Determine the equation in the form y=mx+b for passing through each pair of points (0,8) and (4,3)

Answers

Answer 1

Answer: $y=mx+b\n\nA(0;\ 8);\ B(4;\ 3)\n\nsubstitution\n\n \left\{\begin{array}{ccc}0m+b=8\n4m+b=3\end{array}\right\n\n\left\{\begin{array}{ccc}b=8\n4m+b=3\end{array}\right\n\left\{\begin{array}{ccc}b=8\n4m+8=3\end{array}\right\n\left\{\begin{array}{ccc}b=8\n4m=3-8\end{array}\right\n\left\{\begin{array}{ccc}b=8\n4m=-5&/:4\end{array}\right\left\{\begin{array}{ccc}b=8\nm=-(5)/(4)\end{array}\right$

$Answer:y=-(5)/(4)x+8$

Answer 2

Answer: This requires y2 - y1/ x2 - x1 as the slope. I got y=-5/4x+8 as my answer

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What is the greatest common factor of 42a^5b^3, and 42ab^4

Answers

the greatest common factor of 36x3 and 8x is simply 4X

given the following system of equations, identify the type of system.x y = 6y = 3 - xconsistentinconsistentequivalent

Answers

Inconstant as there is no solution

What two numbers multiply to 44 and add up to 12?

Answers

This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.

let the two numbers be x and y.

Multiply to 44.    x*y = 44 ..........(a)

Add up to 12. x + y = 12 .........(b)

From (b)

y = 12 - x .......(c)

Substitute (c) into (a)

x*y = 44

x*(12 - x) = 44

12x - x² = 44

-x² + 12x = 44

-x² + 12x - 44 = 0.

Multiply both sides by -1

-1(-x² + 12x - 44) = -1*0

x² - 12x + 44 = 0.

This does not look factorizable, so let us just use quadratic formula

comparing to ax² + bx + c = 0, x² - 12x + 44 = 0, a = 1, b = -12, c = 44

x = (-b + √(b² - 4ac)) /2a   or (-b - √(b² - 4ac)) /2a

x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)

x = (12 + √(144 - 176) )/ 2

x = (12 + √-32 )/ 2

√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2

Where i is a complex number. Note the equation has two values. We shall include the second, that has negative sign before the square root.

x = (12 + √-32 )/ 2 or (12 - √-32 )/ 2

x = (12 + 4i√2 )/ 2 (12 - 4i√2 )/ 2

x = 12/2 + (4i√2)/2 12/2 - (4i√2)/2

x = 6 + 2i√2 or    6 - 2i√2

Recall equation (c):

y = 12 - x, When x = 6 + 2i√2, y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2

When x = 6 - 2i√2, y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2

x = 6 + 2i√2, y = 6 - 2i√2

x = 6 - 2i√2, y = 6 + 2i√2

Therefore the two numbers that multiply to 44 and add up to 12 are:

6 + 2i√2 and 6 - 2i√2

$xy=44\n x+y=12\n\n xy=44\n x=12-y\n\n (12-y)y=44\n 12y-y^2=44\n y^2-12y+44=0\n y^2-12y+36+8=0\n (y-6)^2=-8$

No solutions in real numbers.

In complex numbers:
$(y-6)^2=-8\n y-6=-√(-8) \vee y-6=√(-8)\n y=6-2\sqrt2 i \vee y=6+2\sqrt2 i\n\n x=12-(6-2\sqrt2i) \vee x=12-(6+2\sqrt2i)\n x=12-6+2\sqrt2i \vee x=12-6-2\sqrt2i\n x=6+2\sqrt2i \vee x=6-2\sqrt2i$

These numbers are $6-2\sqrt2i$ and $6+2\sqrt2i$ .

Please answer this question

Answers

Answer:

she is running at a constant speed

Step-by-step explanation:

the bar is still because she isnt going faster or slowing down she is constant

Answer:

D: She is at a constant speed.

Step-by-step explanation:

she is not acceleraring or decelerating, so her speed is constant

Israel planted 4 tomato seeds in his garden. Then he planted flower seeds in each of his three neighbor's gardens. Which expression represents the number of seeds Israel planted?A. 4s + 3
B. 4 + 3s
C. 4 – 3s
D. 3s – 4

Answers

The expression that represents the number of seeds that has been planted by Israel is 4 + 3s. Hence, Option B is correct.

What is an expression?

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.

Mathematical symbols can represent variables, operations, functions, brackets, punctuation, and grouping to help specify the logical syntax and order of operations.

But in contemporary mathematics, and particularly in computer algebra, formulae are seen as expressions that can be evaluated as true or false, depending on the values given to the variables present in the expressions.

In the garden, Israel sowed 4 tomato seeds. Then Israel scattered flower seeds throughout the gardens of the three neighbors. Here neighbors will be denoted as x. For this the most suitable expression will be 4 + 3s.

Therefore, Option B is correct.

Learn more about expression from here:

brainly.com/question/14083225

#SPJ2

Answer:

B. 4+3s

Step-by-step explanation:

What is the point of origin on a number line

Answers

0 is the point of origin because it's not really a number, it's more of a starting point for positive and negative numbers.

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