I FORGOT HOW TO DO THIS HHHHHEEEEELP ASAP

What is the vertex of the quadratic function f(x)=(x-6)(x+2)?

Nata [24]

Answer:

(2, -16).

Step-by-step explanation:

(x - 6)(x + 2)

Convert to vertex form:

Expanding the parentheses we have:

x^2 + 2x - 6x - 12

= x^2 - 4x - 12

Completing the square:

= (x - 2)^2 - 4 - 12

= (x - 2)^2 - 16

So the vertex is (2, -16),

4 0

3 years ago

2.2.PS-141You are running a fuel economy study. One of the cars you find is blue. It can travel 39miles on21241 gallons of gasol

svetoff [14.1K]

<h2>Answer:</h2> $\begin{gathered} \text{Unit rate of blue car = 31}\frac{3}{5}mi\text{ per gallon} \\ \text{Unit rate of red car = 28 mi per gallon} \end{gathered}$

The blue car has traveled the greater distance on one gallon of gasoline

<h2>Explanation:</h2>

The formula for calculating the unit rate is expressed as shown:

$\text{Rate = }\frac{Distance}{\text{number of gallons}}$

For the blue car

Distance = 39.5miles

Gallons of gasoline = 1.25 gallons

Get the unit rate:

$\begin{gathered} \text{Unit rate = }\frac{39.5}{1.25} \\ \text{Unit rate = 3}1.6\text{ }miles\text{ per gallon} \end{gathered}$

The unit rate of the blue car as a mixed fraction is 31 3/5 miles per gallon

For the red car

Distance traveled = 22.4 miles

Gallons of gasoline = 0.8 gallons of gasoline

Get the unit rate of the red car;

$\begin{gathered} Unit\text{ rate = }\frac{22.4}{0.8} \\ \text{Unit rate = }28\text{miles per gallon} \end{gathered}$

From the unit rates, we can see that the blue car has traveled the greater distance on one gallon of gasoline since its unit rate is greater than that of the red car.

5 0

1 year ago

The system of equations

ICE Princess25 [194]

Answer:

z = -12

Step-by-step explanation:

Rewritting the equations, we have:

x + y = xy (eq1)

2x + 2z = xz (eq2)

3y + 3z = yz (eq3)

From the first equation:

x = y/(y-1) (eq4)

From the third equation:

y = 3z/(z - 3) (eq5)

Using the value of y from (eq5) in (eq4), we have:

x = [3z/(z - 3)] / [3z/(z - 3) - 1]

x = [3z/(z - 3)] / [(3z - z + 3)/(z - 3)]

x = 3z / (2z + 3) (eq6)

Using the value of x from (eq6) in (eq2), we have:

6z / (2z + 3) + 2z = (3z / (2z + 3))*z

(6z + 4z^2 + 6z) / (2z + 3) = 3z^2 / (2z + 3)

12z + 4z^2 = 3z^2

z^2 = -12z

z = -12

3 0

4 years ago

When the women's soccer team won the state championship, the parent boosters welcomed the team back to school with a balloon b

Ray Of Light [21]

Answer:

Each bouquet included 8 latex balloons and 4 foil balloons

Step-by-step explanation:

Hi there!

Let x be the number of latex balloons and y the number of foil balloons. The total cost of the balloons will be the cost of each latex balloon times the amount (x) added to the cost of each foil balloon times the amount of these balloons (y). Then:

Cost of each latex balloon = 0.14

Amount of latex balloon = x

Cost of each foil balloon = 1.96

Amount of foil balloons = y

0.14 x + 1.96 y = 161.28

We also know that each player received 12 balloons. Since there are 18 players, the number of foil and latex balloons will be 18 · 12 = 216 balloons.

Then:

x + y = 216

So we have a system of equations that we can solve because we have two equations and two unknowns. Let´s solve it!

0.14 x + 1.96 y = 161.28

x + y = 216

Let´s solve the second equation for y:

x + y = 216

y = 216 - x

Now, let´s replace y in the first equation and solve it for x:

0.14 x + 1.96 y = 161.28

0.14 x + 1.96 (216 - x) = 161.28

Apply distributive property:

0.14 x + 423.36 - 1.96 x = 161.28

-1.82 x + 423.36 = 161.28

-1.82 x = 161.28 - 423.36

-1.82 x = -262.08

x = -262.08 / -1.82

x = 144

There are 144 latex balloons

Then:

y = 216 -144 = 72

There are 72 foil balloons

If 144 latex balloons are distributed among the 18 players, each player will receive (144/18) 8 balloons.

In the same way, if the 72 foil balloons are distributed among the players, each will receive (72/ 18) 4 balloons.

Then, each bouquet included 8 latex balloons and 4 foil balloons.

7 0

3 years ago

Find the measure of the smallest angle?

weeeeeb [17]

Answer:

m ∠RMK = 51°

Step-by-step explanation:

m ∠JMK = m ∠RMK + m ∠JMR

10x + 19 = 7x - 26 + 6x + 12

10x +19 = 13x -14

19 = 3x -14

33 = 3x

11 = x

m ∠RMK = 7(11) - 26 = 51°

m ∠JMR = 6 (11) + 12 = 78

6 0

3 years ago