Explain step by step.

Find the equation of the line that cuts through (0,5) and (1, 2)? a. y=-3x + 5 b. y = 3x + 5 c. y = -5x + 3 d. Y = -1/3x + 5. Pl

Dafna11 [192]

Answer:

a. y = -3x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Slope-Intercept Form: y = mx + b

m - slope
b - y-intercept

Step-by-step explanation:

Step 1: Define

y-intercept (0, 5)

Point (1, 2)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute [SF]: $m=\frac{2-5}{1-0}$
Subtract: $m=\frac{-3}{1}$
Divide: $m=-3$

Step 3: Write Equation

Plug in variables into the general form.

y = -3x + 5

8 0

3 years ago

6 points are place on the line a, 4 points are placed on the line b. How many triangles is it possible to form such that their v

yawa3891 [41]

Answer: 96

Step-by-step explanation:

Ok, lines a and b are parallel.

We can separate this problem in two cases:

Case 1: 2 vertex in line a, and one vertex in line b.

Here we use the relation:

"In a group of N elements, the total combinations of sets of K elements is given by"

$C = \frac{N!}{(N - K)!*K!}$

Here, the total number of points in the line is N, and K is the ones that we select to make the vertices of the triangle.

Then if we have two vertices in line a, we have:

N = 6, K = 2

$C = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15$

And the other vertex can be on any of the four points on the line b, so the total number of triangles is:

C = 15*4 = 60.

But we still have the case 2, where we have 2 vertices on line b, and one on line a.

First, the combination for the two vertices in line b is:

We use N = 4 and K = 2.

$C = \frac{4!}{2!*2!} = \frac{4*3}{2} = 6$

And the other vertice of the triangle can be on any of the 6 points in line a, so the total number of triangles that we can make in this case is:

C = 6*6 = 36

Then, putting together the two cases, we have a total of:

60 + 36 = 96 different triangles

3 0

3 years ago

What is length of the altitude of the equilateral triangle below?

Lina20 [59]

Answer: OPTION D.

Step-by-step explanation:

Given the equilateral triangle shown in the figure, you need to find the value of the altitude "a".

In order to find the altitude, you can use the following Trigonometric Identity:

$tan\alpha =\frac{opposite}{adjacent}$

In this case you can identify that:

$\alpha=60\°\\\\opposite=a\\\\adjacent=2\sqrt{3}$

Therefore, you can substitute values into $tan\alpha =\frac{opposite}{adjacent}$ :

$tan(60\°)=\frac{a}{2\sqrt{3}}$

Finally, you must solve for the altitude "a". Then, this is:

$(tan(60\°))(2\sqrt{3})=a\\\\a=6$

Notice that this result matches with the value shown in Option D.

3 0

4 years ago

10 + (2 x 3)2 ÷ 4 × 1 over 2 to the power of 3

diamong [38]

Answer:

The admixture of words and math symbols must be rewritten to allow processing towards a correct answer.

Step-by-step explanation:

Use brackets [ ] and up carrot symbol (^, obtained by pushing the shift key at same time as 6 key) to rewrite the question. The order of operations called GEMA (Grouping, Exponents, Multiplication and Division from left to right and then Addition and Subtraction from left to right) can only be done once the symbols are placed to match the textbook question. Math is a language and its symbols must be used in place of words to assure the correct result.

7 0

4 years ago

Read 2 more answers

PLS HELP ME ASAP FOR 8. A and B (SHOW WORK!!) (for graph PLS use pic) LOTS OF POINTS!

lilavasa [31]

10 books cost $30. To figure it out, it's just 3 times the number of books. XD

3 0

3 years ago

Read 2 more answers