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1 year ago

A rectangle has an area of 48

1 answer:

6 0

Answer: i didnt understand the answer choice but the correct answer is 48/12=width. width=4

Step-by-step explanation:
as we know the area of a rectangle is area=length X width
so we plug in 48 as area and 12 as length

48=12 x width
48/12=width(divide both sides by 12)

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Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)? y squared over 40 minus x square

N76 [4]

The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is $\frac{x^2}{10} + \frac{y^2}{15} = 1$

<h3>How to determine the equation of the hyperbola?</h3>

The given parameters are:

Directrices at x = ±2
Foci at (5, 0) and (−5, 0)

The foci of a hyperbola are represented as:

Foci = (k ± c, h)

The center is:

Center = (h,k)

And the directrix is:

Directrix, x = h ± a²/c

By comparison, we have:

k ± c = ±5

h = 0

h ± a²/c = ±2

Substitute h = 0 in h ± a²/c = ±2

0 ± a²/c = ±2

This gives

a²/c = 2

Multiply both sides by c

a² = 2c

k ± c = ±5 means that:

k ± c = 0 ± 5

By comparison, we have:

k = 0 and c = 5

Substitute c = 5 in a² = 2c

a² = 2 * 5

a² = 10

Next, we calculate b using:

b² = c² - a²

This gives

b² = 5² - 10

Evaluate

b² = 15

The hyperbola is represented as:

$\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1$

So, we have:

$\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1$

Evaluate

$\frac{x^2}{10} + \frac{y^2}{15} = 1$

Hence, the equation of the hyperbola is $\frac{x^2}{10} + \frac{y^2}{15} = 1$

Read more about hyperbola at:

brainly.com/question/3405939

#SPJ1

6 0

1 year ago

For a scavenger hunt, Jim's mom distributed a bag of 875 jelly beans evenly into 25 plastic containers and hid them around the

kupik [55]

Answer:

Jim only found 15 of the containers.

Step-by-step explanation:

If his mom hid 875 jelly beans evenly into 25 containers we can easily multiply 25 x 35 = 875, which means there were 35 jelly beans in each container.

Jim only found an amount of 385 jelly beans. To find out how many containers he found, all you have to do is divide 385 by 25 which gives us 15.4.

15.4 rounded to the nearest whole number is 15. So your answer would be that Jim found only 15 out of 25 containers.

6 0

2 years ago

A bread machine is marked "reduced by 15%, now only $101.15".

Art [367]

(100-15=85%)
85=101.15 how about 100
100 x 101.15 divided by 85=118.882353
$119

8 0

3 years ago

What is the vertex of the graph of the function f(x) = x2 + 8x - 2?

vlabodo [156]

Answer:

Vertex is (-4, -18)

Step-by-step explanation:

f(x) = $ax^{2} +bx +c$

Let (h, k) be the vertex

An easy way to find h is to use the formula h = -b/2a

In your case where f(x) = $x^{2} +8x - 2$ a = 2 and b = 8

So, h = -8/2(1) = -8/2 = -4

Substitue -4 in for x to find k

k = ( $-4^{2}$ ) + 8(-4) - 2

= (16) - 32 - 2

= 16 - 32 - 2

= -18

Vertex is (-4, -18)

Note: Another way to find the vertex is to complete the square, but this can really be difficult in some cases

5 0

2 years ago

A square sheet of paper measures 42 centimeters on each side. What is the length of the diagonal of this paper?

Illusion [34]

59.4cm
Use Pythagorean theorem to find the diagonal (^ means exponent)
a^2 + b^2 = c^2
42^2 + 42^2= c^2
1764+1764=c^2
3528=c^2
square root both sides
c= 59.39696962
round and you get 59.4 cm

5 0

3 years ago