Hector took out a small loan of $900 for 18 months (remember to turn this into

What is the equation of a horizontal line passing through the point (−7, 5)? (1 point)

netineya [11]

If it’s a horizontal line, we focus on the y-coordinates.

(-7,5)

-7 is a x-coordinate
5 is a y-coordinate

The answer is y = 5

6 0

3 years ago

16. PHYSICS The formula h = 1201 - 16t2 gives the height h in feet of an object 1 seconds after it is shot upward from

Murrr4er [49]

<h3><u>Question:</u></h3>

The formula h = 120t-16t^2 gives the height h in feet of an object t seconds after it is shot upward from Earth's surface with an initial velocity of 120 feet per second. What will the height of the object be after 6 seconds?

<h3><u>Answer:</u></h3>

The height of object after 6 seconds is 144 feet

<h3><u>Solution:</u></h3>

<em><u>The formula that gives the height of an object is:</u></em>

$h = 120t - 16t^2$

Where,

h is the height in feet and t is the time in seconds

To find: height of the object be after 6 seconds

To find the height of the object be after 6 seconds, substitute t = 6

$h = 120 \times 6 -16(6)^2\\\\h = 720 - 16 \times 36\\\\h = 720 - 576\\\\h = 144$

Thus height of object after 6 seconds is 144 feet

3 0

3 years ago

Determine whether the two expressions are equivalent. Explain your reasoning.

dlinn [17]

Let us evaluate each pair of expressions one at a time.
8. (n²+4) - n² and 4n.
(n²+4) - n² = n²+ 4 - n² = 4 which is not equal to 4n.
NOT EQUIVALENT

9. 3x + 5 and 2(x + 3)
2(x + 3) = 2x + 6 which is not equal to 3x + 5.
NOT EQUIVALENT

10. 15 - 6x and 15(1 - 6x)
15(1 - 6x) = 15 - 90x which is not equal to 15 - 6x
NOT EQUVALENT

11. (y + y + 2 + y) + 3y and 6y + 2
(y +y +2 + y) + 3y = y+y+y +2 + 3y = 3y + 2 + 3y = 6y + 2.
It matches the other expression.
EQUIVALENT

12. 8y - 3 + 10y and 3(6 - 1)
8y - 3 + 10y = 8y + 10y - 3 = 18y - 3
3(6 - 1) = 3(5) = 15
The two expressions do not match.
NOT EQUIVALENT.

Answer: Only the expressions in number 11 are equivalent.

6 0

3 years ago

Max is scuba diving at elevation of -64.5 feet, when friend signals to come higher. Max makes 2 ascents, each an equal distance

KengaRu [80]

Answer: - 42.95 feet

Explanation:

Let each ascent be x. Thus,

2 equal ascents = 2x

From the information given,

initial position = - 64.5 feet

Final position after 2 ascents = - 21.4 feet

This means that

- 64.5 + 2x = - 21.4

2x = - 21.4 + 64.5

2x = 43.1

x = 43.1/2

x = 21.55

Thus, Max's elevation after the first ascent is

- 64.5 + 21.55

= - 42.95 feet

4 0

1 year ago

Hot dogs come in packages of 10 and hot dog buns come in packages of 8 . What is the least amount of product that you need to Bu

lubasha [3.4K]

This exercise is solved by finding the least common multiple between 10 and 8.

In fact, you have to buy a certain number $h$ of hot dog package, and you will have $10h$ hot dogs, since there are 10 hot dogs in each package. The key concept here is that the number of hot dogs you have in the end is a multiple of the number of hot dogs in each box.

Similarly, you have to buy a certain number $b$ of hot dog buns package, and you will have $8b$ hot dogs, since there are 8 hot dog buns in each package. Again, the key concept here is that the number of hot dog buns you have in the end is a multiple of the number of hot dog buns in each box.

Then, you want to have the same number of hot dogs and hot dog buns, i.e. you want

$10h = 8b$

but you also want $h$ and $b$ to be the first values to satisfy this equation.

This means that you want a multiple of 10 to equal a multiple of 8, and you want the smallest possible number which does the trick. Again, this is exactly the definition of the least common multiple.

To find the least common multiple of two numbers, find their prime factorization, and collect all the primes from both factorizations, with the highest exponent possible. Since $10 = 2\cdot 5$ and $8 = 2^3$ , the primes appearing are 2 and 5. The higher exponent for 2 is 3, and the only exponent for 5 is 1. So, the answer is $2^3\cdot 5 = 40$ .

So, if you buy 4 packages of hot dogs and 5 packages of hot dog buns, you will have 40 hot dogs and 40 hot dog buns, as requested.

4 0

3 years ago

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