Find the equation of the line shown below
Y=mx+c

Answer:

Step-by-step explanation:

Correct Answer: C

We can rely on the guess and check method to easily solve this problem. Let’s first pick arbitrary values of x and y to eliminate some answer choices.

Let’s consider the case where |x| and let x = 3 and y = -10.

Because x/y = -3/10 < 1, answer choice A is incorrect.

Because |x|2 = (3)2 = 9 and |-10| = 10, we have that |x|2 < y, so answer choice B is also incorrect.

Because x2 + 1= (3)2 + 1 = 10 and y2 + 1 = (10)2 + 1 = 101, we have that x2 + 1 < y2 + 1, so answer choice D is also incorrect.

Now, let’s consider the case where |x|>|y| and let x = 3 and y = -2.

Then, x-2 = 1/x2 = 1/9 and y-2 = 1/y2 = 1/4. This means that x-2 < y-2 , so answer choice E is also incorrect.

This means that answer choice C is correct. We can manipulate the inequality to see why this is true: (x/3 – 5) > (y/3 – 5)

We add 5 to both sides: x/3 > y/3

We multiply both sides by 3: x > y.

We know this is true since we are given that x > 1 > -1 > y, which simplifies to x > y.

Answer:

Since y = −2x − 6 and 4x − y = −36, the solution would be B.) (-7, 8).

A solution to the given system of equations is [tex](\frac{100}{3}, \frac{8}{3} )[/tex]

Given the following system of equations:

[tex]y=-2x-64[/tex]  ...equation 1.

[tex]x-y=-36[/tex]   ...equation 2.

To find a solution to the given system of equations, we would use the substitution method:

First of all, we would make x the subject of formula in equation 2.

[tex]x=-36+y[/tex]  ...equation 3.

Substituting eqn. 3 into eqn. 1, we have:

[tex]y = -2(-36+y)-64\\\\y=72-2y-64\\\\y+2y=72-64\\\\3y=8\\\\y=\frac{8}{3}[/tex]

For the value of x:

[tex]x=-36+y\\\\x=-36+\frac{8}{3} \\\\x=\frac{100}{3}[/tex]

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9514 1404 393

Answer:

  (x, y) = (1.25, 8.5)

Step-by-step explanation:

I choose to put these equations into reduced general form, then use the "cross multiplication method" to solve.

  2x -y +6 = 0

  10x -y -4 = 0

d1 = 2(-1) -10(-1) = 8

d2 = -1(-4) -(-1)(6) = 10

d3 = 6(10) -(-4)(2) = 68

Solutions are ...

  x = d2/d1 = 10/8 = 1.25

  y = d3/d1 = 68/8 = 8.5

The solution is (x, y) = (1.25, 8.5).

_____

Additional comment

I like a graphing calculator for a quick and easy solution. When the values are not integers, I like an algebraic solution to see what the exact values are.

__

The "cross multiplication method" is similar to Cramer's rule in that determinants of pairs of coefficients are computed. If you look up this method, videos will show you a variation that is slightly different. Here, we determined d1, d2, and d3 as the 2×2 determinant of the coefficients in adjacent columns of the array you get from the general form equations with the first column repeated:

  [tex]\begin{array}{cccc}2&-1&6&2\\10&-1&-4&10\end{array}[/tex]

In each pair, the determinant is the difference between the product of numbers on the down-diagonal and the product of numbers on the up-diagonal.

The determinants relate to the x- and y-values by ...

  1/d1 = x/d2 = y/d3   ⇒   x = d2/d1, y = d3/d1

There is a Vedic solution method for linear equations that is similar to this, but starts from equations in standard form. As a consequence, the cross-differences are done in a different order.

__

Standard form: ax +by = c

General form: ax +by +c = 0

Answer:

d

Step-by-step explanation:

The recursive formula for the geometric sequence is:

[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]

The recursive equation for a geometric sequence is:

[tex]f(n) = qf(n - 1)[/tex]

In this problem, the sequence is: {-320, -80, -20, -5, . . .}

Hence, the recursive equation is:

[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]

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The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]

The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]

n the following sequence  -320, -80, -20, -5,...

The The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]is given as:

The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]

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Answer:

The average rate of change between x = 1 to x = 2 is 2, from x = 2 to x = 3 is 4 and from x = 3 to x = 4 is 8.

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 times 2 is 12

42 multiplied by 2 is 84

therefore the answer is 12 days.

Answer:

Ms. April will not have enough students.

Step-by-step explanation:

This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.

Answer:

Ms. April will not have enough students.

Step-by-step explanation:

This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.

Answer:  2x for x=3: 2(3) = 6.

Step-by-step explanation:

Answer:

a. ΔMNK =Δ [tex]PRT[/tex]

b. TR=MN

c. [tex]x=7[/tex]

Step-by-step explanation:

I hope this help you

Answer: 12 feet up

Step-by-step explanation:

This problem models a right triangle, in which the ladder is the hypotenuse and the distance away from the wall is one of the legs.  Thus, you may use the Pythagorean Theorem (a^2 + b^2 = c^2)

[tex]a^2+b^2=c^2\\5^2+b^2=13^2\\25+b^2=169\\b^2=144\\b=12[/tex]

N.B. There are some very useful sets of numbers that can help you with this unit.

They are called Pythagorean triplets, and they are the sets of whole numbers that make right triangles.  The important ones are 3, 4, 5, and 5, 12, 13 (And their multiples, like 6, 8, 10(3,4,5 *2))

Hope it helps :) and let me know if you want me to elaborate further.

Answer:

[tex]1\frac{1}{5}[/tex]

Step-by-step explanation:

2 1/4 + 2/5 / (-1/2)-1/4

order of operation states you do division before subtraction or addition

2 1/4 -4/5 -1/4....divide 2/5 by -1/2

2 - 4/5.................combine like terms

6/5........................subtract

1 1/5.......................simplify

Answer:

1+2+3- -9+236359

Step-by-step explanation:

Answer:

y=-4x-7

Step-by-step explanation:

if you use the slope formula, y2-y1 over x2-x1 using any two points from the grid, you get a slope of -4.

if you use the slope intercept form, y=mx+b, and plug in y, m the slope, and x, you get -3=-4(-1)+b

if you solve that, you get -3=4+b

and if you isolate 4 by subtracing 4 from both sides, b=-7.

then you plug slope and y intercept into formula, and get y=-4x+b

Answer:

256, 3125

Step-by-step explanation:

This may be the sequence n^n:  1^1, 2^2, 3^3, 4^4, 5^5, 6^6, ...

Let's check with the numbers we see:

1^1 = 1

2^2 = 4

3^3 = 27

6^6 = 46656

Yes, this is the sequence n^n.

The 4th term is:

4^4 = 256

The 5th term is:

5^5 = 3125

Answer:

L - 10 . W - 5

Step-by-step explanation:

Length = 3*width - 5

area = length * width

50 = (3w-5)* w

50 = 3w^2-5w

0 = 3w^2 - 5w -50

0= (3w+10)(w-5)

w = 5 , w can't equal -10/3 because width can't be negative

width is 5

Length = 3 * 5 - 5

Length = 10 , width = 5

Answer:

first lets say w is the width

50(area)=w(idth)+3(w-5)

50=w+3w+15

50=4w+15

35=4w

8.75=w

w equals 8 3/4

Hope This Helps!!!

Answer:

y = x + 4

Step-by-step explanation:

From point (-1, 3) to point (0, 4), go up 1 (rise = 1) and go right 1 (run = 1).

slope = m = rise/run = 1/1 = 1

The y-intercept is b = 4

y = mx + b

y = x + 4

Answer:

Step-by-step explanation:

3/6 x 8

= ( 3 x 8 ) / 6

= 24 / 6

4/7 x 2

= ( 4 x 2 ) / 7

= 8 / 7

9/2 x 3

= ( 9 x 3 ) / 2

= 27 / 2

8/5 x 7

= ( 8 x 7 ) / 5

= 56 / 5

3/9 x 5

= ( 3 x 5 ) / 9

= 15/9

7/4 x 4

= ( 7 x 4 ) / 4

= 28 / 4

6/2 x 6

= ( 6 x 6 ) / 2

= 36 / 2

8/3 x 9

= ( 8 x 9 ) / 3

= 72 / 3

9/4 x 8

= ( 9 x 8 ) / 4

= 72 / 4

5/3 x 6

= ( 5 x 6 ) / 3

= 30 / 3

2/7 x 3

= ( 2 x 3 ) / 7

= 6 / 7

8/4 x 7

= ( 8 x 7 ) / 4

= 72 / 4

6/4 x 2

= ( 6 x 2 ) / 4

= 12 / 4

28 years

Step-by-step explanation:

The dog is twice as old as the cat

The monkey is twice as old as the dog.

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

Their total age is 4 years 2 months.

1 year has 12 months

=> 4 years have (4 × 12)

= 48 months

Since, the total age is 4 years 2 months, we can express it in "months" by adding "48" and "2".

= 50 months

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

Sum of their ages = 50 months

=> x + 2x + 4x = 50

=> 7x = 50

=>x = 50/ 7 months

If we write this in mixed fractions the whole number will represent the number of years.

=

[tex] \mathsf{7 \frac{1}{7} \: \: months}[/tex]

[tex] = \mathsf{7 \: years \: \frac{1}{7} \: \: months}[/tex]

The value of 1/ 7 is really small,I.e., 0.1428...

So, we can ignore the fraction while rounding off the term that makes it

[tex] \mathsf{x = 7yrs.(approx.)}[/tex]

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

x is the age of the cat.

The monkey's age is "4x"

= 4 × 7

= 28 years.

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

So, the monkey's age is approximately 28 years

Answer:

D Each package has 8 yellow candle chips. A total of 18 packages will have 144 yellow candle chips.

Step-by-step explanation:

8/1 is proportional to 144/18

In option C and D the number of object increases other object also increases. Therefore, options C and D are the correct answers.

Given that, a candle factory makes colored candles to sell in packages.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

A) Does not a represents a proportional relationship

B) Does not a represents a proportional relationship

C) The cost of one package is $1.98 and the cost of 10 packages is $16.99.

Here, the number of packages increases, the cost also increases. So, it is direct proportion.

D) In one package there are 8 yellow candle chips and 18 packages will have 144 yellow candle chips.

Here, the number of packages increases, the number of chips also increases. So, it is direct proportion.

In option C and D the number of object increases other object also increases. Therefore, options C and D are the correct answers.

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Answer:

100º

Step-by-step explanation:

Cooresponding angles are congruent

11x + 1 = 10x + 10

Subtract 10x from both sides

x + 1 = 10

subtract 1 from both sides

x = 9

θ = 11x + 1

θ = 11(9) + 1

θ = 99 + 1

θ = 100º

Answer:

Hope It's Help

Answer:

-1.5

Step-by-step explanation:

To convert a fraction to a decimal number divide the numerator (-3) by denominator (2)

Answer:

-1.5

Step-by-step explanation:

Answer: He sold 1,800 merchandise

Step-by-step explanation: 426 - 300 = 126 ÷0.07 = 1,800

I dont know if im right though

Step-by-step explanation:

All angles of the ∆ are same. So it's a equilateral ∆ . So all sides will also be equal .

16 + y = 46

y = 46 -16 = 30

And ,

60 + x + (180-80) = 180

-20 +x = 0

x = 0 +20

x = 20°