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raketka [301]
3 years ago
10

5-4. Solve each of the following equations for the indicated variable. Use your Equation Mat if it is helpful. Write down each o

f your steps algebraically. Solve for y: 2(y − 3) = 4 Solve for x: 2x + 5y = 10 Solve for y: 6x + 3y = 4y + 11 Solve for x: 3(2x + 4) = 2 + 6x + 10 Solve for x: y = −3x + 6
Mathematics
1 answer:
balu736 [363]3 years ago
5 0
QUESTION 1

The given equation is :

2(y - 3) = 4
We want to solve for y. This means we have to isolate y on one side of the equation while all other constants are also on the other side of the equation,

We first divide both sides by 2 to obtain,

\frac{2(y - 3)}{2} = \frac{4}{2}

We cancel out the common factors to get,

y - 3 = 2

We now group like terms to get,

y = 3 + 2

We simplify to obtain,

y = 5

QUESTION 2

The given equation is

2x + 5y = 10
We want to solve for x. This means that we need to isolate x on one side of the equation, while all other variables and constant are also on the other side of the equation.

This implies that,

2x= 10 - 5y

We now divide through by 2, to obtain,

\frac{2x}{2} = \frac{10}{2} - \frac{5y}{2}

This will now give us,

x = 5 - \frac{5}{2} y

QUESTION 3

The given equation is
6x + 3y = 4y + 11

We want to solve for y. This means that we need to isolate y on one side of the equation, while all other variables and constants are also on the other side of the equation.

We first of all group all the y terms on one side of the equation to obtain,

6x - 11 = 4y - 3y

We simplify to get,

6x - 11 = y

This implies that,

y = 6x - 11

QUESTION 4

The given equation is,

3(2x + 4) = 2 + 6x + 10

We want to solve for x. This means that we need to isolate x on one side of the equation, while all other variables and constant are also on the other side of the equation.

Let us first expand the brackets to get,

6x + 12 = 2 + 6x + 10
This implies that

6x + 12 = 6x + 12

We group like terms to get,

6x - 6x = 12 - 12

We now simplify both sides to get,

0x = 0

We don't want x to vanish, so let us try to divide both sides by zero to get,

x = \frac{0}{0}

This is an indeterminate form, which implies that, x has infinitely many solutions. This means that all the real numbers are solution to the equation.

\therefore \: x \in \: R

QUESTION 5

The given equation is,

y = - 3x + 6

We want to solve for x, so we add the additive inverse of 6, which is -6 to both sides of the equation to get,

y - 6 = - 3x

We rewrite this to obtain,

- 3x = y - 6

We divide through by -3 to get,

\frac{ - 3x}{ - 3} = \frac{y}{ - 3} - \frac{6}{ - 3}

This will give us,

x = - \frac{y}{3} + 2

or

x= 2 - \frac{1}{3} y
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The city of Orlando’s building a dog park in downtown Orlando dog park will be triangular shaped as shown on the coordinate plan
kiruha [24]

Answer:

Perimeter of the dog park = 15.4 yards

Step-by-step explanation:

Coordinates of the vertices of the given triangle are,

P(1, 2), Q(1, 6), R(-4, 2)

Since distance between the two points (x_1, y_1) and (x_2,y_2) is,

d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

Length of PQ = \sqrt{(1-1)^2+(2-6)^2}

PQ = 4

Length of PR = \sqrt{(1+4)^2+(2-2)^2}

PR = 5

Length of QR = \sqrt{(1+4)^2+(6-2)^2}

QR = \sqrt{25+16}

     = \sqrt{41}

     = 6.4 yards

Therefore, perimeter of the given triangle = PQ + QR + PR

                                                                       = 4 + 6.4 + 5

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3 years ago
Two buses leave a station at the same time and travel in opposite directions. One bus travels 15 /kmh faster than the other. If
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Since the buses travel in opposite directions, the speed at which they distance themselves is the sum of their speeds.
One bus travels at speed s.
The other bus travels at speed s + 15.
The sum of the speeds is s + s + 15 = 2s + 15

speed = distance/time

distance = speed * time

366 = (2s + 15) * 2

183 = 2s + 15

168 = 2s

s = 84

The slower bus travels at 84 km/h.

s + 15 = 84 + 15 = 99

The faster bus travels at 99 km/h.

Check:
In 2 hours, the slower bus travels 2 * 84 km = 168 km
In 2 hours, the faster bus travels 2 * 99 km = 198 km
In 2 hours, the buses are 198 km + 168 km = 366 km apart.
Our answer is correct.
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3 years ago
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