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galben [10]
3 years ago
12

Cary is 9 years older than Dan. In 7 years, the sum of their ages will equal 93. Find both of their

Mathematics
1 answer:
a_sh-v [17]3 years ago
3 0
Cary's age is 9 years MORE than Dan's age.
Cary's age is Dan's age, but with 9 more years added to that.
Here is how we can express that,
\rm C=D+9
In 7 years, Cary will be C+7 years old,
and Dan will be D+7 years old.
In 7 years, the sum of their ages,
(C+7) and (D+7) will equal 93.

Here is how we can express that:
\rm (C+7)+(D+7)=93

You have a system of two equations involving two unknowns. You have a couple of nice options here. You can apply substitution or elimination to complete the problem.
You might be interested in
An electric utility company determines the monthly bill for a residential customer by adding an energy charge of 7.32 cents per
Sedaia [141]

Answer:

y(x) = 0.0732x + 17.32

Step-by-step explanation:

The equation for the monthly charge has the following format

y(x) = ax + b

In which y(x) is the cost in function of the number of kilowatt-hours used(x), a is the price of each killowatt hour and b is the fixed(base) charge.

Base charge of $17.32 per month.

This means that b = 17.32

charge of 7.32 cents per kilowatt-hour

Our answer is in dollars. Each dollar is 100 cents. So 7.32 cents is a = 0.0732

Write an equation for the monthly charge y in terms of x, the number of kilowatt-hours used.

y(x) = ax + b

y(x) = 0.0732x + 17.32

6 0
3 years ago
What is the sum of the measures of the interior angles of a regular polygon if leach exterior angle measures 120°?
GREYUIT [131]

Answer:

180

Step-by-step explanation:

180-120 = 60 this is one of all the congruent angles

of the top of my head i know a regular triangle has three 60 degree angles meaning it is 60*3 = 180

5 0
3 years ago
Im to lazy please help.. ;-;
Mumz [18]

Step-by-step explanation:

18h=252

9h=?(x)

9×252=18x

2268=18x

2268/18=x

x=126

5 0
3 years ago
Find the length of the leg of the right triangle leave your answer in simplest radical form
erastova [34]

Answer:

a =12*sqrt(2)

Step-by-step explanation:

3.  The Pythagorean theorem states

a^2 + b^2 = c^2  where a  and b are the legs and c is the hypotenuse

a^2 +21^2 = 27^2

a^2 +441 =729

Subtract 441 from each side

a^2 +441-441 = 729 -441

a^2 =288

Take the square root of each side

sqrt(a^2) = sqrt(288)

sqrt(xy) = sqrt(x)sqrt(y)

a = sqrt(144)sqrt(2)

a =12*sqrt(2)

7 0
3 years ago
What is the range of the function f(x) = 3x2 + 6x – 8?
timama [110]

Answer:

Range is {y | y ≥ –11}


Step-by-step explanation:

This is quadratic equation.

<em>A quadratic equation's range can be found if we find the vertex.</em>

For quadratic equations that have a positive number in front of  x^{2} , it is upward opening and thus <u>all the numbers greater than or equal to the minimum value of vertex is the range.</u>


The formula for vertex of a parabola is:

Vertex =  (-\frac{b}{2a}, f(-\frac{b}{2a})

Where,

  • a is the coefficient of x^{2}
  • b is the coefficient of x

From our equation given, a=3  and  b=6

Now, x coordinate of vertex is  x=-\frac{b}{2a}\\x=-\frac{6}{(2)(3)}\\x=-\frac{6}{6}\\x=-1

y coordinate of the vertex IS THE MINIMUM VALUE that we want. We get this by plugging in the x value [ x=-1 ] into the equation. So we have:

3(-1)^{2}+6(-1)-8\\=-11


Hence, the range would be all numbers greater than or equal to -11  

Third answer choice is the right one.


6 0
3 years ago
Read 2 more answers
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