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Zarrin [17]
2 years ago
10

Which function in vertex form is equivalent to f(x) = x² + x +1?

Mathematics
1 answer:
mylen [45]2 years ago
4 0

Answer:

\left( x+\frac{1}{2} \right)^{2}  + \frac{3}{4}

Step-by-step explanation:

NOTE :

x^2+ax=\left( x+\frac{a}{2} \right)^{2}  -\left( \frac{a}{2} \right)^{2}

………………………………………

f(x) = x² + x +1

     =x^{2}+2\times \frac{x}{2} +1

     =\left( x+\frac{1}{2} \right)^{2}  -\left( \frac{1}{2} \right)^{2}  +1

     =\left( x+\frac{1}{2} \right)^{2}  - \frac{1}{4}+1

     =\left( x+\frac{1}{2} \right)^{2}  + \frac{3}{4}

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On a certain hot​ summer's day, 477 people used the public swimming pool. The daily prices are 1.50 for children and 2.25 for ad
Akimi4 [234]

Answer:

212 children, and 265 adults

Step-by-step explanation:

To find the number of children and adults, we can set up a systems of equations.

x= number of children

y= number of adults

Equation 1: Price

1.50x+2.25y=914.25

Equation 2: Total number of people

x+y=477

Now, let's solve the equation using substitution.

Rearrange the second equation to solve for one variable.

x+y=477

x=477-y

Now plug x equals into the first equation, and solve for y.

1.50x+2.25y=914.25

1.50(477-y)+2.25y=914.25

715.5-1.50y+2.25y=914.25

715.5+0.75y=914.25

0.75y=198.75

y=265

We just solved for the number of adults. Now let's plug y equals into the second equation to find the number of children.

x+y=477

x+265=477

x=212

7 0
2 years ago
In Ethiopia there are 20 premier league soccer teams. in one round how many games are there?​
frosja888 [35]

Answer:

190 games

Step-by-step explanation:

²⁰C₂ = 20!/[(20 - 2)! * 2!] = 190

4 0
2 years ago
line p contains points A(-7,-9) and B(4,0) line q is parallel to line p line r is perpendicular to line q what is the slope of l
igomit [66]
Use the slope formula (y2-y1)/(x2-x1)
(0+9)/(4+7)=9/11
Since q is parallel to r the slope will be the same. 9/11 is the slope of line r
4 0
3 years ago
What is the slope of the line that contains the points (-4;2) and (6;-3) ?
tester [92]

Answer:

-1/2

Step-by-step explanation:

First you use to the formula m=y2-y1/x2-x1 and then you get -5/10 or -1/2. (m= slope)

4 0
3 years ago
Whats going on in this attachment help thanks xD
rodikova [14]

Ratio remains same

\\ \rm\Rrightarrow \dfrac{4}{6x-3}=\dfrac{3}{2}

\\ \rm\Rrightarrow 8=3(6x-3)

\\ \rm\Rrightarrow 8=18x-9

\\ \rm\Rrightarrow 18x=17

\\ \rm\Rrightarrow x=17/18

7 0
2 years ago
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