Given the figure, and MN || QR, what can be concluded?
PM
PN
PQ = PR
Q
M
MN = QR
P
N
R
MP=2-QM
PM
NR
=
PN
MQ

The equation g(x) = (x - 4) (x + 2) is in the factored form.

The x-intercepts are x = -2 and x = 4.

The axis of symmetry is x = 1.

Vertex is (1, -9).

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

g(x) = (x - 4) (x + 2)

This is in the factored form.

Now,

From the graph,

The x-intercepts are x = -2 and x = 4.

The axis of symmetry.

x = -b/2a

x = 2/2

x = 1

i.e

g(x) = (x - 4) (x + 2)

g(x) = x² + 2x - 4x - 8

g(x) = x² - 2x - 8

a = 1, b = -2, and c = -8

Now,

g(x) = x² - 2x - 8

g(x) = x² - 2x + 1 - 1 - 8

g(x) = (x² - 2x + 1) - 9

g(x) = (x - 1)² - 9

This is in the form of f(x) = a(x - h)² + k

So,

Vertex = (h, k) = (1, -9)

Thus,

The statements are completed above.

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The mode, median, mean ,weighted mean, spread of the set of data are: 125, 190, 278429,  765 respectively

We are asked to find the following

Mode:  This is the highest occurred frequency in a set of data and the mode here is 125

The median is the middle frequency when arranged in an order of magnitude the the set of data is  $125,000, $125,000, $178,000, $190,000, $216,000, $225,000, and $890,000. the median is 190

The mean is the average of the data that is: ( $125,000,+$125,000+$178,000+$190,000+$216,000+$225,000+$890,000)/7 = 1949000/7 = 279429

the spread is the range which is the highest frequency minus the lowest frequency =  $890,000 -$125,000= 765000

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Answer:

median

Step-by-step explanation:

The inverse Laplace transform of (2/(s+5)) is f(t) = 2 * e^(-5t)u(t).

To find the inverse Laplace transform of F(s) = (2/(s+5)), we can use partial fraction expansion and then use a table of Laplace transforms to identify the inverse transforms.

Step 1: Perform partial fraction expansion on the fraction:

(2/(s+5)) = (2/5) * (1/(1+(s/5))) = (2/5) * (1/1 + (s/5))

Step 2: Recognize the form of the partial fraction as a geometric series, and use the formula for the sum of a geometric series to find the inverse Laplace transform:

The sum of this geometric series is

(2/5) * (1/(1-(-s/5)))

= (2/5) * (1/(1+s/5))

= (2/5) * (5/5+s)

= (2/(5+s))

Step 3: Use the table of Laplace transforms to find the inverse transform of (2/(5+s)):

f(t) = 2 * e^(-5t)u(t)

where u(t) is the unit step function.

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The congruence theorem that proves that △LON ≅ △LMN is: A. SSS congruence theorem

According to the SSS congruence theorem, if all three corresponding sides of two triangles are congruent, then both triangles are congruent.

here, we have,

In the image given, we have:

ON ≅ MN

LO ≅ LM

LN ≅ LN (reflexive property)

This means all three corresponding sides are congruent, therefore, the congruence theorem that proves both triangles are congruent is:

A. SSS.

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If you read the decimal version of 4.8 out loud, it should be "four and eight-tenths."  This will always give you a good place to start when changing a decimal into an equivalent fraction.

Now, this is a mixed number: 4 and 8/10. To further simplify it as a mixed number, we can leave the 4 alone and reduce the fraction (8/10).  Both the numerator and denominator are divisible by 2, so we can conclude (8/10) = (4/5).  A correct answer in mixed number form is 4 and (4/5).

However, to change 4 and (4/5) to a single (improper) fraction, you first multiply the denominator (5) by the large number out front on the left (4) and ADD this product to the numerator (4).  This number is your new numerator and it will still have the same denominator as before.

Here, 4 and (4/5) = [(5)*(4) + 4]/5 = (20+4)/5 = 24/5.

24 and 5 have no common factors, so this fraction is already in reduced form.

4.8 = 4 8/10 = 4 4/5

Answer:

D

Step-by-step explanation:

bc -1+27 =26

Answer:

6s

Step-by-step explanation:

2+2+3+S+9-10

first we can put these in different group to find out, like number to number, variable to variable. so it will be 2+3+2+9-10=6

second they only one s, so answer is 6s

i hope is helpful

Answer:

w ≈ 12.14 cm

Step-by-step explanation:

using the tangent ratio in the right triangle on the left.

let vertical height be x

tan56° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{3.2}[/tex] ( multiply both sides by 3.2 )

3.2 × tan56° = x , then

x ≈ 4.744

using the cosine ratio in the right triangle on the right

cos67° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{w}[/tex] = [tex]\frac{4.744}{w}[/tex] ( multiply both sides by w )

w × cos67° = 4.744 ( divide both sides by cos67° )

w = [tex]\frac{4.744}{cos67}[/tex] ≈ 12.14 cm (to 2 decimal places )

Answer:

w = 12.14 cm

Step-by-step explanation:

See the attached image. Trigonometric functions will be used

Answer:

  sum = (m+n)(n-m +1)/2

Step-by-step explanation:

You want an expression for the sum of the numbers from m to n.

As the example shows, the sums of the numbers written forward and backward will be the sum of the numbers at the ends of the range:

  m +n

The number of times this sum is repeated is equal to the number of numbers in the range:

  n -m +1

The sum of the numbers in the range will be half the product of these values:

  sum = (m+n)(n-m +1)/2

The cost c of fish varies directly as its weight w in kilograms.

a.Direct variation

b.joint variation

c.combined variation

A SIMPLE RELATIONSHIP BETWEEN TWO VARIABLES IS DESCRIBED AS A DIRECT VARIATION.

When c=kw, where k is the variational constant, we say that c directly varies with w.

2. The quantity of men (n) required to complete a task varies inversely with the duration (d) of the task.

INVERSE VARIATION: Inverse variation occurs when the product of two variables (n and d) ALWAYS equals a fixed value (k). Example,

N=k/d states that the required number of men (n) varies inversely with the number of days (d) required to complete the task.

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The dimensions of width, length and height of the passenger section of the train are 3 meters, 13 meters and 3 meters respectively.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

Given that;

First, plug in the given values into the above formula and solve for x.

V = w × h × l

117 = ( 2x - 7 )( 2x + 3 )( x - 2 )

Expand using FOIL method

( 2x - 7 )( 2x + 3 )( x - 2 ) = 117

( 2x(2x) + 2x(3) - 7(2x) - 7(3) )( x - 2) = 117

( 4x² - 8x - 21 )( x - 2 ) = 117

Expand

4x³ - 16x² - 5x + 42 = 117

4x³ - 16x² - 5x + 42 - 117 = 0

4x³ - 16x² - 5x - 75 = 0

Using rational roots text

(x - 5)(4x² + 4x + 15 ) = 0

( x - 5 ) = 0

x - 5 = 0

x = 5

4x² + 4x + 15 = 0

x = -1±i√14 / 2

Since dimensions are real and positive numbers, we use;

x = 5

To determine the dimensions of the passenger section of the train, plug in x = 5 and simplify.

Width = 2x - 7 = 2( 5 ) - 7 = 10 - 7 = 3 meters

Length = 2x + 3 = 2( 5 ) + 3 = 10 + 3 = 13 meters

Height = x - 2 = 5 - 2 = 3 meters

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The number of terminating zero when the number 6311! is  multiplied out is 252

In mathematics, trailing zeros are a series of digits (usually 0) that follow a number's decimal form or, more broadly, any positional representation.

In mathematics, the term "factorial" refers to the product of all positive integers that are less than or equal to a certain positive integer, which is followed by an exclamation point.

Thus, factorial five is denoted by the symbol 5!, which stands for 1 * 2 * 3 * 4 * 5. Factorial 0 is equivalent to 1 by definition.

For the problem 6311! has 252 trailing zeros

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Answer:

---------------------------

Terminated zeros at the end of number n! is found as the sum of the whole quotients of n and powers of 5 less than n.

Given:

This is greater than 5⁵ = 3125 but less than 5⁶ = 15625.

Find each quotient of 6311 and 5¹ through 5⁵ :

Sum of the quotients is the number of terminating zeros:

Probability has values between 0 and 1.

What is the Probability?

The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

0 represents an impossible event and 1 represents a certain event.

A probability of 0 means that an event will not occur, and a probability of 1 means that an event will certainly occur.

Probabilities between 0 and 1 represent the likelihood of an event occurring, with values closer to 1 indicating a higher likelihood of the event occurring and values closer to 0 indicating a lower likelihood.

Hence, Probability has values between 0 and 1.

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Answer:

ggggghhytyhhh

Step-by-step explanation:

ghdhb

Among the given, only 0.5 can be exactly represented in binary notation with a finite number of bits

Hence, option (d) is the correct choice.

Binary is a base-2 number system in which a number is represented by two states: 0 and 1. We can also refer to it as a true and false condition. A binary number is constructed in the same manner as a decimal number.

Binary data is information expressed or displayed using the binary number system. Binary data is the only type of data that a computer can directly understand and execute. It is represented numerically as a series of zeros and ones.

The binary representation of 0.5 is 0.1_2, and it is the only terminating fraction among the available possibilities.

As a result, it is the only fraction that can be expressed precisely.

All of the other possibilities have a non-terminating fraction portion and hence cannot be expressed accurately with a limited amount of bits.

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The complete question may be:

Which of the following decimal numbers can be exactly represented in binary notation with a finite number of bits?

(a) 0.1

(b) 0.2

(c) 0.4

(d) 0.5

(e) All the above

Answer:

Below

Step-by-step explanation:

(5x2 + 2x + 11) − (7 + 4x − 2x2) = 5x^2 + 2x + 11 - 7 - 4x + 2x^2 =

                                                     (5x^2 + 2x^2 ) + ( 2x-4x) +(11-7) =

                                                                7x^2     - 2x   + 4

The equation −2x+4−7x=−4+5−9x is an inconsistent equation.

Two or more expressions with an Equal sign is called as Equation.

The given equation is −2x+4−7x=−4+5−9x

Add the like terms on both sides

-9x+4=1-9x

inconsistent equation.

A system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system

Hence, the equation −2x+4−7x=−4+5−9x is an inconsistent equation.

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Answer:

observational study to see honestly but this is correct but I don't know the exact reason

[tex]-\sqrt{9y^2} = -1\cdot \sqrt{9}\cdot \sqrt{y^2}[/tex]

I assume you're good with [tex]\sqrt{9}=3[/tex], so this gives us:

          [tex]= -3\cdot \sqrt{y^2}[/tex]

Now the trick on the variable portion is that since y<0, when you square y, you turn it from being a negative number into a positive [tex]y^2[/tex] value.  And when you take the square root of that, you keep the positive value.  So effectively, [tex]\sqrt{y^2} = |y|[/tex], since it just makes the negative number become positive.

          [tex]= -3|y|[/tex]

The answer is,

(iii) (3,-5), and (1,2) Slope of line [tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-5)}{1-3}=\frac{7}{-2}=\frac{-7}{2}$[/tex]

(i) (-3,2) and (1,4) Slope of line [tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{1-(-3)}=\frac{2}{4}=\frac{1}{2}$[/tex]

(ii) [tex]$\left(a_1^2, 2 a_1\right)$[/tex] and [tex]$\left(a t_2^2, 2 a_2\right)$[/tex] Slope of line

[tex]& \frac{y_2-y_1}{x_2-x_1}=\frac{2 a t_2-2 a t_1}{a t_2^2-a t_1^2} \\[/tex]

[tex]& =\frac{2 a\left(t_2-t_1\right)}{a\left(t_2-t_1\right)\left(t_2+t_1\right)}=\frac{2}{t_2+t_1}[/tex]

(iii) (3,-5), and (1,2) Slope of line [tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-5)}{1-3}=\frac{7}{-2}=\frac{-7}{2}$[/tex]

The complete question is,

Find the slope of a line passing through the following points:

(i) (-3,2) and (1,4)

(ii) [tex]$\left(a t_1^2, 2 a_1\right)$[/tex]and [tex]$\left(a t_2^2, 2 \mathrm{at}_2\right)$[/tex]

(iii) (3,-5), and (1,2)

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Answer:

BELOW

Step-by-step explanation:

Assuming no compounding

 then interest = prt = 2000 * .1 * 30 = 6000

    add original deposit to get    8000 total at end of 30 years

Assuming annual compounding

   amount = 2000 ( 1+ .1)^30 = 34 898.80 dollars

     Which definitely shows the POWER of COMPOUNDING !

Answer:

To calculate the value of X, we first need to calculate the total amount of money Miss Saver will have saved by the time she retires at age 60.

We know that her first payment is $1000, and that every subsequent payment increases by 5%. Using this information, we can calculate the total payments made during the 30 years:

$1000 x (1 + 0.05)^30 = $1000 x 3.3201 = $3320.1

This is the total amount of money Miss Saver will have saved by the time she retires at age 60.

Next, we need to calculate the value of each annual withdrawal over the 20 years of withdrawals.

We know that the effective annual interest rate is 2% perpetually, so we can use the formula for the future value of an annuity:

FV = X * ((1 + r)^n - 1) / r

where X is the annual withdrawal, r is the interest rate (0.02), and n is the number of years (20).

We can use this formula to solve for X:

3320.1 = X * ((1 + 0.02)^20 - 1) / 0.02

X = 3320.1 * 0.02 / (1.02^20 - 1)

X = 3320.1 * 0.02 / 0.1135 = $292.36

Therefore, Miss Saver needs to withdraw $292.36 each year for 20 years to deplete her savings account.

Rounded to the nearest integer, the value of X is $292.

The instantaneous rate of change of g(x) = 2/(x + 6) at x = 3 is given as follows:

g'(3) = -0.025.

The function for this problem is defined as follows:

g(x) = 2/(x + 6).

The instantaneous rate of change at x = a is defined as follows:

g'(a).

In exponent format, the function is defined as follows:

g(x) = 2(x + 6)^(-1).

Applying the chain rule, the derivative of g(x) is given as follows:

g'(x) = -2(x + 6)^(-2)[x + 6]'

g'(x) = -2/(x + 6)².

At x = 3, the numeric value of the derivative is given replacing the lone instance of x by 3, hence:

g'(3) = -2/(3 + 6)²

g'(3) = -2/81

g'(3) = -0.025.

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Inequality to show the shaded region in the graph:

x + 3y > -15

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given equation of the line

x + 3y = -15

Shaded region is above the line

Which can be expressed as inequality

x + 3y > -15

Hence, x + 3y > -15 is the inequality to show the shaded region in the graph.

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Answer:

Step-by-step explanation: The above answer is only partially right.  Due to the fact that the line with the arrows is solid, the sign is greater than or equal to.

So, the side with (0,0) is the side where x+3y>−15 and the shaded region (which contains (0,0)) shows the solutions of the inequality x+3y>−15.

Notice that since the boundary line is graphed with a solid line, the inequality includes the equal sign.

The graph shows the inequality x+3y≥−15.

The required, each student will pay $10, as per the given condition.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
The question seems to be incomplete,
Let's assume that the bill is of $50 excluding taxes

Now, each student has to pay = 50 / 5
                                                  = $10 per head

Thus, the required, each student will pay $10, as per the given condition.

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - [tex]\frac{3}{2}[/tex] x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = [tex]\frac{0-3}{0-(-2)}[/tex] = [tex]\frac{-3}{0+2}[/tex] = - [tex]\frac{3}{2}[/tex] , then

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - [tex]\frac{3}{2}[/tex] (0) + c = 0 + c , so

c = 0

y = - [tex]\frac{3}{2}[/tex] x + 0 , that is

y = - [tex]\frac{3}{2}[/tex] x

Answer:

Step-by-step explanation:

Harry winston dillan paul

Answer:

y= 3 y =0

Step-by-step explanation:

find the derivative