Graph line with slope 1/2 passing through the point (-1,3)

The absolute value equation to represent the definition of betweenness is

AB + BC = AC ↔ B ∈ A,C  

Absolute value equation:

An absolute value equation is a function that contains an algebraic expression within absolute value symbols.

Given,

Here we have the statement "If three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.".

Here we need to find the absolute value function for this statement.

In order to find the absolute value equation,

First we have to identify the symbols for the terms mentioned in the statement they are,

between = ∈

if and only if = ↔

sum = +

Now, we have to divide the statement as two parts.

First one is, "c lie on the same line, then b is between a and c"

It can be written as,

B ∈ A,C

Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."

Which can be written as

AB + BC = AC

When we combine it, the we get the absolute value equation as,

B ∈ A,C ↔  AB +BC = AC

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Answer: 1. Complementary

2. Supplementary

3. 116

4. 17

5. A- 28 B-152 C-118

The half life obtained to the nearest tenth is 5.0 days.

The half life is the time taken for only half of the initial amount of the radioactive substance to remain. We know that we have to use the formula;

N=N0e^-kt

N = amount present at time t

No = Amount initially present

k = The constant

t = The half life

We now have that;

HALF LIFE = O.693/k

We have to recall that the term k is the decay constant for the process as shown.

Half life = O.693/0.1394

Half life = 5.0 days

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The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model.

Using an online multiple regression calculator, the estimated multiple linear regression equation that can be used to forecast the annual income using the number of school years completed (Education), length of tenure in the current employment, and age is as follows:

y = - 143481.1924 + 10011.9212x1 - 2193.8838x2 + 2689.2405x3

According to the general form of a multiple linear regression model:

-143481.1924 = intercept(c) ; where regression line crosses the origin

10011.9212x1 - 2193.8838x2 + 2689.2405x3 are weight coefficients of the three predictor variables ; x1, x2, and x3

y = predicted variable

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Given the equation:

You need to solve for "x" in order to find its value:

1. Apply the Addition Property of Equality by adding 0.03 to both sides of the equation:

2. Apply the Division Property of Equality by dividing both sides of the equation by 0.005:

Hence, the answer is:

We will see that the linear equation that passes through the two given points is:

y = 4x + 28

So the y-intercept is y = 28.

First, we need to find the linear equation that passes through the two given points. Remember that for a line that passes through two points (x₁, y₁) and (x₂, y₂), the slope is:

m = (y₂ - y₁)/(x₂ - x₁)

Here our line passes through (-8,-5) and (10, 67), then the slope is:

m = (67 + 5)/(10 + 8) = 4

So we can write:

y = 4*x + b

To find the value of b we can use the point (-8,-5), replacing these values we get:

-5 = 4*-8 + b

-4 + 4*8 = b

28 = b

So the y-intercept is 28.

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If we draw a vertical line and it crosses the figure more than once, then it is not a function.

So, the only graph that a vertical line will intersect the line once is graph A:

B, C and D are intersected more than 1 time, so they are not functions.

Answer: A

A line's equation written using a single point on the line and the line's slope is referred to as the point-slope form. The slope is the rise over run, or the ratio of the change in the y values over the change in the x values, and the point form is denoted as (x,y).

y= 3 / 10x + 8

y=mx+b, where

y=mx+b

y=3/ 10x+8

m=3/10  b=8

Slope: 3/ 10, and the y-intercept is at (0, 8).

x           y

0         8

10        11.

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Step-by-step explanation:

I assume the points D, E and C are also collinear (are on the same straight line).

that is something your teacher forgot to mention. but it is essential.

we have to remember :

1. the sum of all angles in a triangle is always 180°.

2. the sum of all angles around a single point on one side of a line is also always 180°.

3. the angles at the intersection point of 2 lines are the same on both sides of any of the intersecting lines, but they are left-right mirrored.

so,

angle A = 30°

angle DEB = 130°, so,

angle AED = 180 - DEB = 180 - 130 = 50°.

therefore, angle BEC = AED = 50°

therefore, angle D = 180 - 30 - 50 = 100°.

we know, angle B = 90° (AB is perpendicular to BC).

therefore,

angle C = 180 - 90 - 50 = 40°

Answer: Yes

Step-by-step explanation:

because their overall shape it the same, their size is the only thing that sets them apart, so they're not identical

Answer:

8 out of 10.

Step-by-step explanation:

if you flip a coin independent then it doesn't matter what the other outcomes are. So if it's a one out of two chance every time then it's 8 /10.

EXPLANATION:

We are given the original price of a laptop computer at $1,700.

Now the price has been increased to $1,800.

Note that there is a $100 increase over the original price.

For us to calculate the percent increase we shall use the ratio of the increase over the original price and calculate as a percentage.

We can now set up the following equation;

We now cross multiply;

Rounded to one decimal place, the percent increase is;

ANSWER:

We can see the next function:

And we need to translate this function 5 units down, which results in the function g(x).

To find the rule for g(x), we can follow the next steps:

1. We know that the general rule for a function translated k units down is given by:

2. Then if we translate the original function by 5 units down, we will have that:

3. Therefore, g(x) will be:

Hence, in summary, we have that the rule for g(x) is g(x) = 3x + 4 (option A).

Answer:

A 20% B. 45%

Step-by-step explanation:

A 40,000/200000=.2 0r 20%

b. 90,000/200000=.45 or 45%

Answer:

y = 54

Step-by-step explanation:

a) Multiply both sides by 9/(-7).

(9/-7) * (-7/9 y) = (9/-7) * (-42)

y = 54

Answer:

$32,000

Step-by-step explanation:

In the system of equations, the value of the variable 'b' will be 3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of the equations is given below.

Equations 1: - 4 = 9a - 3b + c

Equation 2: 14 = 9a + 3b + c

Equation 3: - 4 = c

Put the value of c in equations 1 and 2, then we have

- 4 = 9a - 3b - 4

9a - 3b = 0                 ...4

14 = 9a + 3b - 4

9a + 3b = 18               ...5

Subtract equation 4 from 5,

9a + 3b - 9a + 3b = 18 - 0

6b = 18

b = 3

In the system of equations, the value of the variable 'b' will be 3.

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A statement which best describes Gary’s error is that: Gary did not use correct factors for 66 in the equation.

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

a(b + c) = ab + ac.

Also, the correct greatest common factor of 66 and 36 is given by:

Greatest common factor (GCF) = 6

By applying the distributive property of multiplication, we have:

66 + 36 = 6(11 + 6)

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The dial for the standard combination lock is fastened to a spindle. The spindle travels through many wheels and a drive cam inside the lock. Every number has one wheel, hence the number of wheels in a wheel pack depends on how many numbers are in the combination.

The lock uses the numbers 0 to 39 and has 64,000 distinct combinations.

How many possible three-number combinations are there?

You have 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit, giving you 10x9x8 = 720 if you want all three possible numbers with no duplication of the digits.

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Answer:

Step-by-step explanation:

40.833 recurring and 9.166 recurring

or 40 5/6 and 9 1/6

Call the small number 's'

Call the big number 'b'

The word problem says:

B+S=50 and also that 5(S-1)=B which multiplied out is 5S-5=B

So, 5S-5=B=50-S

Therefore 6S=55 and the rest history!

Answer:

Step-by-step explanation:

Only $28.25 are available. After Lena uses the card for 15 minutes of calls, there are still 28.25 credits left.

Given that,

Lena spent $30.50 on a prepaid phone card. With this card, calls cost 15 cents each minute. the amount of credit, c (in dollars), remaining on the card following x minutes of calls

It can be written as,

C(x) = 30.50 - 0.15x

C(x) = 30.50-(0.15 x 15)

after Lena uses it for 15 minutes,

C(x) = 30.50 – 2.25 = $28.25 in remaining credits.

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The remainder when 14 is divided by 3 is 2

What is remainder?

When we divide a number by another number if at the end if we have a number less than quotient and we can not divide further we say that the remaining number is remainder.

We are given a number as 14 and we divide 14 by 3

And on dividing 14 by 3 we get the quotient as 4 and remainder as 2.

Hence the remainder we get on dividing 14 by 3 is 2.

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Answer:

76 child tickets were sold

Step-by-step explanation:

let a represent number of adults and c number of child tickets sold, then

a + c = 165 → (1)

5.8a + 8.9c = 1192.6 → (2)

multiplying (1) by - 5.8 and adding to (2) will eliminate a

- 5.8a - 5.8c = - 957 → (3)

add (2) and (3) term by term to eliminate a

0 + 3.1c = 235.6

3.1c = 235.6 ( divide both sides by 3.1 )

c = 76

that is 76 child tickets were sold that day

The monthly payment that Jenna pays for the new car is $1279.411 .

What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/n))^t

Given, total cost of the car = $29,000
Percentage of amount paid while in down payment = 10%
Therefore, amount paid as down payment = (10/100)*29000 = $2900
Now, amount put on loan by Jenna = A = 29000 - 2900 = $26,100
Also, number of years for which amount is loaned = n = 4 years
Annual Percentage Rate of the loan allowed = R = 4.5
Following the formula established in the literature above, we have:
26100 = P (1 + (4.5/4))⁴ ⇒ P = 26100/(1 + (4.5/4))⁴ ⇒ P = 26100/20.4
= 1279.411
The monthly payment that Jenna pays for the new car is $1279.411

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Using a quadratic function, it is found that:

a) The coordinates of the second x-intercept are: (50,0).

b) The vertex shows the maximum flight of the projectile.

c) The coordinates of the vertex are (25, 62).

3) The graph of the equation y = -0.0992(x² - 50x) is given at the end of the answer.

A quadratic function has two x-intercepts, x' and x'', and is defined as follows:

y = a(x - x')(x - x'').

The intercepts are given as follows:

The vertex is found as follows:

Hence the coordinates are: (25, 62).

The equation can be defined as follows:

y = ax(x - 50)

y = a(x² - 50x).

When x = 25, y = 62, hence the leading coefficient is found as follows:

62 = a(25² - 50(25))

-625a = 62

a = -62/625

a = -0.0992.

Hence the equation is:

y = -0.0992(x² - 50x).

The domain of the function is between the roots, hence 0 ≤ x ≤ 50, and the graph is sketched at the end of the answer.

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Using mathematical operations, we know that a wooden piece of (B) 4 feet will have the least unused wood.

So, the piece of wood which will have the least amount of unused wood:

3.31 is more than 3 and less than 4.

So, wooden pieces of 4 feet will have the least unused wood.

Therefore, using mathematical operations, we know that a wooden piece of (B) 4 feet will have the least unused wood.

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Answer: Rs. 360

Step-by-step explanation:

let x of 12 1/2%=45

=> x.25/200=45

=> x/8=45

=> x=45.8

=> x=360

it is Rs 360

The first part of the journey took 4/3 hours (80 minutes)

The last part of the journey too 2/3 hours (40 minutes)

Here, we want to set-up equations to solve

We start by filling the table

Line 1

The rate for the first part of the race is 90 mph

The time for the first part of the race is F

Line 2

The time for the second part of the race is L

The distance (product of the rate and time) is 60L

So, adding these up give us the following equations to be added and solved below;

So, we proceed to solve these equations simultaneously

To get f, we simply substitute l into the first part of the equations;

Since an hour is 60 minutes;

Answer: 1/5

Step-by-step explanation: It might be first easier to put it in decimal form so 8/10 is 0.8 and 0.8 divided by 4 is 0.2. 0.2 as a fraction is 1/5.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

convert element to fraction: 4 = [tex]\frac{4}{1}[/tex]

= [tex]\frac{8}{12}[/tex] ÷[tex]\frac{4}{1}[/tex]

The fraction rule: a/b ÷ c/d = a/b x d/c

= [tex]\frac{8}{12}[/tex] × [tex]\frac{1}{4}[/tex]

Cross - cancel common  factor: 4

= [tex]\frac{2}{12}[/tex]

Cancel the common factor: 2

= [tex]\frac{1}{6}[/tex]

Answer:

128

Step-by-step explanation:

solve for inside parentheses:

-22x21÷4-12

do multiplication and division:

-115.5-12

subtract:

-127.5

Hope this helps