what is the equation for the standard form of the line that has an x-intercept of 3 and a y-intercept of 5​

The simplified value of y in the equation is x = 38 + -3.5y

Simplifying

[tex](14y + -4) + (3x + 11) + (x + 21) = 180[/tex]

Reorder the terms:

[tex](-4 + 14y) + (3x + 11) + (x + 21) = 180[/tex]

Remove parenthesis around (-4 + 14y)

[tex]-4 + 14y + (3x + 11) + (x + 21) = 180[/tex]

Reorder the terms:

[tex]-4 + 14y + (11 + 3x) + (x + 21) = 180[/tex]

Remove parenthesis around (11 + 3x)

[tex]-4 + 14y + 11 + 3x + (x + 21) = 180[/tex]

Reorder the terms:

[tex]-4 + 14y + 11 + 3x + (21 + x) = 180[/tex]

Remove parenthesis around (21 + x)

[tex]-4 + 14y + 11 + 3x + 21 + x = 180[/tex]

Reorder the terms:

[tex]-4 + 11 + 21 + 3x + x + 14y = 180[/tex]

Combine like terms: -4 + 11 = 7

[tex]7 + 21 + 3x + x + 14y = 180[/tex]

Combine like terms: 7 + 21 = 28

[tex]28 + 3x + x + 14y = 180[/tex]

Combine like terms: 3x + x = 4x

[tex]28 + 4x + 14y = 180[/tex]

Solving

[tex]28 + 4x + 14y = 180[/tex]

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-28' to each side of the equation.

[tex]28 + 4x + -28 + 14y = 180 + -28[/tex]

Reorder the terms:

[tex]28 + -28 + 4x + 14y = 180 + -28[/tex]

Combine like terms: 28 + -28 = 0

[tex]0 + 4x + 14y = 180 + -28\\4x + 14y = 180 + -28[/tex]

Combine like terms: 180 + -28 = 152

[tex]4x + 14y = 152[/tex]

Add '-14y' to each side of the equation.

[tex]4x + 14y + -14y = 152 + -14y[/tex]

Combine like terms: 14y + -14y = 0

[tex]4x + 0 = 152 + -14y\\4x = 152 + -14y[/tex]

Divide each side by '4'.

[tex]x = 38 + -3.5y[/tex]

Simplifying

[tex]x = 38 + -3.5y[/tex]

Therefore, we can simplify that the value of y can be expressed as   x = 38 + -3.5y

Learn more about simplifying equation here https://brainly.com/question/17350733

#SPJ1

The values to the nearest tenth are:

a. 1. 43

b. 26. 41

c. 11. 69

d. 4. 57

e. 15. 77

Given the equations;

a. 4. 186 - 2. 758

Find the difference

1. 428

1. 43

b. 72. 05 - 45. 64

Find the difference

26. 41

c. 82. 156 - 41. 31 - 29. 16

Find the difference

11. 686

11. 69

d. 17. 054 - 11. 65 - 0. 83

Find the difference

4. 574

4. 57

e. 29. 16 - 12. 48 - 0. 91

Find the difference

15. 77

Thus, the values to the nearest tenth are 1. 43, 26. 41 , 11. 69, 4. 57, 15. 77

Learn more about subtraction here:

https://brainly.com/question/220101

#SPJ1

The area of the enlarged photograph will be 16 times the area of original photograph.

For the given scale in the question;

Noah enlarges a photograph using the scale 1 inch : 4 inches.

Let the original length of photograph is 'L'.

Let the original width of photograph is 'B'

Old Area  = LB

Thus, the length and width of the scale will get increased by 4 times.

The new length and width will be 4L and 4B.

Thus, the new area will be;

New Area = (4L)(4B)

New Area = 16 LB

New Area = 16 × (old area)

Thus, the new area of the photograph is increased by 16 times.

To know more about the scale, here

https://brainly.com/question/26467371

#SPJ9

[tex]Factor\ by\ grouping:\\\\2x^2+3x-35\\\\(2x-7)(x+5)\\\\2x-7=0\ and\ x+5=0\\\large\boxed{\therefore x=\frac{2}{7}\ and\ x=-5}[/tex]

Answer:  2x^2+3x-35=(x+5)(2x-7)

Step-by-step explanation:

[tex]2x^2+3x-35=\\2x^2+10x-7x-35=\\(2x)(x+5)-(7)(x+5)=\\(x+5)(2x-7)[/tex]

The values of x associated with each case are listed below:

Herein we find two cases of geometric systems generated by two parallel lines and auxiliary line segments, wherein we must use the concept of supplementary angles and triangle properties to determine the value behind angles. Now we proceed to determine the value of the variable x for each case:

Case 1

Case 2

To learn more on triangles: https://brainly.com/question/2269348

#SPJ1

Answer:

1. There exists at least one square that is not a rectangle.

2. Every segment has a midpoint.

Step-by-step explanation:

1.The given statement is: "All squares are rectangles". We have to find the negation of the statement. The statement that gives the negative meaning of the given statement is called the negation of the given statement. So the negation of the given statement is, "There exists at least one square that is not a rectangle".

2.Every segment has a midpoint.

aₙ = 5*(1/5)^(n - 1) is the explicit formula of the sequence.

What is Sequence and example ?

The recursive relation for a geometric sequence is

aₙ = aₙ₋₁*R

where R is the common ratio.

We could write this in a general form as:

aₙ = a₁*(R)^(n - 1)

where a₁ is the first term of the sequence.

In this case we know that:

R = 1/5

And that:

a₆ = 1/625

Then we can replace these values in the above relation to get:

a₆ = (1/625) = a₁*(1/5)^(6 - 1) = a₁*(1/5^5) = a₁*(1/3125)

1/625 = a1*(1/3125)

(3125/625) = a1 = 5

Then the formula will be:

aₙ = 5*(1/5)^(n - 1)

Learn more about sequence

brainly.com/question/21961097

#SPJ9

The value of the angle x is equal to 53°

A) From the image attached, we can solve for the angles as follows;

m ∠RPB = 180 - 115 = 65°

Thus, the angle m∠x =  180° - 65° - 62°

= 53°

B) m∠RPB + m∠PRD = 180° (Internal angle between 2 parallel lines are equal).

Second line:

The 3 angles x, 62 and 65 degrees  are all on the same straight line (AB), so they sum to 180 degrees.

Read more about Measure of Angle at; https://brainly.com/question/25716982

#SPJ1

Answer:

16

Step-by-step explanation:

the first thing is to rearrange terms  

Answer:

LMK and QPM

Step-by-step explanation:

When two lines are crossed by another line (called the transversal), the angles in matching corners are called corresponding angles.

The linear equation which has no solution is  5x+12=5x-7

Given set of linear equations are:

23(9x+6)=6x+4, 5x+12=5x-7, 4x+7=3x+7, -3(2x-5)=15-6x.

We try to solve each equations one-by-one.

Consider the first equation:

23(9x+6)=6x+4

⇒207x+138 = 6x+4

⇒201x = -134

⇒ x =-134/201.

So this linear equation has a solution.

Now consider the second linear equation:

5x+12=5x-7

⇒12 = -7, which has no meaning.

Therefore, this linear equation has no solution.

Now consider 3rd linear equation:

4x+7=3x+7

⇒x = 0

It has a solution.

Consider the 4th linear equation:

-3(2x-5)=15-6x.

⇒ -6x+15=15-6x

⇒ 0=0

In this case, any value for x is a solution. So there are infinitely many solutions.

Learn more about solutions of linear equations at https://brainly.com/question/13729904

#SPJ4

Answer: 5=10.25, 13=26.65, 19=38.95

By elimination, the system of equations, 3x + 2y = 10 , 6x + 4y = 15, has no solutions.

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

First, multiply the first equation by 2.

3x + 2y = 10 ⇒ 6x + 4y = 20     (equation 1)

6x + 4y = 15     (equation 2)

Since the new equation of equation 1 has the same coefficients with those in equation 2, but different constants, then the two lines are in parallel.

Hence, the system of equations has no solutions.

Learn more about solving systems of equations by elimination here: https://brainly.com/question/28405823

#SPJ4

Based on the information, it can be inferred that the number that is the change in height of the elevator is 12 feet.

To complete the table we must take into account the height of the elevator at a given time of seconds. Additionally, we must take into account that the elevator goes down 12 ft every second. So the table would look like this:

To calculate the height of the basement with respect to the first floor, we must take into account the following information:

To calculate this height we must multiply the time it takes for the elevator to go down to the basement by the distance it travels each second.

Learn more about height in: https://brainly.com/question/10726356

#SPJ1

The value of the variable x such that the two lines are perpendicular to each other is equal to 106 / 5.

In accordance with geometry, two lines are perpendicular to each other if and only if the measure of the angle between the two lines is equal to 90°. Then, the angle SXW must be equal to 90° and we need to solve for x in the following equation:

5 · x - 16 = 90

5 · x = 106

x = 106 / 5

The value of the variable x such that the two lines are perpendicular to each other is equal to 106 / 5.

To learn more on perpendicular lines: https://brainly.com/question/18271653

#SPJ1

Answer:

63 hours

Step-by-step explanation:

4 workers = 21 hours

12 workers = g

[tex] \frac{21}{4} \times 12 \\ = 63hours[/tex]

Sarah's charges per hour for working during the week will be $9.5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.

Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be

45x + 5y = 902.5           ...1

50x + 10y = 1045

25x + 5y = 522.5          ...2

Subtract equation 2 from equation 1, then we have

45x - 25x = 902.5 - 522.5

20x = 380

x = 19

And the value of y will be

25 (19) + 5y = 522.5

475 + 5y = 522.5

5y = 47.5

y = 9.5

Sarah's charges per hour for working during the week will be $9.5.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1

Using factorization, In order to have at least $1250 profit, manufacturer should sell the product between $4500 and $500.

Given,

Revenue (R) = 7x

Cost (C) = 1000 + 2x + 0.001x²

Profit ≥ $1250

Using factorization,

⇒ profit = revenue − cost

⇒ Profit= 7x -  1000 - 2x - 0.001x²

⇒  7x -  1000 - 2x - 0.001x² >= 1250

⇒  5x - 0.001x^2 >= 2250

⇒  0.001x^2 - 5x <= - 2250

⇒  0.001x^2 -5x + 2250 >= 0

multiplying 1000 on both sides

⇒  1000x^2 - 5000x + 2250000 > = 0

⇒  x(x - 500) - 4500(x - 500) >=0

⇒  (x- 500) + (x - 4500) >= 0

⇒  x = 500, 4500

To learn more about factorization from given link

https://brainly.com/question/25829061

#SPJ1

The sum of two given expressions will be -

h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex].

We have two expressions.

We have to add them.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it.

According to the question -

f(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex]

g(x) = [tex]-4x^{2} -9x -4x[/tex]

Now -

h(x) = f(x) + g(x) =  [tex]-4x^{2} -3x^{-3} -4x[/tex] + ( [tex]-4x^{2} -9x -4x[/tex])

h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]

Hence, the sum of two given expressions will be -

h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]

To solve more questions on Adding expressions, visit the link below-

https://brainly.com/question/28277126

#SPJ1

The solution of the given system of equations is (-2, -1)

A system of equation can be solved using:

The given system of equations:

2x + 4y = -8  ............   (1)

-5x + 4y = 6  .............. (2)

Since the coefficients of y is the same in both equations, variable y will be immediately cancelled out if we use elimination method.

Substract equation (2) from equation (1)

2x + 4y = -8

-5x + 4y = 6 –

7x         = -14

  x         = -2

Substitute x = -2 into equation (1):

2x + 4y = -8

2. (-2) + 4y = -8

-4 + 4y = -8

Add 4 to both sides

-4 + 4y + 4 = -8 + 4

4y = -4

 y = -1

Hence, the solution is (-2, -1)

Learn more on how to solve system of equations here:

https://brainly.com/question/28405823

#SPJ4

Answer:

The answer is $86.80. The lunch service gains $86.80 in 3 1/2 hours if they get $24.80 per hour.

Step-by-step explanation:

You have to multiply how much they earn per hour, $24.80, by the number of hours they work, 3 1/2. $24.80 times 3 1/2 equals 86.80 so the lunch service earns $86.80 in 3 1/2 hours.

Hope this helps!

If a school has a total of 900 pupils and 400 pupils are boys and the rest are girls, then the ratio of the boys to the girls in the simplest form is 4:5.

A ratio in mathematics can be defined as the number of times a number contains another number or is contained in another number to express the connection between two or more things in quantity or size.

To find the ratio of boys to girls, first, we calculate the number of girls in the school. The number of girls can be found by subtracting the total number of pupils which is 900 from the number of boys which is 400.

Hence,

number of pupils that are girls = total number of pupils - number of boys

number of pupils that are girls = 900 - 400

number of pupils that are girls = 500

Hence the ratio of boys to girls can be given as,

400 : 500

Simplifying,

400/100 : 500/100

4:5

Hence, the simplest ratio of boys to girls is 4:5.

To learn more about ratios, click here:

https://brainly.com/question/25927869

#SPJ4

We can say that ΔHJF ≅ ΔFGH under RHS condition.

So,

To Prove: ΔHJF ≅ ΔFGH

So, ΔHJF ≅ ΔFGH under RHS condition.

(Refer the table given below)

Therefore, ΔHJF ≅ ΔFGH

Know more about the congruency of a triangle here:

brainly.com/question/2938476

#SPJ4

16.  Valid

Reason: congruency can be represented by the symbol ≅ hence  the statement still reads <1 and <2 are congruent.

17. Invalid

Reason: A rectangle also has four right angles, It is only a square when all the sides are equal.

18. Valid

Reason: congruency can be represented by the symbol ≅ hence the statement still reads <JKM and <MKL are congruent.

19. Valid

Reason: The conclusion of the battery dying is in support of the premise giving which is leaving the light on when the car is off.

20.Valid

Reason: The conclusion, Dante obtained a part time job is in line with the premise that obtaining a pert time job, is a way to afford a car payment

21. Valid

Reason: The premise which has that selling 75% of the prom tickets will make the prom hold at country club is fulfilled, hence the prom will be held at the country club

An argument is vailed when the premises or conditions of the argument are all true. when some part of the argument is not true then it will lead to invalid conclusion.

Read more on valid arguments here:

#SPJ1

   For the given parabola:

 We have the following data.

v = (-3,-4)

f = (-3, -3.75)

d  = y = -4.25

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

The canonical equation of a parabola is given by

(x - h)² = 4p(y - k)

The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

  The parabola equation is:

y = x² + 6x + 5

y - 5  + 9 = x² + 6x + 9

y + 4 = x² + 2(3x) + 3²

y + 4 = (x + 3)²

This means that the vertex of this parabola is

v = (h, k)

v = (-3,-4)

f = (-3, -4 + 1/4)

f = (-3, -3.75)

d = y = -4 - 1/4

d  = y = -4.25

Learn more about parabolas in:

brainly.com/question/11780596

#SPJ4

The factors of x²+19x-42 are (H) (x-2).

To find the factors:

Factors are: (x-2) and (x+21)

Therefore, factors of x²+19x-42 are (H) (x-2).

Know more about factorization here:

https://brainly.com/question/25829061

#SPJ4

Answer:

20

Step-by-step explanation:

2+2x45\5

=2+90/5

=2+18

=20

Money received in tenth month: $104

Difference between explicit formula and a recursive formula is: the use of (n-1)th term, nth term and the common difference (d) brings a great difference between the two formulae of an arithmetic progression.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

To find: Money received in tenth month.

Finding:

As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.

That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.

Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.

For a₁ = 50, a₂ = a₁ + 2

=> a₂ = 50 + 2

This way, a₅ = a₄ + 5

=> a₅ = 59 + 5 = 64

a₆ = a₅ + 6

=> a₆ = 64 + 6 = 70

a₇ = a₆ + 7

=> a₇ = 70 + 7 = 77

a₈ = a₇ + 8

=> a₈ = 77 + 8 = 85

a₉ = a₈ + 9

=> a₉ = 85 + 9 = 94

a₁₀ = a₉ + 10

=> a₁₀ = 94 + 10 = 104

Thus, the payment received in tenth month will be $104.

(b) Difference between explicit formula and recursive formula of an arithmetic progression:

To learn more about arithmetic Progressions, refer to the link: https://brainly.com/question/6561461

#SPJ4

The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

Imagine you work for a packaging firm and are building a box with a 36 cm-long rectangular bottom. The box has to be 4 cm tall.

The perimeter is given as,

36 = 2 (L + W)

W = 18 - L

Then the volume is given as,

V = L x W x H

V = L x (18 - L) x 4

V = 72L - 4L²

For the maximum volume, V' = 0

V' = 0

72 - 8L = 0

8L = 72

L = 9

Then the width will be

W = 18 - 9

W = 9

The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².

More about the volume of the rectangular prism link is given below.

https://brainly.com/question/21334693

#SPJ1

Answer:

[tex]c^6h^3[/tex]

Step-by-step explanation:

         [tex]hhh=h^3\\c^3c^2h^3c\\c^3c^2c\\ccc = c^3\\=c^{3 \cdot 2}\\=c^6\\=c^6h^3[/tex]