1. Fill in the missing Statement/Reason for the following proof:
Given: LN bisects ZMLO and LM = LO
Prove: ALMN = ALON
M
STATEMENT
1.
2.
3.
4. LN = LN
5.
ALMN a ALON
REASON
N
1.
2.
3. def of Angle Bisector
4.
5.
| In

Answer:

Theres nothing shown

Step-by-step explanation:

Answer:

Q(x) = 15x^2 + x - 2.

Step-by-step explanation:

To find the height of the water in a pool when both hoses are on, we need to add the values of the two functions, F(x) and P(x), at a given x value. The new function, Q(x), that determines the height of the water in the pool can be expressed as follows:

Q(x) = F(x) + P(x) = 9x^2 + 3x - 5 + 6x^2 - 2x + 3 = 15x^2 + x - 2

So the height of the water in the pool is determined by the function Q(x) = 15x^2 + x - 2.

The equivalent expressions of 45 + 2i are (13 + 4i) + (32 - 6i) and  (9 + 4i) + 2(4 + 7i)(1 - 2i)

From the question, we have the following parameters that can be used in our computation:

Complex number: 45 + 2i

Next, we test the options:

(13 + 4i) + (32 - 6i) = 13 + 4i + 32 - 6i

(13 + 4i) + (32 - 6i) = 45 - 2i --- true

(13 + 4i) + 2(7 + 2i)(2 -i) = (13 + 4i) + 2(14 - 7i + 4i - 2)

(13 + 4i) + 2(7 + 2i)(2 -i) = 13 + 4i + 28 - 14i + 8i - 4

(13 + 4i) + 2(7 + 2i)(2 -i) = 37 - 2i --- false

(2 + 8i) + (30 - 6i) = 2 + 8i + 30 - 6i

(2 + 8i) + (30 - 6i) = 32 + 2i--- false

(9 + 4i) + 2(4 + 7i)(1 - 2i) =  (9 + 4i) + 2(4  - 8i + 7i + 14)

(9 + 4i) + 2(4 + 7i)(1 - 2i) =  9 + 4i + 8  - 16i + 14i + 28

(9 + 4i) + 2(4 + 7i)(1 - 2i) =  45+ 2i --- true

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Roman Rounds normally charges $18 for a large pizza.

What is the equation in one variable?

An equation in one variable is a mathematical statement that uses one variable and an equal sign to relate two expressions. The variable in the equation represents an unknown value, and the goal is often to find the value of the variable that makes the equation true.

Let's use p to represent the normal price of each large pizza charged by Roman Rounds.

Since the price of each pizza was reduced by $2 for the bulk order, the amount Mr. Mosley paid for 12 large pizzas is:

12(p - 2) = $192

We can simplify this equation by first distributing the 12 on the left side:

12p - 24 = $192

Then, we can isolate the variable p on one side of the equation by adding 24 to both sides:

12p = $216

Finally, we can solve for p by dividing both sides by 12:

p = $18

Therefore, Roman Rounds normally charges $18 for a large pizza.

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a.) The number of students that are over 145cm = 13

b.) The number of students with the height between 125 cm and 140 cm = 21 students.

C.) The number of students that were in class = 37

A frequency table is defined as a statistical tool that is used to organize the data given so that it makes it more meaningful and easier to understand.

To calculate the number of students that are over 145cm = 8+4+1 = 13 students.

To calculate the number of students that had a height

between 125 cm and 140 cm = 2+5+6+8 = 21 students.

To calculate the number of students that were in class= 3+2+5+6+8+8+4+1 = 37 students.

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Following are the values of the functions -

1) f(a) = 8a - 4

2) f(a+h) = 8a+ 8h - 4

3)[tex]\frac{f (a+h)-(a) }{h}= 8[/tex]

An expression or relationship with one or more variables is called a function. Both its inputs and outputs are numerous. There is just one output per input. The function explains how the inputs and outputs are related.

To evaluate f(a), we simply substitute the value of "a" into the function:

1) f(a) = 8a - 4

To evaluate f(a+h), we substitute the value of "a+h" into the function:

2) f(a+h) = 8(a+h) - 4

f(a+h) = 8a+ 8h-4

To find the expression for [tex]\frac{f (a+h)-(a) }{h}[/tex], we divide the result by h: L(a+h)-f(a) h we can subtract f(a) from f(a+h) and then

3) [tex]\frac{f (a+h)-(a) }{h}[/tex]

[tex]= \frac{ (8a+8h-4-(8a-4)}{h} \\= \frac{8h}{h}= 8[/tex]

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Answer:

24 people

Step-by-step explanation:

German : 4 + (4/2) = 6

Norwegian : 4 + 4 + (4/2) = 10

Italian : 4 + 4 = 8

Add them all :

6 + 10 + 8 = 24

To find the mean (average) of a set of numbers, you add up all the numbers and then divide by the number of items in the set.

Mean = (79g + 88g + 116g + 109g + 93g) / 5

Mean = (475g) / 5

Mean = 95g

So, the mean of the set of numbers is 95g.

The value of mean of the data set is,

⇒ Mean = 97 g

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Data set is,

79g, 88g, 116g, 109g, 93g

Now, We get;

The mean of data set is,

⇒ Mean = 79g + 88g + 116g + 109g + 93g / 5

⇒ Mean = 485g / 5

⇒ Mean = 97 g

Thus, The value of mean of the data set is,

⇒ Mean = 97 g

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Answer: look at the image for the answer and explanation

Step-by-step explanation:

Answer:

Step-by-step explanation:

perp.: -4/3

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

y - 1 = -4/3x + 4

y = -4/3x + 5

y-int: (0, 5)

Answer:

Step-by-step explanation:

here's a more detailed explanation:

The assistant received a raise of 10%, which means that their salary increased by 10% of the original salary. The new salary after the raise is given as 47,585.

To find the original salary before the raise, we need to reverse the effect of the raise. To do this, we divide the new salary by the factor that represents the increase, which is 1 plus the raise as a decimal.

The raise as a percentage is 10%, which is equivalent to 0.10 as a decimal. Therefore, the factor that represents the increase is 1 + 0.10 = 1.10.

We can now use this factor to find the original salary by dividing the new salary by the factor:

Original salary = New salary / (1 + Raise as a decimal)

Original salary = 47,585 / (1 + 0.10)

Original salary = 47,585 / 1.10

Original salary = 43,259.09

So the salary before the raise was 43,259.09.

Answer:

5x(8-1)=(5x10)-(5x4)

Answer:

It has a Unique solution.

Step-by-step explanation:

The equations are:

y=-2x+1 and y=3x-1

subtracting equation 2 from equation 3

we get,

⇒-5x+2=0

⇒5x=2

⇒x=2/5

substitute x in equation 1, then we get

⇒y=-4/5+1

⇒y=1/5

Hence the equations have a Unique solution.

The value of the fifth term B is 17.

An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).

Given:

The first term of the sequence is 2.

a₁ = 2

And the explicit formula of the sequence,

aₙ = (-2)aₙ₋₁ + 3.

The value of a₂:

a₂ = (-2)a₁+ 3.

a₂ = -2(2) + 3 = -1

And a₃ = -2(-1) + 3 =5

a₄ = -2(5) + 3 = -7

Now, the value of the fifth term,

a₅ = -2(-7) + 3 = 17.

Therefore, the fifth term is 17.

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The length of the lake is 100 ft

Form a right-angled triangle according to the given data in the problem. Chose which trigonometric ratio can be used to find the side that is considered as the side of the lake.  

From the trigonometric ratio table,

Here we have

Yoshi swam across a lake but did not know how far he swam.

He found that it was 100√) feet from point A to point C.

Angle C was a right angle and angle A is 30°.

We represent the given scenario in the form of a right angle triangle as shown in the picture.

Let 'B' be the point where Yoshi swam started and  BC be the length of the lake.  

From the triangle,  

Tan A = BC/AC

From the given data,

Tan 30° = BC/100√3

=> BC = Tan 30°(100√3)

=> BC = (1/√3)(100√3)  

=> BC = 100 ft

Therefore,

The length of the lake is 100 ft

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The proof of the parallelogram has been given below

We have WXYZ as a parallelogram.

XW = ZY

XW // ZY

such that

M ∠VXW = M VZY (This is alternate interior angles,)

M∠VWX = M ∠VYZ

therefore ΔVXW ≅ Δvzy

wv = yv

Then XZ bisects WY

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The percentage of R90 that will give 90c is 4%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

1 cent = R0.04

R1 = 1/0.04

R 90 = 90/0.04 = 2,250c

x/100 × 2250 = 90

2250x = 9000

x = 9000/2250

x= 4%

therefore 4 percent of R 90 is 90c

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Answer:

Step-by-step explanation:

К счастью, другое маленькое дерево поблизости заметило растущее дерево и дало несколько интересных советов о том, как удерживать его распускающиеся листья новыми и интересными способами. Было забавно испытать на других маленьких деревьях множество различных способов расположения листьев. Другие маленькие деревья вскоре заметили это и начали поворачивать свои немногочисленные листья под углом. Другие маленькие деревья могли лишь слегка приподнять свои листья.

Растущее дерево решило, что будет немного приподнимать листья на радость другим деревьям. Но, в конце концов, все маленькие деревья начали отращивать больше листьев на ветвях, которые тянулись еще дальше. С каждым сезоном многие листья невозможно было приподнять. Некоторые из растущих деревьев продолжали шептаться, в то время как некоторые научились громко смеяться, некоторым, казалось, нравилось плакать и падать духом, а некоторые росли вдали от группы из-за того, как многие времена года влияли на них и на другие деревья и животных вокруг них.

За прошедшие годы родительские деревья время от времени мельком смотрели вниз, чтобы увидеть, как растут их семена, и они поднимали свои ветви к небу, чтобы пропустить солнечный свет через полог. Все растущие деревья заметят это и поднимут головы, чтобы насладиться солнечным светом. Те, кто не обращал внимания на поведение своего родительского дерева, обычно подражали другим растущим деревьям и умудрялись собирать немного солнечного света. Иногда растущее дерево переставало расти, потому что не могло достичь солнечного света. Его листья не будут такими обильными, а его ветви будут тянуться дальше, чтобы быть ближе к солнечному свету других растущих деревьев. По прошествии многих сезонов растущие деревья становились все выше и теперь можно было видеть, что их место среди кроны деревьев было довольно тесным.

Explanation:

Let's replace y with 0 and solve for x.

-x+6y = 2

-x+6*0 = 2

-x + 0 = 2

-x = 2

x = -2

We have x = -2 pair up with y = 0 to get the ordered pair (x,y) = (-2,0)

This is the x intercept of the graph. It's where the line crosses the x axis. You can use a tool like Desmos or GeoGebra to confirm.

Since we have infinitely many numbers to replace x or y with, we have infinitely many solution points on this line.

Each point is of the form (-2+6k, k) where k is any real number.  If k = 0, then it leads to (-2,0) found earlier.

The difference in the interest accrued by the end of the first month, given the credit rating and the cost is $ 21. 97

First, find the amount borrowed to pay for the new car or the used car.

New car :

= ( 19, 072 x ( 1 + 4. 5 % sales tax )) - 1, 200 down payment

= $ 18, 730. 24

The used car :

= 15, 635. 00 x ( 1 + 4. 5 %) - 1, 200

= $ 15, 138. 58

The difference in interest at the first month is :

= ( Amount borrowed for new car x Monthly APR for fair credit rating ) - ( Amount borrowed for old car x Monthly APR for fair credit rating )

= ( 18, 730. 24 x 7. 55 % / 12 ) - ( 15, 138. 58 x 7. 60 % / 12 )

= $ 21. 97

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The given series is geometric when r equals negative three-fifths.

What is geometric series?

The geometric series refers to the total of terms with a common ratio between every pair of neighbouring terms. Geometric series can be of two different types: finite and infinite. The sequence is of the form {a, ar, ar², ar³, …….} where, a is the first term, and r is the "common ratio".

where, r = ar/a = (second term)/(first term)

Given, the series 250 – 150 + 90 – 54 + …

So, r = (-150)/250 = -3/5

or, r = 90/(-150) = -3/5

Hence, for the geometric series, r should be equal to negative three-fifths.

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Answer:

B. x=5

Step-by-step explanation:

3x + 6 = 21

Subtract 6 from both sides.

3x = 15

Divide both sides by 3.

x = 5

Answer: B. X=5

Step-by-step explanation:

3x+6=21

subtract 6 on both sides

3x=15

divide by 3 on both sides

x=5

The percentage increase in Marvin's height is 4.51%

Marvin was 1.55m tall a year ago

Now her present height is 1.62m

The first step is to calculate the increase

= 1.62-1.55

= 0.07

The percentage increase can be calculated as follows

0.07/1.55 × 100

= 0.0451 × 100

= 4.51

Hence the percentage increase is 4.51%

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Answer:

The answer is that 1 2/3 and 3/4 common denominate is /12

Step-by-step explanation:

3 x 4 equals 12 then multiply 2 by 4 and 3 by 3 then it’s 1 8/12 and 9/12

Answer:

The correct answer is D.

Step-by-step explanation:

D. y = 0.8x + 4.

Answer:

Step-by-step explanation:

The correct answer is D. m∠6 + m∠7 = 180°.

When a transversal cuts two parallel lines, corresponding angles are equal and alternate interior angles are supplementary. This means that the sum of alternate interior angles is equal to 180°. In this diagram, ∠6 and ∠7 are alternate interior angles, so it is necessarily true that m∠6 + m∠7 = 180°.

The other options are not necessarily true. Option A states that m∠1 = m∠7, but this is only true if the two lines being cut by the transversal are perpendicular. Option B states that m∠3 = m∠6, but this is only true if the two lines being cut by the transversal are parallel. Option C states that m∠5 + m∠8 = 90°, but this is only true if the two lines being cut by the transversal are perpendicular.

Answer:

The set of all numbers less than 17 and greater than or equal to -8 can be expressed in set builder notation as:

{x | -8 <= x < 17}

Step-by-step explanation:

Set builder notation is a way of expressing a set of elements in mathematical terms. The syntax of set builder notation is {x | <condition>}, where x represents an element in the set and the condition specifies the properties that the element must satisfy to be included in the set.

In this case, the set consists of all numbers less than 17 and greater than or equal to -8. The condition for the set is -8 <= x < 17, where x is a real number. This means that x must be greater than or equal to -8 and less than 17 in order to be included in the set.

Therefore, the set of all numbers less than 17 and greater than or equal to -8 can be expressed in set builder notation as:

{x | -8 <= x < 17}.

As per the probability, the value of E(X) is option (a) 0.8

In statistics, the expected value or mean is a measure of central tendency that represents the average outcome of a random variable over an infinite number of trials.

To find the expected value of X, we need to calculate the probability of each possible outcome and multiply it by its corresponding value. In this case, the possible outcomes are 0 and 1, and their probabilities can be calculated as follows:

The probability of drawing a 0 is 4/5 because there are 4 zeros in the list and 5 total numbers.

The probability of drawing a 1 is 1/5 because there is only one 1 in the list and 5 total numbers.

Using these probabilities, we can calculate the expected value of X as follows:

E(X) = (0 x 1/5) + (1 x 4/5)

The first term in this equation represents the probability of drawing a 0, multiplied by its value (which is 0), and the second term represents the probability of drawing a 1, multiplied by its value (which is 1). Simplifying this equation gives:

E(X) = 4/5 =0.8

Therefore, the answer to this problem is (a) 0.8, since the expected value of X is 0.8 of the possible outcomes.

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The graph of the points can be seen at the end, and the relation is not a function.

The coordinate axis has two axis with numbers labeled. For any point (x, y), you need to find the value x on the horizontal axis and the value y on the vertical axis.

Then the graph of the points  ​(-7,5), (-4,-6), (-1,4), (-7,3) will be like the one at the end of the answer.

Now, is this a function?

Not, it is not, because we can see that the input -7 is being mapped into two different outputs, and a relation is a function only if each input is mapped into a single output.

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Answer: The equation "x + y = mb" represents a linear equation in two variables, x and y. In this equation, m is a constant and b is another constant or a known value. The equation states that the sum of x and y is equal to the product of m and b.

This equation can be used to model a variety of real-world situations where two quantities are related and their sum is equal to a constant value. For example, it could represent the amount of money saved by two people, where x and y are the savings of the two people and mb is the total amount of money saved.

To solve for x and y, we can use either substitution or elimination method, or any other method for solving systems of linear equations. The values of x and y that satisfy the equation "x + y = mb" are called the solutions of the equation.

Step-by-step explanation: