a hotel with 75 rooms has 45 for doubles and 30 singles. singles can be booked in any room, but reservations for two or more people must be booked in double rooms. what inequalities represents this situation?

Answers

Answer 1

Answer:

y = 75 - x

Step-by-step explanation:

From the question, we are given variables, and then we can see that

when x = 75 then y = 0

when x = 30 then y = 45

Finding the difference, we have

slope(m) = (45 - 0) / (30 - 75)

slope(m) = 45 / -45

slope(m) = -1

Next, we use the calculated m, to find b, using the formula

y = mx + b

0 = -1 * 75 + b

0 = -75 + b

b = 75

And finally, to get the needed equation, we say that

so y = mX+c

So that

y = -1 * x + 75

y = -x + 75

or y = 75 - x


Related Questions

If you have five red balls and five blue balls in a jar what’s the probability of the first ball being red?

Answers

Answer:

red balls = 5

blue balls = 5

total balls = 5 blue+5 red

= 10

[tex]p(first \: ball \: being \: red) = \frac{red \: balls}{total \: balls} [/tex]

[tex]p(first \: ball \: being \: red) = \frac{5}{10} = \frac{1}{2} [/tex]

Answer:

Step-by-step explanation:

Total number of red balls = 5

Total number of blue balls = 5

Total number of balls in jar = 5 + 5

                                             = 10

Probability of the first ball being red = total number of the red ball/total number of balls in the jar

                                                             = [tex]\frac{5}{10}[/tex]

                                                             = [tex]\frac{1}{2}[/tex]

Therefore, the probability of the first ball being red = [tex]\frac{1}{2}[/tex], 50% or 0.5 (in any way you are instructed to write it in)

0.50(61 + 3s)
Use the Distributive Property to expand the expression.

Answers

Answer:

30.5 + 1.5s

Step-by-step explanation:

k/2 + 9 = 37
too lazy to do this work. lol

Answers

Answer:

K = 56

Step-by-step explanation:

Subtract 9

k/2 = 28

multiply by 2

k = 56

Help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

A, 2 5/8 cups

Step-by-step explanation:

Since six dozen brownies is three times as much as two dozen, we can multiply 7/8 cups by 3. 3 x 7/8 = 21/8 If we simplify this fraction, it is 2 5/8. Therefore the answer is A, 2 5/8 cups.

I think the answer is the last one the 3 and 1/2

Triangle PQR is rotated 180 clockwise about point m and the image of point p is p and the image of point r is r what are the coordinates of the image of point Q

Answers

Answer:

Rotating 180 clockwise would mean that Q is Q if r is r, the coordinates of it pointing to Q would be in your picture , can I see a picture of the problem?

Step-by-step explanation:

describe the relationship between the similarity ratio of two triangles and the ratio of their areas. help plz​

Answers

Answer:

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.

Step-by-step explanation:

Theorem 60: If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b.

Find the are of the semi circle.Either enter an exact answer in terms of pie or use 3.14 and enter your answer as a decimal.The raduis is 4

Answers

12.56
I’m not sure of this is right
I haven’t done this in like 2 years

Find the value of the variable that results in congruent triangles
1.

Answers

Answer:

x = 26

Step-by-step explanation:

m<B = m<E = (x + 17)°

180 - (25 + 112) = (x + 17) (sum of ∆)

180 - 137 = x + 17

43 = x + 17

Subtract both sides by 17

43 - 17 = x

x = 26

Identify the errors made in finding the inverse of
y = x2 + 12x.
x= y2 + 12x
y2 = x - 12x
y2=-11x
y=-11x, for x > 0
Describe the three errors?

Answers

Step-by-step explanation:

y = x2 + 12x.

x= y2 + 12x           would also be 12 y

y2 = x - 12x               would be -x

y2=-11x  

y=[tex]\sqrt{-11x}[/tex], for x > 0    negative  square root not possible

Describe the three errors?

The three errors made in finding the inverse of y = x² + 12x are,

⇒ First mistake to write 12y in place of 12x.

⇒ Second mistake to write the expression y² = x - 12x.

⇒ Third mistake because it never possible negative square root for x > 0.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = x² + 12x

Here, The process are,

⇒ y = x² + 12x.

⇒ x = y² + 12x

There is first mistake to write 12y in place of 12x.

⇒ y² = x - 12x

There is second mistake.

⇒ y² = -11x

⇒ y = √-11x, for x > 0

There is third mistake because it never possible negative square root for x > 0.

Learn more about the mathematical expression visit:

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The cost of 3 scarves is $26.25. What is the unit price? (cost per scarf)

Answers

$8.75 because 26.25 divided by 3 equals $8.75.

hope this helps

Identify proportional relationships
Does the following table show a proportional relationship between the variables g and h?
g
3
6
9
9
36
81

Answers

Answer:

sure easy man the carrot is blue and green and orange there naswer soled

The portion of the parabola y²=4ax above the x-axis, where is form 0 to h is revolved about the x-axis. Show that the surface area generated is
A=8/3π√a[(h+a)³/²-a³/2]
Use the result to find the value of h if the parabola y²=36x when revolved about the x-axis is to have surface area 1000.​

Answers

Answer:

See below for Part A.

Part B)

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

Step-by-step explanation:

Part A)

The parabola given by the equation:

[tex]y^2=4ax[/tex]

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

[tex]y=f(x)=\sqrt{4ax}[/tex]

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

[tex]r(x)=y(x)=\sqrt{4ax}[/tex]

Now, we will need to find f’(x). We know that:

[tex]f(x)=\sqrt{4ax}[/tex]

Then by the chain rule, f’(x) is:

[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]

Combine roots;

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]

Integrate. We can consider using u-substitution. We will let:

[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]

We also need to change our limits of integration. So:

[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]

Hence, our new integral is:

[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]

Simplify and integrate:

[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

FTC:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]

Simplify each term. For the first term, we have:

[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]

We can factor out the 4a:

[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

For the second term, we have:

[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =(2a)^3[/tex]

Hence:

[tex]\displaystyle =8a^3[/tex]

Thus, our equation becomes:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]

We can factor out an 8a^(3/2). Hence:

[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

[tex]y^2=36x[/tex]

We can rewrite this as:

[tex]y^2=4(9)x[/tex]

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

We can write:

[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]

Solve for h. Simplify:

[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]

Divide both sides by 8π:

[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]

Isolate term:

[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]

Raise both sides to 2/3:

[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]

Hence, the value of h is:

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]

[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]

[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]

[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]

[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]

[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]

[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]

[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]

HELPPP I NEED AN ANSWER ASAP

Answers

Answer:

2, 4, and 6 (b, d, f)

Step-by-step explanation:

dont  really know how to explain

1 1/6 as an improper fraction

Answers

Answer:

The mixed number 1 1/6 converted into an improper fraction is 7/6.

Step-by-step explanation:

The improper fraction representation after converting of 1 1/6 is 7/6 where numerator is 7 and denominator is 6

To convert a mixed number to an improper fraction, we follow these steps:

Multiply the whole number by the denominator of the fraction.

In this case,  multiply 1 (the whole number) by 6 (the denominator), which gives  6.

Add the numerator to the result obtained in step 1.

The numerator in this case is 1. Adding 1 to 6 gives 7.

Place the result from step 2 as the numerator of the fraction, and keep the denominator the same.

The denominator remains 6.

Therefore, the improper fraction representation of 1 1/6 is 7/6.

Learn more about converting  fractions here:

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In the lab, Karen has two solutions that contain alcohol and is mixing them with each other. She uses 3 times as much Solution A as Solution B. Solution A is 10% alcohol and Solution B is 15% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 180 milliliters of pure alcohol?

Answers

Answer:

She uses 162 millitiers if Solution B.

Step-by-step explanation:

180 - 10% = 162

Solution A = 18 milliliters

Soultion B = 162 millitiers

helpppppp pleaseeee


question: Why do we need to know the mass of a robot? *
why is this in math why does my teacher does this

Answers

Answer:

To know what the answer is

Step-by-step explanation:

clearly I do not know, but I can say that we do need to know the mass bc in the future there will be more and more androids on the rising making human interaction bad.

to find out the equation take the seed and the time. (this to make it look like i answered) Taking the mass you will be able to find out how manyspeed is found by the time and masstime is found out by the mass and speedi dont know if this helped

Answer:

Step-by-step explanation:

If you rotate figure GTR 270° clockwise about the origin. What will be the coordinates of G’T’R’ (Please Help I need this done in five minutes.)

Answers

Answer:

C.  G' (4,-7), R' (2,-3), T'(6,-4)

Step-by-step explanation:

Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.

"Five less than
the quotient of
a number and
3 is -7°
A. 5 - X/3-7
B. -7 +x/3
C. X3 - 5 =-7
D. 5 - 4/2 = -7

Answers

The answer is C. I hope it helps

It Snowed 1/2 inch on Saturday and 1 3/5 inches on Sunday. How much did it snow altogether, total?

Answers

Answer:

Fraction form: it snowed 2 1/10 inches in total, decimal form: in other words it snowed 2.1 inches.

Step-by-step explanation:

Hurry plz!!
For parts (b) and (c), type each answer in the box below.
b. Explain why the opposite of a positive number will always be a negative
number
C. Explain why zero is its own opposite number.

Answers

C because yes yessssss

rewrite using a single positive exponent 5^6/5^4

Answers

Answer:

Step-by-step explanation:

We can divide exponents by subtract 4 from 6. So, now we have 5^2 or 25.

The other way to solve to check our answer is to do the math.

5^6 = 15625

5^4 = 625

15625/625 = 25

So, we know we have the correct answer.

How do you work this problem? 10x2 +25x

Answers

Answer:

x=-5/2,0

Step-by-step explanation:

It is solved by first factorizing it

10x²+25x=5x(2x+5)=0

Finding the zeros

5x=0x=0/5=0

2x+5=0

x=-5/2

Therefore x is -5/2 or 0

Use special right triangle ratios to find the length of the hypotenuse. Right Triangle Trig.

Answers

Answer:

11 sqrt(2)

Step-by-step explanation:

We know that in a 45 45 90 triangle, the lengths of the sides are x, x ,x sqrt(2)

the length of x is 11

so the lengths of the sides are 11, 11, 11 sqrt(2)

The hypotenuse is 11 sqrt(2)

Please help me fast!!!. Joe and his family are touring Chicago. They want to visit the Willis Tower, hang out at Navy Pier, and shop on Michigan Avenue before their dinner reservations at 5:10 P.M. They plan to spend 1 hour and 10 minutes at the Willis Tower, 3 hours and 10 minutes at Navy Pier, and 1 hour and 15 minutes shopping. What is the latest time Joe's family can start their tour of Chicago and still make it to dinner on time?

Include A.M. or P.M. in your answer.

Answers

Answer:

11:10 am.

Step-by-step explanation:

The first thing I'm going to do is to add all the given time together

Total time = time spent at Willis tower + time spent at Navy Pier + time spent shopping

Total time = 1 HR and 10 minutes + 3 HR and 10 minutes + 1 hour and 15 minutes

Total time = (1 + 3 + 1) hr + (10 + 10 + 15) minutes

Total time = 5 hours + 35 minutes

The question doesn't make mention of how long they spent making the journey so, I'm assuming they spent 35 minutes driving around from Willis to the Pier and finally while shopping

Time = total time + time spent driving

Time = 5 hours 35 minutes + 35 minutes

Time = 6 hours and 10 minutes

Now, this time we've calculated, is what we're going to subtract from the dinner time to get our final answer

Needed time = dinner time - time

Needed time = 5:10 pm - 6:10

Needed time = 17:10 - 6:10

Needed time = 11:10

This means that they ought to start their tour by 11:10 am, so that they can meet their dinner

After the movie premiere 99 out of 130 people surveyed said they liked the movie.
What is the experimental probability that the next person surveyed will say he or she liked the movie?
What is the experimental probability that the next person surveyed will say he or she did not like the movie?

Answers

Answer:

99 over 130 multiplied by 100 over 1

HELP PLEASE I GIVE BRAINLIEST

Answers

Answer:

30

Step-by-step explanation:

Perimeter of rectangle = 5y - 1 + 4y + 2 + 5y - 1 + 4y + 2

                                      = 18y + 2

18y + 2 = 128

18y = 128 - 2

     = 126

y = 126 ÷ 18

y = 7

Length of AD = 4y + 2

                      = 4(7) + 2

                      = 28 + 2

                      = 30

4,0000000000×10,00000000

Answers

Answer:

yes 40

Step-by-step explanation:

she got it correct

The population of Garden City in 1995 was 2,400. In 200, the population was 4,000. Write a linear equation in slope-intercept form that represents this data.

Answers

Answer:

[tex]y = 320x +2080[/tex]

Step-by-step explanation:

Given

Population in 1995 = 2400

Population in 2000 = 4000

Required

Determine the linear equation

Let the years be represented with x.

In 1995, x = 1 i.e. the first year

In 2000, x = 6

Let y represents the population

When x = 1; y = 2400

When x = 6; y = 4000

First, we calculate the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{4000 - 2400}{6 - 1}[/tex]

[tex]m = \frac{1600}{5}[/tex]

[tex]m = 320[/tex]

Next, we calculate the line equation as follows:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex]y - 2400 = 320(x - 1)[/tex]

[tex]y - 2400 = 320x - 320[/tex]

[tex]y = 320x - 320 + 2400[/tex]

[tex]y = 320x +2080[/tex]

which statement is true regarding the functions on the graph?

Answers

Answer:

f(3)=g(3)

Step-by-step explanation:

the only one i see is that

f(3)=g(3)

because the two functions intersect there

that means the two values are the same

Is this a function???

Answers

Answer:

pfft no lol

Step-by-step explanation:

yeah no

have a good day!  :)

plz give me brainliest

Answer:

yes

Step-by-step explanation:

i think,because it goes past the center it all

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