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natulia [17]
3 years ago
14

(1.)Find the slope of the line that passes through the given pair of points. (If an answer is undefined, enter UNDEFINED.) (?a +

3, b ? 3) and (a + 3, ?b) *******(2.)If the line passing through the points (a, 1) and (6, 5) is parallel to the line passing through the points (2, 7) and (a + 2, 1), what is the value of a?
Mathematics
1 answer:
jekas [21]3 years ago
8 0

Answer:

1. The slope of the line is m=\frac{-2b+3}{2a}.

2. The value of a is 18.

Step-by-step explanation:

If a line passes through two points, then the slope of the line is

m=\frac{y_2-y_1}{x_2-x_1}

(1)

It is given that the line passes through the points (-a + 3, b - 3) and (a + 3, -b). So, the slope of the line is

m=\frac{-b-(b-3)}{a+3-(-a+3)}

m=\frac{-b-b+3}{a+3+a-3)}

m=\frac{-2b+3}{2a}

The slope of the line is m=\frac{-2b+3}{2a}.

(2)

If the line passing through the points (a, 1) and (6, 5), then the slope of the line is

m_1=\frac{5-1}{6-a}=\frac{4}{6-a}

If the line passing through the points (2, 7) and (a + 2, 1), then the slope of the line is

m_2=\frac{1-7}{a+2-2}=\frac{-6}{a}

The slopes of two parallel lines are same.

m_1=m_2

\frac{4}{6-a}=\frac{-6}{a}

On cross multiplication we get

4a=-6(6-a)

4a=-36+6a

4a-6a=-36

-2a=-36

Divide both sides by -2.

a=18

Therefore the value of a is 18.

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2=x(7)-3 step by step
lubasha [3.4K]

Regroup terms

2 = 7x - 3

Add 3 to both sides

2 + 3 = 7x

Simplify 2 + 3 to 5

5 = 7x

Divide both sides by 7

5/7 = x

Switch sides

<u>x = 5/7</u>

8 0
3 years ago
Evaluate if x =3 and y = -2<br><br> x2+2xy−4y
Marysya12 [62]

Answer:

5

Step-by-step explanation:

With the equation x^2 + 2xy - 4y, we can substitute the values of x = 3 and y = -2 into the equation to find its result.

(3^2) + (2\cdot3\cdot-2) - (4\cdot-2)\\\\9 + (6\cdot-2) - (-8)\\9 - 12 + 8\\5

Hope this helped!

8 0
3 years ago
What is the value of the power a if 5 to the power of a is equal to 1/125
padilas [110]

First of all, you should know/notice that

125=5^3

You should also know how negative exponents work:

a^{-m}=\dfrac{1}{a^m}

So, if you wanted

5^x=125

the answer would be x=3, but since you want 125 to be at the denominator, the answer is x=-3:

5^{-3}=\dfrac{1}{5^3}=\dfrac{1}{125}

7 0
3 years ago
Find an equation of a sphere if one of its diameters has endpoints (3, 2, 5) and (5, 6, 7). Incorrect: your answer is incorrect.
prohojiy [21]

use midpoint equation

radius = distance between midpoint and one of the endpoints.

midpoint: (3+5)/2, (2+6)/2, (5+7)/2 = (4,4,6)

equation of sphere: (x-4)^2 + (y-4)^2 + (z-6)^2 = r^2

square distance between midpoint and one of the endpoints.

r^2 = 6

Equation: (x-4)^2 + (y-4)^2 + (z-6)^2 = 6

3 0
3 years ago
A new bank account is opened on week 1 with a $200 deposit. After that first week, weekly deposits of $55 are made in the accoun
inysia [295]
Y=55x+200, you multiply the number of weeks by the amount of money, and add 200 because they started with that.   
7 0
3 years ago
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