Sub :- Linear Equations

Answer:

Step-by-step explanation:

The standard form of an equation for a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

We can calculate the slope from the two given points, A(5,7) and B(9,-1).

Slope is Rise/Run, where Rise is the change in y and Run is the change in x.

From the two given points, starting at (5,7) and going to (9,-1):

Rise = (-1 -7) = -8

Run = (9-5) = 4

Rise/Run (slope) = -8/4 or -2

The equation becomes y = -2x + b

We can find b by entering either of the two given points and solving for b. I'll pick (5,7):

y = -2x + b

7 = (-2)*(5) + b

7 = -10 + b

b = 17

The equation is y = -2x + 17

Check this with a DESMOS graph (attached).

The equation of line AB is y= -2x +17

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Points A(5, 7) and B(9, -1)

So, slope for the equation is

sloe= (-1 - 7)/ (9- 5)

slope = -8/ 4

slope= -2

Now, using slope- intercept form

y - b = m ( x- a)

y - 7= -2( x - 5)

y- 7 = -2x + 10

y= -2x + 17

Hence, the equation of line AB is y= -2x +17

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Answer:

(3,5)

1/3

Step-by-step explanation:

The equation is already in point-slope form. Therefore, both the point and slope can easily be found in the equation. Point slope form looks like [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]. In this the point is [tex](x_{1},y_{1})[/tex] and the slope is m. So, the x value is 3 and the y value is 5, making the coordinate (3,5). Finally, the slope is 1/3.

Answer:

Step-by-step explanation:

Add up the equations, it will eliminate x as variable:

Find the value of x:

Given : -

To find : -

Solution : -

3x + 6y = 18

-3x + 4y = 2 +

10y = 20

[tex] \: [/tex]

3x + 6y = 18

3x + 6(2) = 18

3x + 12 = 18

3x = 18 - 12

3x = 6

[tex] \: [/tex]

Answer:

5

Step-by-step explanation:

Eacl side of the square has a length of 5 cm.

Answer:

55%

Step-by-step explanation:

i assume your question is from mathswatch

And this is the answer for it!

Answer:

A. y = –x^2 + 4

Step-by-step explanation:

Find the vertex form.

y = − ( x + 0 ) 2 + 4

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:  

( 0 , 4 )

Focus:  

( 0 , 15 /4 )

Axis of Symmetry:  

x = 0

Directrix:  

y

=

17

4

x

y

−

2

0

−

1

3

0

4

1

3

2

0

Answer:

.25 dollars or 25 cents

Step-by-step explanation:

128/2=64                         32/2=16

64/2=32                          16/2=8                        

32/2=16                           8/2=4

16/2=8                             4/2=2

8/2=4                               2/2=1

4/2=2                               1/2=(1/2)

2/2=1                                (1/2)/2=(1/4)

1/4 of 1 dollar is 25 cents

Answer:

Rate = 100/10 = 10%. ∴ The rate of interest is 10%. ∴ The rate of interest is 10%.

Answer: buddy if you put it in English i can do it I’m a teacher

Step-by-step explanation:

(a) One possibility is 8.45

Rounded to the nearest integer = 8

Rounded to the nearest tenth = 8.5

And rounding this to the nearest integer = 9

(b) The possible numbers are 8.45 to 8.49, inclusively

Answer:

Table is below in explantation

Not proportional

yes, linear

Step-by-step explanation:

We substitute and solve:

TABLE:

X --> Y

0 --> -2 (0-2 = -2)

1 --> -1

2 --> 0

Yes, it is linear, the slope is 1 and is written in slope - intercept form

No, not proportional, the y - intercept is (0, -2) not (0,0)

Answer:

12

Step-by-step explanation:

Assume that lines which appear to be tangent are tangent.

Therefor this is a right triangle.

Use the pythagorean theorem

c^2 = a^2 + b^2

15^2 = ?^2 + 9^2

225 = ?^2 + 81

subtract 81 from both sides

144 = ?^2

Take the square root of both sides

12 = ?

9514 1404 393

Answer:

  ? = 12

Step-by-step explanation:

The tangent makes a right angle with the radius at the point of tangency. That means the Pythagorean theorem can be used to find the missing length.

  ?² +9² = 12²

  ?² = 225 -81 = 144

  ? = √144 = 12

The value of ? is 12.

__

Additional comment

When you see a right triangle with the ratio of hypotenuse to leg of 15:9 = 5:3, you know immediately that it is a multiple of a 3:4:5 right triangle. Here, the scale factor is 3, so the missing side is 3×4 = 12.

Answer:

1/2

Step-by-step explanation:

5/6 • 3/5

15/30 = 1/2

Answer:

1/2

Step-by-step explanation:

For fraction multiplication, multiply the numerators and then multiply the denominators to get

5 × 3/ 6 × 5 = 15/30

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 15 and 30 using

GCF(15,30) = 15

15 ÷ 15/30 ÷ 15 = 1/2

Therefore:

5/6 × 3/5 = 1/2

Answer:

x=5

y=3

then ,

x+2y= 5+2 *3

= 5+6

= 10

Answer:

Simplifying

(n + 9) + -1(2 + -2n) = 0

Reorder the terms:

(9 + n) + -1(2 + -2n) = 0

Remove parenthesis around (9 + n)

9 + n + -1(2 + -2n) = 0

9 + n + (2 * -1 + -2n * -1) = 0

9 + n + (-2 + 2n) = 0

Reorder the terms:

9 + -2 + n + 2n = 0

Combine like terms: 9 + -2 = 7

7 + n + 2n = 0

Combine like terms: n + 2n = 3n

7 + 3n = 0

Solving

7 + 3n = 0

Solving for variable 'n'.

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

Add '-7' to each side of the equation.

7 + -7 + 3n = 0 + -7

Combine like terms: 7 + -7 = 0

0 + 3n = 0 + -7

3n = 0 + -7

Combine like terms: 0 + -7 = -7

3n = -7

Divide each side by '3'.

n = -2.333333333

Simplifying

n = -2.333333333

Step-by-step explanation:

Answer:

Solve the equation for y. See example.

Step-by-step explanation:

I'll use 3x + 5y = 15. First subtract 3x from both sides since it is positive.

[tex]3x + 5y = 15 \\ - 3x \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: - 3x[/tex]

[tex]5y = - 3x + 15[/tex]

Now solve for y by dividing each term by 5.

[tex] \frac{5y}{5} = \frac{ - 3}{5} x + \frac{15}{5} [/tex]

Now simplify.

[tex]y = \frac{ - 3}{5} x + 3[/tex]

The slope is

[tex] - \frac{3}{5} [/tex]

Answer:

i think its the 3rd option

Step-by-step explanation:

i'd'k what it is but you can read it over and over again

(p.s Brainleist?)

Answer:

x=22/3

Step-by-step explanation:

Answer:

(700-42-56)

Step-by-step explanation:

10-x

5-y

4 in a cell of 42 large candles and 56 small candles the total profit would be p equals 40 to 10 - x + 56 * 5 - y

Answer:

17 IS THE ANSWER......................

Answer:

Your answer should be 36.

Answer:

28/5 is the answer.

Step-by-step explanation:

Multiply the denominator by the whole number

5 × 5 = 25 Then we add the answer from the last step to the numerator 25 + 3 = 28 next we write the answer from the last step over the denominator which is 28/5.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5\dfrac{3}{5}}\\\\\mathsf{= \dfrac{5\times5+3}{5}}\\\\\mathsf{= \dfrac{25 + 3}{5}}\\\\\mathsf{= \dfrac{28}{5}}\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{\dfrac{28}{5}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Given that

(2+i)²/(3+i)

On multiplying both numerator and the denominator with (3-i) then

⇛ [(2+i)²/(3+i)]×[(3-i)/(3-i)]

⇛ [(2+i)²(3-i)]/[(3+i)(3-i)]

⇛ [(2+i)²(3-i)]/[(3²-i²)

⇛ [(2+i)²(3-i)]/(9-i²)

⇛ [(2+i)²(3-i)]/[9-(-1)]

Since ,i² = -1

⇛ [(2+i)²(3-i)]/(9+1)

⇛ [(2+i)²(3-i)]/10

⇛ [{2²+i²+2(2)(i)}(3-i)]/10

⇛ (4+i²+4i)(3-i)/10

⇛ (4-1+4i)(3-i)/10

⇛ (3+4i)(3-i)/10

⇛ (9-3i+12i-4i²)/10

⇛ (9+9i-4(-1))/10

Since, i² = -1

⇛(9+9i+4)/10

⇛(13+9i)/10

⇛ (13/10)+ i (9/10)

We know that

The conjugate of a+ib is a-ib

So,

The conjugate of (13/10)+ i (9/10) is

(13/10)-i(9/10) ⇛ (13/10)+i (-9/10)

Answer:-The conjugate of (13/10)+ i (9/10) is (13/10)+i (-9/10)

Additional comment:

Answer:

See below for answer.

Step-by-step explanation:

BA ≅ BC                         Given

DA  ≅ EC                       Given

BA + DA ≅ BC + EC      Congruent  parts are congruent

BD ≅ BE                        Addition

Answer:

$875.00

Step-by-step explanation:

You multiply 1250 by .3 to get 375. Then you subtract that from your total to get your sale price. Hope this helps :))

Using the concept of variation, there is an inverse relationship between the number of attendees and the contribution made by each attendee.

Since the amount of chocolate decreases as the number of attendees increase;

We use inverse variation to model the scenario :

Taking any pair of points :

3000 = k/8

k = 3000 × 8

k = 24000

Therefore, the variation statement is "the amount paid per attendee is inversely proportional to the number of people in attendance.

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answer is 2.2 66 88862 u88272

Answer:

1 # 2 = 4

Step-by-step explanation:

1 # 2 = 2*1 + 2 = 2 + 2 = 4

The equation is y = 0.5x and the slope is 0.5.

A function is said to be linear if it is a straight line graph and it can be represented by the equation:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the height of the tomato after x weeks. Let us assume that the points are (0, 0) and (6, 3), hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{3-0}{6-0} (x-0)\\\\y=0.5x[/tex]

Therefore the equation is y = 0.5x and the slope is 0.5.

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The equation for the scenario "A farmer is measuring the average height y of her tomato plants x weeks after planting sprouts" is y = mx + c

The slope = m

The duration after which the farmer measures the average height of her tomato = x weeks

The average height of the tomato plant after x weeks = y

For the slope to be required, it means the relationship between the average height of the her tomato (y) and the number of weeks (x) is linear

This means that the average height of the tomato will be represented by a linear equation as shown below

y  =  mx   +  c

The slope of the equation is m

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Answer:

Ms. Neville graded 80% of the papers and the student teacher graded 20% of them.

Step-by-step explanation:

Given a total of 75 papers, and Ms. Neville graded 60 of them, 15 remain for the student teacher. 75 - 60 = 15

Ms. Neville graded 60/75 = 0.8 = 80% of papers.

The student teacher graded 15/75 = 0.2 = 20% of papers.

Sanity check: 80% + 20% = 100%