Consider the paragraph proof.

Given: D is the midpoint of AB, and E is the midpoint of AC.
Prove:DE = One-halfBC

On a coordinate plane, triangle A B C is cut by line segment D E. Point D is the midpoint of side A B and point E is the midpoint of side A C. Point A is at (2 b, 2 c), point E is at (a + b, c), point C is at (2 a, 0), point B is at (0, 0), and point D is at (b, c).

It is given that D is the midpoint of AB and E is the midpoint of AC. To prove that DE is half the length of BC, the distance formula, d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot, can be used to determine the lengths of the two segments. The length of BC can be determined with the equation BC = StartRoot (2 a minus 0) squared + (0 minus 0) squared EndRoot, which simplifies to 2a. The length of DE can be determined with the equation DE = StartRoot (a + b minus b) squared + (c minus c) squared EndRoot, which simplifies to ________. Therefore, BC is twice DE, and DE is half BC.

Which is the missing information in the proof?
a
4a
a2
4a2

There are 1,16,280 different recital programs possible.

Given: A pianist plans to play 4 pieces at a recital from her repertoire of 20 pieces and is carefully considering which song to play first, second, etc.

It means the repetition of pieces is not allowed.

When repetition is not allowed, then the number of ways to arrange n things where r things taken together is given by:-

[tex]^{n} P_{r} =\frac{n!}{(n-r)!}[/tex]

Now, the number of different recital programs are:-

[tex]^{20} P_{4} =\frac{20!}{(20-4)!}=\frac{20*19*18*17*16!}{16!}=116280[/tex]

Hence, there are 1,16,280 different recital programs possible.

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Using proportions, it is found that the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each lb has 0,0005 tons. Hence the total weight in tons that we want to put in the elevator is:

T = (175 + 240 + 80 x 50) x 0.0005 = 2.2075 tons.

Hence, the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.

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The reportable square footage for Kinsey's home = 2150square feet.

The main floor of Kinsey's home is 1,425 square feet.

The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet.

The finished basement is 1,425 square feet with 7.5-foot ceilings.

That means the square footage of the upper floor plus the main floor (minus the unfinished laundry area).

Kinsey should report square feet (1425+875- 150)

= 2150square feet.

Hence, The reportable square footage for Kinsey's home = 2150square feet.

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Triangle A was dilated by a scale factor of 1/3 and reflected over the x axis to form triangle A'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

Triangle A was dilated by a scale factor of 1/3 and reflected over the x axis to form triangle A'

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Answer:

b d e

Step-by-step explanation:

The largest possible error in the area of the circle is of 44%.

The area of a circle of radius r is given by:

[tex]A = \pi r^2[/tex]

With a diameter of 20 cm = radius of 10 cm, the area in cm² is given by:

[tex]A = \pi \times 10^2 = 100\pi[/tex]

With the error, with a diameter of 20 x 1.2 = 24 cm = radius of 12 cm, the area in cm² is given by:

[tex]A = \pi \times 12^2 = 144\pi[/tex]

The error is given by:

[tex]E = 144\pi - 100\pi = 44\pi[/tex]

The percent error is the error divided by the initial amount, multiplied by 100%, hence:

[tex]P = \frac{44\pi}{100\pi} \times 100\% = 44\%[/tex]

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Answer:

its an odd number

Step-by-step explanation:

The solution set of -4(x + 3) ≤ -21 is x ≥ 2.25

The inequality is given as:

-4(x + 3) ≤ -21

Divide both sides by -4

x + 3 ≥ 5.25

Subtract 3 from both sides

x ≥ 2.25

This means that the solution set of -4(x + 3) ≤ -21 is x ≥ 2.25

See attachment for the number line

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For the function f(x) = 4|x - 3| + 4, we have that:

The x-intercept of a function is the value of x when y = f(x) = 0, hence:

0 = 4|x - 3| + 4

4|x - 4| = -4

|x - 4| = -1

The absolute value cannot be negative, hence the function has no x-intercepts.

The x-intercept of a function is the value of y = f(x) when x = 0, hence:

f(0) = 4|0 - 3| + 4 = 12 + 4 = 16.

The y-intercept is of y = 16.

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Step-by-step explanation:

[tex] \frac{x}{12} = \frac{x + 4}{5 + 12} \\ [/tex]

[tex] \frac{x}{12} = \frac{x + 4}{17} \\ [/tex]

Now cross multiply...

[tex]12(x + 4) = 17x[/tex]

[tex]12x + 48 = 17x[/tex]

[tex]12x - 17x = - 48[/tex]

[tex] - 5x = - 48[/tex]

Now divide both term by same number

[tex] \frac{ - 5x}{ - 5} = \frac{ - 48}{ - 5} \\ [/tex]

[tex]x = 9.6[/tex]

The equation that has an infinite number of solutions is [tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

An equation that has an infinite number of solutions would be in the form

a = a

This means that both sides of the equation would be the same

Start by simplifying the options

3(x – 1) = x + 2(x + 1) + 1

3x - 3 = x + 3x + 2 + 1

3x - 3 = 4x + 3

Evaluate

x = 6 ----- one solution

x – 4(x + 1) = –3(x + 1) + 1

x - 4x - 4 = -3x - 3 + 1

-3x - 4 = -3x - 2

-4 = -2 ---- no solution

[tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

2x + 3 = 2x + 1 + 2

2x + 3 = 2x + 3

Subtract 2x

3 = 3 ---- infinite solution

Hence, the equation that has an infinite number of solutions is [tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

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Complete question

Which equation has infinite solutions?

3(x – 1) = x + 2(x + 1) + 1

x – 4(x + 1) = –3(x + 1) + 1

[tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

[tex]\frac 13(6x - 3) = 3(x + 1) - x - 2[/tex]

Answer:

B) f≥0.2(375,000) +7,200

Step-by-step explanation:

≥ means 'at least'

answers

6. y = -1/2x + 8

7. y = 15

8. y = -3/4x + 1

9. y = 6x + 3

10. y = 1/3x - 4

steps

equation of the line that is perpendicular means the number next to the x should be a negative reciprocal

number next to the x is the slope

6. y=2x+5

y = mx + b

m = 2

b = -5

negative reciprocal would be

-1/2x

m = -1/2

(2, 7) means x = 2 y = 7

substitute

7 = -1/2(2) + b

7 = -1 + b

b = 8

answer is y = -1/2x + 8

7.

y = 5; (11, 15)

b = 5

m would be 0 because there is no slope

15 = 0*11 + b

b = 15

y = 15

8.

line goes through

(0,-2) and (3,2)

get slope

y2-y1/x2-x1

2-(-2) / 3 - 0

4/3

y = 4/3x

point slope form

y - y1 = m (x-x1)

y - -2 =  4/3 (x - 0)

y+2 =  4/3x

y = 4/3x - 2

negative reciprocal slope would be for perpendicular

-3/4x

(12, 10)

y = mx + b

10 = 3/4(12) + b

10 = 9 + b

1 =  b

b = 1

y = -3/4x + 1

9.

y = -1/6x + 1; (− 2, — 9)

negative reciprocal slope would be for perpendicular

+6x

(− 2, — 9)

y = mx + b

get b

-9 = 6(-2) + b

-9 = -12 + b

b = 3

y = 6x + 3

10.

6x+2y=14; (12, 0)

2y= -6x+14

y= -3x+7

negative reciprocal slope would be for perpendicular

1/3x

y = mx + b

get b

0 = 1/3(12) + b

0 = 4 + b

b = -4

y = 1/3x - 4

The quantities which are squares or multiple of linear things twice grow by square of scale factor. The volume of rectangular prism A = 64 m³

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So, area of first figure = k² × area of second figure

Similarly, Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

Given that the Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 1/2.

Scale factor =  (Length of rectangular prism B)/(Length of rectangular prism A)

1/2 = (Length of rectangular prism B)/(Length of rectangular prism A)

Now, the volume of the rectangular prism can be written as,

(Scale factor)³ = (Volume of rectangular prism B)/(Volume of rectangular prism A)

(1/2)³ = 8 m³ /(Volume of rectangular prism A)

The volume of rectangular prism A = 64 m³

Hence, The volume of rectangular prism A = 64 m³

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a. Find the graph in the attachment

b. As h increases, e tends to 90°

Since you are standing 22 feet from a tall building that has a glass elevator on the exterior wall facing you. You watch the elevator as it ascends to the top of the building.

The height h (in feet) of the elevator above the ground can be modeled by h = 22tane.

To plot the graph, we see that the function is the tangent function.

The tangent function has the value -∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°

Since e is our angle of elevation and e ≥ 0, that is 0 ≤ e ≤ 90°. So, we choose the range of values for which tane ≥ 0. So, 0 ≤ tane ≤ +∞

So, we plot h = 22tane for 0 ≤ e ≤ 90°

Find the graph in the attachment

From the graph, we seet that at high h or as h increases, e tends to 90°

So, as h increases, e tends to 90°

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Answer:

z = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the altitude- on- hypotenuse theorem

(leg of large Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

z² = 8 × (8 + 1) = 8 × 9 = 72 ( take square root of both sides )

z = [tex]\sqrt{72}[/tex] = [tex]\sqrt{36(2)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex] = 6[tex]\sqrt{2}[/tex]

Answer:

[tex]z = 6 \sqrt{2} [/tex]

Step-by-step explanation:

The solution is in the image

Answer:

1, 5

Step-by-step explanation:

-16/4=-4

10/5=2

1/2=1/2

-1/-3=1/3

-1/4/1/2=-1/2

The negative ones are your answer.

The solution of the equations will be the point of intersection of the two lines

A line is the shortest distance between two points. The equation of a line in standard form is given as Ax + By = C

According to the question, we are to pot the following lines.

4y +3x = 0

4y - x = 16

The solution of the equations will be the point of intersection of the two lines as attached.

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Answer: 38.2 degrees

Step-by-step explanation:

[tex]b^2 = a^2 + c^2 - 2ac \cos B\\\\5^2 = 3^2 + 7^2 - 2(3)(7) \cos B\\\\25 = 58-42 \cos B\\\\-42 \cos B=-33\\\\\cos B=\frac{33}{42}\\\\B \approx 38.2^{\circ}[/tex]

Answer:

No, the ratio is not the same.

Step-by-step explanation:

75 total (large tank) / 25 total (small tank) = 3

25 angelfish (large tank) / 5 angelfish (small tank) = 5

The ratio of angelfish to total fish is not the same. When we scale up from the small tank to large tank in terms of total fish, we have a factor of 3. However, when we scale up from the small tank to large tank in terms of angelfish, we have a factor of 5. For the ratio to be the same, these factors would need to be identical.

Answer:0

Step-by-step explanation:

Answer:

I would say b since this would tell him how many people are wiling to join a health club

Hope This Helps!!!

Answer:

16 Liters of the correct answer.

Emil started his lemonade stand with 12 litres of Lemonade.

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:-Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what was left in the afternoon.

When he closes for the day, he has 4 litres of lemonade left. Let the total lemonade he started with is x litres. Now we will form an expression from the given data to calculate the value of x.

x - (x/2) -(1/4)(x/2) - ( 1/4)(x/2)(1/3) = 4

x - ( x/2) - (x/8) - ( x/24) = 4

[ 24x -12x -3x - x][24] = 4

8x  =  96

x = 12 liters

Therefore Emil started his lemonade stand with 12 liters of Lemonade.

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Answer:

could u send a photo please

Answer:5

Step-by-step explanation:

Answer:

[tex]y=\dfrac {60} {x}[/tex]   or   [tex]xy=60[/tex]   (depending on your teacher's format preference)

Step-by-step explanation:

Proportionality is sometimes called "variation".   (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

From these examples, we see that two things:

In our question, y is inversely proportional to x, so the equation we're looking at is the following [tex]y=\dfrac {k} {x}[/tex].

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it:  "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

General Inverse variation equation...

[tex]y=\dfrac {k} {x}[/tex]

Substituting known values...

[tex](12)=\dfrac {k} {(5)}[/tex]

Multiplying both sides by 5...

[tex](12)*5= \left ( \dfrac {k} {5} \right ) *5[/tex]

Simplifying/arithmetic...

[tex]60=k[/tex]

So, for our situation, k=60.  So the inverse proportionality relationship equation for this situation is [tex]y=\dfrac {60} {x}[/tex].

The way your question is phrased, they may prefer the form: [tex]xy=60[/tex]

The logarithm base 10 of the number 10 is 1

We have to find logarithm base 10 of number 10.

Therefore, using logarithm rule

logₐ a = 1

Hence,

log₁₀ 10 = 1

Therefore, logarithm base 10 of the number 10 is 1

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Answer:

1

Step-by-step explanation:

Answer:

If the population of the United States on July 4,2010 was almost 310000000 then, the number in scientific notation is [tex]$3.1 \times 10^{8}$[/tex].

Step-by-step explanation:

- Given

Population of the United States on July 4,2010 was almost 310000000 .

- To write the number in scientific notation.

- Firstly, move the decimal point so that the first factor is greater than or equal to 1 but less than 10 .

- Then, count the number of decimal places, n, that the decimal point was moved.

- Then, write the number as a product with a power of 10.

- Finally, check the scientific notation.

Step 1 of 2

Moving the decimal point-

Move the decimal after 3 . so that 3.10000000 is between 1 and 10 .

Now, we know the decimal point was moved 8 places to the left.

Step 2 of 2

Writing the number as a product with a power of 10 -

Since, 310000000 is greater than 1 so the power of 10 will have the exponent 8 .

Therefore, the number becomes-

[tex]$$31000000=3.1 \times 10^{8}$$[/tex]

Now, checking the scientific notation-

[tex]$$\begin{gathered}3.1 \times 10^{8}=3.1 \times 100000000 \\=310000000\end{gathered}$$[/tex]

[tex]f(x )= - 2x[/tex]

[tex]g(x) = \frac{1}{2} x {}^{2} + 5[/tex]

#1

Domain

Range

#2

Domain

Range

#3

Its graphed

Domain=Range=(-oo,oo)

#4

Domain

Range

[-3,-oo) or (-oo,-3]

The magnitude and direction of line UV is 19.7° South of West for 8.1 miles

The magnitude of the vector line UV is given by the length of the line UV,

d = √[(x₂ - x₁)² + (y₂ - y₁)²] where

Substituting the values of the variables intot he equation, we have

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(-2 - 2)² + (-4 - 3)²]

d = √[(-4)² + (-7)²]

d = √[4² + 7²]

d = √[16 + 49]

d = √65

d = 8.06 miles

d ≅ 8.1 miles

So, the magnitude of vector line UV is 8.1 miles

The direction of the vector line UV is given by Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)] where

Substituting the values of the variables into the equation, we have

Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)]

Ф = tan⁻¹[(-4 - 3)/(-2 - 2)]

Ф = tan⁻¹[(-7)/(-4)]

Ф = tan⁻¹[7/4]

Ф = tan⁻¹[1.75]

Ф = 60.26°

Ф ≅ 60.3°

Its bearing from the north-south line is α = 90° - Ф

= 90° - 60.3°

= 19.7°

So, its direction is 19.7° South of West

So, the magnitude and direction of line UV is 19.7° South of West for 8.1 miles

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Answer:

none of these are correct

Step-by-step explanation: