Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16). Wha

I will designate the hourly rate for weekdays as x and for weekends as y. The equations are arranged as follows:

13x + 14y = $250.90
15x + 8y = $204.70

This gives us a system of equations which can be solved by multiplying the first equation by 4 and the second by -7. This leads to:

52x + 56y = $1003.60
-105x - 56y = -$1432.90

By summing these two equations, we arrive at:

-53x = -$429.30 --> 53x = $429.30 --> (dividing both sides by 53) x = 8.10. This represents her hourly wage on weekdays.

Substituting our value for x allows us to determine y. I will utilize the first equation, but either could work.

$105.30 + 14y = $250.90. To isolate y, subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40

Thus, we find that her earnings are $8.10 per hour on weekdays and $10.40 per hour on weekends. The difference shows she earns $2.30 more on weekends than on weekdays.

The response is B: 5 and 5 square root 3.

Respuesta:

126 pies

Explicación paso a paso:

Dado que:

Ecuación de la línea que representa el sendero de naturaleza:

y = 13x - 4

Distancia del gazebo respecto al sendero de naturaleza:

Cada unidad en el plano de coordenadas = 10 pies

Por lo tanto,

y = 13(10) - 4

y = 130 - 4

y = 126 pies

Answer: To eliminate the y terms and solve for x with minimum steps, we should multiply the first equation by 9 and the second equation by -4.

Step-by-step explanation:

Given: Equation (1) 5x − 4y = 28

Equation (2) 3x - 9y = 30

To eliminate the y-terms and determine x in the fewest operations, it requires us to multiply equation (1) by 9 and equation (2) by -4 to have

9(5x − 4y) =9 (28) ⇒ 45x - 36y = 252

-4(3x - 9y) = -4(30) ⇒ -12x + 36y = -120

By adding both equations together, the y-term is eliminated, leading to 45x - 12x = 132

⇒ 33x = 132 ⇒ x = 4.

Answer:

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)

Step-by-step explanation:

Given the inequality is -3(2x - 5) < 5(2 - x)

First, simplify both sides:

∵ -3(2x - 5) = -3(2x) + -3(-5)

Remember that (-)(-) results in (+)

Thus, -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x)

Remember that (+)(-) results in (-)

Then, 5(2 - x) = 10 - 5x

Now we have: - 6x + 15 < 10 - 5x

Subtract 15 from both sides

So: - 6x < -5 - 5x

Add 5x to both sides

Thus, - x < - 5

Note that since the coefficient of x is negative, we reverse the inequality sign when dividing both sides by it

∵ The coefficient of x is -1

Therefore, dividing both sides by -1 gives us x > 5

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)