The proof below may or may not be correct. If the proof is incorrect, determine the first step number that is not justified and the reason it is not justified.

ANSWER

2, 4 and 8

EXPLANATION

We have that in a triangle ABC, AB = 3 cm and BC = 5 cm.

To find the possible length of AC, we can apply the triangle inequality theorem.

It states that in any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

This means that:

So, we have that:

We have to disregard the third line, since the length of a triangle side can only be positive.

So, using the first 2 lines, we see that:

This means that from the options, the measure of AC can either be 2, 4 or 8.

Different estimates:

The length of the radius of a cylindrical pipe:

Plumber W:

Radius had a length: 3/5 inches.

Plumber X:

Radius had a length: sqrt(3/11) inches.

Plumber Y:

Radius had a length of 9/100 inches.

Plumber Z:

Radius had a length of 3/14/24 inches.

Turn them into decimals:

We can turn each length into decimal:

Plumber W: 3/5 = 0.6.

Plumber X: sqrt(3/11) = 0.522222..

Plumber Y: 9/100 = 0.09

Plumber Z: 3.14/24 = 0.13083

The list from the greatest to least:

We can order this list taking into account the following reasoning: when the number is near to zero, this number is less than the other in the list. Examples: 0.001, 0.0002, 0.00004 are very near to zero.

Additionally, when a number is near 1 (the unit), this number is greater than the other less near to 1.

Examples: 0.69, 0.73, 0.888, 0.99 are near to zero.

The numbers we got in the list are decimals numbers coming from fractions and the square root was taken to the estimation of plumber X. Therefore:

From list 0.6, 0.52222..., 0.09, 0.13083

The number nearest to zero is 0.09. Then, 0.13083 is greater than 0.09 but less than the others. The following number is 0.5222..., and the greatest is 0.6.

The list that shows these lengths in order from the greatest to least is:

{0.6, 0.5222..., 0.13083, 0.09}.

Which is equivalent to:

{3/5, sqrt(3/11), 3.14/24, 9/100}.

Answer: 6 hours

Explanation:

We have that "Ruth studied 2 hours less than twice as many hours as Jackie". I will call the hours that Ruth studied "R" and the hours that Jackie studied "J". The first equation is as follows:

The hours that Ruth studied as 2 less than twice as many as Jackie. This will be referred to as equation 1.

Now, we are told that "Together, their study time was 10 hours" so we have the following equation:

This will be our equation 2.

The next step is to substitute equation 1 into equation 2:

And we solve for J.

Combining like terms:

We add +2 on both sides of the equation to cancel the -2 on the left side:

And we divide both sides by 3:

Jackie studied for 4 hours.

Since we are asked for Ruth, we substitute J=4 into the equation 1:

Ruth studied for 6 hours.

qANSWER

Company B will pay more

Company A =

EXPLANATION

Both companies start by paying $42,000 per year.

Company A offers an increase of $1000 per year.

This means that after n years, he would have earned:

Earnings = 42000 + 1000n

where n = number of years after the first year

So, after 6 years, he would have worked 5 years after the first, so his earnings would be:

Earnings = 42000 + 1000(5) = 42000 + 5000

Earnings = $47000

Company B offers 7% more than the previous year. That means that his earnings are compounded.

His earnings can then be represented as:

where P = initial salary = $42000

r = interest rate = 7%

t = number of years spent = 6 years

Therefore, his earnings after the 6th year will be:

He would have earned $63042.

Therefore, Company B will pay more.

qANSWER

Company B will pay more

Company A =

EXPLANATION

Both companies start by paying $42,000 per year.

Company A offers an increase of $1000 per year.

This means that after n years, he would have earned:

Earnings = 42000 + 1000n

where n = number of years after the first year

So, after 6 years, he would have worked 5 years after the first, so his earnings would be:

Earnings = 42000 + 1000(5) = 42000 + 5000

Earnings = $47000

Company B offers 7% more than the previous year. That means that his earnings are compounded.

His earnings can then be represented as:

where P = initial salary = $42000

r = interest rate = 7%

t = number of years spent = 6 years

Therefore, his earnings after the 6th year will be:

He would have earned $63042.

Therefore, Company B will pay more.

Answer

D. (-3, 0) and (3, -4)

Explanation

Let the coordinate of the points be A(-9, 4) and B(9, -8).

We shall look for the gradient m of line using

m = (y₂ - y₁)/(x₂ - x₁)

Substitute for x₁ = -9, y₁ = 4, x₂ = 9 and y₂ = -8

m = (-8 - 4)/(9 - -9) = -12/18 = -2/3

From option A - D given, only C and D would have the same gradient of -2/3 as line AB

To know the correct option, we shall look for the equation of the line AB, that is,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

(y - 4)/(x - -9) = (-8 - 4)/(9 - -9)

(y -4)/(x + 9) = -12/18

(y - 4)/(x + 9) = -2/3 -----------*

Between option C and D, only D satisfies the equation *

That is, using (-3, 0), we have (0 - 4)/(-3 + 9) = -4/6 = -2/3

Also, using (3, -4), we have (-4 - 4)/(3 + 9) = -8/12 = -2/3

Answers:

Part A.

C. AD = AE

Part B.

BC = 26

Explanation:

Part A.

If DE is a midsegment of triangle ABC, D is a point that divides AB into two equal segments, so option A. 1/2 AB = AD is true.

Additionally, if DE is a midsegment of triangle ABC, its length is equal to half the length of the side that the segment doesn't cross. So:

Therefore, option B is also true.

Triangle ABC is scalene, it means that all their sides have different length, it means that AD is not equal to AE and option C is not true.

Finally, segments AE and EC form AB, so:

AC = AE + EC

AC - AE = AE + EC - AE

AC - AE = EC

So, option D is also true.

Therefore, the answer for part A is C. AD = AE

Part B.

We know that 2DE = BC, so replacing the expression for each segment, we get:

Solving for x:

Now, with the value of x, we get that BC is equal to:

BC = 5x - 4

BC = 5(6) - 4

BC = 30 - 4

BC = 26

So, the answer for part B is 26.

Using the matrix equation, the value of x and y are 5 and 2 respectively.

Consider the 2 by 2 matrix equations,

1/2 [ 4  8     ( x + 3 )   - 4 ] - 3[ 1  y+1    -1  - 2 ] = [ - 1  -5   7  4 ]

[ 2   4       (x+3)/2    -2] + [ - 3   -3y -3   +3  + 6] = [ - 1 - 5    7  4]

[ -1  -3y + 1    (x + 9)/2   + 4]  = [ - 1 - 5   7  4]

Therefore,

- 3y + 1 = - 5

Subtracting 1 from each side of the equation,

- 3y + 1 - 1 = - 5 - 1

- 3y = - 6

Dividing each side of the equation by - 3,

y = 2

And;

( x + 9 )/2 = 7

Multiplying each side by 2,

x + 9 = 14

Subtracting 9 from each side of the equation,

x + 9 - 9 = 14 - 9

x = 5

Therefore, the value of x and y is 5 and 2 respectively.

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So, our answer is 9!

Part 9

we have

(c+2)(c-2)^2

If c=8

substitute the value of c in the expression

so

(8+2)(8-2)^2

(10)(6)^2

(10(36)

360

Part 10

we have

7(3x-2)^2

If x=4

substitute the value of x in the expression

7(3(4)-2)^2

7(10)^2

7(100)

700

This problem invloves the topic of curved lines in a graph, curved lines or more speccifically curve line which looks like letter C (parabola) all follows a certain standard form of equation, which is;

For example you can see that the equation for the black curve line in our picture is y=x² and notice that this equation can also be written as y = (1)x² + 0. Which simillar to the standard form given above where a is just 1 (a=1) and b is just 0 (b=0).

Since our black curve line follows the same standard form of equation as stated above, we can conclude that the RED curve line follows the same form of equation.

To summarize the steps that we must do in order to find the equation of the RED line we will list them as,

1. Sample two(2) points in the graph to be used as reference points.

2. Use the sampled points in our standar eqation in order to find the variables "a" and "b".

3. When we have the variables "a" and "b", we can just directly substitute it into our standard equation to find the equation of our RED line.

Let's start.

1. Sample 2 points to be used as refernce points. (Note that we will find the easiest points

to determine)

Let us use the points (-3, -1) and (-2, 1) as shown in the picture.

2. Use the points (-3, -1) and (-2, 1) in our standard equation.

for our 1st point we have the equation 9a+b = -1, let us now proceed to our next point.

and for our 2nd point we have the equation 4a+b = 1, and by the process of subtitution and elimination we can now find "a" and "b", because we have two equations with two unknowns.

transforming eqatuin number 1 to

then substitue b = -1 -9a to the 2nd equation we have.

since a = -2/5, we can find b using,

therefore our a and b are;

3. We can now proceed in substituting it in our standard equation;

you can also simplify the final equation by multiplying all sides by 5,

therefore our final answer can be,

A number which is 5 more than 8009998 is 8010003

In this question we need to find a number which is 5 more than 8009998.

Let x be a number which is 5 more than 8009998.

We get the required number by adding 5 to 8009998.

so, we write it down as:

x = 8009998 + 5

x = 8010003

Therefore, a number which is 5 more than 8009998 is 8010003

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ok

The sum of the internal angles in a triangle equals 180°

R + B = T = 180

Substitution

19 + 56 + T = 180

T = 180 - 19 - 56

T = 105°

Result:

T = 105°

Answer:

B. SAS
:)

Step-by-step explanation:

Let

x -----> the missing number

we know that

80%=80/100=0.80

so

0.80x=20

solve the linear equation for x

Divide by 0.80 both sides

x=20/0.80

x=25

the answer is 25

2 . 0 5 0

0 . 0 0 4

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

8 2 0 0

+ 0 0 0 0

0 0 0 0

0 0 0 0

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

0 . 0 0 8 2 0 0 =

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

We can calculate the volume as the product of the area of the base and the height.

The area of the base is function of the square of the diameter, so we can write:

Answer: the volume of the box is 1256 cm^2.

if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x

The numebr of shopperes the next day will be

= x(100 + 20)%

= 1.2x

teh number of shoppers the day after

= 1.2x(100 + 20)%

= 1.44x

the next day, the number

= 1.44x (100 + 20)%

= 1.728x

Given that the total number of people that have shopped after 4 days is 671 then

x + 1.2x + 1.44x + 1.728x = 671

5.368x = 671

x = 671/5.368

= 125

if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x

The numebr of shopperes the next day will be

= x(100 + 20)%

= 1.2x

teh number of shoppers the day after

= 1.2x(100 + 20)%

= 1.44x

the next day, the number

= 1.44x (100 + 20)%

= 1.728x

Given that the total number of people that have shopped after 4 days is 671 then

x + 1.2x + 1.44x + 1.728x = 671

5.368x = 671

x = 671/5.368

= 125

Explanation:

The equation is given below as

Step 1:

Collect similar terms, we will have

Hence,

The simplified form of the equation will be

In order to find the greatest common factor (GCF) of the terms, first let's factor the numeric values in their prime factors:

The common factor between these three numbers is the product of the common prime factors, that is, 2 * 2 = 4.

Now, to find the common factor of the variables, we choose for each variable the one with the smaller exponent:

Therefore the common factor is -4(m^5)n.

(we can put the negative signal as well, since all terms are negative).

Equation for a rational function is 10(x2 + 7x + 12) / (x2 + 11x + 30) = 0.

What is Rational Function?

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.

So this will be a rational function with the vertical asymptotes given by the denominators:

(x + 5) and (x + 6).

The x-intercepts will be provided by the numerator,

which will be:

a(x + 3)(x + 4)

The letter an is a constant.

Given that (0,4) is the y intercept, we have:

4 = a(0+3)(0+4) / (0+5)(0+6)

4= 12a / 30

12a = 120

now,

a = 120/12,

a = 10,

and a = 1.

Now,

a(x+3)(x+4) / (x+5)(x+6) = 0

10 (x^2 + 7x + 12) / (x^2 + 11x + 30) = 0

Hence, We have the following equation for a rational function:

10 (x2 + 7x + 12) / (x2 + 11x + 30) = 0.

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Convert 7 liters into gallons

We have the measurement conversion 1 liter= 1.0567 quarts

and the gallons = 4 quarts

So, 7 liters = 7 * 1.0567 quarts = 7.3969 quarts

We will convert from the quarts to gallons as follows:

1 gallons = 4 quarts

x gallons = 7.3969 quarts

so, the value of x will be:

Round to two decimals

so, the answer will be 1.85 gallons

Solution

Step 1:

Write the two given points:

p(4,2) and q(8,12)

Step 2

Find the distance between the two points:

Answer

Answer:

Yes, the set of ordered pairs is a function.

Explanation:

To test whether a given set of ordered pairs represents a function, we have to make sure that it satisfies the definition.

By definition, a function cannot have two outputs for one input. For example, the set of ordered pairs (3, 10 ) and (4, 5) represents a function whereas (3, 10) and (3, 13) does not.

With this in mind, looking at the given set we see that every input gives a unique output; therefore, the set represents a function.

Answer:  expect to lose 679.07 dollars

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

Explanation:

Assuming each free throw is independent of any other, the probability of making the next free throw is 359/449

The probability of making 3 in a row is (359/449)^3 = 0.511145 approximately which represents the probability of earning the $39

That must mean 1-0.511145 = 0.488855 is the approximate probability of losing $43

Let's make a table of outcomes and their associated probabilities.

X = amount of money the player earns (the person shooting the free throws)

[tex]\begin{array}{|c|c|} \cline{1-2}\text{X} & \text{P(X)}\\\cline{1-2}39 & 0.511145\\\cline{1-2}-43 & 0.488855\\\cline{1-2}\end{array}[/tex]

Then from here we'll multiply each X and P(X) value for each separate row.

Example: 39*0.511145 = 19.934655

Let's form a third column of these products

[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{X} & \text{P(X)} & \text{X}*\text{P(X)}\\\cline{1-3}39 & 0.511145 & 19.934655\\\cline{1-3}-43 & 0.488855 & -21.020765\\\cline{1-3}\end{array}[/tex]

Add up everything in the X*P(X) column and you should get roughly -1.08611 which rounds to -1.09

The player expects, on average, to lose about $1.09 each time they play this game. Playing 623 times means they should expect to lose 623*1.09 = 679.07 dollars

Of course, given the nature of this random process, it's not a guarantee they will lose this amount. This is just the average of many attempts.

45/152 is fraction of the students are freshmen.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction is a portion of a whole and is used to represent how many pieces of a particular size there are while speaking in ordinary English, for example, one-half, eight-fifths, and three-quarters. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. There is a proportion there in numerator or denominator of a complicated fraction. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.

Total students = 152

Freshman = 45

Fraction = 45/152

This is the simplest form .

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We can solve this using the next property:

If a

Replace f (x) = - 2x- 5 ​, then:

-21 < f (x) < 0

-21 < -2x-5 < 0

Solve -21 < -2x-5 and -2x-5 < 0

Therefore:

-21 < -2x-5

Add both sides 5

-21+5 < -2x-5 +5

-16 < -2x

(-1)-16 < (-1)(-2x)

16>2x

x<16/2

x<8

and

-2x-5 < 0

Add both sides 5

-2x-5 +5 < 0+5

-2x<5

(-1)-2x < (-1)5

2x > -5

x > -5/2

Hence, the resulting interval is:

-5/2 < x < 8

We have the following

Let's find a, b and c in order to solve the problem

a.

a = 10,000

b.

b=1.0E-16

c.

c=1.0E19

Thus, the value of log [ a^2c/sqrt(c) ] is :

replace:

simplify:

Therefore, the answer is 35

The function given in the graph stretches from negative to positive infinity.

Hence the domain of the function is given by:

The company estimates a residual value of $1,500 and a six-year service life.

It is given that,

Cost of truck delivery = $ 23100

Salvage value = $ 1500

Useful life = 6 years

Depreciation expenses by using the straight-line method are calculated as,

Substituting the value in the formula,

Thu