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3 years ago

Find the equation of the line passing through the points A(3,2) and B(6,3)

Mathematics

1 answer:

icang [17]3 years ago

5 0

Answer:

y = $\frac{1}{3} x+1$

Step-by-step explanation:

m = $m = \frac{change in y}{change in x} \\m = \frac{3 - (2)}{6 - (3)}\\m = \frac{1}{3} \\Find the value of b using the equation of a line \\y = mx+b\\y =( \frac{1}{3} )x + b\\2 =( \frac{1}{3} ) * (3) + b\\cancel common factor\\1 + b = 2\\b = 1\\y = \frac{1}{3} x + 1$

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What are the x-intercepts of the graphed function?

baherus [9]

The x-intercept of the graph is the x-point where graph touches the x-axis. ... Here graph touches the x-axis two times. (c) (–1, 2) and (1, 0): x-intercept are -1 and -1.

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3 years ago

Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. Which expression represents the pro

Elanso [62]

Answer:

<em>Choose the first alternative</em>

$\displaystyle P=\frac{_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C}}{_{2}^{20}\textrm{C}}$

Step-by-step explanation:

<u>Probabilities</u>

The requested probability can be computed as the ratio between the number of ways to choose two sophomores in alternate positions $(N_s)$ and the total number of possible choices $(N_t)$ , i.e.

$\displaystyle P=\frac{N_s}{N_t}$

There are 6 sophomores and 14 freshmen to choose from each separate set. There are 20 students in total

We'll assume the positions of the selections are NOT significative, i.e. student A/student B is the same as student B/student A.

To choose 2 sophomores out of the 6 available, the first position has 6 elements to choose from, the second has now only 5

$_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C} \text{ ways to do it}$

The total number of possible choices is

$_{2}^{20}\textrm{C} \text{ ways to do it}$

The probability is then

$\boxed{\displaystyle P=\frac{_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C}}{_{2}^{20}\textrm{C}}}$

Choose the first alternative

7 0

3 years ago

Read 2 more answers

Please help and show working (please)

Alexxandr [17]

In mathematical notation, ∑ means summation. So wherever you see the symbol, you have to sum over all elements in the set. Let's solve the question.

a. ∑m means, to sum all elements in the set m: ∑m = 12 + 15 + 20 + 30 = 77

b. ∑ $f^{2}$ means to sum all elements in the set f as the square of the elements f = $5^{2} + 9^{2} + 10^{2} + 16^{2} = 25 + 81 + 100 + 256 = 462$

c. ∑mf means to sum all elements as the product of the elements of m and f = (12×5) + (15×9) + (20 $(12^{2}(5)) + (15^{2}(9)) + (20^{2}(10)) + (30^{2}(16)) = 21145$ 10) + (30×16) = 875

d. ∑ $m^{2}f$ means to sum all elements as the product of the square of m and f = $((12*12)(5)) + ((15*15)(9)) + ((20*20)(10)) + ((30*30)(16)) = 21145$

4 0

3 years ago

Find the equation for the plane through the points Upper P 0 (4 comma 5 comma negative 3 )P0(4,5,−3), Upper Q 0 (1 comma 4 comm

alexira [117]

Answer:

4x -4y +z = -7

Step-by-step explanation:

The direction vector will be perpendicular to any/all vectors between the given points. It can be found, for example, using the cross product:

d = (P0Q0) × (P0R0) = (-3, -1, 8) × (-4, -3, 4)

The cross product can be computed by hand or by any of a number of calculators or web tools. Here it will be ...

d = (20, -20, 5)

These can be the coefficients of x, y, and z in the plane equation. However, the equation is better written using coefficients that are mutually prime, so we choose the direction vector to be ...

d = (4, -4, 1)

The constant C in the plane equation

d·(x, y, z) = C

will be the dot product of this direction vector (d) any any of the given points. Using R0, we find the constant to be ...

C = (4, -4, 1)·(0, 2, 1) = 4·0 +(-4)·2 +1·1 = -8+1 = -7

so, the plane equation is ...

4x -4y +z = -7

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3 years ago

What is the equation of the line in slope intercept form? I WILL GIVE BRAINLY

irina [24]

Answer:

y=x+20

Step-by-step explanation:

The y-intercept is 20, as the line is on the y-axis while x is 0. The slope would be 0, because the y and x values both increase by 10, so 10/10 which simplifies to 1. The result would be y=10/10x + 20 simplifying to y=1x+20, which is y=x+20.

Hope this helps!

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4 years ago

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