Https://www.blooket.com/play?id=492019

Ralph is 3 times as old as Sara. In 6 years , Ralph will be only twice as old as Sara will be then. Find Ralph’s age now .

Delvig [45]

Answer:

Ralph's current age is 18.

Step-by-step explanation:

Let r and s represent the current ages of Ralph and Sara respectively. Our task here is to determine r, Ralph's age now.

If Ralph is 3 times as old as Sara now, then r = 3s.

Six years from now, Ralph's age will be r + 6 and Sara's will be s + 6. Ralph will be only twice as old as Sara will be then. This can be represented algebraically as

r + 6 = 2(s + 6).

We now have the following system of linear equations to solve:

r + 6 = 2s + 12, or r - 2s = 6, and r = 3s (found earlier, see above).

r - 2s = 6

r = 3s

Substituting 3s for r in r - 2s = 6, we get 3s = 2s + 6, or s = 6. Sara is 6 years old now, meaning that Ralph is 3(6 years), or 18 years old.

Ralph's current age is 18.

3 0

2 years ago

Given P(x) = 2x3 - 11x2 + 18x - 15 is divided by x – 3. Use synthetic division to find the quotient and the remainder.

katrin [286]

You can find the remainder right away by simply plugging in $x=3$ . The polynomial remainder theorem guarantees that the value of $p(3)$ is the remainder upon dividing $p(x)$ by $x-3$ , but I digress...

Synthetic division yields

3   |   2   -11   18   -15
.    |           6   -15     9
- - - - - - - - - - - - - - - - -
.    |   2     -5     3     -6

which translates to

$\dfrac{2x^3-11x^2+18x-15}{x-3}=2x^2-5x+3-\dfrac6{x-3}$

(and note that $p(3)=2(3)^3-11(3)^2+18(3)-15=-6$ , as expected)

5 0

2 years ago

Find the midpoint of the line segment with the given endpoints: (-1, -6) and (-6, 5).

Vikentia [17]

Answer:

Step-by-step explanation:

First, we will find the midpoint for the x - coordinate first.

Midpoint (x) = $\frac{-1+(-6)}{2} \\=\frac{-1-6}{2} \\=\frac{-7}{2} \\=-3.5$

Now we will find the midpoint for the y - coordinate.

Midpoint (y) = $\frac{-6+5}{2} \\=\frac{-1}{2} \\=-0.5$

Therefore from these 2 values we know that the midpoint of this 2 points is (-3.5,-0.5)

8 0

1 year ago

Which of these is NOT an integer

Tema [17]

Hi there!

»»————-　★　————-««

I believe your answer is:

Option A

»»————-　★　————-««

Here’s why:

⸻⸻⸻⸻

$\boxed{\text{Option A:}}\\\\3^{-5}\\\\\rightarrow \frac{1}{3^5}\\\\\rightarrow \frac{1}{243}\\\\\ \text{This is \textbf{NOT} an integer.}}$

⸻⸻⸻⸻

$\boxed{\text{Option B:}}\\\\-3^5\\\\\rightarrow -3 * -3 * -3 * -3 * -3 \\\\\rightarrow \boxed{-243}\\\\\\\text{This \textbf{IS} an integer.}$

⸻⸻⸻⸻

$\boxed{\text{Option C:}}\\\\\frac{1}{3}^{-5} \\\\\rightarrow \frac{1}{(\frac{1}{3})^5}\\\\\rightarrow \frac{1}{\frac{1}{243} }\\\\\rightarrow \boxed{243}\\\\\\\text{This \textbf{IS} an integer.}$

⸻⸻⸻⸻

$\text{Option \textbf{A} does not simplify into an integer.}$

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

7 0

2 years ago

Find the value of x if a,b, and c are collinear points an b is between a and c

MakcuM [25]

$\sf Hello!$

• $\sf AB = x + 6$
• $\sf BC = 3x - 5$
• $\sf AC = 36 - x$

$\sf We're \:given\: that \:A,\: B\: and \:C \:are \:Collinear\: points$

$\sf Then,$

$\sf AB + BC = AC$

⇒ $\sf x + 6 + 3x - 5 = 36 - x$

⇒ $\sf x + 3x + 6 - 5 = 36 - x$

⇒ $\sf 4x + 1 = 36 - x$

⇒ $\sf 4x + x = 36 - 1$

⇒ $\sf 5x = 35$

⇒ $\sf x = \dfrac{\sf 35}{\sf 5}$

⇒ $\boxed{\sf x = 7}$

$\sf Hence,$

$\sf The\: value\: of\: x\: is\: D.\: 7$

~ $\sf iCarl$

3 0

2 years ago