Help with special right triangles rounding

In the Logarithm prompt above, note that the value of In x when In x = e to the power -x is x = 1/e.

The above assertion is right because the definition of the natural logarithm denoted as In x or ln x, is that it is the inverse function of the exponential function, denoted as e to the power x or ex.

This means that if we have an equation of the form In x = ex, then we can find the value of x by simply taking the inverse of both sides of the equation.

So, if we take the inverse of both sides of the equation In x = ex, we get x = In (ex) = In e to the power x = 1/e.

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Answer: She can buy a total of 33 packets and have 25 cents leftover.

Step-by-step explanation:

Answer:

she will have $1 left

Step-by-step explanation:

265÷8=33.125 or 33 1/8

she will have $1 left

Answer:

Step-by-step explanation:

7.89 is about 8 so we can multiply 215*8 to get 1720 dollars

Answer:

$1696.35

Step-by-step explanation:

$7.89 × 215 = $1696.35

Answer:

in the 50th cube I think it's 250, because your just adding 5 each time, and for the cube equal to 156 that is uh I don't really know, try the 50th one, because 5x50 is 155

Step-by-step explanation:

I am so sorry if I'm wrong.

To make expressions in mathematics we must set a variable value that varies according to the conditions of our problem.

Let's define what a mathematical expression is:

Algebraic expressions are expressions composed of numbers and letters, where the letters are called variables and each of them adopts a specific value according to the process in which it is used.

To make an expression in mathematics you must set a variable, since an expression is a numerical solution of a process, and by having a variable we will have the result on it, for example:

I have a business and every day I earn 2 times more than the previous day:

expression:

x = 2n

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The average of all values is mean and the middle of all values is the median.

Mean is the average taken of the all the values in the data. It is calculated by -

x = (x1+x2+x3+...+xn)/n = ∑ [tex]\frac{Xn}{n}[/tex]

i.e. the sum of all data values divided by the number of data values.

It is used in situations when we need to get an idea of the data.

For ex - the mean of data values 1,2,3,4,5 is given by -

(1+2+3+4+5)/5 = 3.

The median is the middle of the data values. It is calculated differently for both odd and even no. of observations.

For example, the median of 1,2,3,4,5 is 3 as it is the value in the middle.

So, the average of observations is mean and their middle value is median.

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No, AAS ( Angle , Angle , Side) congruence postulate is not same as ASA (Angle, Side, Angle) congruence postulate, because in AAS consists one equal side between both triangles either it PR = AC or PQ = AB . But ASA must include side equality in this case i.e BC = QR and both are not same.

Two triangles are said to be congruent if they have all three same angles as well as same sides. AAS and ASA are basic methods through which we can prove that two triangles are congruent. So, to check that wheather both methods are same we will take one example of two triangles. So, consider two triangles, ∆ABC and ∆PQR as seen above in figure, ∠ ABC = ∠ PQR = 40° and ∠ACB = ∠ PRQ = 80° and AC = QR

According to AAS rule, if two pairs of corresponding angles with opposite or non- including side is same and the equality in opposite sides are equal to each other then the triangles are congruent. We have ,

∠ PRQ = ∠ ACB , ∠ABC = ∠PQR

and either PR = AC or PQ = AB.

if the above three conditions are satisfied then ∆ABC congruent to ∆PQR.

According to ASA rule , if two angles of one triangle with one side contained between two angles are respectively equal to two angles of another triangle and one side contained between them , then triangles are congruent. We have, ∠ R =∠C , ∠B = ∠Q and BC = QR

if the above three conditions are satisfied then both triangles are congruent. As we see clearly both congruence postulates are not same.

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According to this graph of supply and demand schedules, the current cost of the good is:

A demand schedule in economics is a table that displays the quantity demanded of an item or service at various price points. On a graph where the X-axis is quantity and the Y-axis is price, a demand schedule can be represented as a continuous demand curve.

A demand schedule, also known as a tabular representation or statement, displays the various quantities of goods that are wanted at various price points throughout a given time period. The precise quantity of goods and services that will be purchased at each price will be shown on a demand schedule.

The complete question is : Which statement best describes the current price for the good shown in this graph of supply and demand schedules? A. The current price should be raised to reflect lower supply. B. The current price reflects the point where supply and demand are balanced. C. The current price should be lowered to reflect higher supply. D. The current price should be lowered to reflect lower demand.​

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The two steps for calculating the mean:

Add up all the values in the data set.

Divide this number by the number of values.

The mean of a dataset is the sum of all values divided by the total number of values. It’s the most commonly used measure of central tendency and is often referred to as the “average.”

There are two steps for calculating the mean [tex](\bar{x})[/tex]:

(1) Add up all the values in the data set.

Sum of all the observations of given data denoted by [tex]\sum x[/tex]

(2) Divide this number by the number of values.

The total number of values of given data denoted by 'n'

Sample mean:

[tex]$$\overline{x}= \frac{\sum x}{n} $$[/tex]

Example: Find the mean step by step?

42, 13, 31, 87, 24, 58, 76, 69

Solution:

Step 1: Find the sum of the values by adding them all up.

[tex]\sum x=[/tex] 42 + 13 + 31 + 87 + 24 + 58 + 76 + 69 = 400

Step 2: Divide the sum by the number of values

In the formula, n is the number of values in your data set. Our data set has 8 values.

[tex]$$\overline{x}= \frac{\sum x}{n} $$[/tex]

[tex]$$\overline{x}=\frac{400}{8}[/tex]

[tex]$$\overline{x}[/tex] = 50

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Answer: okay so you add all of the numbers in the data set and then divide by how many numbers there were in the set.

Step-by-step explanation:

Answer:-21788

Step-by-step explanation:

Children who are eight years old frequently count up to 1,000 and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

In order to calculate the size of a set, or the number of items in a finite set, one must count. Calculating the amount or total number of items in a collection or group is what is meant when we say we are counting in arithmetic. To count, then, is to speak numbers in sequence while giving each item in a group a value based on a one-to-one correlation. Objects are counted using counting numbers.

Children who are eight  years old frequently count up to 1,000 and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

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the area of 4 cm circle is 12.568 cm² whose radius is 2 cm

the round shaped figure having a fixed center and specific diameter is called circle.

area of a circle having known radius is calculated by the formula

A =πr²

r is the radius of circle

in the above question 4cm circle refer the diameter of circle is 4cm

so, radius is r= 2 cm

Area = 3.142x2²

12.568 square cm

hence, area is 12.568 square centimeters.

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Answer:

i just want the points

Step-by-step explanation:

Answer:

[tex]10.5\%[/tex]

Step-by-step explanation:

[tex]\% \: error = \frac{absolute \: error}{actual \: value} \times 100[/tex]

actual value = 38ml, measurement error = 42ml

absolute error = actual value - measurement error (where actual value > measurement error) OR measurement error - actual value (where actual value < measurement error)

(Note: absolute error is different from measurement error. Absolute error is the distance between the actual value and the measurement error, while measurement error is the error made in measurement).

Therefore, absolute error = 42 - 38 = 4

[tex]\% \: error = \frac{4}{38} \times 100[/tex]

[tex]\% \: error = 10.52[/tex]

Therefore: % error = 10.5 (to the nearest tenth)

Answer: 34cm

Step-by-step explanation:

4cm + 3cm = 7cm

9cm - 7cm = 2cm

The missing value is 2cm

Leading the perimeter to be 34cm

The exact length of the curve is  7.995.

The function  [tex]y=2+8x^{\frac{3}{2} }[/tex]   is given.

0 ≤ x ≤ 1

Differentiating given function with respect to x.

[tex]\frac{dy}{dx}= \frac{d}{dx}2+8x^{\frac{3}{2} }[/tex]

[tex]\frac{dy}{dx}= 12x^{\frac{1}{2} }[/tex]

Length of arc, L = [tex]\int\limits^a_b {\sqrt{1+(\frac{dy}{dx} )^{2} } } \, dx[/tex]

Putting the values,

L = [tex]\int\limits^1_0 {\sqrt{1+144x } } \, dx[/tex]

Let 1 + 144x = z

         144dx = dz

When we plug in "z" and "dz" values to the equation above, we get:

L = [tex]\int\limits^1_0\frac{z^{1/2} }{144} \, dx[/tex]

  = [tex][\frac{z^{3/2} }{144(3/2)} ]^{1} _{0}[/tex]

 = [tex]\frac{1}{216}[z^{3/2} ]^{144} _{1}[/tex]

 = [tex]\frac{1}{216}[144^{3/2}-1^{3/2} ][/tex]

 = [tex]\frac{1}{216}[1728-1][/tex]

 = 1727/216

 = 7.995

Hence, the exact length of the curve is  7.995.

Correct Question :

Find the exact length of the curve,   [tex]y=2+8x^{\frac{3}{2} }[/tex], 0 ≤ x ≤ 1.

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the value of the discriminant of the given equation is -20.

The discriminant of a quadratic equation is a value derived from the coefficients of the equation that can be used to determine the number and type of solutions of the equation. The discriminant of a quadratic equation in the form ax2 + bx + c is calculated by the formula b2 - 4ac. In this case, the equation is 2x2 + 4x + 3. Plugging the coefficients into the formula, we get (4)2 - 4(2)(3) = -20. Therefore, the value of the discriminant of the given equation is -20.

(4)2 - 4(2)(3) = 16 - 24 = -8

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Occupation is a qualitative variable with a nominal level value, annual salary is a quantitative variable with ratio level value, price of a shirt (in dollars) on clearance rack is quantitative with a ratio level value.

Variables can be divided into quantitative or qualitative (categorical).

Quantitative variables are those variables in which the data measures values or counts and is expressed as amounts or numbers. Qualitative variables are any variables whose data are descriptive rather than numerical.

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Therefore, the solution to the given problem of the equation whose factors are (3x - 1)(x + 1).

Examine the equation.

An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. This equation's solution reveals that the value of the variable x is 5.

According to the given question:

Given : 3x² + 2x - 1

Factorizing using splitting the middle term

= 3x² + 3x - x - 1

= 3x(x + 1) - 1(x + 1)

= (3x - 1)(x + 1)

Therefore , the solution to the given problem of the equation whose factors are (3x - 1)(x + 1) .

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The distance traveled by Raven in 1 hour at the given rate is 4 miles.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

Raven can walk 2 (2/5) miles in 3/5 hours.

so,

2 (2/5) = 0.6 hours.

12/5  = 0.6 hours.

2.4 = 0.6 hours.

then,

if 2.4 = 0.6 hour

for  x = 1 hour

By cross multiplying:

x = 2.4/0.6 miles

= 4 miles

Hence, the distance traveled by Raven in 1 hour at the given rate is 4 miles.

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As per the integral value of the closed path, the magnitude of I3 is 3.597

The term magnitude in math refers a measure of the size of a mathematical entity.

Here we have the value of the line integral around the closed path 1.96 x 10⁻⁵.

Now, we have to find the value of the magnitude I3,

Here we have also know that the value of I1 and I2 are 18A and 12 A respectively.

Now, as per the line integral of the magnetic field is written as,

=> 1.96 x 10⁻⁵ = 4π⋅10⁻⁷ (I3 + 12)

When we simplify this one then we get,

=> 1.96 x 10²/4π = I3 + 12

=> 15.597 = I3 + 12

Then the value of the magnitude is calculated as

=> I3 = 3.597

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The graph of Y > -2x + 4 can be drawn by plotting points on a coordinate plane and connecting them with a dashed line. The dashed line should be above the line Y=-2x+4.

A sample graph is shown below:

[Graph of Y > -2x + 4]

(0,4), (1,1), (2,-2), (3,-5), (4,-8)

To graph Y > -2x + 4, you need to plot points on a coordinate plane. Start by finding the intersection point of the line Y=-2x+4 and the x-axis, which will be (0,4). From there, you can calculate the coordinates of the other points by substituting x values into the equation and solving for y. For example, when x=1, y=-2x+4=-2+4=2, so the point (1,2) would be plotted. Then, plot the other points (2,-2), (3,-5), and (4,-8). Finally, connect the points with a dashed line to represent Y > -2x+4.

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The shift in the line's y coordinate relative to its x coordinate is known as the slope of a line. The slope of the given line graph is 3.

The slope of a line is defines as the change in the y coordinate of the line to the x-coordinate. Mathematically, the slope of a line is expressed according to the formula below:

Slope = y₂-y₁/x₂-x₁

Using the following coordinate from the given graph (0, 0) and (1, 3), we will substitute the coordinates into the formula to have:

Slope = 3-0/1-0

Simplify to have:

Slope = 1/3

Slope = 3

Hence the slope of the given line graph is 3.

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The angle 78.125° is rewritten as 78 degrees 7 minutes and 30 seconds.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

The angle is given below.

⇒ 78.125°

Convert the decimal part into minutes and seconds. Then we have

⇒ 78° + 0.125 x 60

⇒ 78°7.5'

⇒ 78°7' + 0.5 x 60

⇒ 78°7'30''

The angle 78.125° is rewritten as 78 degrees 7 minutes and 30 seconds.

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The formula of the set is generally written as follows.

The term set in math is defined as an organized collection of objects and can be represented in set-builder form or roster form.

Here we need to find the formula that can be used in set.

The general formula of the set can be written as follows:

=> n ( P ∪ Q ) = n(P) + n(Q) – n ( P ∩ Q)

where

n(P U Q) refers the number of elements present in one of the sets P or Q.

n(P ⋂ Q) refers the number of elements present in both the sets P & Q.

Where as If P ∩ Q = ∅, then the value is calculated as,

=> n ( P ∪ Q ) = n(P) + n(Q)

Here we have also want to know that sets P and Q are equal only if all the elements they contain intersect, and none of them have any unique elements which are not present in the other set.

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The probability that all adjacent points differ in colour is [tex]\frac{1}{5}[/tex].

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given ,

We have first three colour Green that is g1 , g2 and g3

And We have next three colour red that is r1 , r2 and r3

The probability that all adjacent points differ in colour = 3! * [tex]^{4}C_{3}[/tex] 3! / 6!

=> [tex]\frac{ 3! * 4! *3!}{6!}[/tex]

=> [tex]\frac{1}{5}[/tex]

The probability that all adjacent points differ in colour is [tex]\frac{1}{5}[/tex].

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A man who has hemophilia and a woman who is a carrier has:

A hemophilia carrier is what?

Both an X chromosome from the mother and an X chromosome from the father are passed down to a daughter. Let's say the gene for typical blood coagulation is present on her mother's X chromosome. Let's say her father's X chromosome carries the hemophilia gene.

Since the normal blood clotting gene from the mother is dominant, the daughter won't get hemophilia. The hemophilia gene's instructions cannot be transmitted because of this.

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The possible rational zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.

What is mean of rational zero ?

A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.

By Rational Zero Theorem,

If P(x) is a polynomial with integer coefficients and if is a zero of P(x) i.e.,(P( ) = 0),

then p is a factor of the constant term of P(x)

q is a factor of the leading coefficient of P(x)

Possible value of rational zero is p/q

Have given, f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex]

Here, constant term, p = +20

Leading coefficient, q = +1

The factors of the constant term +20 are ±1, ±2, ±4, ±5, ±10, ±20.

The factor of the leading coefficient is ±1.

Therefore , The possible rational zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.

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Answer:

[tex]f(x)=2(x+3)(x-5)[/tex]

Step-by-step explanation:

Using the roots, [tex]f(x)=a(x+3)(x-5)[/tex].

Using the point [tex](1,-32)[/tex] to solve for [tex]a[/tex],

[tex]-32=a(4)(-4) \\ \\ -32=-16a \\ \\ a=2 \\ \\ \\ \therefore f(x)=2(x+3)(x-5)[/tex]

Given polynomials are,

[tex]\rm{f(x)=x^2+px+q}[/tex]

[tex]\rm{g(x)=x^2+mx+n}[/tex]

According to Remainder Theorem, if (x + a) is a factor of f(x), then,

[tex]\longrightarrow\rm{0=f(-a)}[/tex]

[tex]\longrightarrow\rm{0=(-a)^2+p(-a)+q}[/tex]

[tex]\longrightarrow\rm{0=a^2-pa+q\quad\dots(1)}[/tex]

Similarly, if (x + a) is a factor of g(x), then,

[tex]\longrightarrow\rm{0=g(-a)}[/tex]

[tex]\longrightarrow\rm{0=(-a)^2+m(-a)+n}[/tex]

[tex]\longrightarrow\rm{0=a^2-ma+n\quad\dots(2)}[/tex]

Subtracting (2) from (1),

[tex]\longrightarrow\rm{0=(a^2-pa+q)-(a^2-ma+n)}[/tex]

[tex]\longrightarrow\rm{0=a^2-pa+q-a^2+ma-n}[/tex]

[tex]\longrightarrow\rm{0=(m-p)a+q-n}[/tex]

[tex]\longrightarrow\rm{0=(m-p)a-(n-q)}[/tex]

[tex]\longrightarrow\rm{(m-p)a=n-q}[/tex]

[tex]\longrightarrow\rm{\underline{\underline{a=\dfrac{n-q}{m-p}}}}[/tex]

Hence Proved!