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GuDViN [60]
2 years ago
10

Lilly and Rosie are sisters. The sum of their ages is 19 and the positive difference of their ages is 9. Set up a system of equa

tions involving Lilly’s age, L, and Rosie’s age, R, assuming that Lilly is the older child. Solve the system to find their ages.
Mathematics
1 answer:
likoan [24]2 years ago
7 0

Answer:

14

Step-by-step explanation:

The sum of their age is 19.

This means that when you add their ages together, it will be 19.

L+R=19

The positive difference of their age is 9.

It tells you that Lily is the older child.

Since the difference is a positive number, that means it would be Lily's age minus Rosie's age since Lily is older.

L-R=9

Now you have 2 equations that can be used to find their ages.

Start with the first equation.

L+R=19.

Solve for L.

Subtract R on both sides.

L=19-R

Now use the substitution method (replacing or "substituting" L with 19-R) for the next equation.

L-R=9

(19-R)-R=9

19-2R=9

-2R=-10

R=5

Rosie's age is 5.

Rosie's age is 5. Now use the first equation to find Lily's age.

L+5=19

L=14.

Lily's age is 14.

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Step-by-step explanation:

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6 0
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Step-by-step explanation:

3 0
2 years ago
The graph of the quadratic function y=-x^2-2x+3 is shown below
Karolina [17]

Answer:

The axis of symmetry is at x=-1

The graph has an x-intercept at (1,0)

The graph has a vertex at (-1,4)

Step-by-step explanation:

we have

y=-x^{2}-2x+3

Statements

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The statement is False

Because, the roots of the quadratic equation are the values of x when the value of y is equal to zero (x-intercepts)

Observing the graph, the roots are at -3 and 1

case 2) The axis of symmetry is at x=-1

The statement is True

Observing the graph, the vertex is the point (-1,4)

The axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

so

the equation of the axis of symmetry is x=-1

case 3) The graph has an x-intercept at (1,0)

The statement is True

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case 4)  The graph has an y-intercept at (-3,0)

The statement is False

Because, the y-intercept is the value of y when the value of x is equal to zero

Observing the graph, the y-intercept is the point (0,3)

case 5) The graph has a relative minimum at (-1,4)

The statement is False

Because, is a vertical parabola open downward, therefore the vertex is a maximum

The point (-1,4) represent the vertex of the parabola, so is a maximum

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see the attached figure to better understand the problem

6 0
3 years ago
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NEED HELP ASAP PLEASE
olga nikolaevna [1]

Answers:

  • interest = $75
  • balance at maturity = $3075

=============================================================

Explanation:

The simple interest formula is

i = p*r*t

where in this case,

  • p = 3000 = principal (amount deposited)
  • r = 0.10 = annual interest rate in decimal form
  • t = 3/12 = 0.25 = number of years

So,

i = p*r*t

i = 3000*0.10*0.25

i = 75 is the amount of interest earned

This adds onto the initial deposit to get the final balance when the CD matures (ie when you're able to withdraw the money without penalties)

The balance at maturity is p+i = 3000+75 = 3075 dollars

---------------

In short, you deposit $3000 into the CD and have to wait 3 months for the amount to update to $3075.

7 0
3 years ago
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