Four times the square of a certain number increased by 6 times the number equals 108. Find the number

Answers

Answer 1
-6 and 4.5
So to do this you’ll make an equation x will represent the number so 4x^2+6x=108 so we want the equation to equal 0 so we can solve it to do that you have to subtract 108 from both sides so it ends up being 4x^2+6x-108=0 we want to isolate the x onto one side and division property allows us to divide both sides by 2 the reason it’s two is because 2 is the biggest divisible number that every number in the equation is divisible by so once you divide every number by two you get 2x^2+3x-54=0 now you have to factor cause but since you only have 3x and nothing else to factor with you have to write 3x as a difference so you could do 2x^2+12x-9x-54=0 so you are complicating the problem so you can factor out 2x from the expression so 2x(x+6)- 9(x+6)=0 the 54 got factored because it’s divisible by 9 that 6 is in replace of the 54 cause if you solved it 9x6 is still 54 next factor out x+6 so (x+6) x (2x-9) =0 so one of the two have to equal 0 so right the equations separately x+6=0 minus 6 from both sides and you’ll get x to equal -6 and 2x-9=0 add 9 to both sides and you’ll get 2x=9 divide both sides by 9 and you’ll get x to equal 4.5 when you plug 4.5 and -6 for x the equation works out

Related Questions

The box plots below show the average daily temperatures in January and December for a U.S.
city:
January
December
What can you tell about the means for these two months? (1 point)

Answers

Answer:

The answer is C

Step-by-step explanation:

Took the test!

Plz answer with explanation will give brainliest

Answers

Answer:

B: |8| + (-7)

Step-by-step explanation:

When you are looking for the distance between two numbers, always add. The distance between 8 and -7 is 15 (|8| = 8). If, for instance, the answer was negative, which it is now, just find the absolute value of -15 which equals 15. The answer is B.

angle C is inscribed in circle O AB is a diameter of O what is measure of A

Answers

Answer:

A = 53 degree

90-37 = 53 degree

As the triangle is a right angle triangle we see complimentary to the other angles and as all angles in a triangle equal 180, we see the other two which compliment this.

Step-by-step explanation:

Answer:

53 degrees

Step-by-step explanation:

To find the value of y using the value of x, use ___ equation of the system.

A. Either
B. Neither
C. The First
D. The Second

Answers

Answer:

D, The Second

Step-by-step explanation:

What is w^2 in a verbal expression? Is it w to the power of 2?

Answers

Answer:

w to the power of two, or w squared

Step-by-step explanation:

Yes, one way you can express w^2 verbally, is by saying w to the power of two. However, you can also express this by saying w squared.

When Nick checked his work it did not match the standard form function. Analyze Nick’s work. What was his mistake?
In step 1, he did not put the function in standard form correctly.
In step 2, he should have also factored –7 from the constant term, 17.
In step 3, he did not subtract –7(9) to keep the function equivalent.
In step 4, he did not write the perfect square trinomial correctly as a binomial squared.

Answers

In step 3, he did not subtract –7(9) to keep the function equivalent. Therefore, the correct option is option C among all the given options.

What is mathematical function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a predictor variables (the dependent variable).

In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Paul Dirichlet initially offered the standard concept of function in 1837. When Nick checked his work it did not match the standard form function. In step 3, he did not subtract –7(9) to keep the function equivalent.

Therefore, the correct option is option C.

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Your question is incomplete but most probably your full question was,  

Nick wrote the function p(x) = 17 + 42x – 7x2 in vertex form. His work is below.

p(x) = –7x2 + 42x + 17

p(x) = –7(x2 – 6x) + 17

= 9;

p(x) = –7(x2 – 6x + 9) + 17

p(x) = –7(x – 3)2 + 17

When Nick checked his work it did not match the standard form function. Analyze Nick’s work. What was his mistake?

In step 1, he did not put the function in standard form correctly.

In step 2, he should have also factored –7 from the constant term, 17.

In step 3, he did not subtract –7(9) to keep the function equivalent.

In step 4, he did not write the perfect square trinomial correctly as a binomial squared.

Nick made mistakes in converting to standard form, factoring constants correctly, maintaining equivalence, and writing perfect square trinomials. Correcting these steps will yield an accurate transformation of the equation.

Let's break down the steps Nick likely took and identify where he went wrong in putting the quadratic equation into its standard form.

Step 1: Initially converting the equation to standard form. For the equation x² + 4x + 21 = 0, the equation was already in standard form, so no changes were necessary here. It’s possible that Nick incorrectly adjusted coefficients, which led to errors.Step 2: Factoring out terms. If Nick had an equation like -7x² + 17 = 0, he should have factored out -7 from both the x² term and the constant term, resulting in -7(x² - 17/7) = 0. Missing this step would lead to misrepresentation of the equation.Step 3: Ensuring equivalence. Nick should have subtracted -7(9) correctly to maintain the function's equivalence throughout the transformation.Step 4: Writing the perfect square trinomial correctly. To complete the square, for example, (x + 2)² should be correctly represented as a binomial squared. Not doing so indicates an error in the transformation process.

In summary, Nick’s mistakes include incorrect standard form conversion, improper factoring of constant terms, failing to maintain equivalence, and incorrect representation of perfect square trinomials.

Which number is a common factor of 27 and 45?
A) 5
B) 9
C) 12
D) 15

Answers

Answer:

We found the factors and prime factorization of 27 and 45. The biggest common factor number is the GCF number. So the greatest common factor 27 and 45 is 9.

Step-by-step explanation:

9 is the common factor of both 27 and 45 cause 9 * 5 is 45 and 9*3 is 27

What is the perimeter of the pentagon

Answers

Answer:

60

Step-by-step explanation:

To find the perimeter, you have to add up all the sides, like you have done.

This is 12+12+12+12+12 which is the same as 12*5 which is 60!

Hope this helps!

4(x+2)=2(3x+5)
I need the answer​

Answers

Your answer would be x = -1.

We can find this by first expanding the brackets on both sides of the equation:

4x + 8 = 6x + 10

Now we can rearrange and solve for x:

4x + 8 = 6x + 10

- 4x

8 = 2x + 10

- 10

-2 = 2x

÷ 2

-1 = x

I hope this helps!

Answer:

x = - 1

Step-by-step explanation:

Given

4(x + 2) = 2(3x + 5) ← distribute parenthesis on both sides

4x + 8 = 6x + 10 ( subtract 6x from both sides )

- 2x + 8 = 10 ( subtract 8 from both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

Find the Greatest Common Factor of the terms mn, mnp, n3p

Answers

Answer:

n

Step-by-step explanation:

Solve the system of equations:
2x-5y=-22
X+7y=27

Answers

(x, y) = (-1, 4) please mark brainliest
The answer is y=-3/2x+2.5

10 x ( -9 + (-6) )
--------------------------

Answers

Answer:

This graph will help you.

Step-by-step explanation:

Answer:

Step-by-step explanation:

please help me with this math problem:)

Answers

Answer:

a = 1.08 m

Step-by-step explanation:

Answer:

1.08

Step-by-step explanation:

Approximately what are the zeros of this parabola?

Answers

Answer:

The zeros are approximately -1.65 and 3.65.

Approximately -2 and 4.

Please please help:p

Answers

Answer:

y = [tex]\frac{6}{19}[/tex]

Step-by-step explanation:

Brahmagupta’s solution to a quadratic equation of the form ax2 + bx = c involved only one solution. Which solution would he have found for the equation 3x2 + 4x = 6? x = x = x = x =

Answers

Answer:

A on edg.

Step-by-step explanation:

Snow Mountain Ski Resort offers a special season pass at the beginning of each ski season. The pass costs $35, and an additional $25 is charged each time you ski. Write the equation of this line in slope intercept form.​

Answers

y = 25x + 35

35 is the original amount or your y intercept

25x is the slope since it is how much your cost increases by every time you ski

Solve this problem:



X+7=12

Answers

Answer:

x=5

Step-by-step explanation:

because 5+7=12

you can figure it out by doing 12-7=?

the answer is 5 and thats your x

use the equation tool to complete the table y= -670+33 (X)
Table:
X value Y value
40 650
41 683
42 716
43 749
44 ?

Answers

Answer:

782

Step-by-step explanation:

y = -670 + 33(44)

y = -670 + 1452

y = 782

Step-by-step explanation:

Step 1:  Find y when x is 44

[tex]y = -670 + 33x[/tex]

[tex]y = -670 + 33(44)[/tex]

[tex]y = -670 + 1452[/tex]

[tex]y = 782[/tex]

Answer: [tex]? = 782[/tex]

HELPPPPPPPPPPPPMEEEEEEE

Answers

Answer:

I'm pretty sure it is 21

Which best explains what happens during crossing over?

A. The chromosomes have electrical connections that allow them to line up randomly.
B. Paired chromosomes overlap and portions of DNA switch between chromosome.
C. Genetic material is switched because the chromosomes line up independently.
D. Chromosomes line up randomly and cross genetic information between unpaired chromosomes.

Answers

Answer:

B

Step-by-step explanation:

what is the equation of the line?​

Answers

Answer:

x=3

Step-by-step explanation:

try different values on the line! plug them in and you'll see that every x value is 3!

Answer:

x=3

Step-by-step explanation:

Because there is no slope (or the slope is undefined), there is another way to write the equation. Instead of y=mx+b, it will be either x=b or y=b, y=b being a horizontal line and x=b being vertical. To find b, simply find the value of x or y. The line has infinite points on it with one similarity, being their x value is 3. Hence, the equation is x=3.

The student council at Richmond High School
is made up of 646 female students 229
seniors, and 6% female seniors.
If a student is selected at random, what is the
probability, as a decimal to the nearest
hundredth, that the student is female given that
the student is a senior?

Answers

Answer:

[tex]P(F/S)=0.216[/tex]

Step-by-step explanation:

Let's call F the event that the student is female and S the event that the student is senior.

So, we need to find the probability P(F/S) that a student is female given that  the student is a senior. P(F/S) is calculated as:

P(F/S) = P(F∩S)/P(S)

Then, the probability P(F∩S) that a student is female and senior is equal to 0.06

On the other hand, we can calculate the total number of students x using the following equation as:

[tex]\frac{646}{x}+\frac{229}{x}-0.06=1[/tex]

Where 646/x is the percentage of female students, 229/x is the percentage of senior students and 0.06 is the percentage of female seniors.

Then, solving for x we get that the number of students is 825.4719

Additionally, the probability P(S) that a student is a senior is equal to:

[tex]P=\frac{229}{825.47} =0.2774[/tex]

Because there are 825.47 students and 229 are senior.

So, P(F/S) is equal to:

[tex]P(F/S)=\frac{0.06}{0.2774}=0.216[/tex]

Tarzan is swimming east at 2.4 m/s across a river that is 1660 meters wide and
flows north at 5.2 m/s
What is tarzan’s final rate of swimming?

Answers

The final rate is 6.5 m/s

Tarzan’s final rate of swimming is 4.83 minutes.

What is velocity?

Velocity is the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference.

Now it is given that,

Tarzan is swimming east at Velocity, Vt = 2.4 m/s

River's Velocity flowing north, Vr = 5.2 m/s

Width of river = 1660 meters

So, resultant speed of Tarzan, V = √(Vt² + Vr²)

⇒ V = √(2.4² + 5.2²)

⇒ V = √(5.76 + 27.04²)

⇒ V = √32.8 m/s

⇒ V = 5.73 m/s

Thus, rate of swimming = Width / V

rate of swimming = 1660 / 5.73 s

rate of swimming = 289.70 s

or, rate of swimming = 4.83 minutes

Thus, Tarzan’s final rate of swimming is 4.83 minutes.

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Write the standard equation of the circle with center (0, 1) passing through the point (4, 9).

A. x2 + (y + 1)2 = 40
B. (x − 1)2 − y2 = 80
C. x2 + (y − 1)2 = 80
D. (x + 1)2 + y2 = 40

Answers

the answer is C

explanation:

r² = (4-0)² + (9-1)² = 80

(x-0)² + (y-1)² = r²

x² + (y-1)² = 80

5
= Qu
plete
Cindy went to the salon to get highlights and a haircut. Her total cost
was $95. Cindy decided to tip her stylist 22% because she loved her
hair so much. How much was the tip?
Select one:
O $20.90
O $117
O $115.90
O $74.10

Answers

Answer:

$20.90

Step-by-step explanation:

22% of $95 is $20.90

you should cross multiply and get $20.90

A girl and a boy each randomly grab a piece of candy from a bowl containing 9 pieces of chocolate, 7 fruit chews, 9 lollipops, and 9 peppermints. Find the probability that both events A and B will occur. Give your answer a reduced fraction.

Event A: A girl grabs a lollipop

Event B: A boy grabs a fruit chew

Answers

Step-by-step explanation:

Answer: event a: 11

Event b: 4

Step-by-step explanation:

Since There are 44 cans in total, Event Will get 11 candies and event b Will get 4 candies.

Please Help!!! 25 points!!!!!

Answers

Answer:

32.97

Step-by-step explanation:

because u have to times 10.5 × 3.14

A grocery store clerk put only packages of flour tortillas and packages of corn tortillas on a shelf. The ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 7 to 16.

Which number could be the number of packages of flour tortillas the clerk put on the shelf?

A: 23
B: 18
C: 14
D: 32

Answers

Answer:

would it be c because you can get 14 from 7 and you cant get they other numbers from 7 so maybe?

Step-by-step explanation:

There are many variables that affect the calculation of a patient’s total blood volume. For the purposes of this question, weight and age will be the only variables considered. The Australian Red Cross states that “Blood volume can be estimated as approximately 70mL/kg for adults, 80mL/kg in children…”. Work on the assumption that an adult is a person aged 16 years or over and a child is a person aged 2 to 16 years.

Let:
W = Weight (kg)
P = Plasma volume (mL) and
T = Total blood volume (mL)

Write 2 equations for calculating Total blood volume (T) given Weight (W), expressing T in terms of W, one for adults and one for children:

Answers

Answer:

The two equations are;

For adults, T = W kg × 70 mL/kg ............Equation (1)

For children, T = W kg × 80 mL/kg.............Equation (2)

Step-by-step explanation:

We are told that

Blood volume = 70 mL/kg for adults

Blood volume = 80 mL/kg in children

Therefore, the total blood volume,T  of an adult of weight, W is given by the following relation;

T = W kg × 70 mL/kg ............Equation (1)

The total blood volume,T of a child of weight, W is given by the following relation;

T = W kg × 80 mL/kg.............Equation (2).

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