In a car dealership, all of the vehicles are either
a sedan or a SUV. If 36 sedans are sold and 36
SUVs are added, there will be an equal number
of sedans and SUVs. If 8 SUVs are sold and 8
sedans are added, there will be twice as many
sedans as SUVs. How many sedans were at the
dealership before any vehicle was sold?

Answers

Answer 1

Answer:

The number of sedans before any vehicle was sold is 168

Step-by-step explanation:

Let's define the variables:

x = number of sedans

y = number of SUVs

We know that:

"If 36 sedans are sold and 36  SUVs are added, there will be an equal number  of sedans and SUVs"

If 36 sedans are sold, the new number of sedans is:

x - 36

if 36 SUVs are added, the new number of SUVs is

y + 36

And these numbers are equal, then:

x - 36 = y + 36

We also know that:

" If 8 SUVs are sold and 8  sedans are added, there will be twice as many

sedans as SUVs. "

If 8 SUVs are sold, the new number of SUVs will be:

y - 8

If 8 sedans are added, the new number of sedans wil be:

x + 8

From this we can write the equation:

(x + 8) = 2*(y - 8)

x + 8 = 2*y - 16

Then we have two equations:

x - 36 = y + 36

x + 8 = 2*y - 16

We want to find the number of sedans, x, then we need to isolate the other variable in one of the equations, let's isolate y in the first one:

Let's isolate x in the first one:

x - 36 - 36 = y

x - 72 = y

Now we can replace it in the other equation:

x + 8 = 2*y - 16

x + 8 = 2*(x - 72) - 16

Now we can solve this for x.

x + 8 = 2*x - 144 - 16

8 + 144 + 16 = 2x - x

168  = x

The number of sedans before any vehicle was sold is 168


Related Questions

The probability that Dan buys a sandwich is 0.2.
The probability that Dan gets the bus is 0.9.
Assuming the events are independent, what is the probability that Dan buys a sandwich
and gets the bus?

Answers

Answer:

0.18

Step-by-step explanation:

Find the probability that both independent events occur by multiplying the individual probabilities by each other:

0.2(0.9)

= 0.18

So, the probability is 0.18

A number cube is rolled 14 times and the results are recorded in the table.

What, in simplest form, is the experimental probability that the number cube shows 4?
A. 0
B. 1/6
C. 2/7
D. 5/14

Answers

Answer:

b

Step-by-step explanation:

The experimental probability that the number cube shows 4 is 2/7.

What is an experimental probability?

Experimental probability is a probability that is determined on the basis of a series of experiments.

Given that, a number cube is rolled 14 times, we need to determine the experimental probability that the number cube shows 4,

The formula to calculate the experimental probability is:

P(E) = Number of times an event occurs/Total number of times the experiment is conducted

P(E) = 4/14 = 2/7

Hence, the experimental probability that the number cube shows 4 is 2/7.

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how to find range from a distribution table.​

Answers

Answer:

Range = highest value - lowest value

Explanation:

This is the required formula to find range from a distribution table.

Madam Chong's mass is 72 kg. After participating in a fitness programme, her mass decreases at a rate of 3 kg per month. Find the minimum number of months that Madam Chong has to participate in the programme so that her mass becomes less than 52 kg. (Give your answer to the nearest whole number.)​

Answers

decrease 3kg per month
let x be the months that MC has to participate
72 - 3x < 52
-3x < -20
x > 20/3
about 7 months, i guess hth

Help pleas like please ASAP

Answers

Answer:

(x+9)(x+5)

Step-by-step explanation:

find 2 numbers that add to 14 and multiply to 45

X+9 x+5 hope that helped

Which of the following is the correct factorization of the polynomial below?
x3 + 10x2 + 25x
A. x(x + 5)(x - 5)
B. (x2 + 2x - 5)(x-10)
C. (x2 + 5x - 2)(x-10)
D. x(x + 5)2

Answers

Answer:

x(x+5)^2

Step-by-step explanation:

x^3 + 10x^2 + 25x

Factor out x

x(x^2+10x+25)

What 2 numbers multiply to 25 and add to 10

5*5 = 25

5+5 =10

x(x+5)(x+5)

x(x+5)^2

Answer:

D

Step-by-step explanation:

Given

x³ + 10x² + 25x ← factor out x from each term

= x(x² + 10x + 25) ← perfect square

= x(x + 5)²

Solve the equation 2sin x cos x = cos x, for 0° < x≤ 90°​

Answers

Answer:

2sinx.Cosx=cosx

2sin90°.cos90°=cos90°

2×1.0=0

0=0

A chef got 7 bags of onions. The red onions came in bags of 8 and the yellow onions came in bags of 3. If the chef got a total of 41 onions, how many bags of each type of onion did he get?

Answers

Answer:

[tex]\#\text{ of 8-onion bags: }4,\\\#\text{ of 3-onion bags: }3[/tex]

Step-by-step explanation:

Let [tex]a[/tex] be the number of bags with 8 onions and let [tex]b[/tex] be the number of bags with 3 onions. We have the following system of equations:

[tex]\begin{cases}a+b=7,\\8a+3b=41\end{cases}[/tex]

Subtracting [tex]b[/tex] from both sides of the first equation, we get [tex]a=7-b[/tex]. Substitute this into the second equation:

[tex]8(7-b)+3b=41,\\56-8b+3b=41,\\56-5b=41,\\-5b=-15,\\b=\boxed{3}[/tex]

Therefore, the number of 8-onion bags is:

[tex]a=7-b,\\a=7-3,\\a=\boxed{4}[/tex]

Thus, the chef got 4 8-onion bags and 3 3-onion bags.

ASAP PLEASE HELPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEE

Answers

Answer:

-2/5 is the answer

I hope this will help you

Answer:

-2/5

Step-by-step explanation:

Just add the top numerator together -4 + 2 = -2

Linear equation: -1
2
(6x + 10) = 13

Step 1: –3x – 5 = 13

Step 2: –3x = 18

Step 3: x = –6

Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?

Answers

Answer:

see below

Step-by-step explanation:

-1/2 * (6x + 10) = 13

Distribute -1/2

–3x – 5 = 13

Add 5 to each side

-3x-5+5 = 13+5

–3x = 18

Divide each side by -3

-3x/-3 = 18/-3

x = -6

Suppose the line y = 2.8333x - 22.4967 describes the relation between the​ club-head speed​ (in miles per​ hour), x and the distance a golf ball travels​ (in yards), y.

(a) Predict the distance a golf ball will travel if the club-head speed is 100 mph.

(b) Suppose the observed distance a golf ball traveled when the club-head speed was 100 mph was 265 yards. What is the residual?

(c) The golf ball will travel 260.8 yards. (Round to the nearest tenth as needed.)

(d) The residual is:_________ (Round to the nearest tenth as needed.)

Answers

Answer:

c) The golf ball will travel 260.8 yards.

d) Hence the residual is 4.2 yards.

Step-by-step explanation:

c) y' = 2.8333x - 22.4967

Now the golf ball will travel [tex]= 2.8333\times100 - 22.4967[/tex]= 260.8 yards

here y'= 260.8 yards.

d) The residual is : y - y' = 265 - 260.8 = 4.2 yards.

Answer:

a)  [tex]y=260.8333~yd[/tex]

b) [tex]\Delta d=4.1667~yd[/tex]

c) [tex]y=260~yd[/tex]

d) [tex]\Delta y'=0.8333~yd[/tex]

Step-by-step explanation:

Given:

equation of line, [tex]y=2.8333x-22.4967[/tex]

x = club-head speed​ (in miles per​ hour)

y = the distance a golf ball travels​ (in yards)

a)

x = 100 mph

Then the distance travelled by the ball:

(put the given value of x in the above eq.)

[tex]y=2.8333\times 100-22.4967[/tex]

[tex]y=260.8333~yd[/tex]

b)

If the observed distance in the above case comes out to be 265 yards then the residual value will be:

[tex]\Delta d=265-260.8333[/tex]

[tex]\Delta d=4.1667~yd[/tex]

c)

From the calculated value when rounding it to the nearest tenth:

[tex]y=260~yd[/tex]

d)

The residual on rounding the calculated value to the nearest tenth:

[tex]\Delta y'=260.8333-260[/tex]

[tex]\Delta y'=0.8333~yd[/tex]

i know it’s kinda all hard to see. i have many more questions like this and i can’t do graphs to save my life.. pls help !!

Answers

Answer: D

Step-by-step explanation:

-3 , 1 , 5 , 9 , 13
find the 11th term of this sequence
show your working​

Answers

Answer:

a₁₁ = 37

Step-by-step explanation:

There is a common difference between consecutive terms, that is

1 - (- 3) = 5 - 1 = 9 - 5 = 13 - 9 = 4

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3 and d = 4 , then

a₁₁ = - 3 + (10 × 4) = - 3 + 40 = 37

As displayed on a production possibilities curve, what will an increase in technology allow a society to do? a. Produce more, as long as the resources are also available. c. It will not affect society’s production. b. Produce less, because more resources are spent on developing technology. d. The society will spend more on the same level of production. Please select the best answer from the choices provided A

Answers

Answer:

a. Produce more, as long as the resources are also available

Step-by-step explanation:

from brainly itself

scouteo

Ace

The correct answer is A) produce more, as long as the resources are also available.

As displayed on a production possibilities curve, an increase in technology will allow a society to produce more, as long as the resources are also available.

A production possibilities graph is a valid representation of the available ways an economy is able to use the resources. In this case, an increase in technology will allow a society to produce more, as long as the resources are also available means that as long there are enough resources in the market, technology in a country helps with the production of more things to be consumed or traded.  

please help me out (geometry)

Answers

Answer:

x = 15

Step-by-step explanation:

2x+10+4x+80=180

or, 2x+4x=180-80-10

or, 6x=90

or, x=15

Answered by GAUTHMATH

Ecuación de la hipérbola con centro en (0;0), focos en abrir paréntesis 0 coma espacio menos raíz cuadrada de 28 cerrar paréntesis espacio y espacio abrir paréntesis 0 coma espacio raíz cuadrada de 28 cerrar paréntesis espacio ,eje conjugado = 2 raíz cuadrada de 3

Answers

Answer:

[tex]\frac{y^{2}}{25}-\frac{x^{2}}{3}=1[/tex]

Step-by-step explanation:

Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:

centro: (0,0)

focos: [tex](0,-\sqrt{28}),(0,\sqrt{28})[/tex]

eje conjugado = [tex]2\sqrt{3}[/tex]

por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:

[tex]\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1[/tex]

de los focos podemos obtener que:

[tex]c=\sqrt{28}[/tex]

y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:

[tex]b=\sqrt{3}[/tex]

podemos utilizar la siguiente fórmula para obtener a:

[tex]c^{2}-a^{2}=b^{2}[/tex]

si despejamos a en la ecuación obtenemos lo siguiente:

[tex]a=\sqrt{c^{2}-b^{2}}[/tex]

ahora podemos sustituir los valores:

[tex]a=\sqrt{(\sqrt{28})^{2}-(\sqrt{3})^{2}}[/tex]

[tex]a=\sqrt{28-3}[/tex]

[tex]a=\sqrt{25}[/tex]

a=5

así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:

[tex]\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1[/tex]

[tex]\frac{y^{2}}{(5)^{2}}+\frac{x^{2}}{(\sqrt{3})^{2}}=1[/tex]

[tex]\frac{y^{2}}{25}+\frac{x^{2}}{3}=1[/tex]

si graficamos la hipérbola, queda como en el documento adjunto.

Brooke and Lamont ran a half marathon Brooke finished in 1 hour 50 minutes Lamont finished in 100 minutes who had the faster time​

Answers

Answer:

Brooke = 1 hr 50 min

Lamont = 100 min = 1 hr 40 min

Because 60 min = 1 hr

Lamont was faster

Hope this helped

What is the value of c in the interval (5,8) guaranteed by Rolle's Theorem for the function g(x)=−7x3+91x2−280x−9? Note that g(5)=g(8)=−9. (Do not include "c=" in your answer.)

Answers

Answer:

[tex]\displaystyle c = \frac{20}{3}[/tex]

Step-by-step explanation:

According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one c within (a, b) such that f'(c) = 0.

We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a c in (5, 8) such that g'(c) = 0.

So, differentiate the function. We can take the derivative of both sides with respect to x:

[tex]\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right][/tex]

Differentiate:

[tex]g'(x) = -21x^2+182x-280[/tex]

Let g'(x) = 0:

[tex]0 = -21x^2+182x-280[/tex]

Solve for x. First, divide everything by negative seven:

[tex]0=3x^2-26x+40[/tex]

Factor:

[tex]0=(x-2)(3x-20)[/tex]

Zero Product Property:

[tex]x-2=0 \text{ or } 3x-20=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle x=2 \text{ or } x = \frac{20}{3}[/tex]

Since the first solution is not within our interval, we can ignore it.

Therefore:

[tex]\displaystyle c = \frac{20}{3}[/tex]

Resuelve el siguiente problema un buzo en una laguna decendio 8m en una hora.Si cada hora bojo la misma cantidad de metros, ¿cuantos metros bojo en 4 horas

Answers

Answer:

X = 32 meters.

Step-by-step explanation:

Let the unknown distance be X.

Given the following data;

Distance = 8 meters per hourTime = 4 hours

To find how many meters he would cover in four hours;

1 hour = 8 meters

4 hours = X meters

Cross-multiplying, we have;

X = 8 * 4

X = 32 meters.

In a city of 26,000 population 5000 read English news paper, 12000 read Nepali La News paper and 1000 read both of these. What percent read neither English nor Ne newspaper. ​

Answers

Answer:

38.46%

Step-by-step explanation:

We are given;

Total population; n(S) = 26000

Number that read English news paper; n(E) = 5000

Number of people that read nepali; n(N) = 12000

Number that read both English and nepali; n(E n N) = 1000

Thus from probability laws, number that read either English or nepali is;

n(E u N) = n(N) + n(E) - n(N n E)

n(E u N) = 12000 + 5000 - 1000 = 16000

Thus;

number that read neither English nor nepali is;

n(E' u N') = n(S) - n(E u N)

n(E' u N') = 26000 - 16000 = 10000

Thus, the percentage is;

10000/26000 × 100% = 38.46%

Which situation does the graph illustrate?

Answers

Answer:

eju 48, 23w6yuw43wdgn

Step-by-step explanation:

The range of cells in column D and rows 1 to 10 is represented as:

1:10 D1:D10 D:D

Answers

Answer:

how?

Step-by-step explanation:

I didnt get question

One of the legs of a right triangle measures 9 cm and its hypotenuse measures 16 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answers

Answer:

13.2 cm

Step-by-step explanation:

using the Pythagorean theorem, we can find the length of the other leg, since this is a right triangle. The equation is a^2 + b^2 = c^2, A and B being the legs and C being the hypotenuse. Since we are finding the other leg, we can switch the equation around to find A/B instead. (A/B being the legs). so we get: B^2 = C^2 - A^2 ; then we simplify [tex]b=\sqrt{c^2-a^2}[/tex]

We plug in the numbers given:

[tex]b = \sqrt{16^2-9^2}\\b=\sqrt{256-81}\\b=\sqrt{175} \\b= 13.229[/tex]

rounded to nearest tenth: 13.2

The measure of the other leg in the right triangle is 13.22 cm.

What is a right triangle?

A triangle with one angle measuring 90° is called a right triangle.

Given that, a right triangle has a leg measuring 9 cm and its hypotenuse is 16 cm longs, we need to find the other side,

So, using the Pythagoras theorem,

16² = 9² + x²

x = √256-81

x = √175

x = 13.22

Hence, the measure of the other leg in the right triangle is 13.22 cm.

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What is the value of X?​

Answers

Answer:

x=2

Step-by-step explanation:

A line that intersects a circle in two points is called a secant line, and this is the case for both line DE and AE.

For two secant lines that intersect outside of the circle, such as the ones here, we can say that

CE * DE = BE * AE

Therefore, we need to then define these lines.

CE is x+4, BE is x+1, AE = (BE + AB) = 11+x+1 = 12+x, and DE = (CE + DC) = 1+x+4 = 5+x

We then have

(x+4) * (5+x) = (x+1) * (12+x)

expand

5x + x² + 20 + 4x = 12x+x²+12+x

x²+9x + 20 = x²+13x+12

Next, we want to congregate all values to one side so we can solve for x. This can be done by subtracting both sides by (x²+13x+12) to get

-4x + 8 = 0

subtract 8 from both sides to isolate the x and its coefficient

-4x = -8

divide both sides by -4 to isolate the x

x = 2

Answer: A

Explanation: I just took a test on it

Edwin hiked to a famous point with a beautiful view. It took 2 hours and 55 minutes to hike to the viewpoint and 25 minutes to hike back. Edwin spent 25 minutes enjoying the view at the top. He finished the hike at 11:45 A.M. What time did Edwin start the hike to the viewpoint?

Answers

Answer:

= 8:00 A.M.

Step-by-step explanation:

▪You first find the total time taken which will be :

2 hrs 55 min + 25 min

= 3 hrs 20 min + 25 min

= 3 hrs 45min

▪ Beginning time = Arrival time - Time taken

= 11:45 - 3:45

= 8:00 am

¿

Find the value of x rounded to the nearest tenth.

Answers

Answer:

The answer to the equation is C

please help me divide this fractions, showboat work.
O_O​

Answers

solution given;

36:5/5

38:86/69

To divide fractions, you basically just multiply the first fraction by the reciprocal of the second. To find the reciprocal, you just flip the numerator and the denominator.

For number 36, you have 2/3÷8/15. To solve this, you just multiply 2/3 by 15/8.

2/3×15/8 is 30/24, which is 5/4 or 1 1/4.

To answer the second problem, you have to convert the mixed numbers to improper fractions.

7 1/6 as an improper fraction is 43/6. 5 3/4 as an improper fraction is 23/4.

Do the same procedure; 43/6×4/23 is 86/69 or 1 17/69.

On a pie chart, a category representing 20% of the whole should correspond to a central angle of 20°.

Answers

Answer:

No! 20% does not correspond to a central angle 20°.

Step-by-step explanation:

The central angle for pie chart is 360°.

So, a category represents 20% is 20%(360) for central angle.

Let's simplify it to get the angle,

[tex]\frac{20}{100} * 360[/tex]

Simplify it,

72°

So, 20% does not correspond to a central angle 20°.

An animal shelter takes in an average of 5 animals per day. The shelter must keep its total occupancy below 300. Currently, the shelter has 165 animals. If none of the animals get adopted, which inequality represents how many more days, x, the shelter can continue to take in animals without exceeding its occupancy limit?

Answers

Answer:

5x less than 300  - 165

Step-by-step explanation:

It will take 27 days to take in animals without exceeding its occupy limit.

What is algebraic expression ?

An expression which is made up of variables and constants , along with algebraic operation (addition , subtraction etc ) is called Algebraic expression.

According to the question :

165 + (x) 5 = 300

5x = 135

x = 27

Hence , it will take 27 days to occupy the limit

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Which function is represented by the graph

Answers

Answer: A

Screenshot of calculator

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