Connor went to New York for vacation. He spent 3 nights at a hotel and rented a car for 4 days. Jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. If Connor paid $675 and Jillian paid $875, how much did one night at the hotel cost?

Answers

Answer 1

Answer: The answer for the question in problem would be $125 is the price of hotel per night. This is computed by establishing the equations from the given statements, 3x + 4y = 625 and 4x +5y = 875. And by substitution you would get the answer of 125 as the price per night n the hotel and 75 per day for the rental of car.

Answer 2

Answer:

Answer:

The cost of one night at the hotel is $125

Step-by-step explanation:

Let the cost of each night spend in hotel is = $x

Let the cost of each day of car rented = $y

Cannor spent 3 nights at a hotel and rented a car for 4 days paid $675.

$\Rightarrow3x+4y=675$ ......(1)

Jillian also spent 4 nights in same hotel and rented a car for 5 days paid $875.

$\Rightarrow4x+5y=875$ .......(2)

Now, we solve equation (1) and (2) by substitution method

From (1) take the value of x, $x=(675-4y)/(3)$

then put in equation (2) $4*(675-4y)/(3)+5y=875$

solve,

$\Rightarrow 4*(675-4y)+5y*3=875*3$ (Taking LCM)

$\Rightarrow2700-16y+15y=2625$

$\Rightarrow y=2700-2625=75$

Now, put value of $y=75$ in value of $x=(675-4y)/(3)$

$\Rightarrow x=(675-4(75))/(3)$

$\Rightarrow x=(675-300)/(3)$

$\Rightarrow x=(375)/(3)$

$\Rightarrow x=125$

Therefore, the cost of one night at the hotel is $125

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In a problem it says that x is "at most –5." What does this mean?

Answers

It means exactly what it says. It means that x can be negative five at the MOST, but it can also be any number before that. If you were writing this for an equation it would be x is greater than or equal to five. I hope this helps you :)

it means that -5 is the range of your answer, it will be less than that.

3It takes 47 yd of fabric to make a costume for a school play. How much fabric would be needed for 10 costumes?

Answers

47 per costume X 10 costumes
47x10
470

What is true about the domain and range of the function?The graph of the function f(x) = (x +2)(x + 6) is shown
below.
у
6
The domain is all real numbers, and the range is all
real numbers greater than or equal to 4.
O The domain is all real numbers greater than or equal to
4, and the range is all real numbers.
O The domain is all real numbers such that -65x3-2,
and the range is all real numbers greater than or equal
to-4.
The domain is all real numbers greater than or equal to
4, and the range is all real numbers such that -63x3
-2.
4
N
-6 -4 +2
4
6
х
N
-2-
-4
6t

Answers

Answer:

The domain is all real numbers and the range is all real numbers greater than or equal to -4

Step-by-step explanation:

←→ is parallel to CD←→. AC¯¯¯¯¯ and BD¯¯¯¯¯ are perpendicular to AB←→ and CD←→ . What is the relationship between AC¯¯¯¯¯ and BD¯¯¯¯¯ ?

Answers

If AC and BD are perpendicular to AB and CD which are parallel. It means they face the same direction and are parallel to one another.

AB=CD

"When two lines are parallel, the perpendicular distance between the two lines is the same throughout."

A pool is being drained at a constant rate. The amount of water is a function of the number of minutes the pool has been draining, as shown in the table. Write an equation in slope-intercept form that represents the function. Then find the water in the pool after two and a half hours. Time (mi) 12--------20------50
Volumne (gal) 4962--4754--3974

Answers

The equation in the slope-intercept form is $y=-26x+5274$ and there will be $1374$ gallons of water in the pool after $2$ and a half hours.

The equation of a line that passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ is $(y-y_1)=(y_2-y_1)/(x_2-x_1)(x-x_1)$ .

Take points $(12, 4962)$ and $(20, 4754)$ .

Here, $x_1=12, y_1=4962, x_2=20, y_2=4754$ .

The equation is :

$(y-4962)=(4754-4962)/(20-12)(x-12)$

$(y-4962)=(-208)/(8)(x-12)$

$8(y-4962)=-208(x-12)$

$8y-39696=-208x+2496$

$208x+8y-39696-2496=0$

$208x+8y-42192=0$

$8y=-208x+42192$

$y=-(208)/(8)x+(42192)/(8)$

$y=-26x+5274.$

The slope intercept form is $y=mx+c$ , where $m$ is the slope and $c$ is the $y$ -intercept.

After $2$ and a half hours or $150$ minutes.

Put $x=150$ in the equation $y=-26x+5274.$

$y=-26* 150+5274$

$y=-3900+5274$

$y=1374$

So, there will be $1374$ gallons of water in the pool after $2$ and a half hours.

Learn more about slope-intercept form here:

brainly.com/question/21366542?referrer=searchResults

Answer:

Using the first two values in the table, we can first find the slope to write an equation of a line, so we have

[4754 - 4962 ] / [20 - 12 ] = -26

So we have

y - 4754 = -26(x - 20)

y - 4754 = -26x + 520

y = -26x + 5274

Let's confirm that the amount after 50 minutes is correct

y = -26(50) + 5274 = 3974

So after 2 + 1/2 hrs (150 min) we have

y = -26(150) + 5274 = 1374 gallons

Step-by-step explanation:

In march, a customer spent $8.55 at an office-supply store for some 12-packs of pens. At that time, the store was selling packages of one dozen pens for $1.35. Any customer who bought more than 4 packages, received a discount of $0.30 on the price of each package in excess of 4 packages. In september, the same customer went back to the store to buy the same number of pens. By then, the price per 12-pack of pens had been raised to $1.50 each, with the same discount for more than 4 packages. How much more did the customer have to pay in September than in March?

Answers

We can start by making an equation from the information given on the month of March to find how many packs he bought.
$4(1.35)+x(1.05)=8.55$ This equation shows that for the first 4 packs he bought, he payed $1.35. Then, consequently, for each pack after that, he payed $0.30 less, and we don't know how many more he bought, so we set it up as shown. Finally, we set it all equal to $8.55 since that's how much he payed that month. We get that x=3, meaning that he bought a total of 7 packs of pens that month.
Knowing this, we can now make an equation for the month of September.
$4(1.50)+3(1.20)=x$ This time, we know the entire left side, that he paid $1.50 for the first 4 packs and $0.30 less for the last 3. We get x=$9.60
Knowing this, we can subtract the amount he paid in September by the amount he paid in March to get the answer... $9.60-$8.55=$1.05

I hope this helped!

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