

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Answer:

There are 182.88 cm in 6 feet, given that 1 inch = 2.54 cm.

Step-by-step explanation:

Given that 1 inch = 2.54 cm, how many centimeters are there in 6 feet?

12 inches = 1 foot

We have 6 feet, so:

6 feet x 12 inches = 72 inches

If 1 inch is 2.54 cm, multiply by the number of inches by 2.54 to get the number of cm.

2.54 x 72 = 182.88

There are 182.88 cm in 6 feet, given that 1 inch = 2.54 cm.

The graph of the compound inequality is described by the third choice. A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right

From the question, we are top determine the graph of the given compound inequality

First, we will determine the solution to the compound inequality

Solving the first inequality

x - 3 < - 11

Add 3 to both sides

x - 3 + 3 < - 11 + 3

x < -8

Solving the second inequality

x + 5 ≥ 14

Subtract 5 from both sides

x + 5 - 5 ≥ 14 - 5

x ≥ 9

Thus,

The solution to the given compound inequality is x < -8 or x ≥ 9

Hence, the graph of the compound inequality is described by the third choice. A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right.

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Answer:

2,000

Step-by-step explanation:

because the 8 in the hundreds place is more than 5 and allows the number to be rounded up

Answer: 2,000

Step-by-step explanation:

the 1 next to the 8 makes that 1 to round up to a 2 which makes it 2,000.

Answer:

y≥−3/2x−2

Step-by-step explanation:

the inequality is represented by the graph is y≥−3/2x−2

For  f(x)=2 x+5 and g(x)=x²-3 x+2 , the values of the composite function 3 f(x)-2 = 6x+ 13

The domain of a function is the set of input values, the function can take.

The functions are given as:

f(x)=2 x+5

g(x)=x²-3 x+2

To find:

3 f(x)-2 = ?

3 ×(2 x+5) - 2 = 6x + 15 - 2

= 6x+ 13

Therefore,

The function operation of 3 f(x)-2 = 6x+ 13

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Two or more expressions separated with an equal sign is called as equation. y=24-x is the value for y of equation 4x-y=24.

Two or more expressions separated with an equal sign is called as equation.

The given equation is

4x-y=24.

In the given equation x and y are variables.

We are required to solve for y variable.

subtract both sides by -4x

4x-y-4x=24-4x

-y=24-4x

Multiply both sides by minus

y=-24+4x

y=4x-24

Therefore the solution for y is 4x-24.

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Answer:

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step-by-step explanation:

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step 1: Understand the problem.

Step 2: Devise a plan (translate).

Step 3: Carry out the plan (solve).

Step 4: Look back (check and interpret).

The example using the polya's 4-steps in problem solving is created along with the answer.

Let's apply Polya's 4-step problem-solving process to the following word problem:

Problem: Lily has twice as many apples as John. Together, they have 27 apples. How many apples does each person have?

Step 1 - Understand the Problem:

To solve this problem, we need to find the number of apples that Lily and John each have. We know that Lily has twice as many apples as John, and together, they have 27 apples. We need to determine the number of apples for each person.

Step 2 - Devise a Plan:

Let's use algebra to represent the number of apples. Let's say the number of apples John has is "x." Since Lily has twice as many apples as John, the number of apples she has is "2x." We know that together, they have 27 apples, so we can set up an equation:

x + 2x = 27

Step 3 - Execute the Plan:

Now, we'll solve the equation to find the value of "x."

3x = 27

x = 27 / 3

x = 9

So, John has 9 apples. Now, we can find the number of apples Lily has:

Lily's apples = 2 * 9 = 18

Step 4 - Review the Solution:

John has 9 apples, and Lily has 18 apples. Together, they have 9 + 18 = 27 apples, which matches the information given in the problem. Therefore, the solution is correct.

Answer:

John has 9 apples, and Lily has 18 apples.

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As per coordinate geometry, a) 7.48 meters is the parameter for the path the ladybug flies between the points, including the domain. b) 1.87-meter distance does the ladybug travel per second

This is a problem from coordinate geometry and we can crack it with a few steps. First of all, the required formula to solve it is,

l = √ ( x₁ - x₂ )² + ( y₁ - y₂ )² + ( z₁ - z₂)²

where, x₁, y₁, z₁ is the coordinate of the first point and x₂, y₂, z₂ is the coordinate of the second point and l is the distance between two points.

Here x₁ = 2, y₁ = 7, z₁ = 1

and x₂ = 4, y₂ = 1, z₂ = 5

Now we have to put values in the formula,

l = √ ( 2 - 4 )² + ( 1 - 7 )² + ( 5 - 1 )²

l = √ 2² + 6² + 4²

l = √ 4 + 36 + 16

l = √ 56 = 7.48 meter

So, the ladybug flies 7.48 meters while traveling from point one to point two.

The speed taken to fly along this path is, l/t = S, where S is denoted as speed.

S = 7.48 / 4 = 1.87 meters/ second.

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The answers to all the subparts are:

So,

Given:

(1) An equation to model the situation:

(2) Money in the account after 4 years:

(3) To find how will it be until there is $5000 in the account:

Therefore, the answers to all the subparts are:

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The complete question is given below;
$1500 is put into an account earning 7% annual interest, compounded continuously.

1. Write an equation to model the situation

2. How much money will be in the account after 4 years?

3. How will it be until there is $5000 in the account?

Answer:

The following tables show how many words each person can text in a given amount of time. Compare the rates of texting for each person using the ratio table.

Step-by-step explanation: