In which section of the number line is √13?

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 interval over which the function is continuous equation is (-∞, 3) U (3, +∞).

The function f(x) = (x2 - 5x - 6)/(x - 3) is continuous over all real numbers except x = 3, since the denominator is equal to 0 at x = 3.

We can use the properties of combinations of continuous functions to determine the interval(s) over which the function f(x) is continuous equation.

First, we need to consider the function f(x) in two parts. The first part is f(x) when x ≠ 3, and the second part is when x = 3.

For the first part, when x ≠ 3, the function f(x) is continuous over all real numbers, since both the numerator and denominator are continuous over all real numbers.

For the second part, when x = 3, the function f(x) is discontinuous, since the denominator is equal to 0.

Therefore, the interval over which the function f(x) is continuous is (-∞, 3) U (3, +∞).

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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:

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

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 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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$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:

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

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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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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The total distance traveled by the particle over 5 units of time is 140 units.

What is the total distance?

To find the total distance a particle travels over a certain time interval, we need to find the definite integral of its velocity function over that interval. The velocity function is the derivative of the position function.

In this case, the position function of the particle is x(t) = t³ - 6t + 9t - 2 and we need to find the total distance traveled by the particle over 5 units of time.

The velocity function is x'(t) = 3t² - 6 + 9 = 3t² + 3

The total distance traveled over 5 units of time is the definite integral of the velocity function evaluated between 0 and 5.

∫(3t²+3) dt from 0 to 5

= [t³ + 3t] from 0 to 5

= (5³ + 3*5) - (0 + 0) = 125 + 15 = 140

The total distance traveled by the particle over 5 units of time is 140 units.

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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 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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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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Answer: ASA postulate

Step-by-step explanation:

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

The general statement for the previous question is that if a homogeneous system of equations has at least one non-zero solution, then it has infinitely many solutions, which can be found by taking multiples of the non-zero solution.

(a) (i)

Let p = (1,3,4) and q = (5,8,12) be two points in R3. The line joining p and q can be written as lq + (1-\p) where l is a real number. By substituting in the coordinates of p and q, we get l(5,8,12) + (1-\1,3,4) = (l + 1-\, l+3-\, l+4-\). This is the equation for the line joining p and q, where l can be any real number.

(ii)

To check that all points on the line joining p and q are also solutions to the system of linear equations, we substitute the equation of the line into the system of equations.

01111 + 212.22 + 213.43 = 21

(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 21

Simplifying, this gives: l + 6 - \ = 21. Therefore, all points on the line joining p and q are solutions to the system.

(b)

To check that any multiple of p, i.e., a vector of the form (1,3,4) where is any real number, is also a solution of the system, we substitute the equation of the multiple of p into the system.

01111 + 212.22 + 213.23 = 0

(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 0

Simplifying, this gives: l + 6 - \ = 0. Therefore, all multiples of p are solutions to the system.

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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

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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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:

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

Answer:

2290

Step-by-step explanation:

2290*3 gives 6870

Answer:

-2

Step-by-step explanation:

y = −2− x 2 y = - 2 - x 2

Answer:

[tex]24x^{2}y^2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)!}\\\end{minipage}}[/tex]

We can use the Binomial Theorem to find any term of a binomial expansion.  

The first term is when k = 0, so the third term is when k = 2.

Compare the given expression (x + 2y)⁴ with the formula to find the values of a, b and n.  

Therefore:

Substitute the values into the formula to find the third term:

[tex]\implies \displaystyle\binom{4}{2}x^{4-2}(2y)^2[/tex]

[tex]\implies \dfrac{4!}{2!(4-2)!}x^{2}2^2y^2[/tex]

[tex]\implies \dfrac{4 \times 3\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}{2\times 1\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}\;x^{2}4y^2[/tex]

[tex]\implies \dfrac{12}{2}\:x^24y^2[/tex]

[tex]\implies 6x^{2}4y^2[/tex]

[tex]\implies 24x^{2}y^2[/tex]

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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An inequality which represents the value of t for which the water temperature is still safe is t ≤ 2 and it has been plotted in the graph attached below.

In order to write, solve, and graph an inequality that represents the value of t for which the water temperature is still safe, we would take note of the following important information;

Now, we can write an inequality that represents the value of t for which the water temperature is still safe as follows;

102 + t ≤ 104

By subtracting 102 from both sides of the inequality, we have the following:

102 - 102 + t ≤ 104 - 102

t ≤ 2

Next, we would use an online graphing calculator to graph the above inequality as shown in the image attached below.

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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: 27 28 29

Step-by-step explanation:

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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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 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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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°