Una mujer de 5 pies de altura esta de pie cerca de un farol que tiene 12 pies de altura, . Encuentre una función que modele la longitud de su sombra en términos de distancia desde la base del farol. un triangulo isósceles tiene un perímetro de 8cm. Encuentre una función que moldee su área a en términos de la longitud de su base

Number handshakes in each case

i) 6

ii)10

iii) 55

The formula for the number of handshakes possible at a party with n people is

handshakes = n*(n - 1)/2.

This is because each of the n people can shake hands with n - 1 people (they would not shake their own hand), and the handshake between two people is not counted twice.

Now using the formula for handshake

= n*(n - 1)/2.

i) 5 people at party

=  n*(n - 1)/2.

= 5(5-1) /2

=5 x 4 /2

=10

ii) 4 people at party

=  n*(n - 1)/2.

= 4(4-1) /2

=4 x 3 /2

= 6

iii)  11 people at party

=  n*(n - 1)/2.

= 11(11-1) /2

= 11 x 10 /2

= 55

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Answer:

The equation: 2n - 3 ≤ -21

The answer to the equation: n ≤ 9

Step-by-step explanation:

How to get the equation:

The difference of symbolizes subtraction. Because we are subtracting twice a number and 3, the first part of the equation can be written as 2n - 3. The n symbolizes the number.

is at most symbolizes a less than or equal to sign. That sign is ≤. And what is it less than or equal to? -21.

Now are equation is 2n - 3 ≤ -21

How to solve it:

2n - 3 ≤ -21

Add 3 to both sides of the equation

2n ≤ 18

Divide both sides of the equation by 2

n ≤ 9

So the probability that a randomly selected song had 501-1,000 plays given that the song was country is 7/12, or approximately 0.583.

To find the probability that a randomly selected song had 501-1,000 plays given that the song was country, we need to use conditional probability.

Using Bayes' theorem, we have:

P(B|A) = P(A|B) * P(B) / P(A)

We can find each of these probabilities from the given information:

P(A) = (7+3)/(7+3) = 1 (since all songs recorded were either country or rock)

P(B) = (7+2)/(7+3+2) = 9/12 (since 9 out of the 12 songs recorded had 501-1,000 plays)

P(A|B) = P(A and B) / P(B) = 7/9 (since out of the 9 songs with 501-1,000 plays, 7 were country)

Therefore,

P(B|A) = (7/9) * (9/12) / 1

P(B|A) = 7/12

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Answer:

Ben needs to get a 99% on his second test

Step-by-step explanation:

The average is the sum of both test scores, divided by the total number of test scores (2).

Let x by the grade Ben must receive on his second test.

(89 + x)/2 = 94

Multiply by 2 on both sides

89 + x = 188

Subtract 89 on both sides

x = 99

Check work:

(89 + 99)/2 = 188/2 = 99

Answer: 99

Concept:

Here, we need to know the idea of the average value.

In mathematics, average refers to the sum of a group of values divided by n, where n is the number of values in the group.

Average = Sum of value / number of values

Solve:

Given information

Scoring on first test = 89

Scoring on second test = x

Number of tests = 2

Average = 94

Given expression

Average = Sum of value / number of values

Substitute values into the expression

94 = (89 + x) / 2

Multiply 2 on both sides

94 × 2 = (89 + x) / 2 × 2

188 = 89 + x

Subtract 89 on both sides

188 - 89 = 89 + x - 89

\(\boxed{x=99}\)

Hope this helps!! :)

Please let me know if you have any questions

The Percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.

To find the percentage error, we need to calculate the difference between the recorded value and the true value, then divide that difference by the true value and multiply by 100 to get a percentage.

True value = 1,500

Recorded value = 900

Difference = True value - Recorded value

Difference = 1,500 - 900

Difference = 600

Percentage error = (Difference / True value) x 100

Percentage error = (600 / 1,500) x 100

Percentage error = 40

Therefore, the percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.

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Answer:

5

Step-by-step explanation:

like my answer please...

The size of the angle QUP in the system formed by the equilateral triangle QUR, the equilateral triangle PUT and the square RUTS is equal to 150°.

By Euclidean geometry we know that squares are quadrilaterals with four sides of equal length and four right angles and triangles are equilateral when its three sides have equal length and three angles with a measure of 60°. In addition, a complete revolution has a measure of 360°.

Finally, we must solve the following equation for the angle QUP:

m∠QUR + m∠QUP + m∠PUT + m∠RUT = 360

60 + m∠QUP + 60 + 90 = 360

m∠QUP + 210 = 360

m∠QUP = 150

The size of the angle QUP in the system formed by the equilateral triangle QUR, the equilateral triangle PUT and the square RUTS is equal to 150°. \(\blacksquare\)

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Therefore , the solution of the given problem of expressions comes out to be (x - 2)(x - 6) = x² - 8x + 12.

It is advisable to employ shifting numbers, which may also prove to be increasing variable, diminishing, or blocking, rather than random estimations. Only by exchanging tools, information, or answers to problems could they assist one another. The statement of truth equation may comprise the arguments, elements, or quantitative remarks for strategies like increased disagreement, production, and blending.

Here,

Using long division, one can divide x² - 8x + 12 by x - 2 as follows:

    x - 6

   -------------

x - 2 | x^2 - 8x + 12

      - (x^2 - 2x)

      ------------

            -6x + 12

            -(-6x + 12)

            -----------

                     0

As a result, we have:

x² - 8x + 12 = (x - 2)(x - 6) + 0

The remainder is 0, and the quotient is x - 6. We may validate our response by doing the following:

(x - 2)(x - 6) = x² - 8x + 12

It is the primary polynomial that we initially used.

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Answer:

see below

Step-by-step explanation:

10 are blue, 30 are yellow, 20 are red, and 40 are green.

There are 100 marbles in the bag

The color that has the most marbles is green

P( green) = 40/100 = 40%

P( yellow) = 30/100 = 30%

P( red) = 20/100 = 20%

P( blue) = 10/100 = 10%

You will be more likely to pick a green marble

a. The equation to show the amount of money Adam has after any number of days can be written as:

m = 20d + 11

b. The dependent variable is the amount of money Adam has (m), and the independent variable is the number of days (d).

c. The slope of the equation is 20, which represents Adam's daily income from his job. For every additional day that he works, he earns $20 more.

d. The y-intercept of the equation is 11, which represents the amount of money Adam had before he started working. In other words, he already had $11 saved up before he began earning money from his job.

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For an arithmetic sequence a,= 7+3(n-1)

when n is 31

For an arithmetic sequence a,= 7+3(31-1)

An arithmetic sequence a,= 7+3(30)

An arithmetic sequence a,= 7+90

An arithmetic sequence a= 97

THE CORRESCT

Answer:

Step-by-step explanation:

\(10[2x-4]=100\\\\\mathrm{Divide\:both\:sides\:by\:}10\\\frac{10\left(2x-4\right)}{10}=\frac{100}{10}\\\\Simplify\\2x -4=10\\\\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\2x-4+4=10+4\\\\Simplify\\2x =14\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\frac{2x}{2}=\frac{14}{2}\\\\Simplify\\x = 7\)

When the sine function  sinθ = 0.5126 then the angle θ  is 30.001°

Given sinθ = 0.5126

We have to find the value of θ or the angle θ.

We know that the sine function is a ratio of opposite side and hypotenuse.

As given value sinθ = 0.5126

To find θ value, we take sin⁻¹ on both sides of the equation.

sin⁻¹(sinθ)=sin⁻¹(0.5126)

On left side the sine and its inverse will be cancelled and left with angle θ.

Now θ = sin⁻¹(0.5126)

To find the value of sin⁻¹(0.5126), you can use the inverse sine function or arcsin function.

θ = 30.001°

Hence, when the sine function  sinθ = 0.5126 then the angle θ  is 30.001°

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Answer:

A vector graphic consists of a set of instructions for creating a picture is a true statement.

Step-by-step explanation:

A vector graphic is an image format that represents images as a set of mathematical instructions or geometric primitives such as lines, curves, and shapes. Instead of using a grid of pixels like raster graphics, vector graphics define images based on mathematical formulas and coordinates.

These instructions or mathematical representations describe the shapes, colors, and other visual attributes of the image. They allow the image to be scaled, resized, and manipulated without loss of quality since the instructions can be recalculated and redrawn at any resolution or size.

Vector graphics are often created and edited using specialized software such as Adobe Illustrator, CorelDRAW, or Inkscape. They are commonly used for logos, illustrations, diagrams, typography, and other graphical elements where scalability and flexibility are important.

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Answer:

true

Step-by-step explanation:

the triangle can be acute or obtuse depending on the angles between its two legs

Considering that y is between x and z, we have that:

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

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Answer:

Explanation: We need to find the unknown side "x" using the Pythagorean theorem, it can be done as follows:

Answer:

DE

Step-by-step explanation:

a tangent is a straight line that only touches the circle at one point.

9514 1404 393

Answer:

  B.  3, 4, 5

Step-by-step explanation:

The Pythagorean triple (3, 4, 5) is the only Pythagorean triple that is an arithmetic sequence. It is also the triple with the smallest integers. It is useful to remember this triple, as it is seen a lot in algebra, geometry, and trig problems.

__

Side length 1, 2, 3 do not form a triangle.

Side lengths 5, 6, 7 form an acute triangle.

Side lengths 3, 4, 5 form a right triangle.

The absolute value of a number is its distance from zero on the number line. It provides the positive value of a number, disregarding its sign.

In mathematics, the absolute value is a function that gives the distance of a number from zero on the number line. It is denoted by the symbol "| |" or two vertical bars. The absolute value of a number "a," denoted as |a|, is defined as follows:

If "a" is positive or zero, then |a| = a.

If "a" is negative, then |a| = -a.

In simpler terms, the absolute value of a number disregards its sign and returns the magnitude or distance of the number from zero. It represents the positive value of the number, regardless of whether the original number was positive or negative.

For example:

The absolute value of 5 is |5| = 5, since 5 is already positive.

The absolute value of -7 is |-7| = 7, since the negative sign is removed, and the resulting value is positive.

The absolute value of 0 is |0| = 0, as it is equidistant from zero in both directions.

The absolute value function is useful in various mathematical concepts, such as solving equations involving inequalities, finding the distance between two numbers, defining the magnitude of vectors, and determining the modulus of complex numbers.

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Answer:

\(\displaystyle \frac{9}{\sqrt{7}-2}=3\sqrt{7}+6\)

Step-by-step explanation:

Rationalizing the Denominator

Rationalizing the denominator means to get rid of any radicals in the denominator.

We use the conjugate of the denominator to rationalize. The conjugate of a binomial is obtained by changing the sign that is between the two terms while keeping the same order of the terms. For example, the conjugate of

\(\sqrt{7}-2\) is \(\sqrt{7}+2\).

We need to use the algebraic identity:

\((a-b)(a+b)=a^2-b^2\)

Let's rationalize

\(\displaystyle \frac{9}{\sqrt{7}-2}\)

Multiply numerator and denominator by the conjugate of the denominator:

\(\displaystyle \frac{9}{\sqrt{7}-2}=\frac{9}{\sqrt{7}-2}\cdot\frac{\sqrt{7}+2}{\sqrt{7}+2}\)

Operate in the numerator and apply the identity in the denominator

\(\displaystyle \frac{9}{\sqrt{7}-2}=\frac{9(\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)}\)

\(\displaystyle \frac{9}{\sqrt{7}-2}=\frac{9\sqrt{7}+18}{(\sqrt{7})^2-2^2}\)

\(\displaystyle \frac{9}{\sqrt{7}-2}=\frac{9\sqrt{7}+18}{7-4}=\frac{9\sqrt{7}+18}{3}\)

Dividing:

\(\boxed{\displaystyle \frac{9}{\sqrt{7}-2}=3\sqrt{7}+6}\)

Answer:kkkkkkk

Step-by-step explanation:

From the two methods to find the surface area, the method used by student 2 is most desirable as the smaller regular objects are easily interpreted to solve.

We want to find the area of the irregular composite polygon figure. Now, there are two ways to do this which are;

1) To divide the internal part of the irregular polygon into regular shapes and find the respective areas and add up to get the total area.

2) To inscribe the irregular polygon into a regular shape like a rectangle or square, Then divide into regular shapes the external parts of the irregular polygon that share boundary with the bigger regular shape. Then add up the areas and subtract from the area of the big regular shape.

Now, looking at the two options to find the surface area, the method used by student 2 is most desirable as the smaller regular objects are easily interpreted to solve.

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The volume of the right circular cone is approximately 1.6 cubic centimeters (rounding this answer to the nearest tenth of a cubic centimeter).

What is volume ?

Volume is a physical quantity that measures the amount of three-dimensional space that a substance or object occupies.

The volume of a right circular cone is given by the formula

\(V = (1/3)\pi r^2h\) , where r is the radius of the base and h is the height of the cone. We are given the height of the cone, which is 14.9 cm. To find the radius of the base, we need to use the given circumference of the base, which is 2.9 cm.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. We can rearrange this formula to solve for r, which gives us r = C/(2π). Plugging in the given circumference of 2.9 cm, we get:

r = 2.9/(2π) ≈ 0.461

Now, we can substitute the values of r and h into the formula for the volume of a cone and solve for V:

V = (1/3)π(\(0.461^2\))(14.9) ≈ 1.564 \(cm^3\)

Rounding this answer to the nearest tenth of a cubic centimeter gives us a final volume of approximately \(1.6 cm^3\). Therefore, the volume of the right circular cone is approximately 1.6 cubic centimeters.

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Answer: in explanation

Step-by-step explanation:

Rate is simplest form, so 3 napkins for 5 cents.

Unit rate is for 1 x value, so 1 napkin for 0,6 cents.

Answer:

Yes what is the question I would surely love to help u

Step-by-step explanation:

Answer:

I think that complementary angles

(a)The equation of the plane P is r. n = a. n0[x, y, z] . [1, 2, 1] = [0, 1, 2] . [1, 2, 1]x+2y+z=5 (b)Therefore, X = [4/3, 5/3, 4/3], and the distance from L to P is the distance from X to P is,  (5√6)/18

(a) Equation of the plane P that passes through the point P(0,1,2) and is perpendicular to the vector n=[1,2,1].An equation of the plane P that passes through the point P(0,1,2) and is perpendicular to the vector n=[1,2,1] is obtained as follows.

The vector equation of a plane P can be given by: r. n = a. n, where r is the position vector of any point (x,y,z) on the plane and a is the known point on the plane.

Therefore, the equation of the plane P is r. n = a. n0[x, y, z] . [1, 2, 1] = [0, 1, 2] . [1, 2, 1]x+2y+z=5

(b) Let E be the line in R^3 given by x=[1,2,1]+t[1,−1,1],tE. Explain why C does not intersect P and find the distance from L to P

.The equation of the line E is given by: x = a + tb, where a = [1, 2, 1] and b = [1, −1, 1].Since P (0, 1, 2) is not on the line E, there is no point of intersection between C and P. The vector n = [1, 2, 1] is a normal vector of P. Let D be the point on P closest to E.

Then, the line PD is perpendicular to P. Hence, it must be parallel to the normal vector n of P.

Hence, the direction vector of PD is parallel to n. Thus, we obtain a new point D′ by projecting P onto E, and PD′ is perpendicular to P. Therefore, D′ lies on the line E, and hence, D′ can be written as x = [1, 2, 1] + t[1, −1, 1].To find the distance from L to P, we first find the point of intersection of line E and plane P. If the point of intersection is X, then the distance from L to P is the distance from X to P.

In order to find X, we need to solve the system of equations:x = a + tb, x.n = c.nwhere a = [1, 2, 1], b = [1, −1, 1], c = [0, 1, 2], and n = [1, 2, 1].Substituting x = a + tb, we get [1+t, 2−t, 1+t].n=[1, 2, 1][1+t, 2-t, 1+t] = 5

Simplifying, we get 6t = 2, or t = 1/3.Substituting t = 1/3, we get x = [4/3, 5/3, 4/3].

Therefore, X = [4/3, 5/3, 4/3], and the distance from L to P is the distance from X to P, which is given by the formula d = (|(x - 0) · n|)/|n| = |5/3|/√6 = (5√6)/18

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Answer:

Step-by-step explanation:

distance between 2 points = d = √(x2 - x1)² + (y2 - y1)²

JI = √(3--2)² + (4-4)² = √5² = 5

GH = √(5--5)² + (0-0)² = √10² = 10

sum of bases JI + GH = 10 + 5 = 15

1/2 sum of bases = 15/2

JG = √(-5--2)² + (0-4)² = √9 + 16 = √25 = 5

JK = 5/2 = KG

IH = √(5-3)² + (0-4)² = √4 + 16 = √20 = 2√5

IL = 2√5/2 = √5 = LH

coordinates of K:  (-5+-2)/2, (0+4)/2 = (-7/2, 2)

coordinates of L:  (5+3)/2, (0+4)/2 = (4, 2)

KL = √(4--7/2)² + (2-2)² = 15/2