Lindsay sketches a right triangle with lengths f, g, and h as shown. She uses the Pythagorean Theorem to write the equation f2 + g2 = h2 to represent the triangle. How can Lindsay correct her error? Explain your reasoning.

Answer:

Step-by-step explanation:

[tex]1) \overline{BA} \cong \overline{BC}, \overline{DA} \cong \overline{EC} \text{ (given)}\\2) \overline{BD} \cong \overline{BE}[/tex]  (congruent segments subtracted from congruent segments form congruent segments)

The height of the skyscraper is 177.51 m which is 331 m from the base of skyscraper.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here, h₀ = 1.52 m,      angle of elevation = 28⁰

         d = 331 m

Now, tan 28⁰ = h/d

         h = d. tan 28⁰

         h = 331 X 0.5317

         h = 175.99 m

Total height = h + h₀

                    = 175.99 + 1.52

                    = 177.51 m

Thus, the height of the skyscraper is 177.51 m which is 331 m from the base of skyscraper..

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Answer:

Step-by-step explanation:

The answer is 177.5 dont add the .1

The standard deviation of the sample mean differences is; 0.6898

From online research, the sample size of the session regarding the number of people who will purchase the red box is; N₁ = 45

From online research, the sample size of the session regarding the number of people who will purchase the blue box is; N₂ = 60

Formula for standard deviation of the sample mean differences is;

σm₁ - σm₂ = √[(σ₁²/n₁) + (σ₂²/n₂)]

Thus;

σm₁ - σm₂ = √[(3.868²/45) + (2.933²/60)]

σm₁ - σm₂ = 0.6898

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Based on the property of the consecutive angles of a parallelogram, the value of x is calculated as: E. 37.

In a parallelogram, the angles that are opposite to each other are congruent while consecutive angles are supplementary.

Angles F and G are consecutive angles and are therefore supplementary (have a sum of 180 degrees.)

Angle F + angle G = 180

4x - 2 + 34 = 180

4x + 32 = 180

4x = 180 - 32

4x = 148

x = 148/4

x = 37

Value of x is: E. 37.

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Answer:

scale factor = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{V'W'}{VW}[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

[tex]p\left( A|B\right) =0[/tex]

Step-by-step explanation:

Formula:

[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]

The only prime outcome is 3

Then

The set A = {3}

1 and 2 are the divisors of 2

Then

The set B = {1 , 2}

Therefore , p(A∩B) = 0

Also p(B) = 0.4+0.1 = 0.5

[tex]\Longrightarrow p\left( A|B\right) =\frac{0 }{0.5 }=0[/tex]

Answer:

Approx. 2140.16 cubic centimeters

Step-by-step explanation:

[tex]Volume=\frac{4}{3}\pi r^{3} \\V=\frac{4}{3}(3.14)(8)^{3} \\V=4.18(8)^{3} \\V=4.18(512) \\V=2140.16[/tex]

Answer: 8

Step-by-step explanation:

To find the diagonal, we need to use two formulas:

Area of a square: [tex]A = s^{2}[/tex] (Area = side * side)

Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]  

Since  every side of a square is the same:

[tex]a^2 = b^2\\a = b = \sqrt{32} \\a^{2} = 32\\b^2 = 32[/tex]

Our equation:

[tex]32 + 32 = c^2\\64 = c^2\\8 = c[/tex]

The picture below visually explains the problem

Hope this helps!

The average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon

The given parameters can be represented as:

M(0) = 30680

M(20) = 30970

The average rate of change is calculated as:

M'(t) = (M(20) - M(0))/(20 - 0)

This gives

M'(t) = (30970 - 30680)/(20 - 0)

M'(t) = 14.5

Hence, the average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon

The average rate of change of M as t changes from 8 to 16.

This is calculated using

M'(t) = (M(16) - M(8))/(16 - 8)

M'(t) = (20 - 10)/(16 - 8)

M'(t) = 1.25

The average rate of change of M as t changes from 16 to 24.

This is calculated using

M'(t) = (M(24) - M(16))/(24 - 16)

M'(t) = (25 - 20)/(24 - 16)

M'(t) = 0.625

The average rate of change of M as t changes from 24 to 32.

This is calculated using

M'(t) = (M(32) - M(24))/(32 - 24)

M'(t) = (25 - 25)/(32 - 24)

M'(t) = 0

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The solution to the equation is y = 5.5 + x , for any real number x greater than or equal to zero and y any real number greater than or equal to 5.5.

Analysis:

since number of items cannot be negative x and y are real number numbers since y or x can be a decimal so we do not use integers alone.

so  y = 5.5 + x , for any real number x greater than or equal to zero and y any real number greater than or equal to 5.5.

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Answer: C

Step-by-step explanation:

Answer:

a/b = c/d

a*d = b*c

Ex:

a/2 = 2/4

4a = 4

a = 1

1/2 = 2/4

Answer:

6

Step-by-step explanation:

I use the information I from my Nathan teacher

Answer:

Mean: 4.7

Mode: 2

Median: 4.5

Step-by-step explanation:

Answer:

Hi,

number of ways: 8

Step-by-step explanation:

[tex]\begin{array}{|c|c|c|}Quater&dime&nickel\\------&---&---\\0&0&9\\0&1&7\\0&2&5\\0&3&3\\0&4&1\\1&0&4\\1&1&2\\1&2&0\\------&---&---\\\end{array}[/tex]

The distance between library and park is 6√2 miles and the distance between park and field is 6√11 miles.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Here, mark the park as A, Home as B, Library as C and field as D.

  Now, CD = 18 miles

            BC = 4 miles

we have to find AC (distance between library and park)

   BD = BC + CD = 18 + 4 = 22 miles

 Using property of similar triangles,

        AD² = BD X CD

         AD² = 22 X 18

         AD = √22 X √18

         AD = 6√11 miles

By Pythagoras theorem,

         AD² = AC² + CD²

        396 = AC² + 324

         AC² = 396 - 324

         AC² = 72

           AC = √72

           AC = 6√2 miles

Thus, the distance between library and park is 6√2 miles and the distance between park and field is 6√11 miles.

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Answer: -12

Step-by-step explanation: When solving this problem, PEMDAS is a key component. What is PEMDAS?

PEMDAS stands for the following:

P- Parentheses

E- Exponents

M-Multiplication

D- Division

A-Addition

S-Subtraction

This is also known as order of operations. Following this order, we can easily simplify the problem.

P-Parentheses

(-2)(-3)^2-2(2-5)

Our parentheses is (2-5). We can simply this to -3. Our problem now is

(-2)(-3)^2-2(-3)

E-Exponents

We have one set of exponents in this. It is -3^2. This simplifies to 9. Our problem now is

(-2)(9)-2(-3)

M- Multiplication

We can simply to.

-18+6

These simplifies into

-12

Answer:

-12

Step-by-step explanation:

-2*9-2(2-5) : Raise -3 to the power of 2

-18-2(2-5) : Multiply -2 by 9

-18-2*-3 : Subtract 5 from 2

-18+6 : Multiply -2 by -3

-12 : Add -18 and 6

The area of the sector is 188.9 km².

A sector is a plane figure enclosed by two radii and an arc between them.

To calculate the area of the sector, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the area of the sector is 188.9 km².

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Answer:

(14, -2)

Step-by-step explanation:

The coordinates of the midpoint is equal to the mean of the coordinates of the endpoints.

=============================================================

Solving :

⇒ 5 = -4 + x / 2

⇒ x - 4 = 10

⇒ x = 14

⇒ 2 = 6 + y / 2

⇒ y + 6 = 4

⇒ y = -2

===========================================================

Coordinates of Point Y :

⇒ Y = (x, y)

⇒ Y = (14, -2)

Answer:

Y (14, - 2 )

Step-by-step explanation:

using the midpoint formula for (x₁, y₁ ) and (x₂, y₂ ) , then

midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1+y_{2} } }{2}[/tex] )

equating the x- coordinates and the y- coordinates

let coordinates of Y = (x, y )

[tex]\frac{x-4}{2}[/tex] = 5 ( multiply both sides by 2 )

x - 4 = 10 ( add 4 to both sides )

x = 14

and

[tex]\frac{y+6}{2}[/tex] = 2 ( multiply both sides by 2 )

y + 6 = 4 ( subtract 6 from both sides )

y = - 2

coordinates of Y = (14, - 2 )

Answer: D

Step-by-step explanation:

As the measure of the 75 degree angle is less than the measure of the 80 degree angle, rule out RS.

Also, the two triangles with the 80 degree angle are congruent, so PQ=QR.

This leavesc us with SP

Answer: 1:0.75

Step-by-step explanation:

Ratio 4 to 3 = 4:3

Simplified Ratio 4.00:3.00

Ratio in Form 1:n 1:0.75

Ratio in Form n:1 1.33:1

The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.

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Answer:

D

Step-by-step explanation:

Reflection over the X-axis

All point passes, (x,-y)

Answer:

D.

Step-by-step explanation:

Reflection over the x-axis because the quadrilateral reflected.

Answer:

x=  -4, y = 4.

Step-by-step explanation:

first, divide the first equation by its G.C.D (5), to obtain its simplest form.

5x/5 + 5y/5 = 0/5 to obtain x + y = 0.

Then, find the value of y by rearranging the second equation.

y = 36 + 8x. (Rem; when 8x moves to the other side of the equation, it changes the sign)

Now substitute the value of y (36 + 8x) in the first equation which is x + y = 0.

x + 36+8x = 0

Put like terms together.

36 + 9x = 0

move 9x to the other side and change its sign.

36 = -9x

divide both sides by 9,

x = -4.

Lastly, find the value of y by replacing the value of x in either equation.

-8(-4) + y = 36

32 + y = 36

rearrange to obtain

y = 36 - 32

y = 4.

The price of one pen will be $1.5 and one highlighter is $4.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The cost of the pen and the highlighter will be calculated by forming the two expressions from the given data in the question the expressions are as follows:-

6p  +  3h  = 21

2p  +  4 h = 19

Solving the above linear equations by elimination method:-

( 6p  +  3h  = 21 ) x 2

( 2p  +  4 h = 19 ) x 6

The new equations are:-

12p  + 6h  =  42

12p  + 24h  = 114

Substracting the below equation from the above equation we will get:-

6h - 24h  =  -72

-18 h = -72

h  =  $4

Put the value of h in any of the above equations:-

2p  +  4 h = 19

2p  +  4 ( 4 )  = 19

2p  +  16  =  19

p  =  3 / 2

P  = $1.5

Therefore the price of one pen will be $1.5 and one highlighter is $4.

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Answer:

The answer to the question is F

Step-by-step explanation:

Why it is an Scalene Triangle ,it because all the sides and angle are not equal

Step-by-step explanation:

since there is triangle , you use the formula

1/2 × b × h

as you can see the base is 6 and the height is 4, so

1/2 × b × h

= 1/2 × 6 × 4

=12

12 × 2 = 24 , you times by 2 because there is 2 triangle

There is also rectangle in the diagram, so you use the formula , length × breadth , the length is 8 and the breadth is 5, so

length x breath

= 5 × 8

=35

35 × 2 = 70 , times by 2 because you can see 2 rectangles with the same length and breadth

length x breath

= 8 × 6

= 48

this one is different because the length is 8 and the breadth is 6.

SA = 48 + 35 + 24

= 107 cm ²

Sorry for my bad eng ,its not my first language.

Answer:

Step-by-step explanation:

Comment

There was a flat fee of 10 dollars

Each 1/4 hour brought in 3,75

The total charge was 55 dollars.

Equation

Charge = 10 + 4*3.75*x                     as an hourly rate,

Solution

55 = 10 + 4*3.75x                                Combine

55 = 10 + 15x                                       Subtract 10 from both sides

55-10= 10-10 + 15x

45 = 15x                                               Divide by 15

45/15 = 15x/15

x = 3 hours

Answer 3 hours