Find The Slope of Each Line

The residual column is given by the difference between the given values

and the values from the fitted line.

Reasons:

The line of best fit equation is; y = 2.55·x - 3.15

The 4-column table is presented s follows;

[tex]\begin{tabular}{|c|c|c|c|}\underline{x}&\underline{Given}&\underline{Predicted}&\underline{Residual}\\1&-0.7&-0.6&-0.1\\2&2.3&1.95&0.35\\3&4.1&4.5&a\\4&7.2&7.02&b\end{array}\right][/tex]

Required:

The values of a and b

Solution;

The residual is given by the difference between actually observed value and the predicted value

RESID = [tex]\mathbf{y_i}[/tex] - [tex]\mathbf{x_i}[/tex]·b

Where;

[tex]y_i[/tex] = The given value at point i

[tex]x_i[/tex]·b = The predicted value at point i

Therefore;

At x = 1, the residual = -0.7 - (-0.6) = -0.1

At x = 2, the residual = 2.3 - 1.95 = 0.35

At x = 3, the residual = a = 4.1 - 4.5 = -0.4

Therefore;

At x = 4, the residual = b = 7.2 - 7.02 = 0.18

Therefore;

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Answer:

[tex](x + 7) - (x - 2)[/tex]

x²-2x+7x-14

Answer:

x2+5x-14

Step-by-step explanation:

Answer:

The slope (m = rate of growth) for this function is 3/5. So, m= 3/5.

The y-intercept (b) for this function is located at (0,3). So, b=3.

Therefore, h(x) = 3/5x + 3

Step-by-step explanation:

Let the independent variable be x and dependent variable be y

y=h(x)

h is a linear function so it is represented in the general form of y=mx+c where

m is slope and c is the y-intercept.

Given "the dependent variable decreases 3 units for every 5 units the independent variable increases."

When x increases by 5, y decreases by 3

So the slope = rate of change of y / rate of change of x = -3/5

Given h(0)=3, h(0)=m(0)+c=3

c=3

Combining slope and y-intercept, y=-3/5*x+3

x-intercept is when y=0

0=-3/5*x+3

3/5*x=3

x=3*5/3=5

x-intercept=5

The slope of the linear function 3/5.

The y - intercept of the linear function - 3.

The x - intercept of the linear function - 5.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

A linear function g models a relationship in which the dependent variable decreases 3 units for every 5 units the independent variable increases.

And, g(0) = - 3

Now,

Since, A linear function g models a relationship in which the dependent variable decreases 3 units for every 5 units the independent variable increases.

So, Slope = Rate of growth

               = - 3 / 5

Thus, The slope of the linear function - 3/5.

Hence, The general form of equation of line is,

⇒ y = mx + c

⇒ g (x) = - 3/5x + c

Since, g (0) = - 3

⇒ g (0) = - 3/5 × 0 + c

⇒ - 3 = c

Thus, The y - intercept of the linear function - 3.

Hence, We get the general form of equation of line as;

⇒ g (x) = - 3/5x - 3

For x - intercept put g (x) = 0, we get;

⇒ 0 = - 3/5x - 3

⇒ - 3/5x = 3

⇒ x = - 5

Thus, The x - intercept of the linear function - 5.

Therefore, The slope of the linear function 3/5.

The y - intercept of the linear function - 3.

The x - intercept of the linear function - 5.

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Answer:

a² - b² = (a+b)(a-b)

Step-by-step explanation:

= 2x² - 7x²

=(2x + 7x)(2x - 7x)

Answer:

-5x²

Step-by-step explanation:

combine like terms in 2x²-7x²

Answer:

linear functions have no exponents higher than 1, and a graph that looks like a straight line. non-linear functions have at least one exponent higher than 1, and a graph that isn't a straight line.

Step-by-step explanation:

Answer:

X = 17

Step-by-step explanation:

Mid segment theorem: the segment joining the midpoints of two sides of a triangle is half the length of the third side.

Step-by-step explanation:

I hope you understand it. Thank you for 50 points

Refer to the attachment

they look the same size but because of the 2 in front meaning it's going to be double than what the real answer it is (and it twelve Ike it's counter part) it would be six... yet someone already answered before me so credits to him.

ANSWER 6

Answer:  [tex]y < -\frac{1}{2}x+3[/tex]

This is the same as writing y < (-1/2)x+3

==============================================================

Explanation:

The dashed boundary line goes through (0,3) and (4,1)

Apply the slope formula for those two points

m = (y2-y1)/(x2-x1)

m = (1-3)/(4-0)

m = -2/4

m = -1/2

The slope of the dashed line is -1/2. The y intercept is 3. So we go from y = mx+b to y = (-1/2)x+3 to represent the equation of the dashed line. This is the same as writing [tex]y = -\frac{1}{2}x+3[/tex]

We shade below the dashed line to represent the inequality [tex]y < -\frac{1}{2}x+3[/tex]. Points in the shaded region are solutions to the inequality. One example point is (0,0).

Note that we don't have "or equal to" as part of the inequality sign because we are not including points on the boundary. A solid line, rather than a dashed line, would include points on the boundary.

Answer:

Step-by-step explanation:

32,000

×. 4

Answer:

$33,280

Step-by-step explanation:

Since your salary is $32,000, you would take 4% from $32,000 and add it to the current salary. 4% can be shown as .04 in decimal form. If you multiply 32,000 by .04 you get 1280. Add 1,280 to 32,000 and you get 33,280.

Answer:Whats the question or add a picture

Answer:

127 degree I guess because I don't see a picture

Step-by-step explanation:

is the picture showing 53 degrees

Answer:

yyyyyyyyyyyyyyyyyyyyyyyyyyyyy

Answer:

0.02a

Step-by-step explanation:

Since 0.02 is equal to 2 cents, he would get 0.02a annually. This is because a represents the income from interest and 0.02 is the amount of money made for interest.

Answer:B.27

Step-by-step explanation:

If right please mark as brainly

Answer:

d = 3

Step-by-step explanation:

The sum to n terms of an AP is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( a + l)

where a is the first term and l the last term

Here a = 2, l = 59 and sum = 610 , then

[tex]\frac{n}{2}[/tex] (2 + 59) = 610

[tex]\frac{n}{2}[/tex] × 61 = 610 ( divide both sides by 61 )

[tex]\frac{n}{2}[/tex] = 10 ( multiply both sides by 2 to clear the fraction )

n = 20

Then the sequence has 20 terms with a₂₀ = 59

The nth term of an AP is

[tex]a_{n}[/tex] = a + (n - 1)d

where d is the common difference , then

2 + 19d = 59 ( subtract 2 from both sides )

19d = 57 ( divide both sides by 19 )

d = 3

Answer:

the first option; b = 5 minus three-halves r

Step-by-step explanation:

4b+6r=20

4b=20-6r

b=5-3/2r

Answer: A

Step-by-step explanation: This is the answer for edge 2021 im a student

Answer:

Slope=5

Step-by-step explanation:

Using slope formula, we have -9-(-14)/-1-(-2) which is 5/1, so our slope is 5

Answer:

slope is 5

Step-by-step explanation:

get 2 points and apply:

(-14-(-9))/(-2-(-1))=-5/-1=5

Answer:

y=10x-4

Step-by-step explanation:

Answer:

y=10x-4

Step-by-step explanation:

Answer:

128/512 or 1/4

Step-by-step explanation:

(2 x 2 x 2 x 2) x (2 x 2 x 2)= 16 x 8 = 128

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

(2 x 2 x 2 x 2 x 2) x (2 x 2 x 2 x 2)= 32 x 16 = 512

Answer:

B. m[tex]\geq 2\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]m\geq \frac{5}{2}[/tex]

[tex]\sqrt{x(x+2)} = 0 <=> x(x+2)=0\\<=> x=0 /or/ x+2=0 <=> x=0 /or/ x=-2[/tex]

ok done. Thank to me :>

Step-by-step explanation:

step 1:-group the first two terms together and then the last terms together.

step 2:-factor out a GCF from each separate binomial.

step3:-factor out the binomial

Answer:

w [tex]\leq[/tex] 3,600

Step-by-step explanation:

[tex]\leq[/tex]  means less than or equal to.

Answer:

answer is d

by using rise over run you get 3/6 which is then simplified into 1/2

Answer: She did not create it correctly because we have two science students and six music students instead of three science students and five music students. I believe pie charts work well because they give a quick overview of the students.

Would appreciate brainly <3

Answer:

a = 1

b = -9

c = 18

Answer:

b. (6,3)

Step-by-step explanation:

10+2=12

12/2=6

The line is always on 3, so that will be the y coordinate!

The midpoint of the line segment are (6, 3). Therefore, option B is the correct answer.

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

The formula to find the midpoint of line segment is (x, y) = [(x₁+x₂)/2, (y₁+y₂)/2]

From the graph, the coordinate points of ends of line segment are (2, 3) and (10,3).

Here, midpoint = [(2+10)/2, (3+3)/2]

= (6, 3)

Therefore, option B is the correct answer.

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Answer:

f(x) = 2x + 1.

Step-by-step explanation:

In order to determine the function rule for the given table of values, we must start by finding the slope or the rate of change. Choose two ordered pairs from the table: (0, 1) and (1, 3).

Let (x₁, y₁) = (0, 1)

     (x₂, y₂) = (1, 3)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (3 - 1)/(1 - 0)

m = 2/1 = 2

Therefore, the slope of the function is, m = 2.

Next, we must determine the y-intercept, which is the point on the graph where it crosses the y-axis, with coordinates of (0, b ). From the given table of values, the y-intercept is (0, 1), for which its y-coordinate is the value of b = 1.

Therefore, the function rule that represents the given table of values is: