Which of these relations is a function?

The Distance from bottom of lamppost is 57.142 ft.

Triangles with the same shape but different sizes are called similar triangles. Examples of similar objects include squares with any side length and all equilateral triangles. To put it another way, if two triangles are similar, their angles are the same and their sides are the same size. The "~" symbol indicates the triangular resemblance here.

Given the height of lamp post is 20 ft

height of man is 6 ft

man walking away with speed of 5 ft per sec

distance covered 8 sec is 8 x 5 = 40 ft

let us consider a triangle ΔABC and consider the triangle with man ΔDEC

which is inside ΔABC as shown in figure,

AB = 20 ft, DE = 5 ft and AD = 40 ft

consider   ΔABC and ΔDEC

∠BAC = ∠EDC = 90⁰

∠BCA = ∠ECD = common angle

so    ΔABC ~ ΔDEC by (AA property)

according to similar triangles

AB/DE = AC/DC

let DC be x and AC is 40 + x

substitute the values

20/6 = (40 + x)/x

20x = (40 + x)6

20x = 240 + 6x

14x = 240

x = 17.142ft

AC = AD + DC = 40 + 17.142 = 57.142 ft

Hence the Distance from bottom of lamp post to the end of shadow is 57.142 ft.

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Answer:

Step-by-step explanation:

12x^2+17x = 5

12x^2+17x-5 = 0

(4x - 1)(3x+5) = 0

Solve (4x-1) and (3x +5)

4x - 1 = 0

4x = 1

x = 1/4

3x + 5 = 0

3x = -5

x = -5/3

x = { 1/4, -5/3 }

Step-by-step explanation:

The answer is in the image above

Answer:        

Step-by-step explanation:

Apply  distributive property.

5i(3+2i)

5i⋅3+5i(2i)

Multiply

3 by 5.15i+5i(2i)

Multiply

5i(2i) .

15i + 10i2

Simplify each term.

Rewrite

i2 as −1.15i+10⋅−1

Multiply

10 by −1.15i−10

Reorder

15i and −10.−10+15i

hope it helps :)

The component form of two vectors 2u - v is (10, 0), no magnitude in the second direction.

A vector is a quantity that has both magnitude and direction.

Given are two vectors u = (4, - 1) and v = (-2, - 2).

∴ The value of 2u - v in component form is 2(4, - 1) - (-2, - 2).

2u - v = (8, - 2) - (-2, - 2).

2u - v = (8+2, - 2+2).

2u - v = 10

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Answer:

The y-intercept of the given line is 7/9.

Step-by-step explanation:

The y-intercept of a line is the point where the line crosses the y-axis.

So, to find the point where the line crosses the y-axis we must do x=0.

By substituting x=0 in the following equation, we get

=> 9y + 4(0) = 7

=> 9y = 7

=> y = 7/9

Hence, y = 7/9 is the y-intercept of the given line.

Answer: decimal form 20.5

Step-by-step explanation:

Finding line J's slope is the first step.The simplest approach to achieve this is to change the equation's format to y=mx+b, where m represents the slope.

9x-y=10

Take 9x off of both sides.

9x-y-9x=10-9x

Simpllify -y=-9x+10

Divide both sides by (-9x+10)-1, or -1 -y/-1.

Simplify y=9x-10

m=-1/9.

The notation (x1,y1) y-y1=m(x-x1) y-1=-1/9(x- -8) which reduces to y-1=-1/9(x+8)

y-1=-1/9x-8/9

then multiply both sides by 1.

y-1+1=-1/9x-8/9+9/9

(Using 9/9 as 1 makes it easier to use the common denominator to simplify the fractions.)

As the penultimate step, simplify.

y-1/9x+1/9

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Without using the triangle sum theorem, the proof that shows that m∠G + m∠K + m∠GHK = 180° is proved below.

Based on the triangle angle sum theorem, all the interior angles in a triangle will add up to the sum of 180 degrees.

The complete proof that shows that m∠G + m∠K + m∠GHK = 180 degrees is explained below.

Statement                                    Reason                                          

1. GK║HJ                                     1. Given

2. ∠G ≅ ∠IHJ                              2. Corresponding angles theorem

3. ∠K ≅ ∠JHK                             3. Alternate interior ∠s theorem

4. m∠IHK = m∠IHJ + m∠JHK     4. Additive property of angle measure

5. m∠IHK = m∠G + m∠K            5. Substitution

6. m∠IHK + m∠GHK = 180°        6. Angles forming a linear pair sum of 180°

7. m∠G + m∠K + m∠GHK = 180° 7. Substitution

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Answer:

14

Step-by-step explanation:

x+8=? x= 6. i do know it

lower control threshold for the data is LCL = -0.007

The lower control limit on a control chart is the value below which any particular data point would be deemed to be out of statistical control owing to specific cause variation. It is represented by a line below the centerline.

The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]

To date,

Size of sample = n

Sample size is 12 samples.

Televisions with defects = X

We have a sample defect = p

p chart week with n = 200

x = 4, 7, 5, 6, 8, 3, 12, 4, 4, 5, 6, 2.

P = x/n

p = 4/200 = 0.02

p = 7/200 = 0.035

p = 5/200 = 0.025

p = 6/200 = 0.03

p = 8/200 = 0.04

p = 3/200 = 0.015

p = 12/200 = 0.06

p = 4/200 = 0.02

p = 4/200 = 0.02

p = 5/200 = 0.025

p = 6/200 = 0.03

p = 2/200 = 0.01

total will be 0.33

p bar = 0.33/12

p bar = 0.0275

The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]

LCL =  0.0275 - 3[tex]\sqrt{ 0.0275 (1- 0.0275/200}[/tex]

LCL = -0.007

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If the length of the garden is one digit whole number and the width is 5 meter, then the lease possible area is 5 meters

The shape of the region is rectangular

The length of the garden is one digit whole number

One digit whole numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

The width of the rectangular region = 5 meters

We know the area of the rectangle = Length × Width

Here we have to find the least possible area

So the width is given but the length of the garden is unknown but it is a one digit whole number

To get least possible area, the length should be least number, because the area is the product of length and width

The length of the garden = 1

The least possible area = 1 × 5

= 5 meter square

Therefore, the least possible area is 5 meter square

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Answer:

3

Step-by-step explanation:

h(2) we find by looking at what y equals when x is 2

when x is 2 y or h(2) is about 3

hopes this helps please mark brainliest

Answer:

The intercepts are: (0, 3/7) and (-3/4, 0)

Step-by-step explanation:

If X=0

-4(0) + 7y = 3

7y = 3

Y = 3/7

If Y=0

-4x + 7(0) = 3

-4x = 3

X = -3/4

The time taken by the horizon to develop is calculated with the half-life which is 675 years.

Organic matter particles have more negatively charged particles, which hold on the positively charged particles.

The organic matter in the soil affects the water holding capacity of the soil. Thus is if there are more organic matter, this means that the organic matter is more. Thus the farmer has to add more organic matter.

In order to reduce the the acidity, the farmers add Calcium oxide, Calsium hydroxide and so on.

The horizon s formed after years of sediment formation. Thus the process can take years.

This is the half-life of the soil and with the formula of half-life we get 225 * 3 = 675 years.

Therefore, the time taken by the horizon to develop is 675 years.

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Answer:

14.56 

Step-by-step explanation:

Answer:

the answer is D. the 3 is simply a scalar multiple so multiply each term by 3

Answer:

D

Step-by-step explanation:

I believe that it's D since all you have to do is multiply 3 by each of the numbers that are supposedly n.

Given that WXZ and YXZ are congruent based on side-angle-side congruency, we can prove the theorem that states "A point on the perpendicular bisector of a line segment is equidistant from the segment’s endpoints." This theorem is often referred to as the "Perpendicular Bisector Theorem."

The required details for "Perpendicular Bisector Theorem" in given paragraph

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a line segment, then it is equidistant from the segment's endpoints. This means that if we draw a line through a point that is perpendicular to a line segment, and that line passes through the midpoint of the segment, then the point is equidistant from the endpoints of the segment. In this case, we are given that line L is the perpendicular bisector of segment WY, and that Z is a point on L. We are also told that WXZ and YXZ are congruent based on side-angle-side congruency. Since WXZ and YXZ are congruent, it follows that WX and YX are congruent and that WZ and YZ are congruent. This means that the distances from Z to W and Y are equal, so Z is equidistant from W and Y.

Therefore, we can conclude that Z is a point on the perpendicular bisector of segment WY, and the Perpendicular Bisector Theorem is proved. The answer is C. "A point on the perpendicular bisector of a line segment is equidistant from the segment’s endpoints."

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The solution for the inequality |r| - 3 > 2 is r < -5 or r > 5.

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

|r| - 3 > 2.

Simplify the inequality,

|r| > 5,

Implies that,

r < -5 or r > 5

Interval notation (-∞, -5) ∪ (5, ∞).

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Answer:

Step-by-step explanation:

You want the discriminant, roots, and graph of the quadratic function ...

 f(x) = 1/2x² -2x +10

The discriminant of the quadratic function

  y = ax² +bx +c

is ...

  d = b² -4ac

The given function has a=1/2, b=-2, c=10, so the discriminant is ...

  d = (-2)² -4(1/2)(10) = 4 -20 = -16

The discriminant of -16 means there will be two distinct complex conjugate roots.

The roots are ...

  x = (-b ±√d)/(2a)

  x = (-(-2) ±√(-16))/(2(1/2)) = 2 ±4i

A graph of the function is attached.

Graph with their Turning Point is shown with different degree of different degree Equation

Where a graph changes, either from increasing to decreasing, or from decreasing to increasing, is called a turning point.

Factorization Technique

The turning point of the parabola lies exactly at the midway between the (two) x-intercepts of a quadratic function, as shown by the fact that a vertical line of symmetry divides the parabola into two equal half and crosses it. In light of this, we can use a factorisation-based method to locate the solution of a quadratic equation. The process involves five steps.

Step 1: By looking at the coefficient of x2, determine if the graph is a minimum or maximum;

Factorize the supplied quadratic function in Step 2 and set it to Zero;

Step 3: Define the function's antecedents;

Take the midpoint of the pair of roots to find the x-coordinate of the turning point in step 4;

2 turning points

Let f(x)=x³+ax²+bx+c, where the coefficients a, b and c are real numbers. The figure below shows a section of the graph of y=f(x). The curve has two distinct turning points; these are located at A and B, as shown.

But there is come limitations in this case too, a function has to follow certain conditions to have two turning points.

3 turning points

If we get 4 roots of any equation it may be containing 3 turning Points.

With some limitations in this as well.

4 turning points

If we get 5 roots of any quadratic equation it may be containing 4 turning points with some limitations in this as well.

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By solving the given equation  20 + 0.44x = 19 + 1.69x we get x=0.8.

When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. For instance, an equation in French is described as having one or more variables, whereas in English, an equation is any properly written formula that consists of two expressions linked by the equals sign.

Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.

Given,

20 + 0.44x = 19 + 1.69x

20-19=1.69x-0.44x

1=1.25x

x=0.8

Therefore, by solving the given equation  20 + 0.44x = 19 + 1.69x we get x=0.8.

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Answer:

35,875

Step-by-step explanation:

35000x(1+2.5%)

35000x1.025%

35,875

(sorry if it's wrong I'm assuming it is the answer because i saw a similar equation and i used the same format..)

An experiment can be assumed to have internal validity if random assignment and experimental control is employed. So the option c is correct.

The degree to which a study reliably establishes a cause-and-effect link is a sign of its internal validity. The procedures used in the study and the level of care done have a significant impact on this type of validity.

Internal validity is essential because, if proven, it enables alternate explanations for a discovery to be disregarded.

An experiment can be assumed to have internal validity if  random assignment and experimental control is employed. So the option c is correct.

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The right question is:

An experiment can be assumed to have internal validity if:

A. the dependent variable is valid.

B. there is a strong manipulation of the independent variable.

C. random assignment and experimental control is employed.

D. confounding variables are present.

Mr. Henderson paid a total of $98.40 for phone service and $79.20 for garbage pickup last year. To find his average cost per month for these two services, we need to divide the total amount he paid by the number of months in a year.

Since there are 12 months in a year, we can divide the total amount Mr. Henderson paid for phone service and garbage pickup by 12 to find his average cost per month. This is calculated as follows:

Average cost per month = (98.40 + 79.20) / 12

Average cost per month = 177.60 / 12

Average cost per month = $14.80

Therefore, Mr. Henderson's average cost per month for phone service and garbage pickup last year was $14.80. This means that, on average, he paid about $14.80 per month for these two services.

Answer: 9x = 288, 32 hours

Step-by-step explanation:

x can be the variable and it represents the hours he worked. 9 is the amount made each hour, so it is multiplied by x. 288 is the total made, so 9x=288.

9x = 288 Divide by 9 on both sides to isolate x
x = 32 hours. Kevin worked 32 hours this week

Answer:32

Step-by-step explanation: 32x9=288

The value of b is 20.

What is Pythagorean theorem?

The Pythagoras theorem is a mathematical law that states that the sum of squares of the lengths of the two short sides of the right triangle is equal to the square of the length of the hypotenuse.

According to the given question:

∠S and ∠Q are right angles in RSTQ quadrilateral.

RTS and RTQ are right angled triangles.

Applying Pythagorean theorem on both the triangles

sin 35° = b + 60 / RT ⇒ RT = b + 60 / sin 35°

sin 35° = 4b / RT ⇒ RT = 4b / sin 35°

Since RT is common in both equations

b + 60 / sin 35° = 4b / sin 35°

b + 60 = 4b

3b = 60

b = 20

Hence the value of b is 20

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The rental cost for each movie is  $3.75

The rental cost for each video game is  $5.75

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

let the cost of renting movies be m and let the cost of video game rental be v

One month Ivan rented 9 movies and 7 video game $74

9m + 7v = $74

3 movies and 5 video games for a total of $40

3m + 5v = $40

The simultaneous equation

9m + 7v = $74

3m + 5v = $40

solving the equation gives

m = $3.75

v = $5.75

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Answer:1/2

Step-by-step explanation:

3/4+(-1/2)-(-1/4)

3/4-1/2+1/4

1-1/2=1/2