question 4 (essay worth 15 points) (06.05, 06.06 hc) students were asked to prove the identity (sec x)(csc x)

Smaller number = 7

Larger number = 14

An algebraic equation can be solved in a variety of ways.

The method you use to solve an equation depends on the type of equation and the information you are given.

Some of the most common methods to solve algebraic equations include using factoring, using the quadratic formula, completing the square, graphing, and using the substitution method.

This question uses the algebraic equation solving technique.

Step 1: Create an equation that relates the two numbers.

Let x = the smaller number

Let y = the larger number

2x + 3y = 86

Step 2: Substitute the given information into the equation.

We know that y = x + 7, so we can substitute that into the equation.

2x + 3(x + 7) = 86

Step 3: Solve the equation.

2x + 3x + 21 = 86

5x + 21 = 86

5x = 65

x = 13

Step 4: Substitute the value for x into the expression for y.

y = x + 7

y = 13 + 7

y = 20

Therefore, the two numbers are 7 and 14.

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The bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to describe the relationship between two quantities, or to express a rate or change in a quantity over time. The symbol for percent is "%".

For example, if a pizza is marked up by 20%, it means the price has increased by 20/100 or 1/5 of the original price. If a student scores 80% on a test, it means they got 80 out of 100 questions correct. If a stock's value increases by 10%, it means the value has gone up by 10/100 or 1/10 of the original value.

The current admission price is $3 + $3 * 50% = $3 + $1.50 = $4.50.

150% of the price 5 years ago is $3 * 150% = $3 * 1.5 = $4.50.

So, the bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.

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Answer:

26

Step-by-step explanation:

32 - 14 + 26 - (81/9)2

Dividing

32 - 14 + 26 - (9)2

Multiplying

32 - 14 + 26 - 18

Adding & Subtracting from left to right

18 + 26 - 18

44 - 18

26

$1.15

Let's call the cost of the bike horn "x".

Dirk paid $5.33 and received $4.18 in change, so he must have paid x + $4.18 = $5.33.

Solving for x, we get x = $5.33 - $4.18 = $1.15.

Therefore, the bike horn cost $1.15.

Answer:

Cayley earned per day: 4 x 5 = 20

: Her earning per week-  3 x 20 = 60

: Her earning for 8 weeks- 8 x 60 = 480

Cayley earns $480 per week.

Answer: 27 28 29

Step-by-step explanation:

Answer:

2290
ignore this--> (I need 20 words to answer the question lol)

Answer:

2290

Step-by-step explanation:

2290*3 gives 6870

Answer:

=> A/Q,

m + 3m + 2m+ 3m 360° =

9m = 360°

m = 360/9

m = 40°

Angle A = m = 40°

Angle B = 3m = 120°

Angle C 2m = 80° =

Angle D = 3m = 120°

The lithosphere is: a. the rigid outer part of the earth, consisting of the crust and upper mantle.

The Lithosphere is the solid outer shell of the Earth that forms the Earth's surface, including the continents and the ocean floor. It is the uppermost layer of the Earth's solid surface, composed mostly of the minerals, such as silicon and oxygen, that form rocks like granite and basalt.

The lithosphere is composed of the Earth's crust and the uppermost part of the Earth's mantle. It is broken up into tectonic plates that are in constant motion and are responsible for the earthquakes, volcanoes, and the creation and destruction of land masses. The lithosphere is also the layer that supports all life on Earth.

Therefore, we can state that the correct description of the lithosphere is: a. the rigid outer part of the earth, consisting of the crust and upper mantle.

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The measure of the angle ∠ABC  is given by 45°

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: ΔABC with AB=√2, AM=1,BM=1 and BC=2

Now in ΔABM we have two sides equal AM=1,BM=1

and AB=√2

Thus AM²+BM²=AB²

Thus the triangle must be a right angled triangle with AB as its hypotenuse

let ∠B=Ф then we have TanФ=1/1

                                         ⇒ Ф=45°

Hence, The measure of the angle ∠ABC  is given by 45°

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If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B that is option E.

In mathematics, digits are single numbers that are used to represent values. In math, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in various combinations and repetitions to represent all of the values. A digit is a symbol that can represent any of the ten numbers from 0 to 9. If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B. A digit can be any of the following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A number is a measurement of something. It can be written with one, two, three, or more digits.

Here,

If a and b are nonzero digits, the number of digits (which does not have to be the same) in the sum of the three whole numbers is determined by the values of A and B that is option E.

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The number of years after 2003 that the car's value will be $11,250 is t = 7.5 years.

In 2003, the price of a certain automobile was approximately with a depreciation of 1,750 per year. After how many years will the cars value be $11,250 A) write an equation to model the problem. Let the represent the number of years after 2003.

A) The equation to model the problem is:

Price in year t = 2003 Price - (t - 1)(1,750)

B) To solve the equation for t, we can rearrange it to isolate t:

t = (2003 Price - 11,250) / 1,750

Therefore, the number of years after 2003 that the car's value will be $11,250 is t = 7.5 years. This means that the car's value will be $11,250 in the year 2010.5.

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Answer:

Sum of two polynomials:
[tex]3x^2 - x - 4[/tex]        Choice C   (read explanation carefully)

Product of the two polynomials:
[tex]2x^4-5x^3-14x^2+30x-12\\\\[/tex]     Choice C   (read explanation carefully)

In both cases, your answer choice copy/paste messed up the formatting. I looked at the coefficients and came up with the choices.

You should compare the actual terms with the choices I have provided to make sure they match

Step-by-step explanation:

The two polynomials are
2x² + 3x - 6

and

x² - 4x + 2

Addition

To add these two polynomials together group like terms and add their coefficients:

(2x² + 3x - 6) + (x² - 4x + 2)

= 2x² + 3x - 6 + x² - 4x + 2

= (2x² + x²) + (3x -4x) + (-6 + 2)

= 3x² - x - 4

Your answer choices have lost formatting during copy paste. You will have to compare and choose the right one. I think it is C because it has a 3x² term and the last term is - 4

Multiplication

[tex]\left(2x^2\:+\:3x\:-\:6\right)\cdot \left(x^2-4x\:+\:2\right)\\\\\\[/tex]
Distribute the parentheses - multiply each term in the second polynomial by each term in the first polynomial and simplify

[tex]\left(2x^2\:+\:3x\:-\:6\right)\cdot \left(x^2-4x\:+\:2\right)\\\\= 2x^2x^2+2x^2\left(-4x\right)+2x^2\cdot \:2+3xx^2+3x\left(-4x\right)+3x\cdot \:2-6x^2-6\left(-4x\right)-6\cdot \:2\\\\= 2x^4-8x^3+4x^2+3x^3-12x^2+6x-6x^2+24x-12\\\\\textrm{Add similar terms}\\=2x^4 +(-8x^3+3x^3)+ (4x^2-12x^2-6x^2) + (6x+24x) -12\\\\[/tex]

[tex]=2x^4-5x^3-14x^2+30x-12\\\\[/tex]    (Answer)

Again your answer choices have lost formatting but my best guess from looking at the coefficients is that it is choice C

Using the concept of change of subject of formula, we can express the radius r₁ and r₂ as r₁ = r₂² / 18π

The formula of volume of a cylinder is given as;

V = πr²h

The equation for the volume of the cylindrical tank is V1 = 36πr₁ and the equation for the volume of the neighborhood pool is V2 = 1/2(4/3πr₂²).

Since V₁ = V₂, we can set the two equations equal to each other and solve for r₁:

36πr₁ = 1/2(4/3πr₂²)

To solve for r₁, we can first multiply both sides of the equation by 2/4/3, which gives:

18πr₁ = r₂²

Then we can divide both sides of the equation by 18π to get:

r₁ = r₂² / 18π

So we can say that r₁ is a function of r₂ because it can be expressed in terms of r₂.

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Answer: ASA postulate

Step-by-step explanation:

There is a congruent side included between two pairs of congruent angles.

Answer:

Your answer is: A) [tex]96cm^{2}[/tex]

Step-by-step explanation:

The area of the rectangle having a length of 12 cm and a width of 8 cm

is 96 cm².

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the area of a rectangle is (length×width).

Given, one side of a rectangle is 8 cm and the other side of the rectangle is 12 cm.

Therefore, The area of this rectangle is,

= (12×8) cm².

= 96 cm².

So, the area of the rectangle is 96 cm².

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Answer:

To solve the equation 9x² = 3³x-2, we can follow these steps:

First, we need to simplify the right side of the equation. 3³ = 27, so we can replace 3³ with 27. The equation now becomes: 9x² = 27x - 2

Next, we'll want to get all the x terms on one side of the equation and all the constants on the other side. To do this, we'll add 2 to both sides of the equation: 9x² = 27x - 2 + 2 = 27x. This gives us: 9x² = 27x

Next, we'll divide both sides of the equation by 9. This will give us x² = 3x.

Finally, we can divide both sides by 3. This will give us x = 1.

So the solution is x = 1

The incorrect code contained two errors. The first was that the variable 'resistance' was initialized with a string value from the prompt, and the second was that the inverse value was not rounded off to two decimal places.

// incorrect code

//

// let resistance = prompt("Enter the resistance: ");

// inverse = 1.0 / resistance;

// console.log("The inverse of resistance is " + inverse);

// correct code

let resistance = parseFloat(prompt("Enter the resistance: "));

let inverse = 1.0 / resistance;

console.log("The inverse of resistance is " + inverse.toFixed(2));

1. In the incorrect code we have a variable 'resistance' that is initialized with a string value from the prompt. To fix this we have used the parseFloat function to convert this string to a float value.

2. In the incorrect code the inverse value is not rounded off to 2 decimal places. To do this we have used the toFixed(2) method to round off the inverse value to 2 decimal places.

The incorrect code contained two errors. The first was that the variable 'resistance' was initialized with a string value from the prompt, and the second was that the inverse value was not rounded off to two decimal places. To fix these errors, the parseFloat function was used to convert the string value of 'resistance' to a float value, and the toFixed(2) method was used to round off the inverse value to two decimal places.

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Step-by-step explanation:

The given system of equations models the scenario where Jason spent all of his money on buying CDs and magazines, and that if he had bought one more CD, he would have run out of money. The system of equations is:

4x + 2y = 32 (Equation 1)

5x + 2y = 36 (Equation 2)

The first equation represents the total amount of money Jason spent on 4 CDs (x dollars each) and 2 magazines (y dollars each). The second equation represents the total amount of money Jason would have spent if he had bought one more CD. By subtracting equation 1 from equation 2, we get:

x = 4 (Equation 3)

This equation tells us that each CD costs $4.

By substituting this value into equation 1, we get:

4(4) + 2y = 32

16 + 2y = 32

2y = 16

y = 8 (Equation 4)

This equation tells us that each magazine costs $8.

So, Jason spent $4 for each CD and $8 for each magazine.

The value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest. The solution is obtained by using the arithmetic operations.

What are arithmetic operations?

In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

We are given first expression as 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex]

The answer for this expression can be a positive or a negative number depending on the fact which of the terms is greater.

The second expression is (-7[tex]\frac{5}{6}[/tex] ) + (- 9[tex]\frac{3}{4}[/tex])

The answer for this expression will be a negative number because addition of two negative numbers is always negative.

The third expression is (-7[tex]\frac{5}{6}[/tex] ) . 9[tex]\frac{3}{4}[/tex]

The answer for this expression will be a negative number because multiplication of one negative number and one positive number is always  negative.

The fourth expression is (-7[tex]\frac{5}{6}[/tex] ) ÷ (- 9[tex]\frac{3}{4}[/tex])

The answer for this expression will be a positive number because division of two negative numbers is always positive. But, dividing two numbers will give us value close to 1 because the numbers 7 and 9 are very close to each other.

Hence, the value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest.

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The solution of the system of equations is:

(-3/2, 1/2)

Here we have two lines of the form:

y = a*x + b

one passes through (0, 0) and (1, -3)

For the first point we know that the constant is 0, and replacing the values of the second point we get:

1 = a*-3

1/-3 = a

The line is:

y = (-1/3)*x

The second line passes through (0, 2) and (-1, 1) from the first point we can see that:

y = a*x + 2

And replacing the values of the second point we get:

1 = a*-1 + 2

1 - 2 = -a

-1 = - a

1 = a

This line is y = x + 2

Then the system of equations is:

y = x + 2

y = (-1/3)*x

We can replace use the substitution method to write:

x + 2 =  (-1/3)*x

x + 1/3*x = -2

(4/3)*x = -2

x = -2*(3/4)

x = -3/2

And the y-value is:

y = -3/2 + 2

y = 1/2

The solution is (-3/2, 1/2)

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If a polynomial can be expressed as a polynomial divided by a polynomial, that function is deemed rational. x is 3, the sole zero in the denominator.

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Each measure in a 4/4 time signature has four quarter note beats; each measure in a ¾ time signature has three quarter note beats; and each measure in a 2/4 time signature has two quarter note beats.

A 4/4 time signature does not imply that each measure contains simply four quarter notes. It signifies that each measure only contains four beats. These beats may comprise half notes, quarter notes, eighth notes, pauses, or whatever the composer desires, but all note and rest values must add up to no more or less than the time signature’s top number (or numerator).

The most popular musical meter is 4/4. Because it is so widespread, it is also known as common time, and the two numerals in the time signature are sometimes substituted with the letter C. The stacking digits in 4/4 indicate that each measure comprises four quarter note beats. To count 4/4 meter, tap the beat every time you tap the beat.

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The area of the rectangle is A = 172.5 m^2

The area of a rectangle can be found by using the formula A = lw, where l is the length and w is the width. In this case, we are given that the length is 8 meters more than twice the width, so we can let l = 2w + 8. We are also given the perimeter, which is the sum of the length and width multiplied by two, or 2l + 2w. We can set this equal to 46 and solve for w:

2(2w + 8) + 2w = 46

4w + 16 = 46

4w = 30

w = 7.5

Therefore, the width of the rectangle is 7.5 meters and the length is 2(7.5) + 8 = 23 meters. The area of the rectangle can then be found by substituting these values into the area formula:

A = lw

A = (23)(7.5)

A = 172.5 m^2

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The starting pay was $ 168.6 and has climbed by $ 3,000 annually since 2008 at a consistent rate.

Since it is a percent increase, they will receive a 2% salary raise in year two, which will amount to $30,000. As a result, it would be 1.2, and we'll now try to identify a pattern. We know that the pay will be 30,000 because of the 2% increase because the power in this situation is one and the salary is in the eleventh year.

At this moment, I would have accepted ten times the 2% rise. During the first year, it would not have occurred. If you want to proceed, divide it by one less than 1.2 to get the temperature. After we calculate it, we'll receive a value for their entire compensation for the next 10 years.

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Answer:

she is 0 blocks away from home because you said she started at home

Answer:

a) Malavika is 8 blocks west from home

b) Traveled 20 blocks total

Step-by-step explanation:

a) According to a compass: 3 west (left), then 6 east (right) and that puts you at 3 east (right). Then back 11 west (left) puts you at 8 west (left)

b) Add up all blocks traveled: 3 + 6 + 11 = 20

For equation 1, substitution x=4tanθ is the most helpful. For 2, substitution x=4sinθ is the most helpful. For 3, substitution x=4secθ is the most helpful. For 4, substitution x=4sinθ is the most helpful. For 5, substitution x=4tanθ is the most helpful.

Substitutions are often used to simplify indefinite integrals. For example, in the first integral ∫√(x^2-16) dx, substitution x=4tanθ is the most helpful. This is because it will allow us to simplify the expression under the radical. After substituting, we have ∫√(16tan^2θ-16) dθ. The 16tan^2θ can be factored to give 16(tan^2θ-1), which is equal to 16sec^2θ-16. This simplifies the integral, making it easier to integrate. In a similar way, substitution can also be used to simplify the other integrals. For example, for the fourth integral ∫(x^2 – 16)^(5/2) dx, substitution x=4sinθ is the most helpful. After substituting, we have ∫(16sin^2θ-16)^(5/2) dθ. This simplifies the integral, making it easier to integrate. In general, the substitutions chosen for each integral should be the ones that simplify the expression the most, allowing for easier integration.

1. A. x = 4tanθ

2. B. x = 4sinθ

3. C. x = 4secθ

4. B. x = 4sinθ

5. A. x = 4tanθ

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