Mathematics College

An item is regularly priced at
$80
. It is now priced at a discount of
85%
off the regular price. What is the price now?

Answers

Answer 1

85% = 0.85

1-0.85 = 0.15

80 x 0.15 = 12

the price now is $12

Related Questions

How tall is a building that casts a 73 foot shadow when the angle of elevation of the sun is 29

Answers

We use trigonometry for this problem. You might have learned about SOH CAH TOA. In right triangles, when given an angle, you can name the three sides of the triangle a certain part: Opposite, Adjacent, and Hypotenuse.

For this problem, we are given the angle and the ADJACENT length (73). We want to find the OPPOSITE side's length.
TOA
We must use the tangent function.

TOA helps us remember this relationship:
tan( theta ) = opposite / adjacent.

Plug in our values:

tan(29 degrees) = opposite / 73

Multiply by 73 to isolate "opposite" and solve for it.

73 * tan(29) = opposite.

Using a calculator, the answer is approximately 40.46 ft.
Final answer:

The height of the building is approximately 40.39 feet.

Explanation:

To find the height of the building, we can use the concept of similar triangles. The height of the building is proportional to the length of its shadow. We can set up a proportion using the angle of elevation of the sun and the length of the shadow.

Let x be the height of the building. The proportion can be set up as:

(x / 73) = tan(29°)

Using a calculator, we can find the value of tan(29°) to be approximately 0.5543. Solving for x, we get:

x = (73 * 0.5543)

Therefore, the height of the building is approximately 40.39 feet.

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f(x)=2× if x<0
|x| if x>0

Answers

If the question is about graphing the piecewise-defined function, the attached image shows it.

The graph is in two parts: graph y = 2^x, but use only the part which is to the right of the y-axis (for x > 0), and the other part is the graph of y = |x| which lies to the left of the y-axis (for x < 0).

The open circles are to indicate that the function has no assigned value at x = 0.

which situation could be modeled by using a linear function

Answers

if the ice-cream is cheaper, I buy more pints... say the initial price of the ice-cream gallon(8 pints) is hmmm $10, then I'd buy 1 pint

[tex]\bf \begin{array}{ccllll} \begin{array}{llll} price\ of\\ gallon \end{array}& \begin{array}{llll} pints\\ bought \end{array}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 10&1\\ 9&2\\ 7&3\\ 6&4 \end{array}\impliedby \begin{array}{llll} \textit{now if you graph that}\\ \textit{will give you a \underline{line}}\\ \textit{thus a \underline{line}ar function} \end{array}[/tex]

Which trinomial is a perfect square trinomial?


A) a^2 - 12a + 36
B) a^2 - 8a + 64
C) a^2 - 6a + 36
D) a^2 - 4a + 64

Answers

Which trinomial is a perfect square trinomial?


A) a^2 - 12a + 36
B) a^2 - 8a + 64
C) a^2 - 6a + 36
D) a^2 - 4a + 64

Answer:

d is the answer

1. The function f(x) = –0.05(x2 – 26x – 120) represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent? (1 point)

2. What do the zeros of this function represent? Remember the zeros are where f(x) = 0. (1 point)

3. Will the zeros tell you where the net should be placed? Why or why not? (1 point)

4. To find the zeros, set the function equal to 0, and then factor the polynomial. Start by setting the function equal to 0. (1 point)

Factor the polynomial.

The polynomial (x2 – 26x – 120) is in the form x2 + bx + c which can be factored as (x + p)(x + q) .

5. Next factor the polynomial x2 – 26x – 120. To identify the factors, complete the table: Note: This table does not contain all the factors of –120, but it has enough to let you factor the polynomial. (2 points: 0.5 points for each row)

p q p + q
10 –12
–10 12
30 –4
4 –30

6. Which values of p and q give the correct factors? (1 point)

7. Factor the polynomial completely: (2 points: 1 point for each factor)
0 = –0.05(x2 – 26x – 120)

8. Find the roots of the equation by setting each factor equal to 0 and solving for x.
Hint: There are three factors, but the constant factor, –0.05, does not equal zero. Solve for x with the other two factors. (2 points: 1 point for each factor)

9. Identify the roots. (2 points: 1 point for each root)

10. What are the zeros of this function? Circle them on the graph. (1 point)

11. Are these zeros the same as the roots you found? (1 point)

12. What does a negative zero mean in terms of this problem? (1 point)

13. Following this trajectory, will Nik hit a net that is 30 feet from the cannon? How do you know? (1 point)

Answers

Question 1

f(x) represents the distance of the cannon from the ground

Question 2

When f(x) = 0, there will two values of 'x'. The point on the positive x-axis where the graph crosses represent the point where the cannon hits the ground.

Question 3

Yes, it would. By knowing the spot where the cannon will hit the ground, we can set the net at the spot.

Question 4

f(x) = 0
-0.05 (x² - 26x -120) = 0
x² - 26x - 120 = 0

Question 5

Please refer to the table attached below

Question 6

The value of p and q that gives the correct factors are -30 and 4 since it gives p+q = -26

Question 7

Factorising the equation completely

-0.05 (x² - 26x - 120) = 0
-0.05 (x+4) (x-30) = 0 
(x+4) (x-30) = 0

Question 8
 
Solving the equation

x+4 = 0 and x-30=0
x=-4 and x=30 

Question 9 

The roots of the equation is x = -4 and x = 30

Question 10

Please refer to the third graph

Question 11

Yes

Question 12

The negative zero means the initial distance of the cannon, where it was fired from

Question 13

The distance between x = -4 and x = 30 is 34 units. If the cannon was fired from the point when x = -4, the cannon will hit the ground again 34 units from the point it was fired from. If Nik put a net 30 units from the firing point, the cannon will fly pass it. 

The motion of the projectile (cannonball), given by the (quadratic)

polynomial function is the path of a parabola.

Response:

Vertical heightThe point the projectile is at ground levelYes, because is it where the projectile will landx² - 26·x - 120 = 0(x - 30)·(x + 4) = x² - 26·x - 120 p = -30, and q = 4-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4) x - 30 = 0 and x + 4 = 0 Which gives; x = 30 or x = -4x = 30 or x = -4The zeros of the function are x = 30, and x = -4YesThe negative zero (x = -4) means that the ground level is a point before the location at which the cannonball is launched (x = 0). It also means that the cannonball was launched above ground level.Yes, because the projectile hits the ground 30 feet from the cannon

Which methods can be used to evaluate the polynomial?

1. f(x) is the output of the projectile function, where;

x = The input which is the distance

Therefore;

f(x) = The vertical distance (height) of the cannonball at point x.

2. The zeros are the points where the height, f(x) = 0

Therefore;

The zeros represent the points at which the cannonball is at ground level

3. The net should be placed where the cannonball is expected to reach ground level.

Therefore;

The zeros indicates where the net should be placed

4. The given polynomial can be equated to 0 as follows;

x² - 26·x - 120 = 0

5. x² - 26·x - 120 = x² - 30·x + 4·x- 120

Which gives;

x·(x - 30) + 4·(x- 30) = (x - 30)·(x + 4)

(x - 30)·(x + 4) = x² - 26·x - 120

6. Where; (x + p)·(x + q) = a·x² + b·x + c

We have;

The values of p and q that give the correct factors are;

p = -30, and q = 4

7. The polynomial, -0.05·(x² - 26·x - 120) = 0 in factored form is therefore;

-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4)

8. From the factors, we have;

-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4)

The roots of the equations, are given as follows;

x - 30 = 0 and x + 4 = 0

Which gives;

x = 30 or x = -4

9. The roots of the equation are therefore;

x = 30, and x = -4

10. The zeros for the function, are the values of x at which f(x) = 0

At x = 30 f(30) = -0.05 × (30² - 26 × 30 - 120) = 0

At x = -4, f(-4) =  -0.05 × ((-4)² - 26 × (-4) - 120) = 0

The zeros of the function are x = 30, and x = -4

11. Yes. The zeros are the same as the roots found given that at the roots, f(x) = 0

12. The zeros of the function are x = 30 and x = -4, which are points at

which the projectile (cannonball) is at ground level. The negative zero, x

= -4, means that, apart from the point x = 30, the projectile can (also/only)

be at ground level at a point before the location where the projectile is

launched, (-4) which means that at the point at which the cannonball is

launched, which is at x = 0, the cannonball was not on the ground, but

at the lip of the barrel or at a more elevated position.

What the negative zero means are therefore;

It is a location before the point where the cannonball is launchedThe cannonball is launched from a height above ground level

13. At 30 feet, x = 30, which is a zero of the function, and the cannonball

is at ground level, such that a net placed at 30 feet from the cannon

will be hit by the cannonball.

Therefore;

Yes Nik will hit a net that is 30 feet from the cannon

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A map scale has a scale of 1 inch equals 35 miles what is the actual distance if the distance on the map is 3.5 in

Answers

Let's set up a proportion.

1 in/ 35 miles = 3.5 in/ x miles

1*3.5=3.5
35*3.5=122.5

x=122.5

Final answer: 122.5 miles

Allen's monthly take-home pay is $3000, and his monthly rent is $750. If both his monthly take-home pay and his rent increase by $200, what percentage of Allen's take-home pay will be used to pay rent?

Answers

well, if they both increase by 200 each, that means his take-home pay is 3200 and his rent is 950

ok... if we take 3200 as the 100%, what is 950 in percentage of it?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 3200&100\\ 950&x \end{array}\implies \cfrac{3200}{950}=\cfrac{100}{x}[/tex]

solve for "x".

Answer:

29.68%

Step-by-step explanation:

Allen's monthly take-home pay is $3000

His monthly rent is $750

Now both his monthly take-home pay and his rent increase by $200

So, After increase Allen's monthly take-home pay =$3000+$200= $3200

After increase His monthly rent = $750+200=$950

Now we are supposed to find what percentage of Allen's take-home pay will be used to pay rent

So, percentage = [tex]\frac{\text{Rent after increase}}{\text {Take- home pay after increase}} \times 100[/tex]

                          = [tex]\frac{950}{3200}\times 100[/tex]  

                          = [tex]\frac{950}{32}[/tex]  

                          = [tex]29.68\%[/tex]  

Hence 29.68% of Allen's take-home pay will be used to pay rent.                          

To be eligible for a basketball tournament, a basketball team must win at least 60% of its remaining games. If the team has 21 game remaining, how many games must the team win to qualify for the tournament?

Answers

They would have to win 12.6 games. You need to find 60% of 21

Final answer:

The basketball team must win at least 13 out of their 21 remaining games to qualify for the tournament, as they need to win at least 60% of the games.

Explanation:

To determine how many games a basketball team must win out of 21 to qualify for a tournament, given they must win at least 60%, we perform the following calculation:

First, multiply the total number of remaining games, which is 21, by 60% (or 0.60) to find the minimum number of games they need to win.Next, solve for the number: 21 games × 0.60 = 12.6.Since a team can't win a fraction of a game, they must win at least the next whole number of games, which is 13.

Therefore, the team must win at least 13 games out of the remaining 21 to be eligible for the tournament.

3(b-4)+5b=44

what number is b.

Answers

3(b-4)+5b=44
3b-12+5b=44
8b=44+12
8b=56
b=56/8
b=7
you can rewrite this as:
3b - 12 + 5b = 44

Then you can add the individual sides:
8b - 12 = 44

Then you can move the 12 over to the other side:
8b = 44 + 12

Sum the sides again:
8b = 56

Then you divide both sides by 8:
b = 7

Hope this helps! :)

Jessica and Franklin are volunteering to paint one of their community member’s fences for service hours. If Jessica could complete the job in 6 hours and Franklin could complete the job in 4.5 hours, how long would it take them to complete the job together, to the nearest minute?

Answers

2.57 hours approximately
[tex] \frac{1}{t} = \frac{1}{6} + \frac{1}{4.5} = \frac{3+4}{18} = \frac{7}{18} [/tex]
t=18/7=2.57 hour =154 min

The figure has ____ lines of symmetry. A. 0 B. 4 C. 6 D. 8

Answers

Answer:

  B.  4

Step-by-step explanation:

Vertical and horizontal lines through the vertices farthest from center are two of the lines of symmetry.

The other two lines of symmetry are the diagonal lines through the vertices closest to center.

There are a total of 4 lines of symmetry.

Answer:

4

Step-by-step explanation:

hope it helps

We deal from a well-shuffled 52-card deck. calculate the probability that the 13th card is the first king to be dealt.

Answers

Final answer:

The probability that the 13th card is the first king to be dealt is 1/52.

Explanation:

To calculate the probability that the 13th card is the first king to be dealt from a well-shuffled 52-card deck, we need to consider the number of favorable outcomes and the total number of possible outcomes. There are 4 kings in the deck, so the probability of the first king being the 13th card is 1/52.

Final answer:

The probability that the 13th card is the first king to be dealt in a shuffled 52-card deck is 1/13.

Explanation:

In a well-shuffled 52-card deck, the probability that the 13th card is the first king to be dealt can be calculated as follows:

First, let's determine the number of favorable outcomes. Since there are 4 kings in the deck, there are 4 possible kings that can be the first king dealt.

Next, let's determine the number of possible outcomes. Since there are 52 cards in the deck, there are 52 possible cards to be the 13th card dealt.

Therefore, the probability is calculated as:

Probability = Number of favorable outcomes / Number of possible outcomes

Probability = 4 / 52

Probability = 1 / 13

So, the probability that the 13th card is the first king to be dealt is 1/13.

The number of chicken legs depends on how many chickens are in the coop. This is modeled by y=2x and is an example of _____ variation.

Answers

this is an example of direct variation

Answer:

y=2x is an example of direct variation.

Step-by-step explanation:

Direct variation is mathematical relationship in between two variables which can be expressed by an equation where one variable is equal to a constant multiplied by the other variable.

In the equation y=2x, x and y are the variables and 2 is a constant.

Here it is expressed as an equation where the variable y is equal to the constant 2 multiplied by the other variable x.

Thus we can say that it is an example of direct variation.

find the x-intercepts of the parabola with vertex (2,13) and y intercept (0,5)
round to the nearest hundredth
i have no idea how to do this problem please help!

Answers

To get the x-intercept we need the equation of the parabola;
the vertex form of the equation is given by:
y=a(x-h)^2+k

where:
(2,13) is the vertex:
Therefore;
y=a(x-2)^2+13
when x=0, y=5
Therefore the value of a will be:
5=a(0-2)^2+13
5-13=4a
4a=-8
a=-2
therefore the equation of the parabola will be:
y=-2(x-2)^2+13
y=-2x^2+8x+5
the x-intercept will be:
x=2-sqrt(7.5)
or
x=2+sqrt(7.5)

Answer:

What is the vertex of the parabola?

Round to the nearest hundredth.

✔ (8.33, 236.67)

Step-by-step explanation:

the directions for mixing water and powdered milk say that one should use 3 cups of water for each cup of powdered milk. how many cups of powdered milk are needed if 5 cups of water are used

Answers

Set up conversion problems so that you can cancel out units that you don't want and introduce units that you do want for your final solution.

5w(m/3w)=15m

So you will need 15 cups of milk if 5 cups of water are used.

If a company has 5 employees with annual salaries of $30,000, $50,000, $30,000, $80,000, and $70,000, respectively, what is the mean annual salary at the company?

Answers

$52,000, if you add all and divide, then you get the mean/average.

Answer:

Annual mean salary at the company is $52,000

Step-by-step explanation:

Given :  If a company has 5 employees with annual salaries of $30,000, $50,000, $30,000, $80,000, and $70,000, respectively.

We have to determine the mean annual salary at the company.

Consider the given salaries of 5 employee of the company

$30,000, $50,000, $30,000, $80,000, and $70,000

The annual mean salary at the company is the sum of salary of the employees divided by the number of employees.

Annual mean salary =[tex]\dfrac{30,000+50,000+30,000+70,000+80,000}{5}=\frac{2,60,000}{5}[/tex]

Thus, Annual mean salary at the company is $52,000

A parallelogram is cut out of a 12-inch by 8-inch sheet of paper. There are four right triangle remnants. Two have the dimensions 2 inches by 9 inches, and the other two have the dimensions 3 inches by 6 inches. The resulting parallelogram has a base of approximately 9.22 inches. Complete the following steps to calculate the altitude of the parallelogram using area methods. The area of the sheet of paper is square inches. The combined area of the triangle cutouts is square inches. The area of the parallelogram is square inches. The altitude of the parallelogram rounded to two decimals is square inches.

Answers

Answer:

96

36

60

6.51

Step-by-step explanation:


The area of a shape is the amount of space it occupies.

The area of the paper is 96 square inchesThe combined area of the triangle cutouts is 36 square inchesThe area of the parallelogram is 60 square inchesThe altitude of the parallelogram is 6.51 inches

The dimension of the paper is given as: 12-inch by 8-inch

So, its area is:

[tex]\mathbf{A_1 =12 \times 8}[/tex]

[tex]\mathbf{A_1 =96}[/tex]

The dimensions of the 4 right triangles are: Two 2 inches by 9 inches, and two 3 inches by 6 inches

So, the combined area is:

[tex]\mathbf{A_2 = 2 \times \frac 12 \times 2 \times 9 + 2 \times \frac 12 \times 3 \times 6}[/tex]

[tex]\mathbf{A_2 = 36}[/tex]

The area of the parallelogram is the difference between the areas of the paper and the four right triangles.

So, we have:

[tex]\mathbf{A_3 = A_1 - A_2}[/tex]

[tex]\mathbf{A_3 = 96 - 36}[/tex]

[tex]\mathbf{A_3 = 60}[/tex]

The area of a parallelogram is:

[tex]\mathbf{Area = Base \times Altitude}[/tex]

The base is given as 9.22

So, we have:

[tex]\mathbf{60 = 9.22\times Altitude}[/tex]

Divide both sides by 9.22

[tex]\mathbf{6.51 = Altitude}[/tex]

Rewrite as:

[tex]\mathbf{Altitude = 6.51}[/tex]

Hence, the altitude of the parallelogram is 6.51 inches

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Assume that the risk-free rate is 8 percent the required rate of return on the market is 13 percent and the required rate of return on acme healthcare stock is 15 percent what is the implied beta coefficient

Answers

This is the formula for computing the required rate of return in a market: E(R) = Rf + ß( Rmarket - Rf ). This is called as the Capital Asset Pricing Model (CAPM). The E(R) represents the required rate of return; the Rf is the risk-free rate; the ß is the beta coefficient (which we are looking for); and the Rmarket is the rate of return on the market. Substituting the values to this formula, you can come up with the beta coefficient of 1.4.

How long will it take a $800 investment to be worth $900 if it is continuously compounded at 11% per year?

Answers

Final answer:

It takes approximately 1.083 years, or around 1 year and 1 month for an $800 investment to grow to $900 when continuously compounded with an 11% yearly interest rate.

Explanation:

To calculate how long it will take for an $800 investment to grow to $900 with continuous compounding at an 11% yearly interest rate, we use the formula for continuously compounded interest, P = Pert, where P is the final amount, Pe is the original principal, r is the interest rate, and t is time in years.

Rearranging the equation to find t, we have, t = ln(P/Pe) / r.

Substitute P as $900, Pe as $800, and r as 0.11 into the formula.

Therefore, t = ln(900/800) / 0.11 = approximately 1.083 years or around 1 year and 1 month.

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Sonya can walk 6 km in 3 hours. If she has to walk 10 km, how much time will it take her?

Answers

it will take sonya 20 hours

I don't understand what the question is asking?

Answers

OK for this question you need to find out how many more post are needed. If you look at the diagram it shows that one side is 50 feet.  Now there are two sides that will need post, because the barn side need no more.  Now if there are two side both 50 feet, and you need a post every ten feet. How many posts are needed? 

check the picture below.

bear in mind that 100/10 is 10, however, we have to include the very first post, which is not spaced away 10' from anywhere, is simply touching the barn wall.  So the total is 10 spaced 10' from each other plus the starting post which is touching the barnwall.  And you can start doing the counting from either side A or B and you'd get 11 total.

Notice the angle "tickmarks" btw, that means those two angles are equal, that means the triangle is an isosceles, and thus both of those sides are equal, so, if one is 50', the other is also 50'.

Tomas's grandfather is 100 years old.Tomas's grandfather is 10 times as old as Tomas.How old is Tomas? Can someone​give me the answer to this plz

Answers

Tomas should be 10

If his grandfather is 100, then divide 100 by 10 and you will get Tomas's age.

Please correct me if I'm wrong.


Tomas is 10 years old

100 years old ÷ 10 = 10 years old


Hope this helps : )

Which input value produces the same output value for the two functions on the graph?

x = −3
x = −2
x = −1
x = 3

Answers

Answer:

x = -2

Explanation:

The line represents the output value (y) for a given input value (x). Where the lines cross, the output values are equal. These lines cross at x=-2.

Answer:x=-2

Step-by-step explanation:

got it right on edg

The RideEm Bicycles factory can produce 160 bicycles in a day at a total cost of $10,100. It can produce 180 bicycles in a day at a total cost of $11,000. What are the company's daily fixed costs

Answers

Answer:

$2,900

Step-by-step explanation:

The additional 180 - 160 = 20 bicycles cost an additional $11,000 - 10,100 = $900. That means the 180 bicycles cost 9·$900 = $8100, and the fixed costs are $11,000 - 8,100 = $2,900.

_____

Each group of 20 bikes costs $900, so 9 groups of 20 (180 bikes) cost 9×$900 = $8100.

Final answer:

To find the daily fixed costs of RideEm Bicycles factory, subtract the variable cost from the total cost.

Explanation:

To find the daily fixed costs of RideEm Bicycles factory, we need to determine the fixed cost component of the total cost. We can do this by subtracting the variable cost from the total cost. The formula for calculating fixed cost is:



Fixed Cost = Total Cost - (Variable Cost per Unit x Number of Units)



Using the given information:


 Number of bicycles produced when the total cost is $10,100: 160 bicycles
 Number of bicycles produced when the total cost is $11,000: 180 bicycles
 Variable cost per unit: (Total Cost - Fixed Cost) / Number of Units

By plugging in the values and solving the equations, we can find the daily fixed costs of the company.

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If a cow has a mass of 9×1029×102 kilograms, and a blue whale has a mass of 1.8×1051.8×105 kilograms, which of these statements is true?

A.) The blue whale has about 200200 times more mass.
B.)The blue whale has about 500500 times more mass.
C.)The cow has about 200200 times more mass.
D.)There is no way to compare the masses.

Answers

cow : 9 x 10^2 = 9 * 100 = 900
whale : 1.8 x 10^5 = 1.8 * 100,000 = 180,000

180,000/900 = 200

The blue whale has about 200 times more mass <==


Answer:

The blue whale has about 200 times more mass.

The area of Desert A is nine times the area of Desert B. If the sum of their areas is 2,000,000 square miles, find the area of each desert.

Answers

a=9b

a+b=2000000, using a from above we have:

9b+b=2000000  combine like terms on left side

10b=2000000  divide both sides by 10

b=200000, since a=9b

a=1800000

A=1,800,000 mi^2 and B=200,000 mi^2

Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.

a.Divide all terms in the equation by a.
b.Subtract the constant (the term without an x) from both sides.
c.Add a constant (in terms of a and b) that will complete the square.
d.Take the square root of both sides of the equation.
e.Solve for x.

Answers

Everyone should do this derivation, because otherwise the "quadratic formula" is some sort of "magic" LOL...

ax^2+bx+c=0  

x^2+bx/a+c/a=0

x^2+bx/a=-c/a

x^2+bx/a+b^2x/(4a^2)=b^2/(4a^2)-c/a

(x+b/(2a))^2=(b^2-4ac)/(4a^2)

x+b/(2a)=±√(b^2-4ac)/(2a)

x=-b/(2a)±√(b^2-4ac)/(2a)

x=(-b±√b^2-4ac)/(2a)

Answer:

See below.

Step-by-step explanation:

We are going to take the quadratic formula ax²+bx+c=0

a.Divide all terms in the equation by a.

[tex]\frac{ax^{2} }{a} +\frac{b}{a}x+\frac{c}{a}=0\\\\x^{2} +\frac{b}{a}x+\frac{c}{a}  =0[/tex]

b.Subtract the constant (the term without an x) from both sides.

[tex]x^{2} +\frac{b}{a}x+\frac{c}{a} -\frac{c}{a}  =\frac{-c}{a} \\\\x^{2} +\frac{b}{a}x=-\frac{c}{a}[/tex]

c.Add a constant (in terms of a and b) that will complete the square.

[tex]x^{2} +\frac{b}{a}x=-\frac{c}{a}\\\\[tex]x^{2} +\frac{b}{a}x+\frac{b^{2} }{4a^{2} }  =-\frac{c}{a} +\frac{b^{2} }{4a^{2}}\\\\(x+\frac{b}{2a}) ^{2}  =\frac{-4ac+b^{2} }{4a^{2} }[/tex]

d.Take the square root of both sides of the equation.

[tex]x+\frac{b}{2a}  =[tex]\\x+\frac{b}{2a} =\frac{\sqrt{-4ac+b^{2} } }{2a}\\x=\frac{\sqrt{-4ac+b^{2} } }{2a}-\frac{b}{2a} [/tex]

e.Solve for x.

[tex]x=-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]

identity the two rational numbers

Answers

B and D are both rational.

A rational number is a number that can be represented as a ratio fo two integers.

-7/3 is rational because both -7 and 3 are integers. 2.777... equals 25/9. 25 and 9 are both rational numbers.

On average, Donna's Cafe has 84 customers, which represents 24% of the total approved occupancy by the fire department. a. What is the total approved occupancy of the cafe by the fire department?

Answers

well, let's say is "x", so "x" is the 100%, now if 84 is the 24%, what is "x"?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 84&24\\ x&100 \end{array}\implies \cfrac{84}{x}=\cfrac{24}{100}[/tex]

solve for "x".

Can someone please solve this?

Answers

[tex]|-8-6|=|-14|=14[/tex]
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