Dad is 4 times as old as his son Jim. In 10 years, Dad's age will be 20 years more than twice Jim's age. How old is Jim?If D = dad's age now and J = Jim's age now, which of the following systems could be used to solve the problem?

a. D = 4J and D + 10 = 2J + 20
b. D = 4J and D + 10 = 2(4J + 10) + 20
c. D = 4J and D + 10 = 2(J + 10) + 20

Answers

Answer 1

Answer: Let's focus on the "In 10 years" part

in 10 years
D will be (D + 10)
and J will be (J + 10)

"twice Jim's age" would then be 2(J + 10)
and
"20 years more than" that would be 2(J + 10) + 20

so
the answer with
D + 10 = 2(J + 10) + 20
would be your answer
that is, C.

Answer 2

Answer:

Answer: The correct answer would be C:

Step-by-step explanation:

D=4J and D+10=2(J+10)+20

f(x) = 2x² + x – 1

Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

Let us now tackle the problem!

An axis of symmetry of quadratic equation y = ax² + bx + c is :

$\large {\boxed {x = (-b)/(2a) } }$

Option 1 :

f(x) = 2x² + x – 1 → a = 2 , b = 1 , c = -1

Axis of symmetry → $x = (-b)/(2a) = (-1)/(2(2)) = -(1)/(4)$

Option 2 :

f(x) = 2x² – x + 1 → a = 2 , b = -1 , c = 1

Axis of symmetry → $x = (-b)/(2a) = (-(-1))/(2(2)) = (1)/(4)$

Option 3 :

f(x) = x² + 2x – 1 → a = 1 , b = 2 , c = -1

Axis of symmetry → $x = (-b)/(2a) = (-2)/(2(1)) = -1$

Option 4 :

f(x) = x² – 2x + 1 → a = 1 , b = -2 , c = 1

Axis of symmetry → $x = (-b)/(2a) = (-(-2))/(2(1)) = 1$

Learn more

Solving Quadratic Equations by Factoring : brainly.com/question/12182022
Determine the Discriminant : brainly.com/question/4600943
Formula of Quadratic Equations : brainly.com/question/3776858

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number

The graph of function $\boxed{f(x)=2x^(2)+x-1}$ has an axis of symmetry as $\boxed{x=-(1)/(4)}$ .

Further explanation:

The standard form of a quadratic equation is as follows:

$\boxed{f(x)=ax^(2)+bx+c}$

The vertex form of a quadratic equation is as follows:

$\boxed{g(x)=a(x-h)^(2)+k}$

Axis of symmetry is the line which divides the graph of the parabola in two perfect halves.

The formula for axis of symmetry of a quadratic function is given as follows:

$\boxed{x=-(b)/(2a)}$

The first function is given as follows:

$f(x)=2x^(2)+x-1$

The above function is in standard form with $a=2$ , $b=1$ and $c=-1$ .

Then its axis of symmetry is calculated as,

$\begin{aligned}x&=-(b)/(2a)\n&=-(1)/(2*2)\n&=-(1)/(4)\end{aligned}$

The axis of symmetry of first function is $x=-(1)/(4)$ .

Express the function $f(x)=2x^(2)+x-1$ in its vertex form,

$\begin{aligned}f(x)&=2x^(2)+x-1\n&=(√(2)x)^(2)+\left(2* √(2)x* (1)/(2√(2))\right)-1+\left((1)/(2√(2))\right)^(2)-\left((1)/(√(2))\right)^(2)\n&=\left(√(2)x+(1)/(2√(2))\right)^(2)-1-(1)/(8)\n&=\left[√(2)\left(x+(1)/(4)\right)\right]^(2)-(9)/(8)\n&=2\left(x-\left(-(1)/(4)\right)\right)^(2)-(9)/(8)\end{aligned}$