1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bumek [7]
3 years ago
13

The function f(x) = 2x2 + 3x + 5, when evaluated, gives a value of 19. What is the function’s input value?

Mathematics
1 answer:
goldenfox [79]3 years ago
8 0
f(x)=\quad 2{ x }^{ 2 }+3x+5

Let's called the input 'z'

When we plug 'z' in the function we get ;

f(z)=\quad 2{ z }^{ 2 }+3z+5

And we know that, this is equal to 19, so ;

2{ z }^{ 2 }+3z+5=\quad 19

Let's rearrange the equation.

2{ z }^{ 2 }+3z+5=\quad 19\\ \\ 2{ z }^{ 2 }+3z=\quad 19-5\\ \\ 2{ z }^{ 2 }+3z=\quad 14\\ \\ 2{ z }^{ 2 }+3z-14=\quad 0

So we have a quadratic equation here.

We'll use this formula to solve it :

\frac { -b\pm \sqrt { { b }^{ 2 }-4ac }  }{ 2a }

The formula is used in equation formed like this :

a{ x }^{ 2 }+bx+c=0

In our equation,

a=2 , b=3 and c=-14

Let's plug in the values in the formula to solve,

a=2\quad b=3\quad c=-14\\ \\ \frac { -3\pm \sqrt { 9-(4\cdot 2\cdot -14) }  }{ 4 } \\ \\ \frac { -3\pm \sqrt { 9-(-112) }  }{ 4 } \\ \\ \frac { -3\pm \sqrt { 9+112 }  }{ 4 } \\ \\ \frac { -3\pm \sqrt { 121 }  }{ 4 } \\ \\ \frac { -3\pm 11 }{ 4 }

So,

z=\quad \frac { -3+11 }{ 4 } \quad ,\quad \frac { -3-11 }{ 4 } \\ \\ z=\quad \frac { 8 }{ 4 } \quad ,\quad \frac { -14 }{ 4 } \\ \\ z=\quad 2,\quad -\frac { 7 }{ 2 }

So the input can be both, 2 and -\frac{7}{2}

You might be interested in
Find the midpoint of segment JP, given J(-4,6) and P(-12,-2).
grin007 [14]

Answer:

The answer is

<h2>( - 8 , 2)</h2>

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

<h3>M = ( \frac{x1 + x2}{2}  ,  \:  \frac{y1 + y2}{2} )</h3>

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

J(-4,6) and P(-12,-2)

The midpoint is

<h3>M = ( \frac{ - 4 - 12}{2}  ,  \:  \frac{6 - 2}{2} ) \\  = ( -  \frac{16}{2} ,  \:  \frac{4}{2} )</h3>

We have the final answer as

<h3>( - 8 , 2)</h3>

Hope this helps you

6 0
3 years ago
Please help<br> Is that right?
Cloud [144]

Answer:

Yep your very smart

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A Write an equivalent equation that does NOT contain decimals.
vampirchik [111]

                                                     <span>0.5x - 0.1 = -2.9

When you multiply each side of an equation by the same number,
you don't change the equation or its solution.  If you want to get rid
of the decimals, you could  multiply each side by  10.  Then the
equation is

                                                     5x - 1  =  -29

You should be able to solve that without help.
But I'm about to take your points, so here's
how to solve that equation:

                                            </span><span><span>5x - 1  =  -29

Add  1  to each side:        5x        =  -28

Divide each side by  5 :     x         =  -28 / 5

Simplify the solution:          x         =  -5 and 4/5 .

Again ... this is the same solution as the original equation
if we hadn't gotten rid of the decimals.

</span></span>
5 0
3 years ago
Use the data from problem 1 to complete this problem. Compare the range of the prices of Felix's books and of Tyler's books. Wha
Alborosie

Hello, I am The HumanSpider your answer is ready.

Answer:

Felix books are less expensive.

Tyler's books vary in price more.

Step-by-step explanation:

Screw that!

Note: My answer came from Yahoo answer also there are some good reviews from that answer.

~

Don't be a fool stay cool

Your Pal

The HumanSpider

3 0
3 years ago
What is the slope and y-intercept of y = 4x
Sphinxa [80]

Answer: Slope: 4 Y-intercept: 0

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • The model at the right represents a garden. The total area of the garden shown can be represented by the expression 8x2+12x. If
    10·1 answer
  • Solve the answer y=6x−8<br> Thanks for helping
    6·1 answer
  • Can anyone help me with my algebra homework please ?
    8·1 answer
  • Do you have to regroup to find 523 - 141?
    14·2 answers
  • Airplanes are sometimes used to fight fires . A certain airplane can deliver 3.9 * 10^4 liters of water in one trip . How much w
    12·1 answer
  • Which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f? m∠4 = 110° and
    7·1 answer
  • Six possibilities are equally likely and have payoffs of $2, $4, $6, $8, $10, and $12. the expected value is:
    5·1 answer
  • Dylan is working on a magic trick with a deck of cards. He pulled out and replaced one card 80 times
    8·1 answer
  • QUICK HURRY!!!!!!!!!!!!!!!!!!!<br><br> 20 1/7 SIMPLIFIED IS:
    7·1 answer
  • Point F lies between points G and M. GF What is the value of x? 10x +4, FM = 20, and GM = 13x​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!