Why is it useful to have different forms of linear equations?

Answers

Answer 1
It is also useful because we can read the slope and y-intercept from the equation. Often, when we are given equations in other forms, we can rewrite it in slope-intercept form to get the slope and y-intercept.
Answer 2

Linear equation is the equation of a straight line.

Forms of a linear equation

The forms of a linear equation are:

Slope intercept form - [tex]\mathbf{y = mx + b}[/tex].Point slope form - [tex]\mathbf{y - y_1 = m (x - x_1)}[/tex].Standard form - [tex]\mathbf{Ax +Bx = C}[/tex].

Slope intercept form

From the slope intercept form, one can easily deduce the slope and the y-intercept of the linear equation

Point slope form

From the point-slope form, one can easily deduce the slope and the points of the graph of the linear equation

Standard form

From the standard form, the values of x and y can be easily calculated.

Hence, the usefulness of having different forms of linear equation is that they all serve different purposes, even through they represent the same graph.

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Related Questions

Pls help Which of the following exponential equations is equivalent to the logarithmic equation below ? In x = 7

Answers

Answer:

Step-by-step explanation:

Let's write that out completely:

[tex]ln_e(x)=7[/tex] The rule for going from log to exponential is what I call the "circular rule" in my classes and the kids never forget it. Take the base of the log, raise it to the power of the number on the other side of the equals sign, and then circle back to set it equal to the argument.

e is the base. Raise e to the 7th and circle back to set the whole thing equal to x (x is called the argument):

[tex]e^7=x[/tex] choice C.

Brianna's Bakery offers 3 flavors of bagels. Customers can choose from plain, cinnamon, or blueberry bagels. Yesterday, a customer ordered 144 bagels for a company meeting. The order was for twice as many blueberry bagels as plain bagels and 3 times as many cinnamon bagels as blueberry bagels.
How many cinnamon bagels did the customer order

Answers

Answer:

96 darling

Step-by-step explanation:

youre gonna take all the times this was teice as mich as that

like this:blueberrybagel twice as much 2

than plain bagels 1

cinnamonbags 3 times as much than

blueberry bagels 2×3= 6+

=9

EACH portion contains144:9=16 bagels

blueberry ones16×2=32

plain ones16×1=16

cinnamon ones 3×32=96


question 1…. help please

Answers

Answer: The number = 3 /4 or 4 / 3

Concept:

Here, we need to know the idea of a reciprocal.

Reciprocal is also called the multiplicative inverse.  It is similar to turning the number upside down which is found by interchanging the numerator and denominator.

Number ⇒ Reciprocal = 1 / Number

Solve:

STEP ONE: Set up the equation

Let x = the number

Let 1 / x = the reciprocal

x + 1 / x = 25 / 12

STEP TWO: Multiply x on both sides

(x + 1 / x) · x = (25 / 12) · x

x² + 1 = 25x / 12

STEP THREE: Multiply 12 on both sides

(x² + 1) × 12 = (25x / 12) × 12

12x² + 12 = 25x

STEP FOUR: Subtract 25x on both sides

12x² + 12 - 25x = 25x - 25x

12x² - 25x + 12 = 0

STEP FIVE: Solve for the quadratic equation

(3x - 4) (4x - 3) = 0 ⇔ (Factorization of the equation)

(x - 4 / 3) (x - 3 / 4) = 0

x = 4 / 3 or x = 3 / 4

Hope this helps!! :)

Please let me know if you have any questions

SOMEONE HELP ME PLEASE

Answers

i dont know if this help

Add.
(3x2 – 2x) + (4x-3)
O A. 7x2- 5x
O B. 12x3 - 14x2 + 6x
O C. 3x2 - 6x + 3
O D. 3x2 + 2x-3

Answers

Answer:

O D. 3x2 + 2x-3

Answer:

A.7x2-5x questions 2of 20

the perimeter of a rectangular plot of land whose length is (2x+5)m and width (x-10)m is 80m. Find the
i)value of x
ii)area​

Answers

Answer:

P.=2(2x+5)+2(x-10)=80cm

6x-10=80

x=90/6=15cm

Area= L*W= 35*5=175 squared cm= 0.0175 squared m

Verify the identity.

[tex]cot (x-\frac{\pi }{2})=-tan[/tex]

Answers

Answer:

True

Step-by-step explanation:

assuming that you meant to write

cot (x-π//2) = - tan x

the identity is TRUE because,

- you can graph cot (x-π//2)  and  - tan x, and see that the graphs overlap

OR

-you solve for cot (x-π/2)

useful to know is that :

cot x=1/tan x, tan x = sin x/cos x,  

cos(x) =cos(-x), sin(-x) = -sin x,

cos(π/2 -x) =sin x, sin (π/2-x) =cos x

cot (x-π/2) = 1/tan (x-π/2) , yet tangent is sin x/cos x

cot (x-π/2) = cos (x-π/2) /sin (x-π/2) , factor -1

cot (x-π/2) = cos -(π/2-x) /sin -(π/2-x),  use facts: cos(x) =cos(-x), sin(-x) = -sin x

cot (x-π/2) = cos (π/2-x) / -sin (π/2-x), use cos(π/2 -x) =sin x, sin (π/2-x) =cos x

cot (x-π/2) = sin x / -cos x , again sin x /cos x = tan x

cot (x-π/2) = -tan x

I will mark as the brillianest plzzzzzzzzzzzzzzzzzzzz be helpful to me ......
c) If C.P. = Rs 750, loss percent = 8% find S.P.​

Answers

Answer: SP is Rs 690

Step-by-step explanation:

CP= Rs 750

loss percent = 8%

so

loss = 8% of CP

= 8/100 * 750

= Rs 60

Loss = Rs 60

so

SP = Rs 750-60

= Rs 690

Answer:

here,

CP=750

loss%=8%

now,

SP= (100-L)×cp/100

= (100-8)×750/100

= (92×750)/100

= 69000/100

= 690

hence the SP of the article is Rs 690

any problem then comment it

hope this helped you ☺️

solve for x on the diagram below

Answers

Answer:

20 is the answer

Step-by-step explanation:

x+3x+10=90(right angle triangle)

4x=90-10

x=80/4

x=20°

Answer:

x = 20

Step-by-step explanation:

Based on the square indication at the corner of the angle, we can assume it's a right angle, so 90°. This means that x + 3x + 10 = 90. Solve it like any algebraic equation, isolating x. add x to 3x + 10, this would net you 4x + 10 = 90. Subtract 10 on both sides of the equation to further isolate x, meaning 4x = 80. Simplify this, dividing 4 on both sides, meaning x = 20.

Please Help!!
To find the distance AB across a river, a distance BC of 786 m is laid off on one side of the river. It is found that B = 110.2° and C = 13.5°. Find AB. I don't understand how to do this but I know you need to use the Law of Sines, so please show work.

Answers

Answer:

~ 220.6

Step-by-step explanation:

sine rule : a/sinA =b/sinB = c/sinC

AB/sinC =BC/sinA

A = 180 - 110.2 - 13.5 = 56.3 degrees

AB/sin13.5 = 786/sin56.3

AB = 786sin13.5/sin56.3 = 220.5506

The distance across the river of AB is 220.55 m.

What is Law of Sines?

Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.

That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Given a triangle ABC.

We have,

∠B = 110.2° and ∠C = 13.5°

We know that the sum of the interior angles of a triangle is 180°.

∠A = 180 - (110.2 + 13.5) = 56.3°

Using the law of sines,

BC / Sin A = AB / Sin C

Substituting the values,

786 / sin (56.3°) = AB / sin (13.5°)

AB = (786 / sin (56.3°)) sin (13.5°)

     = 220.55 m

Hence the distance is 220.55 m.

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Find the value of x.

Answers

Answer:

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ᴀꜱ ꜱɪʟʟʏ ᴀꜱ ꜰᴜɴ

ᴀꜱ ᴄᴏʟᴅ ❄️ ᴀꜱ ᴀ ᴛʀᴇᴇ

ᴀꜱ ꜱᴄᴀʀʏ ᴀꜱ ꜱᴇᴀ

ᴀꜱ ʜᴏᴛ ᴀꜱ ꜰɪʀᴇ

ᴀꜱ ᴄᴏʟᴅ ᴀꜱ ɪᴄᴇ

ꜱᴡᴇᴇᴛ ᴀꜱ ꜱᴜɢᴀʀ

ᴀɴᴅ ᴇᴠᴇʀʏᴛʜɪɴɢ ɴɪᴄᴇ

ᴀꜱ ᴏʟᴅ ᴀꜱ ᴛɪᴍᴇ ⌛

ᴀꜱ ꜱᴛʀᴀɪɢʜᴛ ᴀꜱ ʟɪɴᴇ ➖

ᴀꜱ ʀᴏʏᴀʟ ᴀꜱ ᴀ ᴀɴɢᴇʟ☺️

ᴀꜱ ʙᴜᴢᴢᴇᴅ ᴀꜱ ʙᴇᴇ

ᴀꜱ ꜱᴛᴇᴀʟᴛʜ ᴀꜱ ᴛɪɢᴇʀ

ꜱᴍᴏᴏᴛʜ ᴀꜱ ɢʟɪᴅᴇʀ

ᴘᴜʀᴇ ᴀꜱ ʜᴇᴀʀᴛ ❤️

ᴘᴜʀᴇ ᴀꜱ ɪ ᴡᴀɴɴᴀ ʙᴇ

Step-by-step explanation:

hehehehehe I'm xxxxxd

Saniya........ Khan ❤️

Find cos A and cot B exactly if a=15 and b=11 , what will Cos A be and Cot B be?

Answers

Answer:

D. <15/√346>

Have a nice day! :)

find the value of a) 4:12

Answers

Step-by-step explanation:

1:4 bcos u need to divide both sides by 4

what is the value of x

Answers

Answer: 24(option A) is the answer

exterior angle = 360/n

so, n = 15

then, 360/15 = 24

Goalie is determined using the formula A = 60 a equals 60 left-parenthesis StartFraction g Over t EndFraction right-parenthesis.. In

Answers

Answer:

g = At/60

Step-by-step explanation:

A = 60(g/t)

To solve for 'g'

Open the bracket

A = 60g/t

Multiply both sides by t

At = 60g

Divide both sides by 60

At/60 = 60g/60

At/60 = g

Urgent ! Help me please

Answers

Answer:

B

Step-by-step explanation:

x -> x and y -> y+5

-1 -> - 1 and - 3 -> 2, so b is the correct answer.

Find the indicated side of the
right triangle.
45°
y
6
45°

Answers

Answer:

6

Step-by-step explanation:

tan 45 = 6 / x

1 = 6 / x

x = 6

Note :

Tan 45 value = 1

Answer:

x=6

Step-by-step explanation:

Since this is an isosceles triangle, the sides must be equal next to the base angles that are equal

x=6

the sum of two numbers is 10, the sum of their squares is 58 determine the two numbers​

Answers

Answer:

7 and 3

Step-by-step explanation:

Using the given information, one can form an equation. Let the first number be (x) and the second (y).  For two equations based on the given information.

"the sum of two numbers is 10"

x + y = 10

" the sum of their squares is 58 determine"

[tex]x^2+y^2=58[/tex]

Solve for the equation for (x), then substitute the expression for (x) into the second equation. Simplify and solve to find the value of (y), and backsolve for the value of (x).

x + y =10

x = 10 -y

Substitute into the other equation:

[tex]x^2+y^2=58[/tex]

[tex](10-y)^2+y^2=58[/tex]

Simplify, remember the pattern for opening a binomial squared:

[tex](a - b)^2=a^2-2ab+b^2[/tex]

Apply this pattern here to simplify,

[tex](10-y)^2+y^2=58[/tex]

[tex]100-20y+y^2+y^2=58[/tex]

Simplify further,

[tex]100-20y+y^2+y^2=58[/tex]

[tex]2y^2-20y+100=58[/tex]

Inverse operations,

[tex]2y^2-20y+100=58[/tex]

[tex]2y^2-20y+42=0[/tex]

Factor, take out a common factor that all of the terms have. Then rewrite the quadratic trinomial as the product of two linear binomials. Remember the general pattern for factoring, add the inverse of the factors of the constant term to the variable, the sum of these factors must equal the coefficient of the linear term of the quadratic trinomial.

[tex]2y^2-20y+42=0[/tex]

[tex]2(y^2-10y+21)=0[/tex]

[tex]2(y-7)(y-3)=0[/tex]

Now use the zero product property to solve, the zero product property states that any number times zero equals zero.

[tex]2(y-7)(y-3)=0[/tex]

[tex]y = 7, y = 3[/tex]

Since the sum of (7) and (3) is (10), one has found the values of (y), it can be either (7) or (3), it doesn't matter which equals which.

A square has a perimeter of of 28 m. What is the length of each side

Answers

Answer:

a square has 4 sides therefore the formula for perimeter of a square would be 4a where a is the number of sides. in this case, we want to know the length of each side so we divide total length (28) by number of sides which is 4 and we get 7m

Answer:

the side lengths of a square are equal. Second, know that the sum of all 4 side lengths gives us the perimeter.

A right triangle has a 12in base and an 8in height. What is the area of the triangle, in in??​

Answers

Answer:

48

Step-by-step explanation:

using the formula 1/2 b*h

8*12=96

96/2=48

Can u please solve this

Answers

Answer:

522.5in^3

Step-by-step explanation:

4/3 ×3.14×5^3

4/3×3.14×125

1.33×3.14×125

4.18×125

522.5

Step-by-step explanation:

[tex]v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3 \times {5}^{3} \\ = 4 \times 125 \\ = 500 {in}^{3} \\ thank \: you[/tex]

f(x) = (x - 5) (2x - 7) (7x - 3) has zeros at x = -3.5, x = 3/7, and x = 5.

what is the sign of f on the interval 3/7 < x < 5 ?

1. f is always positive on the interval.
2. f is always negative on the interval.
3. f is sometimes positive and sometimes negative on the interval.

Answers

The function f(x) will be sometimes positive and sometimes negative on the interval so option (3) will be correct.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

In other terms, a function is a relationship between variables, and the type of relationship that exists between the variables defines the function, such as y = sinx and y = x +6.

Given function is

f(x) = (x - 5) (2x - 7) (7x - 3)

The term (x - 5) will be negative if x < 5.

The term (2x - 7) will be negative if x<3.5

Let's say if x = 4 then (x - 5) will be negative but (2x - 7) will be positive and hence overall value will be negative.

But if x = 3 then (x - 5) will be negative and (2x - 7)  will also be negative and hence overall value will be negative

Hence the function f is sometimes positive and sometimes negative on the interval.

For more about the function

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Answer:

always negative the other guy was wrong because when you wrote 2x - 7 you meant 2x + 7 I know this because it’s on Khan Academy

Step-by-step explanation:

HELP!!!!!! so many points for this one!!!!!! x^2+y^2+4x-2y=-1
The equation of a circle in the xy-plane is shown above. What is the radius of the circle

A.2
B.3
C.4
D.9

Answers

Answer:

A. 2

Step-by-step explanation:

Given circle:

x² + y² + 4x - 2y = -1

Convert the equation into the standard form of (x - k)² + (y - h)² = r²:

x² + 4x + 4 + y² - 2y + 1 = -1 + 4 + 1(x + 2)² + (y - 1)² = 2²

As per above:

r = 2

Correct choice is A

A.2

Answer:

Solution given:

equation of a circle is:

x²+y²+4x-2y=-1

x²+y²+4x-2y+1=0

Comparing above equation with

ax²+by²+2gx+2fy+c=0

we get

a=1

b=1

g=2

f=-1

c=1

now

radius of a circle (r)=[tex]\sqrt{g²+f²-c}[/tex]

substituting value

r=[tex]\sqrt{2²+(-1)²-1}=2[/tex]

therefore radius of a circle is 2 units

What is the initial value of the sequence?
1
2
3
8

Answers

Answer:

2

Step-by-step explanation:

The initial value is the y value of the first term shown ( when x=1)

y = 2 when x=1

The initial value is 2

Answer:

What is the initial value of the sequence?

1 2 <<<CORRECT 3 8

Step-by-step explanation:

Edge 2021

Show that the line 4y = 5x-10 is perpendicular to the line 5y + 4x = 35 ​

Answers

Step-by-step explanation:

concept :concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:Given equations of lines areconcept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:Given equations of lines are4y = 5x-10concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:Given equations of lines are4y = 5x-10or, y = (5/4)x(5/2). .....(1)5y + 4x = 355y + 4x = 35ory = (-4/5)x + 7. ......(2)Let m and n be the slope of equations i and ii, respectively.Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4n= -4/5Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4n= -4/5therefore, mx n = -1Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4n= -4/5therefore, mx n = -1Hence, the lines are perpendicular.

Express -5/8 as a rational number with -24 as the denominator​

Answers

Answer:

Step-by-step explanation:

Hello!

-5/8 = (-5*-3)/ (8*-3) = 15/-24

Someone Help! PLEASE!
Jesse is taking the tests needed to join the math team. His scores were 89, 92, 94. What's the lowest score he can get on the fourth test and still have a 90 average?

Answers

Answer:

The lowest score could be 85

Step-by-step explanation:

Let the  lowest score = x

(x + 89 + 92 + 94)/4 = 90                     Add the 3 scores you know

(x + 275)/4 = 90                                    Multiply both sides by 4

(x + 275) = 360                                     Remove the brackets.

x + 275 = 360                                       Subtract 275

x = 360 - 275

x = 85

First, find the length of each edge of the cube.
Then, find the volume.

Answers

the length of each edge of the cube would be 6cm, and to find the volume you would do 6x6x6 which is 326 cm cubed

since in a cube length, width and height are equal,

h = 6

w = 6

l = 6

and volume is 6³ = 216cm³

hope it helps :)

Daphne borrows $2500 from a financial institution that charges 6% annual interest, compounded monthly, for 2 years. The amount that Daphne will need to pay back at the end of the term is

Answers

1350$ is the right answer to your problem trust me I know this

help
1) find the value of x
2)find length of a side of the square

Answers

Answer:

x = 12 , s = 41

Step-by-step explanation:

The sides of a square are equal , so

4x - 7 = 3x + 5 ( subtract 3x from both sides )

x - 7 = 5 ( add 7 to both sides )

x = 12

Then

length of side s is

s = 4x - 7 = 4(12) - 7 = 48 - 7 = 41

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