Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Write a system of linear inequalities to represent this situation.

Answers

Answer 1

The answer is :

x + y ≤ 14

2x + 3y ≤ 18

Answer 2

The inequality for the given statement will be equal to x +y ≤ 18 or,

2x + 3y ≤ 18.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given information in the question,

The price of fuel x = $2/gallon

The price of fuel y = $3/gallon

Total money to spend on fuel = $18

Then, the inequality in this situation will be,

x +y ≤ 18 or,

2x + 3y ≤ 18.

To know more about Inequality:

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Related Questions

what is true about the equation y = 4x2 + 28x + 49

Answers

Answer:

What are the answer choices for this question. It would help me know what they are asking you to do.

all square numbers from 1 to 15

Answers

Answer:

1,4,9

Step by step explanation

[tex] {1}^{2} = 1 \times 1 = 1 \\ {2}^{2} = 2 \times 2 = 4 \\ {3}^{2} = 3 \times 3 = 9 \\

{4}^{2} = 4 \times 4 = 16 \\ {5}^{2} = 5 \times 5 = 25 \\ {6}^{2} = 6 \times 6 = 36 \\ {7}^{2} = 7 \times 7 = 49 \\ {8}^{2} = 8 \times 8 = 64 \\ {9}^{2} = 9 \times 9 = 81 \\ {10}^{2} = 10 \times 10 = 100 \\ {11}^{2} = 11 \times 11 = 121 \\ {12}^{2} = 12 \times 12 = 144 \\ {13}^{2} = 13 \times 13 = 169 \\ {14}^{2} = 14 \times 14 = 196 \\ {15}^{2} = 15 \times 15 = 225[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Rewrite the equation by completing the square.

2 x^2 -11 x +14 = 0

Answers

Answer:

x^2 - (11/2)x + 121/16 = -7

Step-by-step explanation:

In a newspaper,it was reported that the number of yearly robberies in springfield in 2011 was 240, and then went up by 5% in 2012.How many robberies were there in springfield in 2012?

Answers

Answer:

There were 252 robberies in 2012.

Step-by-step explanation:

Number of robberies in 2011 = 240

5% Increase =

[tex]5/100*240=12[/tex]

Therefore, new number of robberies in 2012 =

[tex]240+12=252[/tex].

To confirm this figure, we use the formula,

% increase = Increase / Original number * 100

Increase= 12

Original number= 240

Therefore,

12 / 240*100 = 5

This confirms that, indeed, there was a 5% increase in 2012.

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 22 feet and a height of 12 feet. Container B has a diameter of 18 feet and a height of 19 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.

Answers

Answer:

a) 4561.59 ft^3

b) 17.93 ft

Step-by-step explanation:

Given:-

- Container A and B are of cylindrical shape

- The diameter of container A, da = 22 ft

- The height of container A, ha = 12 ft

- The diameter of container B, db = 18 ft

- The height of container B, hb = 19 ft

- Container A is initially full while container B is empty.

- Water is pumped from container A to container B until container A is empty.

Find:-

a) The volume of water in container B

b) The level of water in container B

Solution:-

- The cylinder is initially full to the top. The volume of the water in container A takes the shape of container A. The volume of a cylindrical container is mathematically expressed as function of diameter and height, as follows:

                        [tex]V = \pi \frac{d^2}{4}*h[/tex]

- The volume of water in container A of diameter ( da ) and height ( ha ):

                       [tex]V_a = \pi \frac{d_a^2}{4}*h_a\\\\V_a= \pi \frac{22^2}{4}*12\\\\V_a = 4561.59253 ft^3[/tex]

- We are given that the water is pumped from the container A to B until all the water ( Volume ) is emptied from container A:

- The total amount of water available in container A, is V_a is all pumped into container B. Therefore, after the process of pumping container B will have the volume of water equivalent to the volume of water in container A before the pumping process started ( assuming no loss of water ):

                       [tex]V_b = V_a = 4561.59253 ft^3[/tex] .. Answer ( a )

- The volume of water contained in container also takes the shape of cylinder and can be expressed as:

                     [tex]V_b = \pi \frac{d_b^2}{4}*h\\\\h= \frac{4*V_b}{\pi*d_b^2 }\\\\h = \frac{4*4561.59253}{\pi*18^2 } \\\\ h = 17.926 ft[/tex]

Answer: The level of water in container B is h = 17.93 ft

When's the 3 digit number is rounded to the nearest hundred it round to 400.The digit in the ones place is the fourth odd number you count beginning with 1.The sum of the digits is 12.What is the number

Answers

Answer:

417

Step-by-step explanation:

count 1, 3, 5, (7) is the fourth one

it needs to be rounded to 400 so it is between 350 and 450

lets try in the 300s, 12 -(3 + 7) = 2. but 327 does not round to 400 so it does not work

lets try in the 400s, 12 - (4 + 7) = 1. put that one in the middle and you get 417 which fits the entire description

Answer:

Cannot be determined since the question is wrong.

Step-by-step explanation:

The fourth odd number is: 1, 3, 5, 7

h+t+o=12

h+t+7=12

Subtract 7 from both sides

h+t=5

If it rounds up to 400, h must be 3.

3+t=5

Subtract 3 from both sides

t=2

So our number is 327? It doesn't round up to 400 so the question is probably wrong. You probably got a typo in their like the numbers adding up to 12 or rounding to 300.

what is the difference between very crowded and rowdy

Answers

If you mean by term definition, Crowded is full of many and rowdy is rambunctious and rough

Answer:

Crowded means full of people

Rowdy means noisy and disorderly.

Crowded and Rowdy are adjectives.

Lucy knows about 6 Web sites that sell a designer T-shirt she loves. The mean price of the T-shirt is $14 and the range of prices is $7. Which of the following are possible prices for the T-shirt? A. $14, $14, $14, $14, $7, $7 B. $14, $14, $14, $14, $14, $21 C. $13, $13, $13, $15, $15, $15 D. $13, $12, $15, $15, $11, $18

Answers

Answer:

D

Step-by-step explanation:

When we talk of the range, that means the difference between the highest and the lowest figure in the data set

The mean refers to the sum of the values in the data set divided by the count of the value in the data set.

let’s take a look at data set option A;

mean = [4(14) + 2(7)]/6 = (56 + 14)/6 = 70/6 which is definitely not 14 which makes the option wrong

Let’s take a look at option C

mean = {13(3) + 15)3)}/6 = (39 + 45)/6 = 84/6 = 14

While the range is 15-13 = 2 which does not make it right too

Now, a look at option D

mean = (13 + 12 + 15 + 15 + 11 + 18)/6 = 84/6 = 14

range = 18-11 = 7 (highway number in the set minus lowest number)

This makes option D our answer

Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine this area.

Answers

Answer:

Using Geometry to answer the question would be the simplest:

Step-by-step explanation:

Remembering the formula for the area of a triangle which is [tex]A=\frac12bh[/tex]. One can then tackle the question by doing the following:

Step 1 Find the y-intercepts

The y-intercepts are found by substituting in [tex]x=0[/tex].

Which gives you this when you plug it into both equations:

[tex]-y=1\\y=-1\\y=8[/tex]

So the y-intercepts for the graphs are [tex](0,-1)\\[/tex], and [tex](0,8)[/tex] respectively.

Now one has to use elimination to solve the problems by adding up the equations we get:

[tex]x-y=1\\2x+y=8\\3x=9\\x=3[/tex]

Now to solve for the y component substitute:

[tex]2(3)+y=8\\y=2[/tex]

Therefore, the graphs intersect at the following:

[tex](3,2)[/tex]

Now we have our triangle which is accompanied by the graph.

now to solve it we must figure out how long the base is:

[tex]b=8-(-1)\\b=9[/tex]

The height must also be accounted for which is the following:

[tex]h=3[/tex]

Now the formula can be used:

[tex]A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2[/tex]

Answer: 13.5 units²

Step-by-step explanation:

Geometry Solution:

The base is along the y-axis from -1 to 8 = 9 units

The height is the largest x-value = 3

[tex]Area=\dfrac{base\times height}{2}\quad =\dfrac{9\times 3}{2}\quad =\dfrac{27}{2}\quad =\large\boxed{13.5}[/tex]

Calculus Solution:

[tex]\int^3_0[(-2x+8)-(x-1)]dx\\\\\\=\int^3_0(-3x+9)dx\\\\\\=\bigg(\dfrac{-3x^2}{2}+9x\bigg)\bigg|^3_0\\\\\\=\bigg(\dfrac{-3(3)^2}{2}+9(3)\bigg)-\bigg(\dfrac{-3(0)^2}{2}+9(0)\bigg)\\\\\\=\dfrac{-27}{2}+27-0-0\\\\\\=\dfrac{27}{2}\quad =\large\boxed{13.5}[/tex]

WHAT IS 5 times negative 1 and 2/5

PLEASE ANSWER ASAP WILL GIVE BRAINLIEST AND TONS OF POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! PLEASE SHOW YOUR WORK

Answers

Answer:

-7

Step-by-step explanation:

5*-1 2/5=-7

5*-1=-5

-2/5*5=-2

5+2=-7

un autobus de linea hace cuatro viajes cada dia. en cada viaje transporta 119 viajeros. ¿ cuántos pasajeros transporta al dia?

Answers

Answer:

son 119 pasajeros por vieje y hace 4 viajes ,murtiplicas la cantidad de pasajeros por la cantidad de los viajes osea 119x4 el total seria:476 pasajeros

What is the area of the regular pentagon with 5 inch sides and apothem that measures 4.2 inches?
52.5 in2
21 in2
105in2
10.5 in2

Answers

Answer:

The area of the pentagon is 52.5 in²

Step-by-step explanation:

The area of a regular pentagon is given by:

area = (5*l*a)/2

Where l is the length of each side and a is the length of the apothem. Applying the data from the problem we have:

area = (5*5*4.2)/2

area = (105)/2

area = 52.5 in²

The area of the pentagon is 52.5 in²

Find the value of m, if (3/5) raise to −3 multiply 5/3 raise to 11 equals 3/5 raise to 3m+1

Answers

Answer:

[tex]m=-5[/tex]

Step-by-step explanation:

[tex]\left(\frac{3}{5}\right)^{-3}\left(\frac{5}{3}\right)^{11}=\left(\frac{3}{5}\right)^{3m+1}\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(\left(\frac{3}{5}\right)^{-3}\left(\frac{5}{3}\right)^{11}\right)=\ln \left(\left(\frac{3}{5}\right)^{3m+1}\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]

[tex]\ln \left(\left(\frac{3}{5}\right)^{3m+1}\right)=\left(3m+1\right)\ln \left(\frac{3}{5}\right)\\\ln \left(\left(\frac{3}{5}\right)^{-3}\left(\frac{5}{3}\right)^{11}\right)=\left(3m+1\right)\ln \left(\frac{3}{5}\right)\\\mathrm{Solve\:}\:\ln \left(\left(\frac{3}{5}\right)^{-3}\left(\frac{5}{3}\right)^{11}\right)=\left(3m+1\right)\ln \left(\frac{3}{5}\right):\quad m=\frac{14\ln \left(5\right)-14\ln \left(3\right)-\ln \left(\frac{3}{5}\right)}{3\ln \left(\frac{3}{5}\right)}[/tex]

[tex]m=\frac{14\ln \left(5\right)-14\ln \left(3\right)-\ln \left(\frac{3}{5}\right)}{3\ln \left(\frac{3}{5}\right)}\\\mathrm{Decimal}:\quad m=-5[/tex]

Felipe dice que su calculadora no funciona. Para cambiar solo el 9 del 39.200 sumó 1.000 pero obtuvo 40.200. ¿Cómo le explicarías a Felipe por qué no cambió solo el 9?

Answers

Answer:

Felipe dio un paso incorrecto de acuerdo con el sistema de valor posicional al sumar la suma de 1,000 a 39,200. La manera correcta en que Felipe debe abordar esto se muestra en la explicación a continuación.

Step-by-step explanation:

En el sistema de valor posicional; cada número representa una entidad particular; ya sea unidad, decenas, cientos, mil, diez mil etc. En la pregunta dada, el número 39200 indica que 9 está en el valor posicional de mil, es decir, 9000.

Entonces, si Felipe desea cambiar de 8 a 9, entonces necesita restar 9000-8000 = 1000

Sin embargo; si quiere cambiar 9 a cero; entonces restará 9000 de 9000; pero ya que 9 no funciona; Primero debe restar 8000 y luego restar 1000.

Which graph represents an exponential equation ​

Answers

Answer:

4.

Step-by-step explanation:

It is exponential equation because exponential equations have those unprece curves or increasing/decreasing curves.

PLZ MARK BRAINLIEST!!!

Find the approximate height of the cylinder. Use 3.14 for π.

Volume = 146.952 cm3 A cylinder is shown. The diameter is labeled six centimeters.

Answers

Answer:  The height is 5.2 cm.

Step-by-step explanation:

146.952 = n r^2 h

146.952= 3.14 * 9 *h

146.952= 28.26 h  divide both sides by 28.26

h = 5.2

Find the area of the the regular polygon.

Answers

Answer:

Area of Regular Polygon = ( About ) 332.6 units^2; Option C

Step-by-step explanation:

~ Let us first declare consecutive notes. If we were to draw an altitude in this triangle, it would be perpendicular to the base, by definition. At the same time this shape is a regular polygon, so all sides ( and angles ) are ≅. This would mean that, by Coincidence Theorem, the altitude divides the base into the two ≅ parts. ~

1. If that is so, the altitude would split this base into parts ⇒ ( 16√3 )/2 = 8√3.

2. This would mean that the altitude can be found through Pythagorean Theorem, provided that by definition it forms a 90 degree angle at the base. Let us say x ⇒ the length of the altitude, ( 8√3 )^2 + ( x )^2 = ( 16√3 )^2 ⇒ 192 + x^2 = 768 ⇒ x^2 = 576 ⇒ length of altitude - 24 units

3. With the base 16√3 units, and the the altitude/height 24 units, we can find the area of this regular polygon to be ⇒ 1/2 * base * height ⇒ 1/2 * 16√3 * 24 ⇒ 192√3 units^2

4. That being said that area would be 192 * 1.732050808...... ⇒

Area of Regular Polygon = ( About ) 332.6 units^2

Please Help It is for my hw

Answers

Answer:

step 1: distribute -1

step 2: combine like terms

step 3: subtract 4 on both sides

step 4: divided both sides by -8, so u can isolate M alone

M=-2

Step-by-step explanation:

What are the coordinates of the x-intercept(s) of the graph of y=(x-6)(x+5)

Answers

Answer:

(-5 , 0) and (6 , 0)

Step-by-step explanation:

In order to get the coordinates of the x-intercept(s) of the graph of y=(x-6)(x+5)

we need to solve for x the equation (x-6)(x+5) = 0

(x-6)(x+5) = 0

x - 6 = 0  or  x + 5 = 0

x = 6  or  x = -5

therefore

the coordinates are :

(-5 , 0) and (6 , 0)

__________________________

:)

Solve the triangle if B=78 degrees and a=41. Round to the nearest tenth.

Answers

Answer:

b=197.6cm

Step-by-step explanation:

Given that a = 41 and B =78°

From the diagram of the triangle,

Tan θ = opp/adj

Where θ=78°

Tan78°= b/41

b = tan78×41

b = 4.70× 41

b = 197.5944cm

To the nearest tenth

b=197.6cm

Someone help pleaseeee!!!!!!!!!!!

Answers

Answer:

(-1,2)

Step-by-step explanation:

The solutions to the system is where the lines intersect

The lines intersect at the point  (-1,2)

-1,2 should be right but yeah

The population of a town is growing at a rate of 2.1% per year. Given a starting population of 40,000 people, when will the population double?

Answers

Answer:

48 years

Step-by-step explanation:

Square root of 72x^2 z^3

Answers

The answer would be 6xz sqr2z

A tennis ball is 4 centimeters in diameter. What is the surface area of this ball?

Answers

Answer:

The answer is approximately 50.27cm²

Answer:

Here is the solution of your problem.

Please mark as brainlist!

Bobby catches 8 passes in 3 football games. At this rate how many passes dose he catch in 15 games?expine

Answers

Answer: 40

Step-by-step explanation:

I can see the answer is 40, but let's try to figure out how to do it.

I like to use the rule of 3. Let's put the number of passes on the left side and the number of games on the right side.

[tex]\frac{8}{x}=\frac{3}{15}[/tex]

''x'' represents the number of passes in 15 games.

Solve for x;

[tex]x=\frac{15*8}{3}\\ x=\frac{120}{3}\\ x=40[/tex]

What type of triangles does the Pythagorean Theorem apply to?

Answers

Answer: right angle triangle

Step-by-step explanation:

we only use Pythagorean theorem to find the length of the missing side of a right angle triangle only.

From end zone to end zone, a football field is 120 yards long. How long is the
football field in feet?
1) 360 feet
)) 40 feet
(1) 60 feet
()) 240 feet

Answers

Answer:

120x3 = 360

Step-by-step explanation:

Answer:

360 I GOT IT RIGHT!!!

Step-by-step explanation:

Please help! Correct answers only please!

You pick a card at random. Without putting the first card back, you pick a second card at random.

What is the probability of picking an even number and then picking an even number?

Simplify your answer and write it as a fraction or whole number.

Answers

Answer:

1/6

Step-by-step explanation:

Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!

write each of the following numbers in words 7070 75​

Answers

Answer:

7070- Seven thousand seventy/Seven thousand and seventy

75- Seventy five

Step-by-step explanation:

7070- Seven thousand seventy/Seven thousand and seventy

75- Seventy five

Enter the slope intercept equation of the line shown below

Answers

Answer:

y = -x + 1

Step-by-step explanation:

you know that it must be y = mx + b form so you know that b is the y-intercept and the only time it touches is on positive one so you know it needs a positive one. then to find the slope you need to use the two points that are given. Rise/Run(rise over run) it only goes up one and over -1 so divide and you get -1 for the slope.

hope this helps!

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