Does Sarah’s argument make sense

The third side of the right angle triangle is 4√3 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles of a right triangle is 180 degrees.

Therefore, the sides of a right triangle can be found using Pythagoras's theorem.

Hence,

c² = a² + b²

where

The hypotenuse side is the longest side of a right triangle.

Therefore,

8² - 4² = b²

64 - 16 = b²

b² = 48

b = √48

b = √16 × 3

b = 4√3 units

Therefore,

third side =  4√3 units

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The function that represent the total number of gold pieces as a function of the number of magical broom is g = 50 + 125x.

Bob the Wizard makes magical brooms. He charges 125 gold pieces for each magical broom he makes for his customers.

He also charges a one-time fee of 50 gold pieces for his initial consultation.  

The total number g of gold pieces Bob charges as a function of x, the number of magical broom he makes can be represented as a function as follows;

Therefore.

x = number of magical brooms

g = total number of gold pieces.

Hence, the function is as follows:

g = 50 + 125x

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Answer:

The answer is G=125x+50.

Step-by-step explanation:

Answer:B

Step-by-step explanation: i got it right

She saved 324 number of 20p coins altogether.

And, Halley need 176 more 20p coins to saved £100.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Halley saves up twenty-pence coins.

And, At the last count she had saved £64.80.

Now,

We know that;

Number of 20p coins in £1 = 5

So, Number of 20p coins in £64.80 = 5 × 64.80

                                                       = 324

And, Number of 20p coins in £100 = 5 × 100

                                                      = 500

So, He need number of 20p coins = 500 - 324

                                                      = 176

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Step-by-step explanation:

6x + 2y = 10

2y = -6x + 10

y=-6/2x +10/2

y= -3x + 5

x + 2y = 4

2y = -x + 4

y= -1/2x + 4/2

y=-1/2x +2

The probability that the next coin flip will yield a head is 50%, as each coin flip has an equal chance of landing either heads or tails.

Probability is an incredibly important concept to understand in our everyday lives. Understanding probability helps us make informed decisions about the chances of something happening. For example, when playing a game of chance, understanding probabilities can give us a better idea of the likelihood of winning or losing. Knowing the probability of an event happening can also help us make decisions in other areas of life, such as investing.

In the context of coin flipping, it is important to remember that the probability of a coin landing on heads or tails is always 50%. This means that no matter how many times the coin is flipped and no matter what the previous outcome, the probability of the next flip being heads or tails remains the same. This concept is the basis of probability theory, which can be applied to many other areas of life.

Understanding probabilities is also useful in understanding the chances of certain events occurring in the world. For example, understanding the probability of an earthquake happening in a certain area can help us make decisions about where to live or how to prepare for a potential disaster. Similarly, understanding the probability of a successful business venture can help us decide whether or not to invest in it.

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The limit is evaluated by using the series expansion of 1 - cos(2x) and 1 + 2x - e^2x. The series expansion of 1 - cos(2x) is 2x^2 - (2/3)x^4 + (1/5)x^6 - (1/42)x^8 + ... and the series expansion of 1 + 2x - e^2x is 2x - (2/3)x^3 + (2/5)x^5 - (4/21)x^7 + ... Therefore, the limit of both series is 0 as x approaches 0.

The limit of 1 - cos(2x) as x approaches 0 is calculated by taking the series expansion of 1 - cos(2x), which is

2x^2 - (2/3)x^4 + (1/5)x^6 - (1/42)x^8 + ...

When x is 0, all terms in the series are 0, so the limit is 0. Similarly, the limit of 1 + 2x - e^2x as x approaches 0 is calculated by taking the series expansion of 1 + 2x - e^2x, which is

2x - (2/3)x^3 + (2/5)x^5 - (4/21)x^7 + ....

When x is 0, all terms in the series are 0, so the limit is also 0.

The limit of 1 - cos(2x) as x approaches 0 is also calculated numerically. When x is

0.0001, 1 - cos(2x) is 0.000399980.

When x is 0.00001, 1 - cos(2x) is 0.0000039998.

As x becomes closer to 0, the value of 1 - cos(2x) approaches 0. The same is true for

1 + 2x - e^2x.

When x is 0.0001, 1 + 2x - e^2x is 0.000399980.

When x is 0.00001, 1 + 2x - e^2x is 0.0000039998.

As x becomes closer to 0, the value of

1 + 2x - e^2x also approaches 0.

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An amount of 150.478 kilojoules of thermal energy are needed to heat a quart of water from 30 °C to 68 °C.

In this problem we have the case of a quart of water being heated from 30 °C to 68 °C, the heating process does not involve any phase change, that is, the process is entirely sensible. The thermal energy required (Q), in kilojoules, is described by the following formula:

Q = m · c · (T' - T)

Where:

Please notice that a quart of water has 0.946 kilograms of water. If we know that m = 0.946 kg, c = 4.186 kJ / (kg · °C), T = 30 °C and T' = 68 °C, then the thermal energy needed is:

Q = (0.946 kg) · [4.186 kJ / (kg · °C)] · (68 °C - 30 °C)

Q = 150.478 kJ

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Answer:

5/3

Step-by-step explanation:

The formula of finding slopes are:

Change in y over change in x, which is:

(10 - 5) / (4 - 1)

= 5/3

To prove that angle 1 is supplementary to angle 3, we must demonstrate that the two angles add up to 180 degrees.

Angle is a term used to describe the shape formed when two straight lines cross or intersect. It is measured in degrees, and is typically represented by the symbol ∠. Angles are important in geometry, architecture, engineering and construction. They are also used in navigation and astronomy. Angles are a fundamental part of understanding the physical world around us.

Since line m is parallel to line n, then the two lines are essentially parallel lines, meaning that all of the angles made with the lines are the same. In this case, the angles made with line m and line n are both 90 degrees. Since the two angles are the same, then that means that angle 1 and angle 3 are also the same.

Since angle 1 and angle 3 are the same, then that means that the two angles add up to 180 degrees. Therefore, angle 1 is supplementary to angle 3.

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Answer:

no

Step-by-step explanation:

the greatest power is not 2 it is 3

Answer:

0.56

Step-by-step explanation:  

24/43 as decimal is approximately: 0.55814 (Rounded to fifth decimal place)

B) a translation 10 units down followed by a translation 8 units to the right.

As in rotation, reflection and translation the transformed image is congruent to the original figure(i.e all the points undergo same change), so analyzing any one point will give the series of transformation undertaken.

Taking point A(-6, 4) into consideration.

Translating a point (x, y) k units down, it becomes (x, y-k).

So translated 10 units down point A, it becomes (-6, -6).

Translating a point (x, y) k units right, it becomes (x+k, y)

So translated 8 units right point (-6, -6), it becomes (2, -6)

This is the coordinates for A'.

Therefore, quadrilateral ABCD underwent a translation 10 units down followed by a translation 8 units to the right.

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The standard form of the quadratic inequality represented by the description is; y <  -2x² + 160x - 2400

An inequality with a quadratic expression is referred to as a quadratic inequality.

It is of the form y = ax² + bx + c (or substitute <,≥ or ≤ for > ) represents a region of the plane that a parabola encircles.

Let's assume that the equation is y = a(x - h)² + k

Where (h, k) is the coordinate of the vertex. Thus;

y = a(x - 40)² + 800

Put the point (60, 0) in the equation

0 = a(60 - 40)² + 800

0 = a(20)² + 800

-800 = 400a

a = -800/400

a = -2

Thus, the equation is;

y = -2(x - 40)² + 800

The inequality is a dashed line and shaded below the parabola and is;

y <  -2(x - 40)² + 800

= y <  -2(x² - 80x + 1600) + 800

y <  -2x² + 160x - 3200 + 800

y <  -2x² + 160x - 2400

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An equation of the line that passes through the point (6,3) and is parallel to the line x+3y=24 is x+3y=33.

To calculate this equation, we must first consider the parameters of the line x+3y=24. This equation can be rearranged to solve for y, which gives us y=8-1/3x.

Now, we need to find the slope of the line, which we can calculate using the two points (6,3) and (8,0). Using the slope formula (rise/run), we calculate the slope as m=(3-0)/(6-8) = -3/2. We now know that the slope of the line is -3/2.

Next, we need to use the point-slope formula (y-y1=m(x-x1)) to calculate the equation for the line that passes through (6,3) and has a slope of -3/2. Plugging in the values, we get y-3=-3/2(x-6). Simplifying, we get 2y=-3x+33. Rearranging gives us x+3y=33.

Therefore, the equation of the line that passes through the point (6,3) and is parallel to the line x+3y=24 is x+3y=33.

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An equation of the line that passes through the point (6, 3) and is parallel to the line x + 3y = 24 is y = -1/3 x + 5

In this question we have been given an equation of line x + 3y = 24

We need to find an equation of the line that passes through the point (6, 3) and is parallel to the given line x + 3y = 24

Let m1 be tha slope of the required line and m2 be the slope of line x + 3y = 24

We write  equation of line x + 3y = 24 in slope-intercept form.

x + 3y = 24

3y = 24 - x

y = (24 - x)/3

y = 8 - x/3

y = -1/3 x + 8

so, m2 = -1/3

We know that the slopes of parallel lines are equal.

So, m1 = m2

m1 = -1/3

i.e.,, the slope of the required line is -1/3

We know that the point - slope form of equation of line is:

(y - y1) = m(x - x1)

Let (x1, y1) = (6, 3)

Substituting values in above equation,

(y - 3) = -1/3(x - 6)

y - 3 = -1/3x + 1/3 (6)

y - 3 = -1/3 x + 2

y = -1/3 x + 2 + 3

y = -1/3 x + 5

Therefore, equation of the required line is y = -1/3 x + 5

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Answer: 1/5

Step-by-step explanation:

7/10 - w = 1/2

7/10 - w = 5/10

7-5 = 2

2/10 = 1/5

Answer w=.2

Explanation: −w+7/10=1/2

−

Answer: Greatest common factor is x.

Step-by-step explanation:

([tex]x^2[/tex]) (4x)

Both terms share x.  x is the Greatest Common factor, and the only factor in this manner.

If you were to simplify and take out the x, you would have:

x  (x)*(4)

Based on the sequence formula, the number of cubes in the 5th pattern is 9

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

Number of cubes in the nth pattern = 2n - 1

Also from the question, we have the pattern to be the 5th pattern

This means that n = 5

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

Number of cubes in the 5th pattern = 2 * 5 - 1

Evaluate the product

Number of cubes in the 5th pattern = 10 - 1

Evaluate the difference

Number of cubes in the 5th pattern = 9

Hence, the number of cubes is 9

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Complete question

a pattern using cubes is shown to the right. the number of cubes at a particular place in the pattern can be calculated using the expression. 2n-1 the variable n represents the place in the pattern

How many cubes are in the 5th pattern

Can drive cannot drive row totals Likes to fly 0.60 / 0.55 = 1.09 0.09 Do not like to fly 0.18 / 0.45 = 0.40 0.40 Column totals 0.55 0.45 1.00

1. Calculate the relative frequency of those who like to fly and can drive by dividing the frequency of those who like to fly and can drive (0.60) by the total frequency of those who can drive (0.55).

0.60 / 0.55 = 1.09

2. Calculate the relative frequency of those who like to fly and cannot drive by dividing the frequency of those who like to fly and cannot drive (0.18) by the total frequency of those who cannot drive (0.45).

0.18 / 0.45 = 0.40

3. Enter the relative frequencies into the table.

Can drive cannot drive row totals Likes to fly 1.09 0.09 Do not like to fly 0.40 0.40 Column totals 0.55 0.45 1.00

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Students do not likes to fly, can drive is 0.13. Therefore, the completed  relative frequency table is given below.

In the given question, on a recent survey, students were asked if they like to fly and if they can drive.

We have to complete the relative frequency table, showing all necessary calculations.

From the table

Likes to fly

Row totals = Can drive + Cannot drive

0.32 + Cannot drive = 0.70

Subtract 0.32 on both side, we get

Cannot drive = 0.38

Can drive:

Column totals = Likes to fly + Do not likes to fly

0.32 + Do not likes to fly = 0.45

Subtract 0.32 on both side, we get

Do not likes to fly = 0.13

Cannot drive:

Column totals = Likes to fly + Do not likes to fly

0.38 + Do not likes to fly =0.55

Subtract 0.38 on both side, we get

Do not likes to fly = 0.55-0.38

Do not likes to fly = 0.17

Row totals = 0.13 + 0.17

Row totals = 30

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The complete question is:

On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.

Complete the relative frequency table, showing all necessary calculations.

                              Can drive              cannot drive              row totals

likes to fly                 0.32                                                           0.70

do not like to fly  

column totals           0.45                          0.55                          1.00

You use Descartes's rule of signs to find complex roots by locating the polynomials.

Descartes' rule of signs is a useful tool for finding complex roots of polynomial equations. This technique can help you identify the possible number of positive, negative, and imaginary roots of a given polynomial equation.

To use the rule of signs, first you must identify the polynomial's leading coefficient, degree, and number of sign changes in the coefficients. The leading coefficient indicates the highest degree of the polynomial, and the degree indicates the number of roots the equation has.

Finally, the number of sign changes in the coefficients is used to determine the number of positive, negative, and imaginary roots the equation has. With these values, you can determine the number of complex roots the equation has by applying Descartes' rule of signs.

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If you know the value of x, you can substitute it into the equation and get the perimeter of the larger triangle.

What is the equilateral triangle?

An equilateral triangle is a type of triangle in which all three sides have the same length. The three angles in an equilateral triangle are also congruent and measure 60 degrees each. This means that all the angles in an equilateral triangle are always equal to 60 degrees. An equilateral triangle can also be referred to as an equiangular triangle.

The diagram shows two proportional right triangles, with triangle ABC and triangle DEF.

We know that AB = 6, AC = 10, and BC = 8 for triangle ABC, and EF = 16 for triangle DEF.

Since the two triangles are similar and proportional, the ratio of the corresponding sides is the same for both triangles.

We know that AB/EF = AC/EC = BC/DE

Since we know that AB = 6 and EF = 16, we can calculate the value of DE (the length of the hypotenuse of the larger triangle) using the proportion:

6/DE = 16/x

We can solve for DE by multiplying both sides by x:

DE = 16 * 6 / x

Now we can calculate the perimeter of the larger triangle by adding the lengths of all three sides:

Perimeter = DE + DE + 16 = (16 * 6 / x) + (16 * 6 / x) + 16

However, if you know the value of x, you can substitute it into the equation and get the perimeter of the larger triangle.

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Answer:

m = -1/2

Step-by-step explanation:

Slope can be calculated using the following formula

slope(m) = (y2 - y1) / (x2 - x1)

Where the values of x and y derive from points (x1,y1) and (x2,y2) which can be found in the table.

Here the values of x and y may vary depending on the chosen points however I have chosen (-4,3) and (-2,2)

If we use these points then (x1,y1) = (-4,3) and (x2,y2) = (-2,2)

So, x1 = -4, y1 = 3, x2 = -2 and y2 = 2

We now plug these values into the formula

m = (y2 - y1) / (x2 - x1)

plug in x1 = -4, y1 = 3, x2 = -2 and y2 = 2

m = (2-3) / (-2-(-4)

==> simplify parenthesis

m = -1/2

No further simplification can be done so m = -1/2 is the final answer

Answer:

2 obv

Step-by-step explanation:

slope of -4 and 3 is 2

because -xcoefficient/ycoefficient

and the - × - becomes +

so it will be 4/2 and the answer is 2

U rnt supposed to be cheating on a test but hope this helps. Its 2500.

Answer:

Below

Step-by-step explanation:

.014 g / .0022 cm^3   = 6.364  gm / cc   = 6364 kg/m^3

    density is too low to be pure gold  

An equation of the line that passes through the point (1,7) and perpendicular to the line x+6y=42 is y = 6x + 1

In this question we have been given an equation of line x + 6y = 42

We need to find an equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y = 42

Let m be tha slope of the required line.

We write  equation of line x + 6y = 42 in slope-intercept form.

y = (42 - x)/7

y = 6 - x/6

y = -1/6 x + 6

Let m1 be the slope of line x + 6y = 42

m1 = -1/6

We know that the product of slopes of perpendicular lines is -1.

So, m * m1 = -1

m * (-1/6) = -1

m = (-1) * (-6)

m = 6

So, the slope of the required line is 6

We know that the point - slope form of equation of line is:

(y - y1) = m(x - x1)

Let (x1, y1) = (1, 7)

Substituting values in above equation,

(y - 7) = 6(x - 1)

y - 7 = 6x - 6

y = 6x - 6 + 7

y = 6x + 1

Therefore, equation of the required line is y = 6x + 1

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The equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42 is y = -6x - 5.

The equation of a line that passes through the given point (1,7) and is perpendicular to the line x+6y=42 can be determined by using the slope-intercept form of the equation of a line.

The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope of the line, and b is the y-intercept.

First, we need to determine the slope of the line x+6y=42. To determine the slope, we can solve for y by subtracting x from both sides of the equation, yielding 6y = -x + 42. Then, we can divide both sides of the equation by 6 to obtain y = -x/6 + 7. Thus, the slope of the line x+6y=42 is -x/6.

Now, the slope of a line perpendicular to the line x+6y=42 is the negative reciprocal of the slope of x+6y=42, which is 6/-x.

The equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42 can then be determined using the point-slope form of the equation of a line, which is given by y - y1 = m(x - x1). Substituting the coordinates of the point (1,7) and the slope 6/-x, we obtain

y - 7 = 6/(-x)(x - 1)

Simplifying, we obtain

y = -6x - 5

Thus, the equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42 is y = -6x - 5.

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We have been given the expression 2^5/8=2^2  was used to simplify this expression. 2 to the fifth power, over 8 = 22.

8 can be rewritten as 2^3

Hence, the given expression becomes

2^5/2^3=2^2

After subtracting the exponents on left hand side of the equation we get:

2^2=2^2

we can do it by simplifying 8 to 2^3 to make both powers base two, and subtracting the exponents.

Linear expressions or equations are expressions in which the highest power of the variable is one.

Quadratic expressions or equations are expressions in which the highest power of the variable is two.

Cubic expressions or equations are expressions in which the highest power of the variable is three.

Quartic expressions or equations are expressions in which the highest power of the variable is four.

From the expression, 5x + 2 given,

the highest power of x is one. So it is a linear expression.

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The result is 4

A number's exponent indicates how many times the number has been multiplied by itself. Example: Since 2 is multiplied by itself 4 times, 2222 can be expressed as 24. Here, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base." Generally speaking, xn denotes that x has been multiplied by itself n times.

The quotient of powers property states that if you have an expression in the form (a^m)/(a^n) where 'a' is the base and 'm' and 'n' are integers, it can be simplified to (a^(m-n)).

In the given expression, 2 to the fifth power (2^5) can be divided by 8 (which is equal to 2^3), using the quotient of powers property. The result is 2^(5-3) = 2^2 = 4

So 2^5 / 8 = 4

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Six factorial (6!) is equal to six multiplied by five multiplied by four multiplied by three multiplied by two multiplied by one, divided by three multiplied by two multiplied by one expression  (3 × 2 × 1).

6! (6-3)!

= 6 × 5 × 4 × 3 × 2 × 1 / 3 × 2 × 1

= 6 × 5 × 4 / 3 × 2 × 1

= 120 / 6

= 20

6! (6-3)! is a mathematical expression that can be simplified by breaking it down into two parts. The first part is 6! which stands for 6 factorial and is equal to 6 multiplied by 5 multiplied by 4 multiplied by 3 multiplied by 2 multiplied by 1. The second part is (6-3)! which stands for (6 minus 3) factorial and is equal to 3 multiplied by 2 multiplied by 1. When these two parts are combined, the expression can be simplified to 6 × 5 × 4 divided by 3 × 2 × 1, which equals 120 divided by 6, which is equal to 20.

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The length of the curve y (x) = ₁∫ˣ √(t³ − 1) dt , 4 ≤ x ≤ 9, is 211/4.

In calculus, arc length of curve is the distance between two points along a portion of the curve. Finding the length of an irregular arc segment by approximating the arc segments as connected (straight) line segments is also known as the integral variation of the curve-corrected distance formula. Arc length formula is

ₐ∫ᵇ√[ 1 + (dy/dx)²] dx --(*)

Where, x is the arc length,

We have calculate the length of curve means the length of arc of curve.

Now, y = y (x) = ₁∫ˣ √(t³ − 1) dt

differentiate both sides with respect to x

=> dy/dx= d/dx( ₁∫ˣ√(t³ − 1 ) dt)

Using the fundamental theorem of calculus,

=> dy/dx = dy/dt × dt/dx

let t = x => dt/dx = 1

dy/dt = √x³ - 1 ( from leibnitz rule )

dy/dx = √x³ - 1

Required length of curve = ₄∫⁹√[ 1 + (√x³ - 1)²] dx

= ₄∫⁹√[ 1 + x³ - 1] dx

= ₄∫⁹√x³ dx

[tex] = ₄∫⁹{x}^{ \frac{3}{2} } dx[/tex]

[tex] = \frac{2}{5} ( {9}^{ \frac{5}{2} } - {4}^{ \frac{5}{2} } )[/tex]

[tex]= 211/4[/tex]

So, the required length is 211/4.

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Complete question:

Find out length of the curve

y (x) = ₁∫ˣ √(t³ − 1) dt , 4 ≤ x ≤ 9.

102,566,767, 1,9044828e-10, and 297,060 are the answers to the questions.

The questions above use addition and multiplication to solve the problem.

101,455,348 + 1,111,419 = 102,566,767

0.000000612 x 0.00031119 = 1,9044828e-10

297,060 + 0.0004839 = 297,060

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