CHECK YOUR KNOWLEDGE

Airida [17]

5x - 14y = 22 ⇒ 5x - 14y = 22
-6x + 7y = 3 ⇒ 12x - 14y = -6
 -7x = 28
 -7 -7
 x = -4
 5x - 14y = 22
 5(-4) - 14y = 22
 -20 - 14y = 22
 + 20 + 20
 -14y = 42
 -14 -14
 y = -3
 (x, y) = (-4, -3)

3 0

3 years ago

PLEASE HELP!!! very confused

Leni [432]

Answer:

Step-by-step explanation:

The vertices lie on the x-axis, as is determined by their coordinates. This makes the center of this hyperbola (0, 0) because the center is directly between the vertices. The fact that the foci also lie on the x-axis tells us that this is the main axis. What this also tells us is which way the hyperbola "opens". This one opens to the left and the right as opposed to up and down. The standard form for this hyperbola is:

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$ and so far we have that h = 0 and k = 0.

By definition, a is the distance between the center and the vertices. So a = 5, and a-squared is 25. So we're getting there. Now here's the tricky part.

The expressions for the foci are (h-c, k) and (h+c, k). Since we know the foci lie at +/-13, we can use that to solve for c:

If h+c = 13 and h = 0, then

0 + c = 13 and c = 13.

We need that c value to help us find b:

$c^2=a^2+b^2$ and

$13^2=5^2+b^2$ and

$169=25+b^2$ and

$144=b^2$ so

b = 12. Now we're ready to fill in the equation:

$\frac{x^2}{25}-\frac{y^2}{144}=1$ and there you go!

3 0

2 years ago

Ruby will buy3 ivory silk lilac trees or 2 bur oak trees. He wants to buy the trees that cost less. What trees will he buy? How

baherus [9]

Rudy will buy 3 Ivory Silk Lilac trees; $4

22 × 3 = 66; 35 × 2 = 70

$70 − $66 = $4

Hope this helped.

I got this same exact question in third grade and this was my answer.

3 0

3 years ago

Please help, i cannot solve.

Ludmilka [50]

Im sorry im in sixgh grade i was so close to solving it but that didnt work, i tried

3 0

3 years ago

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes.

Paladinen [302]

Answer:

Answer:

\{ {{20x+30y=280} \atop {y=4x}} .{

y=4x

20x+30y=280

.

Where xx is the number of small boxes sent and yy is the number of large boxes sent.

Step-by-step explanation:

Let be xx the number of small boxes sent and yy the number of large boxes sent.

Since each small box can hold 20 books (20x20x ), each large box can hold 30 books (30y30y )and altogether can hold a total of 280 books, we can write the following equation to represent this:

20x+30y=28020x+30y=280

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation:

y=4xy=4x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is:

\{ {{20x+30y=280} \atop {y=4x}} .{

y=4x

20x+30y=280

.

7 0

3 years ago