In the following triangle, point O is the midpoint of LM, and point P is the midpoint if LN.

Below is the proof that OP||MN. The proof is divided into four parts, where the title of each part indicates its main purpose.
Complete part D of the proof.

Part A: Prove LM/LO=2

Part B: Prove LN/LP=2

Part C: Prove LMN ~ LOP

Part D: Prove OP||MN

The number makes the expression a perfect square trinomial is 25.

Hence, we have v² - 10v + 25.

Given the expression; v² - 10v

To determine the number that makes the expression a perfect square trinomial, we divide the coefficient of v by 2 and square the result.

( -1 × 10/2 )²

(-1 × 5)²

( -5 )²

25

We add 25 to the expression to get a perfect square trinomial.

v² - 10v + 25.

Therefore, the number makes the expression a perfect square trinomial is 25.

Hence, we have v² - 10v + 25.

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Answer:

slope = 11/2

Step-by-step explanation:

If you are given two points, you can find the slope using the point-slope equation. The equation looks like this:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from one point, and "x₂" and "y₂" represent the values from the other point. You can plug the values from the points into the equation and simplify to find the slope.

Point 1: (-4, 7)                Point 2: (-6, -4)

x₁ = -4                              x₂ = -6

y₁ = 7                               y₂ = -4

y₁ - y₂ = m(x₁ - x₂)                               <----- Point-slope form

7 - (-4) = m(-4 - (-6))                            <----- Insert values

11 = m(2)                                             <----- Simplify

11/2 = m                                             <----- Divide both sides by 2

[tex]\huge\boxed{\frac{11}{2}}[/tex]

The slope is equivalent to vertical change divided by horizontal change, otherwise known as "rise over run".

Therefore, the slope can be represented with the following equation, where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are your points:

[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values and simplify to find the answer.

[tex]\dfrac{(-4)-7}{(-6)-(-4)}[/tex]

[tex]\dfrac{-4-7}{-6+4}[/tex]

[tex]\dfrac{-11}{-2}[/tex]

[tex]\boxed{\frac{11}{2}}[/tex]

let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".

[tex]\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}[/tex]

Using the z-distribution, it is found that she should take a sample of 46 students.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence, by the Empirical Rule the standard deviation is found as follows:

[tex]6\sigma = 800 - 200[/tex]

[tex]6\sigma = 600[/tex]

[tex]\sigma = 100[/tex]

The sample size is n when M = 29, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]29 = 1.96\frac{100}{\sqrt{n}}[/tex]

[tex]29\sqrt{n} = 196[/tex]

[tex]\sqrt{n} = \frac{196}{29}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{196}{29}\right)^2[/tex]

n = 45.67.

Rounding up, a sample of 46 students should be taken.

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Answer:

True. empty set is the subset of any set

Step-by-step explanation:

Let take the first derivative

[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]

The second derivative

[tex] - {x}^{ - 2} [/tex]

The third derivative

[tex]2 {x}^{ - 3} [/tex]

The fourth derivative

[tex] - 6 {x}^{ - 4} [/tex]

The fifth derivative

[tex]24 {x}^{ - 5} [/tex]

Let create a pattern,

The values always have x in it so

our nth derivative will have x in it.

The nth derivative matches the negative nth power so the nth derivative so far is

[tex] {x}^{ - n} [/tex]

Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because

1!=1

2!=2

3!=6

4!=24

5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor

so our constant are

[tex](n - 1)[/tex]

So far, our nth derivative is

[tex](n - 1)!x {}^{ - n} [/tex]

Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)

[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]

That is our nth derivative

Answer:

about 19.31 years

Step-by-step explanation:

[tex]10000( {1.11}^{x} ) = 75000[/tex]

[tex] {1.11}^{x} = 7.5[/tex]

[tex]x ln(1.11) = ln(7.5) [/tex]

[tex]x = \frac{ ln(7.5) }{ ln(1.11) } = 19.31[/tex]

[tex]\square[/tex] The function is continuous. [False]

Both pieces of the function are continuous, so the overall continuity of [tex]g(x)[/tex] depends on continuity at [tex]x=0[/tex].

We have

[tex]\displaystyle \lim_{x\to0^-} g(x) = \lim_{x\to0} \left(\frac1{2^x} + 3\right) = 1 + 3 = 4[/tex]

and

[tex]\displaystyle \lim_{x\to0^+} g(x) = \lim_{x\to0} (-x^2+2) = 2[/tex]

The one-sided limits do not match, so [tex]g[/tex] is not continuous at [tex]x=0[/tex].

[tex]\square[/tex] As [tex]x[/tex] approaches positive infinity, [tex]g(x)[/tex] approaches positive infinity. [False]

[tex]g(x)[/tex] is a large negative number when [tex]x[/tex] is very large, so [tex]g(x)[/tex] is approaching negative infinity.

[tex]\boxed{\checkmark}[/tex] The function is decreasing over its entire domain. [True]

This requires [tex]g'(x) \le 0[/tex] on the entire real line. Compute the derivative of [tex]g[/tex].

[tex]g'(x) = \begin{cases}-\ln(2)\left(\dfrac12\right)^x & x<0 \\\\ ? & x=0 \\\\ -2x & x>0 \end{cases}[/tex]

• [tex]\left(\frac12\right)^x > 0[/tex] for all real [tex]x[/tex], so [tex]g'(x)<0[/tex] whenever [tex]x<0[/tex].

• [tex]x^2\ge0[/tex] for all real [tex]x[/tex], so [tex]-x^2\le0[/tex] and [tex]-x^2+2\le2[/tex]. Equality occurs only for [tex]x=0[/tex], which does not belong to [tex]x>0[/tex].

Whether the derivative at [tex]x=0[/tex] exists or not is actually irrelevant. The point is that [tex]g(b) < g(a)[/tex] if [tex]b>a[/tex] for all real [tex]a,b[/tex].

[tex]\boxed{\checkmark}[/tex] The domain is all real numbers. [True]

There are no infinite/nonremovable discontinuities, so all good here.

[tex]\boxed{\checkmark}[/tex] The [tex]y[/tex]-intercept is 2. [True]

When [tex]x=0[/tex],

[tex]g(0) = -0^2 + 2 = 2[/tex]

Answer:

The Third would be 72

Step-by-step explanation:

The sum of the two is 16+22=38. the third one is 72-38=34

These are the laws of indices. You just have to memorise it, sorry : (

Hope it helps : )

[tex]m = \frac{f(5) - f(0)}{5 - 0} [/tex]

[tex]m = \frac{ - 10 - 10}{5} = \frac{ - 20}{5} = - 4[/tex]

Step-by-step explanation:

the average rate of change is

(f(high interval end) - f(low interval end))/(high interval end - low interval end)

in our case here

(f(5) - f(0)) / (5 - 0)

(-10 - 10) / 5 = -20/5 = -4

The given coordinates are actually a rectangle

The coordinates are given as:

A (3, 1), B (1, 5), C (9, 9), and D (11, 5).

Calculate the distance between the coordinates using:

[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(3 -1)^2 +(1-5)^2} =\sqrt {20[/tex]

[tex]BC = \sqrt{(1 -9)^2 +(5-9)^2} =\sqrt {80[/tex]

[tex]CD = \sqrt{(9 -11)^2 +(9-5)^2} =\sqrt {20[/tex]

[tex]DA = \sqrt{(11 -3)^2 +(5-1)^2} =\sqrt {80[/tex]

The above shows that the opposite sides are congruent

Next, we calculate the slopes using:

m = (y2- y1)/(x2- x1)

So, we have:

AB = (1- 5)/(3-1) = -2

BC = (5- 9)/(1-9) = 1/2

CD = (9- 5)/(9-11) = -2

DA = (5- 1)/(11-3) = 1/2

The slopes of adjacent sides are opposite reciprocals.

This means that the sides are perpendicular

Hence, the given coordinates are actually a rectangle

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It would take the brave night 20 hours on his horse from one kingdom to another in 2 days.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let us assume that he travelled at 20 mph on the second day.  If he traveled exactly the same amount of time each day and went 300 miles, find how many hours it took the knight to travel from one kingdom to another.

Let t represent the time in hours travelled each day.

Total distance travelled in day one = 10t

Total distance travelled in day one = 20t

Hence:

10t + 20t = 300

t = 10 hours

Total time = 10 + 10 = 20 hours

It would take the brave night 20 hours on his horse from one kingdom to another in 2 days.

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Answer:

the answer to the question is 1

Answer:

-26 Is the correct answer

Step-by-step explanation:

The equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.

Given the expression; (z−3)4z−6

First, we apply distributive property.

(z−3)4z−6

(z−3)4z−6

z(4z) - 3(4z) - 6

We remove the parentheses

4z² - 12z - 6

Therefore, the equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.

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The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let f(n) represent the total cost of shoe rentals for n games, hence:

The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

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Answer:

30, 50, and 120

Step-by-step explanation:

3/20 × 200 = 30

5/20 × 200 = 50

12/20 × 200 = 120

The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.

Given that:

The sum of the measures of three angles = 200.

Let the ratios be x.

The ratio of first angle be 3x

The ratio of second angle be 5x

The ratio of third angle be 12x

According to the question,

3x+ 5x+ 12x = 200

20x = 200

Divide both sides by x

x = 200/20

x = 10

The ratio of first angle be 3x = 3(10) = 30 degrees

The ratio of second angle be 5x = 5(10) = 50 degrees

The ratio of third angle be 12x = 12(10) = 120 degrees

The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.

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The probability of selecting from the platter a chocolate cupcake and then a yellow cupcake is  0.10.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of selecting a chocolate cupcake and then a yellow cupcake = (number of chocolate cupcake / total number of cupcakes) x (number of yellow cupcakes / total number of cupcakes - 1)

(13 / 38) x (11 / 37) = 0.10

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

[tex]5P2 = \frac{5!}{(5 - 2)!} = \frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} = 20[/tex]

Answer:

3) 194 feet

Step-by-step explanation:

The other house:

"a house that is 33 ft wide and 50 ft long"

area = LW = (33 ft)(50 ft) = 1650 ft²

This house:

LW = A

L × 22 ft = 1650 ft²

L = 75 ft

P = 2(L + W)

P = 2(75 ft + 22 ft)

P = 194 ft

Answer: 3) 194 feet

Answer:

3) P = 194 ft.

Step-by-step explanation:

[tex]A=wl[/tex]

[tex](30)(50)=22l[/tex]

[tex]1650=22l[/tex]

[tex]l=1650/22=75[/tex]

the dimensions of the house are: (22 × 75)

Perimeter:

[tex]p=2(22)+2(75)=44+150=194[/tex]

Hope this helps

Answer:

1/21

Step-by-Step Explanation:

Let's solve your equation step-by-step.

3(1−5x)=2(3x+1)

Step 1: Simplify both sides of the equation.

3(1−5x)=2(3x+1)

(3)(1)+(3)(−5x)=(2)(3x)+(2)(1)(Distribute)

3+−15x=6x+2

−15x+3=6x+2

Step 2: Subtract 6x from both sides.

−15x+3−6x=6x+2−6x

−21x+3=2

Step 3: Subtract 3 from both sides.

−21x+3−3=2−3

−21x=−1

Step 4: Divide both sides by -21.

-21x/-21=-1/-21

x=1/21

[tex]\boldsymbol{\sf{3(1-5x)=2(3x+1)}}[/tex]

Reorder terms

Distribute

Subtract 3x from both sides.

Simplify

Subtract 6x from both sides.

Simplify

Divide both sides by the same factor

Simplify

1. The amount of the adjusting entry for Uncollectible Accounts is $1,250.

2. The adjusted balances of Accounts Receivable Allowance for Doubtful Accounts Bad Debt Expense are:

Accounts Receivable = $3,545,000

Allowance for Doubtful = $7,250

Accounts Bad Debt Expense = $1,250

3. The net realizable value of the accounts receivable is $3,537.750 ($3,545,000 - $7,250).

                               Accounts Receivable    Allowance for Doubtful Accounts

Beginning balance     $645,000 DR               $6,000 CR

Sales                          2,900,000

Bad Debt Estimate = $7,250 ($2,900,000 x 0.0025)

Ending balance      $3,545,000                     $7,250 CR

Bad Debts Expense = $1,250 ($7,250 - $6,000)

Thus, the net realizable value of the accounts receivable shows the amount that the company expects to recover from customers after allowing for doubtful accounts.

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1. Determine the amount of the adjusting entry for uncollectible accounts.

2. Determine the adjusted balances of Accounts Receivable, Allowance for Doubtful Accounts, and Bad Debt Expenses.

3. Determine the net realizable value of accounts receivable

The number of bacteria when t = 8 is approximately 66 bacterias

Given the function that gives the number of bacteria in a population as a function of time in hour expressed as:

P=48∙e^((0.045t))

If the value of t is 8, hence;

P=48∙e^((0.045(8))

P = 48e^0.36

P = 65.933

Hence the number of bacteria when t = 8 is approximately 66 bacterias

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Answer:

Step-by-step explanation:

...You need to subtract that number of units from the function equation.

Example:  given y = x^2, and wanting to shift the entire graph down 3 units, we subtract 3 from y = x^2, obtaining y = x^2 - 3.

Answer:

b

Step-by-step explanation:

(-4(-1)-8)(3(2)^2+2=4-8×12+2

-4×14=-56

Answer:

$4800

Step-by-step explanation:

Let's use the simple interest formula, P(1+rt), to find the final amount of the loan

10000(1+.12*4) = 14800, the final amount

14800 - 10000 = 4800 total in interest

Using the simple interest formula, it is found that the APR for the loan is of 4.472%.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

The parameters for this problem are:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

We solve the equation for r to find the APR.

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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The probability of all three events happening when the dies are rolled is; 0.0083

A) On the first die, it has 6 sides and 3 must come out, that is, 1 event out of 6 possible, therefore the probability is: 1/6

B) On the second die, it has 20 sides and if 19 or 20 can come out, that is 2 events out of 20 possible, so the probability is: 2/20 = 1/10

C) On the third die, which is 12 sides, an odd number can come out. The odd numbers would be 1, 3, 5, 7, 9, 11; i.e, 6 events out of 12 possible numbers.

Thus, the probability would be: 6/12 = 1/2

The final probability would be;

(1/6) * (1/10) * (1/2) = 0.0083

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Answer:

[tex]2xy^2(xy-1)(xy-3)[/tex]

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

Given expression

[tex]2x^3y^4-8x^2y^3+6xy^2[/tex]

The greatest common factor of all three terms is [tex]2xy^2[/tex].

Factor this out:

[tex]2xy^2(x^2y^2-4xy+3)[/tex]

Complete the square:

[tex]2xy^2(x^2y^2-4xy+4-1)=[/tex]

[tex]2xy^2((xy-2)^2-1)[/tex]

Factorize further using the identity for the difference of squares:

[tex]2xy^2(xy-2+1)(xy-2-1)=[/tex]

[tex]2xy^2(xy-1)(xy-3)[/tex]