6 times a number is 27 less than the square of that number. Find the
positive solution.


Answers

Answer 1

Answer:

x = 9

Step-by-step explanation:

To solve these problems, you first set up an equation representing the information given.

6x = x² - 27

This turns into a quadratic equation which you need to factor out.

0 = x² - 6x - 27

You want to choose two numbers that multiply to -27, and add up to -6

0 = (x - 9)(x + 3)

If you're unfamiliar with factoring, you take the opposite sign of the number in the parentheses because it's a shortcut when setting it equal to 0.

x = 9, -3

Since it asks for the positive solution only, the answer is x = 9.

I hope this helps!


Related Questions

The 1st graders at City Elementary were asked whether they like dogs or cats best. The results are shown in the table. Relative Frequency Table by Row What conclusion can you draw about the relative frequency of the results?
A) A girl in this group is most likely to prefer cats.
B) A boy in this group is most likely to prefer cats.
C) A boy in this group is most likely to prefer dogs.
D) There is no association between the variables.

Answer: A girl in this group is most likely to prefer dogs

Answers

Answer:

I'm thinking the ANS is letter B

I feel like it’s letter b

Using the graph
Order the lines from the steepest slope to the least steel slope

Answers

Answer:

The steepest slope is that of the line that is closest to being vertical.

Step-by-step explanation:

Hope this helps!!!!

Answer:

B, A, C, D

Step-by-step explanation:

rise over run

slope: the ratio of the change in the dependent values (outputs) to the change in the independent values (inputs) between two points on a line

Aaron is 5 years younger than
Roy. Four years later, Roy will be
twice as old as Aaron. Find their
present ages

Answers

Answer:

Roy is 6 years old and Aaron is 1 year old.

Step-by-step explanation:

A is Aaron's age,

R is roy's age,

A = R - 5

R + 4 = 2(A+4)

We can distribute first,

R + 4 = 2A + 8

Subtract 4 from each side,

R = 2A + 4

Since A = R - 5, you can substitute in R - 5 for A in the equation,

R = 2(R-5) + 4

Distribute,

R = 2R - 10 + 4

Since - 10 + 4 = -6, we can do this,

R = 2R - 6

Subtract R from both sides,

0 = R - 6

Add 6 to both sides and you have part of your answer;

R = 6

Since A = R - 5,

A = 6 - 5

A = 1, so Aaron's age is 1.

Consider the function represented by the table. What is f(0)?

Answers

Answer:

The table isn't shown, but f(0) will be found when you put zero in for x.

El caño de una fuente está inclinado 60° sobre la horizontal. Si el agua sale del caño con una velocidad inicial de 10 m/s: a) ¿Qué dibujo forma el chorro de agua? B) ¿Qué altura máxima alcanza el agua? C) ¿A qué distancia del caño hay que colocar el sumidero? D) ¿Cuál es el módulo de la velocidad del agua cuando esta cae al sumidero

Answers

Answer:

A) Parabola; B) 3.83 m; C) 8.84 m; D) 10 m/s

Step-by-step explanation:

A) Shape of water jet

The water jet has the shape of a parabola.

B) Maximum height

Data:

θ = 60°

u = 10 m/s

a = 9.8 m·s⁻²

Calculations:

1. Calculate the horizontal and vertical components of the velocity

[tex]u_{\text{h}} = u \cos \theta = \text{10 m/s} \times \cos 60 ^{\circ} = \text{10 m/s} \times 0.5 = \text{5 m/s}\\u_{\text{v}} = u \sin \theta = \text{10 m/s} \times \sin 60 ^{\circ} = \text{10 m/s} \times 0.866 = \text{8.66 m/s}[/tex]

2. Maximum height

[tex]H = \dfrac{(u_{\text{v}})^{2}}{2a} = \dfrac{8.66^{2}}{2\times 9.8} =\textbf{3.83 m}[/tex]

C) Range

1. Calculate the time of flight

Use the vertical component of velocity to calculate the time to the maximum height of the stream.

[tex]u_{\text{v}} = at\\t = \dfrac{ u_{\text{v}}}{a} = \dfrac{\text{8.66 m$\cdot$s}^{-1}}{\text{9.8 m$\cdot$s}^{-2}}= \text{0.884 s}[/tex]

It will take the same time to reach the ground.

Thus,

Time of flight = 2t = 2 × 0.884 s  = 1.77 s

2. Calculate the horizontal distance

s = vt = 5 m·s⁻¹ × 1.77 s = 8.84 m  

You should place the drain 8.84 m from the pipe.}

D) Modulus of velocity

The stream of water will hit the drain with the same velocity as when it left the pipe.

Thus, the modulus of the velocity is 10 m/s.

The graph below shows the trajectory of the water stream.

Which expression is equivalent to 6x2 – 19x – 55?
(2x – 11)(3x + 5)
(2x + 11)(3x - 5)
(6x – 11)(x + 5)
(6x + 11)(x - 5)

Answers

So the right answer is of option D.

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

(6x + 11)(x – 5)

Step-by-step explanation:

It's D on edg

Brandon wants to buy a shirt that originally costs $P. He recieved a 15% discount on the original cost, so he paid a discounted price of $R. This can be represented by the following equation.



How is the discounted price, $R, related to the original cost, $P?
A.
R is 15% of the original cost.
B.
R is 0.85% of the original cost.
C.
R is 0.15% of the original cost.
D.
R is 85% of the original cost.

Answers

loading...
loading...

Answer:

D

Step-by-step explanation:

Original price minus 15%  was the cost so he paid the other 85%  

A line that includes the points (8,0) and (9,s) has a slope of 9. What is the value of s?

Answers

Answer:

s = 9

Step-by-step explanation:

We can find the slope given two points

m = (y2-y1)/(x2-x1)

 9 = (s-0)/(9-8)

 9 = (s)/1

S = 9

This strip is 12 cm long Find the length of 25% of the strip

Answers

Answer:

If the strip is 12cm and it is asking for 25% of it, you can divide 12 by 4, as 25 is 1/4 of 100.

The answer will be 3cm

Answer:

3

Step-by-step explanation:

Twenty five percent of the 12 cm strip means 25÷ 100 = 0.25 .

so 0.25 x 12 = 3.

1) Uma sala tem o formato de um trapézio, determine a área dessa sala.(a) 10,4 m² (b) 25,6 m² (c) 12,8 m² (d) 15,2 m²

Answers

Answer:

A opção correta é;

c) 12,8 m²

Step-by-step explanation:

A área de um trapézio = 1/2 × (distância perpendicular entre os lados paralelos) × (soma dos comprimentos dos lados paralelos)

No diagrama da pergunta, os comprimentos dos lados paralelos são;

3,8 me 2,6 m

A distância perpendicular entre os lados paralelos = 4 m

∴ área do trapézio = 1/2 (3,8 + 2,6) × 4 = 12,8 m²

Portanto, a área da sala = 12,8 m².

Solve the inequality. Graph the solution. −6n>54 The solution of the inequality is .

Answers

Answer:

n =-9

Step-by-step explanation:

-6n>54

Divided by negative 6

n=we change the Sign

n=-9

the difference between 9 fifty-sixes and 3 fifty-sixes.

Answers

Nine fifty sixes is more then three fifty sixes

Javier and Serah are both travelling by train. Javier's train travels 130 km in 75 minutes. Serah's train travels 377 km. It leaves at 9:35 and arrives at 12:50. Work out the difference, in km/h, between the average speed of their trains.

Answers

Answer:

The difference between the average speed is 12 kilometers per hour, where Serah's train has the greatest speed.

Step-by-step explanation:

Givens

Javier's train travels 130 km in 75 minutes.Serah's train travels 377 km from 9:35 to 12:50.

The average speed is defined as

[tex]s=\frac{d}{t}[/tex]

To finde Javier's speed, we need to transform 75 minutes into hours, we know that 1 hour is equivalent to 60 minutes.

[tex]h=75min \times \frac{1hr}{60min} =1.25 \ hr[/tex]

Now, we find the average speed

[tex]s_{Javier}=\frac{130km}{1.25hr}=104 \ km/hr[/tex]

Therefore, Javier's train travels 104 kilometers per hour.

On the other hand, Serah's traing travels from 9:35 to 12:50, which is equivalent to 3 hours and 15 minutes, but 15 minutes is equivalent to 0.25, so the total time is 3.25 hours, so the average speed is

[tex]s_{Serah}=\frac{377km}{3.25hr}= 116 \ km/hr[/tex]

So, the difference would be

[tex]116-104=12 \ km/hr[/tex]

Therefore, the difference between the average speed is 12 kilometers per hour, where Serah's train has the greatest speed.

Answer:

12 km/h

Step-by-step explanation:

Only do question 4

50 points

Topic: Percentage

Answers

Answer:

a 1

b 6

c 15

Step-by-step explanation:

101% 101/100 = 1 1/100

is 1  complete 100 grid and 1/100 of another grid so you will need 2 grids

589% 589/100 = 5 89/100

is 5 complete 100 grids and 89/100 of another grid so you will need 6 grids

1450% 1450/100 = 14 50/100

is 14 complete grids and 50/100 of another grid so you will need 15 grids

Generally, how long are budgets are created for?

Answers

Answer:

In the general scenario, the duration of capital expenditures spans one year, sometimes spannering two or three fiscal years. Companies utilise various approaches to measure their capital expenditures than their normal budgeting processes.

Step-by-step explanation:

The answer is above

Hope this helps.

Answer: One Year

Step-by-step explanation:   A budget is a list of probable EXPENSES and expected INCOME during a given period, most often one year.

Angles A and B together create a 90° angle. ∠A = 4x −10 and ∠B = 2x − 20. Find the angle measures (what will

Answers

Answer:

see below

Step-by-step explanation:

A+ B = 90

4x-10 + 2x-10 = 90

Combine like terms

6x -20 = 90

Add 20 to each side

6x -20+20 = 90+20

6x = 110

Divide by 6

6x/6 = 110/6

x = 55/3

A = 4x-10  = 4(55/3)  -10

A=63 1/3

B = 2x-10 = 2(55/3) -10  

     26 2/3

Approximate the square root to the nearest integer.
37

Answers

6.083 would be the answer

Answer:

We know that 6² = 36 , which is very close to 37 . Thus square root of 37 will be very close to 6

The spinner to the right is spun 20 times. It lands on red 6 times, yellow 2 times, green 8 times, and blue 4 times.

Based on the data, what is the experimental probability of landing on yellow?

You may give your answer as a simplified fraction, decimal, or percent.

Answers

Answer:

0.1

Step-by-step explanation:

Given: The spinner lands on red 6 times, yellow 2 times, green 8 times, and blue 4 times. when it is spun 20 times.

To find: experimental probability of landing on yellow

Solution:

Probability refers to chances of occurring of some event.

Probability = number of favourable outcomes total number of outcomes

As the spinner lands on yellow 2 times,

number of favourable outcomes = 2

Total number of outcomes = 20

Probability = 2/20 = 1/10 =0.1

What is 1/7 * -1/2 please help

Answers

Answer: If you are asking what (1/7) x -(1/2)

Than the answer is -0.07

Step-by-step explanation:

Answer:

-0.07142857142

Step-by-step explanation:

Guys I really need help I will make u BRANLIEST!!!

Answers

Answer:

h=12 in

Step-by-step explanation:

volume of cube=1/3πr²h

113.04=1/3×3.14×3²×h

h=113.04/(3.14×3)=37.68/3.14=12 in.

Answer:

12 in

Step-by-step explanation:

It's right

A coordinate grid with 2 lines. The first line is labeled y equals 0.5 x plus 3.5 and passes through (negative 3, 1), (negative 2.7, 2.1), and (0, 3.5). The second line is labeled y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction and passes through the points (negative 4, 3), (negative 2.7, 2.1), and (StartFraction 1 over 3 EndFraction, 0). Which is the approximate solution to the system y = 0.5x + 3.5 and y = −A system of equations. y equals 0.5 x plus 3.5. y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction.x + shown on the graph? (–2.7, 2.1) (–2.1, 2.7) (2.1, 2.7) (2.7, 2.1)

Answers

Answer:

2.1 2.7

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

edge test ;)

Mila reads at a rate of 3 paragraphs per minute.
After reading for 4 minutes, she had read a total of 12 paragraphs.
This situation can be represented with a linear equation written in point-slope form,
where x represents the number of minutes and y represents the number of
paragraphs
Use this information to complete each statement about the linear equation.
CL
The slope of the linear equation is

Answers

Y=3x because that slope is 3 and if you times it by 4 you get 12

Answer:

Y=3x because that slope is 3 and if you times it by 4 you get 12

Step-by-step explanation:

HELP HELP HELP HELP
show the steps too. I'll give BRAINLIEST!​

Answers

Move constant to the right-hand side and change its sign

2x^2 + 8 = -2 + 7
-2 + 7 = 5

Divide both sides of the equation by

x^2 + 4x = 5/2

Add (4/2^2) to both sides of the equation

x^2 + 4x + (4/2)^2 = 5/2 + (4/2)^2

factor the expression

(x + 4/2)^2 = 13/2

reduce the fraction by 2

(x + 2)^2 = 13/2

now solve equation for x




During a basketball game, Jeremy scored triple the number of points as Donovan. Kolby scored double the number of points as Donovan. So, if the three boys scored 36 points, how many points did Jeremy score? And how many points did Donovan score?

Answers

Answer: Jeremy score 18 points; Donovan score 6 points.

Step-by-step explanation:

Let Jeremy's points be a

Let Donovan's point be b

Let Kolby point be c

Jeremy scored triple the number of points as Donovan. This is:

a = 3b

Kolby scored double the number of points as Donovan. This will be:

c = 2b

The the three boys scored 36 points. This will be:

a + b + c = 36

Since a = 3b and c = 2b

Plug the equations for a and c into the equation. This will be:

a + b + c = 36

3b + b + 2b = 36

6b = 36

b = 36/6

b = 6

Donovan has 6 points

Jeremy will have:

a = 3b

a = 3 × 6

a = 18

Jeremy has 18 points.

Kolby will have:

c = 2b

c = 2 × 6

c = 12

Kolby will have 12 points.

Kareem is participating in a 5-day cross-country biking challenge. He biked for 67, 62, 59, and 47 miles on the first four days. How many miles does he need to bike on the last day so that his average (mean) is 60 miles per day? miles

Answers

Answer:65miles

Step-by-step explanation:

Let the needed miles be x

(67+62+59+47+x)/5=60

235+x=60×5

235+x=300

x=300-235

x=65miles

a right triangle is shown, m

Answers

Answer:

WHAT

Step-by-step explanation:

Answer: 7[tex]\sqrt{2}[/tex]

Step-by-step explanation: Khan Academy

Factor the polynomial: 2x2(x - 5) - 3(x - 5)
O A. (x - 5)(2x2 - 3)
B. (x - 5)(2x - 3)
O c. 2x2(x - 5)
O D. (x - 5)(2x + 3)

Answers

Answer:

A

Step-by-step explanation:

[tex]2x^2(x-5)-3(x-5)=\\2x^3-10x^2-3x+15=\\(x-5)(2x^2-3)[/tex]

Therefore, the correct answer is choice A. Hope this helps!

The factor of the polynomial is (x - 5)(2x² - 3).

Option A is the correct answer.

What is a polynomial?

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

We can factor the polynomial 2x² (x - 5) - 3(x - 5) by first factoring out the common factor of (x - 5).

This gives:

2x² (x - 5) - 3(x - 5)

= (x - 5)(2x^2 - 3)

Thus,

The factor of the polynomial is (x - 5)(2x² - 3).

Learn more about polynomials here:

https://brainly.com/question/2284746

#SPJ7

At an electric store, a heater costs } more than a food mixer.
A blender costs $27. If the total cost of the three items is $139,
what is the cost of the blender as percent of the cost of the
food-mixer?
%

Answers

Answer:

19%

Step-by-step explanation:

27/139 is equal to .194 and rounding down gives us .19 or 19%.

which quadrilateral always has four sides of the same length

Answers

Answer:

Either a square or a rhombus.

Step-by-step explanation:

A square always has four equal sides with an additional four 90 degree angles.

A rhombus always has four equal sides, but that is it.

Choose your pick on which shape you want to be your answer.

Answer:

a square and a rhombus

Step-by-step explanation:

i have the same question

Solve the inequality d/7 > 15. Then graph the solution.

Answers

Answer:

yes answer question?

Step-by-step explanation:

Answer:dE (105,infinity)

Step-by-step explanation:

"Find a number which, when added to 3, yields 7"

may be written as:

3 + ? = 7, 3 + n = 7, 3 + x = 1

and so on, where the symbols ?, n, and x represent the number we want to find. We call such shorthand versions of stated problems equations, or symbolic sentences. Equations such as x + 3 = 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in the equation x + 3 = 7, the left-hand member is x + 3 and the right-hand member is 7.

EQUIVALENT EQUATIONS

Equivalent equations are equations that have identical solutions. Thus,

3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5

are equivalent equations, because 5 is the only solution of each of them. Notice in the equation 3x + 3 = x + 13, the solution 5 is not evident by inspection but in the equation x = 5, the solution 5 is evident by inspection. In solving any equation, we transform a given equation whose solution may not be obvious to an equivalent equation whose solution is easily noted.

The following property, sometimes called the addition-subtraction property, is one way that we can generate equivalent equations.

If the same quantity is added to or subtracted from both members of an equation, the resulting equation is equivalent to the original equation.

In symbols,

a - b, a + c = b + c, and a - c = b - c

are equivalent equations.

Example 1 Write an equation equivalent to

x + 3 = 7

by subtracting 3 from each member.

Solution Subtracting 3 from each member yields

x + 3 - 3 = 7 - 3

or

x = 4

Notice that x + 3 = 7 and x = 4 are equivalent equations since the solution is the same for both, namely 4. The next example shows how we can generate equivalent equations by first simplifying one or both members of an equation.

Example 2 Write an equation equivalent to

4x- 2-3x = 4 + 6

by combining like terms and then by adding 2 to each member.

Combining like terms yields

x - 2 = 10

Adding 2 to each member yields

x-2+2 =10+2

x = 12

To solve an equation, we use the addition-subtraction property to transform a given equation to an equivalent equation of the form x = a, from which we can find the solution by inspection.

Example 3 Solve 2x + 1 = x - 2.

We want to obtain an equivalent equation in which all terms containing x are in one member and all terms not containing x are in the other. If we first add -1 to (or subtract 1 from) each member, we get

2x + 1- 1 = x - 2- 1

2x = x - 3

If we now add -x to (or subtract x from) each member, we get

2x-x = x - 3 - x

x = -3

where the solution -3 is obvious.

The solution of the original equation is the number -3; however, the answer is often displayed in the form of the equation x = -3.

Since each equation obtained in the process is equivalent to the original equation, -3 is also a solution of 2x + 1 = x - 2. In the above example, we can check the solution by substituting - 3 for x in the original equation

2(-3) + 1 = (-3) - 2

-5 = -5

The symmetric property of equality is also helpful in the solution of equations. This property states

If a = b then b = a

This enables us to interchange the members of an equation whenever we please without having to be concerned with any changes of sign. Thus,

If 4 = x + 2 then x + 2 = 4

If x + 3 = 2x - 5 then 2x - 5 = x + 3

If d = rt then rt = d

There may be several different ways to apply the addition property above. Sometimes one method is better than another, and in some cases, the symmetric property of equality is also helpful.

Example 4 Solve 2x = 3x - 9. (1)

Solution If we first add -3x to each member, we get

2x - 3x = 3x - 9 - 3x

-x = -9

where the variable has a negative coefficient. Although we can see by inspection that the solution is 9, because -(9) = -9, we can avoid the negative coefficient by adding -2x and +9 to each member of Equation (1). In this case, we get

2x-2x + 9 = 3x- 9-2x+ 9

9 = x

from which the solution 9 is obvious. If we wish, we can write the last equation as x = 9 by the symmetric property of equality.

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