All categories

3 years ago

Ralph is 3 times as old as Sarah. in six years, Ralph will be only twice as old is Sarah will be then. find Ralphs age now.

2 answers:

8 0

First, we start with the equation that the problem told us, which is:

R + 6 = 2 * (x + 6)

Then, we distribute the two:

R + 6 = 2x + 12

Now, we put R on its own side.

R = 2x +6

So, the answer must be C, 2x + 6

loris [4]3 years ago

8 0

Answer:

The expression for Ralph's age in 6 years is 3x +6

Present age of Ralph is 18 years.

Step-by-step explanation:

Let the present age of Sarah's is x.

Hence, present age of Ralph is 3x

In 6 years, it has been given that Ralph will be only twice as old is Sarah will be then. Thus, we must add 6 to the present age of both.

Sarah's age is x+6

Ralphs's age is 3x+6

Hence, we have

3x+6 =2(x+6)

Solving the equation for x

3x + 6 = 2x +12

x = 6

Hence, Ralph's present age is

= 3×6

= 18

The expression for Ralph's age in 6 years is 3x +6

Present age of Ralph is 18 years.

You might be interested in

Convert the following systems of equations to an augmented matrix and use Gauss-Jordan reduction to convert to an equilivalent m

Rasek [7]

Answer:

System of equations:

$x_1+2x_2+2x_3=6\\2x_1+x_2+x_3=6\\x_1+x_2+3x_3=6$

Augmented matrix:

$\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]$

Reduced Row Echelon matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]$

Step-by-step explanation:

Convert the system into an augmented matrix:

$\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]$

For notation, R_n is the new nth row and r_n the unchanged one.

1. Operations:

$R_2=-2r_1+r_2\\R_3=-r_1+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&-3&-3&-6\\0&-1&1&0\end{array}\right]$

2. Operations:

$R_2=-\frac{1}{3}r_2$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&-1&1&0\end{array}\right]$

3. Operations:

$R_3=r_2+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&2&2\end{array}\right]$

4. Operations:

$R_3=\frac{1}{2}r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]$

4 0

3 years ago

Hello Guys, I really need help with these questions. Here they are.

Slav-nsk [51]

Answer:

See below.

Step-by-step explanation:

It can really help to think when you see |expression| that it means the distance from expression to zero.

(a) |x| < 7 means the distance from x to 0 is less than 7. That puts x between -7 and 7. The solution set is -7 < x < 7.

(b) |x + 3| < 9 means that the distance from x + 3 to 0 is less than 9. That puts x + 3 between -9 and 9:

-9 < x + 3 < 9 Now subtract 3 from all three parts.

-12 < x < 6

(c) |y - 8| > 11 means that the distance from y - 8 to 0 is more than 11 units. That puts y - 8 in one of two places: left of -11 or right of 11.

$y-8 < -11 \text{ or } y-8 > 11\\\\y < -3 \text{ or } y > 19$

(g) $|3x-1| \ge 18$ means that the distance from 3x - 1 to 0 is more than (or equal to) 18. Another way to say it is, 3x - 1 is farther from 0 than 18 units. That puts 3x - 1 in one of two places: to the left of -18 or to the right of 18.

$3x-1 \le -18 \text{ or } 3x-1 \ge 18\\\\3x \le -17 \text{ or } 3x \ge 19\\\\x \le -\frac{17}{3} \text{ or } x \ge \frac{19}{3}$

$|4y+3| \le 13$ means that 4y + 3 is closer to 0 than 13; it is between -13 and 13.

$-13 \le 4y+3 \le 13\\\\-16 \le 4y \le 10\\\\-4 \le y \le \frac{5}{2}$

(That last fraction is 10/4 simplified.)

3 0

2 years ago

Read 2 more answers

Find the distance traveled in 35 seconds by an object traveling at a velocity of v(t) = 20 + 5cos(t) feet per second

rosijanka [135]

$s(t)= \int\limits^{35}_0 {v(t)} \, dt \\ =\int\limits^{35}_0 {(20+5cos(t))} \, dt \\ =[20t+5sin(t)]^{35}_0 \\ =(20(35)+5sin(35))-(20(0)+5sin(0)) \\ =700+2.868=702.868 \, feet$

8 0

3 years ago

The number of miles USC employees commute to campus is normally distributed. To estimate the mean of this distribution, four emp

Aleksandr [31]

Yfiyfidy. It’s soot ioydotdi

It’s Bc. H. Dey h. Yes so I’m hehe what crazy now

7 0

2 years ago

Look at image please

Kay [80]

Answer:

Step-by-step explanation:

It begins at the point (0, -1200). 0 tickets sold, $1200 spent.

$5 for a ticket means that slope =5.

(600, 1800) and (0,-1200)

m= (1800-(-1200))/(600-0)=3000/600=5

slope=5

Answer is a.

8 0

3 years ago