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Zarrin [17]
3 years ago
5

Which ordered pair in the form(x,y) is a solution of this equation?

Mathematics
1 answer:
Gnom [1K]3 years ago
8 0

The ordered pair is (-2, -3)

Step-by-step explanation:

  • Step 1: To find whether an ordered pair is a solution, substitute values of x and y and see whether it satisfies the equation.

(-3, -2) ⇒ 7 × -3 - 5 × -2 = -21 + 10 = -11 ≠ 1

(-2, -3) ⇒ 7 × -2 - 5 × -3 = -14 + 15 = 1

(0, 4) ⇒ 0 - 5 × 4 = 20 ≠ 1

(4, 0) ⇒ 7 × 4 - 0 = 28 ≠ 1

So the ordered pair is (-2, -3)

You might be interested in
17.
Marta_Voda [28]

Answer:

a) 50 meters

b) 2354 meters

c) 12 seconds

d) 24.13 seconds

Step-by-step explanation:

Hello!

<h3>a) How far is Lincoln above the ground when he shoots the gun?</h3>

We need to really understand what the variables represent in this question. Given that t is time, and h is height, the time at which he shoots the bullet will be 0, as the bullet hasn't started traveling yet. This means that we can solve for the original height of the bullet by plugging in 0 for time in the equation.

Equation: h = -16t^2 + 384t + 50

Plug in 0 for t:

  • h = -16t^2 + 384t + 50
  • h = -16(0)^2 + 384(0) + 50
  • h = 50

The height at which Lincoln shot the bullet is 50 meters.

We can also look at this graphically. The height of origin will simply be when the x-value (in this case t-value) is 0. That means it is the point at which the graph intersects the y-axis, known as the y-intercept.

Standard form of a Parabola: y = ax^2 + bx + c

The y-intercept is the "c" value.

Given our equation: h = -16t^2 + 384t + 50

The c-value is 50. This proves that the y-intercept is 50.

<h3 /><h3>b)How high does the bullet travel vertically relative to the ground?</h3>

We want to find the highest point of the graph. To do that, we can find the vertex.

We can utilize the Axis of Symmetry (AOS) to find the Vertex.

First, find the AOS using the formula: AOS = -\frac{b}{2a}

  • a = -16
  • b = 384

Plug it into the formula:

  • AOS = -\frac{b}{2a}
  • AOS = -\frac{384}{2(-16)}
  • AOS = \frac{384}{32}
  • AOS = 12

Plug in 12 for t in the equation:

  • h = -16t^2 + 384t + 50
  • h = -16(12)^2 + 384(12) + 50
  • h = -2304 + 4608 + 50
  • h = 2304+50
  • h = 2354

Therefore, the highest point of the bullet is 2354 meters.

<h3>c)How long does it take the bullet to reach its greatest height?</h3>

We answered this in the last question. The t-value when h is at its highest is 12.

<h3>d)After how many seconds (round to nearest 100th) does the bullet hit the ground?</h3>

We have to solve for the values of t when h is 0 (when it touches the ground).

Set the equation to 0, and solve using the quadratic formula.

Quadratic formula: x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}

  • x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}
  • x = \frac{-384\pm\sqrt{384^2 - 4(-16)(50)}}{2(-16)}
  • x = \frac{-384\pm\sqrt{147456 +3200}}{-32}
  • x = \frac{-384\pm\sqrt{150656}}{-32}
  • x = \frac{-384\pm388.14}{-32}
  • x = -\frac{4.14}{32}, x = \frac{772.14}{32}

We are only going to take the positive solution, as we can't have a negative time. The solution that doesn't work is called an extraneous solution.

  • x = \frac{772.14}{32}
  • x = 24.13

It takes approximately 24.13 seconds for the bullet to hit the ground.

6 0
2 years ago
Which equation represents this number sentence?
olasank [31]

Answer:

The answer to your question is: the second option

Step-by-step explanation:

a) This is not the right answer, the sentence to this option could be: fourteen more than the quotient of five and a number is 23.

b) This is the right option, the sentence is given in the description.

c)  This is not the right answer, the sentence to thi option could be: the quotient of fourteen plus a number and five is 23.

d) This is not the right answer, the sentence of this option could be: the quotient of five and the addition of a number and fourteen is 23.

4 0
3 years ago
Peter's dog eats 0.3 kilograms of dog food each day. How much dog food will Peter's dog eat
11111nata11111 [884]

All you have to do is multiply 0.3 by 8.

8×0.3=2.4

The dog will eat 2.4 kilograms of food in 8 days. Hope that helps!

8 0
3 years ago
Read 2 more answers
What is 6 1/4 - 3 1/3
Anettt [7]
Hey There!

Remember, first find the gcf of 4,3 in this problem it is 12.

Steps to solve

1.6\frac{1}{4} - 3\frac{1}{3}

2.6\frac{1}{4} - 3 \frac{1}{3} = 2\frac{11}{12}

So, The answer is <span>2\frac{11}{12}</span>

Hope This Helps :)
6 0
3 years ago
Read 2 more answers
Find the 22th term in the arithmetic sequence<br> 23,14,5,-4
Darya [45]

Answer:

-45

Step-by-step explanation: no explanation

3 0
3 years ago
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