What is the midpoint of the line segment with endpoints (-5.5, -6.1) and (-0.5, 9.1)?

60 dollars for 12 hamburgers how much dollars per hamburger

natali 33 [55]

5. 60/12 is 5 :) hope this helps

6 0

2 years ago

Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2

tekilochka [14]

Answer:

1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

1. 2x^2 - 7x + 3

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

a = 2
b = -7
c = 3

we can use the quadratic formula: $x = \frac{-b~\pm~\sqrt{b^2~-~4ac} }{2a}$

Substitute the a, b, and c values into the quadratic formula: $x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)} }{2(2)}$

Now simplify using the laws of pemdas: $x=\frac{7\pm\sqrt{(49)-(24)} }{4}$

Simplify even further: $x=\frac{7\pm\sqrt{(25)} }{4} \rightarrow x=\frac{7\pm (5) }{4}$

Now split this equation into two equations to solve for x: $x=\frac{12 }{4} ~~and~~ x=\frac{2 }{4}$

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

$\boxed {x=3,\frac{1}{2} }$

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

x - 3 = 0
2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

2. 3x^2 + 7x + 2

To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.

Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

3x + 1 = 0
x + 2 = 0

Solve.

First factor: 3x + 1 = 0

Subtract 1 from both sides.

3x = -1

Divide both sides by 3.

x = -1/3

Second factor: x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

$\boxed {x = -\frac{1}{3} , -2}$

7 0

2 years ago

9. A contestant on a game show must guess the price of a new car. The contestant will

iren [92.7K]

Given :

A contestant on a game show must guess the price of a new car. The contestant will win if his guess is within $1000 of the price of the car.

To Find :

If the price of the car is $24,995 and the contestant's guess is represented by g, what absolute value inequality represents this situation.

Solution :

Let, range in which participant guess would be considered correct is r.

So, r should be in range $( 24,995 ± 1000 ).

( 24,995 - 1000 ) ≤ r ≤ ( 24,995 + 1000 )

23,995 ≤ r ≤ 25,995

Therefore, the correct inequality is 23,995 ≤ r ≤ 25,995 .

Hence, this is the required solution.

4 0

2 years ago

Translate each phrase into an algebraic inequality:

Nonamiya [84]

Let hours = x

She can work a maximum of 30 hours so x can be any number from 30 or below.

The inequality would be: X <= 30

5 0

2 years ago

Read 2 more answers

28)A regression equation is obtained for a collection of paired data. It is found that the total variation is 24.488, the explai

Doss [256]

Answer: The coefficient of determination = 0.6291

Step-by-step explanation:

Given: Total variation is 24.488, the explained variation is 15.405, and the unexplained variation is 9.083.

The coefficient of determination is computed as:

$\text{ coefficient of determination} =\frac{\text{explained variation }}{\text{total variation}}$

Substituting given values, we get

$\text{coefficient of determination} =\frac{15.405}{24.488}$

$=0.6291$

Therefore, the coefficient of determination = 0.6291

7 0

1 year ago