Why do the roots of a quadratic equation have the opposite sign of the factors of a quadratic equation

Answer: You can drive, at most, 2.95 miles per day.

x ≤ 2.95

Step-by-step explanation:

In a single day, you can spend at most $90

Then if C represents the cost of renting the car, then we will have the inequality:

C ≤ $90

Now let's find the equation for C.

We know that we have a fixed cost of $25 plus $22 per mile, then if you drive x miles, the total cost will be $25 plus x times $22, or:

C = $25 + x*$22.

We can now replace that in the inequality:

$25 + x*$22 ≤ $90

Now let's isolate the variable x

x*$22 ≤ $90 - $25

x*$22 ≤ $65

x ≤ $65/$22 = 2.95

x ≤ 2.95

You can drive at most, 2.95 miles per day.

To find other inequalities with the same solution we can start with the solution:

x ≤ 2.95

Now let's multiply both sides by a number (the units of the number can be dollars, in that way we can make a similar problem)

Let's multiply both sides by $10:

x*$10 ≤ 2.95*$10 = $29.5

x*$10 ≤ $29.5

Now let's add the same number in both sides, for example, $5.

x*$10 + $5 ≤ $29.5 + $5 = $34.5

x*$10 + $5 ≤ $34.5

We could write this problem as:

"To rent a cab in your city, you have an initial cost of $5, plus $10 for each mile driven. How many miles could you drive if at most you can spend $34.50?"

You could be more creative with the problem, but this is the way in which you can craft problems of this type when you already know the solution.

Answer: 268

Step-by-step explanation:

From the question, we are informed that 67 out of 206 species of birds found in the Badlands nest there and that 824 species were found in the Badlands. The number of those that nest there would be:

= 67 × 824/206

= 67 × 4

= 268

Answer:

There is no solution to the problem.

Step-by-step explanation:

Key skills: Absolute Value, Division, One Variable Equation

1) We have the equation 3|-3x+9|=-18

2) First, divide by 3 on both sides.

-18/3 is -6

3) This means --> |-3x+9| = -6

4) Absolute Value cannot be negative so there is no solution.

Hope you understood and have a nice day!! :D

Answer:

x/2.

Step-by-step explanation:

We replace the x in g(x) by f(x):

g(f(x)) = 1((x + 2/2) - 1

= (x + 2)/2 - 1

= (x + 2 - 2)/2

= x/2.

Answer:

x/2

Step-by-step explanation:

g(f(x)) = (x+2/2) - 1

         = [tex]\frac{x+2}{2}[/tex] - [tex]\frac{2}{2}[/tex]

          = (x + 2 - 2) / 2

           = x/2

hello there!

it would be C

because

6/3=2 and 2*5=10 and 7*2=14

hope this helps

have a fantastic day/night

Answer:

aₙ = 75 x 0.2ⁿ⁻¹   or 75 x (1/5)ⁿ⁻¹

Step-by-step explanation:

a₁ = 75

a₂ = 75 x 0.2¹ = 75 x 0.2 ²⁻¹ = 15

a₃ = 75 x 0.2² = 75 x 0.2³⁻¹ = 3

.......

aₙ = 75 x 0.2ⁿ⁻¹   or 75 x (1/5)ⁿ⁻¹

Answer:

y=1

Step-by-step explanation:

the slope is 0 and the y-intercept is 1, so y=0x+1, y=1

Answer:

12

Step-by-step explanation:

60 x 20% = 12

Answer:

12

Step-by-step explanation:

Answer:

[tex]\displaystyle 6[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{7^2 - 13}{24 - 18}[/tex]

Step 2: Evaluate

Answer:

Step-by-step explanation:

If Buddy the Elf stands 6'3" tall and looks up at the Empire State Building (1454' high), what is the angle of elevation if Buddy is 206' from the base of the Empire State Building?

We are to find the angle of elevation which is calculated using the Trigonometric function of Tangent.

tan θ = Opposite/Adjacent

Where:

Opposite = 1454'

Adjacent = 206

tan θ = 1454'/206

Answer:

(4, 18)

Step-by-step explanation:

Answer: No

Step-by-step explanation:

$12-$4.50= $7.50

$7.50*15= $112.50

The Total cost is $135 She will only be making $112.50 in profits.

Answer:

The student multiplied by 5 instead of dividing by 5

Step-by-step explanation:

At the fourth step, the student multiplied each side by 5 rather than dividing it by 5. The opposite opperation from multiplication is division so they should have divided 5x and 60 by 5 here instead of multiplying it by 5. If this equation was done correctly, the correct answer would be x=12.

Answer and explanation:

Profit from sale of model boats = Sales -costs(costs of goods purchases + expenses or charges by the local fair)

John's profit from the sale of model boats can be represented by the equation:

P= 50x-(5x+80)

Where P is profit from the sale of the model boats and x is number of model boats bought and sold. The 80 is constant as it is a fixed cost paid to the local fair.

For example if John buys and sells 20 model boats, he would make profit of:

Substitute x=20 in equation above

P= 50×20-(5×20+80)

P=1000-180

P=$820

It could be said that John is in a very profitable business and his profit is also dependent on volume of sales because the lower his sales the closer he gets to making a loss and not profit

Answer:

52 cars

Step-by-step explanation:

During the first six months of the year the car dealership sold

53 cars

47 cars

62 cars

56 cars

46 cars

48 cars

Therefore the average number of cars sold per month can be calculated as follows

= 53+47+62+56+46+48/6

= 312/6

= 52

Hence an average of 52 cars is sold monthly

Answer:

1.

The slope is 2

The y-intercept is -10

equation: y = 2x - 10

2.

Slope: 2.5

y-intercept: 1

Equation: y = 2.4x + 1

Step-by-step explanation:

1.

x      y

2      12

4      16

8      24

10     28

from 12 to 16 you add 4

from 2 to 4 you add 2

y/x = 4/2 = 2

The slope is 2

The y-intercept is -10

equation: y = 2x - 10

I got the y-intercept because I went from 12 to 0 which is -12, and then 2 - 12 and it's -10

__________________________________________________________

2.

x       y

5      4

20   10

30    14

35    16

from 4 to 10, u add 6

from 5 to 20 you add 15

y/x = 15/6 = 2.5

Slope: 2.5

y-intercept: 1

Equation: y = 2.4x + 1

I got the y-intercept because I went from 4 to 0 which is -4, and 5 - 4 is 1.

Hope this helped

I'm pretty sure it's 28 but sorry if I'm wrong it might be 44

Answer:

x=12.87298334

Step-by-step explanation:

Answer:

36° and 54°

Step-by-step explanation:

Let one of the acute angle be "x"

We are told that the other acute angle is 1.5 times the other angle = 1.5x

The right angle = 90°

Find the value of x:

Therefore:

90 + 1.5x + x = 180 (sum of interior angles of triangle)

Add like terms

90 + 2.5x = 180

2.5x = 180 - 90

2.5x = 90

x = 90/2.5

x = 36° (one acute angle)

✔️Second acute angle = 1.5x

Plug in the value of x

= 1.5(36)

= 54°

Answer:

I think the person with the greatest debt is Marcus cause he has -25 dollars in his bank account.

Step-by-step explanation:

Sara and Maria both have positive numbers as their bank amount.  Samuel have to deposit 10 dollars into his bank account to not be in debt while Marcus has to deposit 25 dollars. 

Answer:

$80.625

Step-by-step explanation:

$75 for the iPod times 0.075 = 5.625 which is the sales tax.

Then $75 (Cost of iPod) + 5.625 (Sales Tax) = $80.625 (Price of the iPod including the sales tax)

Sorry, if I am wrong. I tried my best and Hope this helps ;)

Answer:

The similarity postulate that applies is;

C. Similar - AA

Step-by-step explanation:

The given parameters are;

ΔABC with angles ∠BAC = 30°, ∠ABC = 100° and ∠BCA = 50°

ΔDEF with angles ∠EDF = 30°, ∠DEF = 100° and ∠DFE = 50°

Therefore, the interior angles of ΔABC are equal to the corresponding interior angles of ΔDEF, which satisfies the Angle-Angle (AA) condition for similarity of two triangles based on the congruency of two interior angles of one triangle to two interior angles of the other triangle.

Answer:

£187,500

Step-by-step explanation:

Cost of houses one year ago = £150000

Percent increase a year after = 25%

Increment = 25% * 150000

Increment = 0.25 * 150000

Increment = £37500

New cost of house after increment =  £150000+ £37500

New cost of house after increment = £187,500

Answer:

314 sq.feet

Step-by-step explanation:

r= 10 feet

as you know r= d/2

As pool is circular

Area of circle = πr^2

Area of circle= 3.14*10^2 = 314square feet

9514 1404 393

Answer:

  0.5f -20.4

Step-by-step explanation:

There is only one term containing a variable (0.5f), but there are three constant terms. The constant terms can be combined by finding their sum in the usual way.

 -2.4 +0.5f -14 -4

  = 0.5f -(2.4 +14 +4)

  = 0.5f -20.4

Answer:

3cm

Step-by-step explanation:

so the long sides are 6cm and the short sides are 3cm

Answer:

C = 12 + 15(x - 4)

C = 15x - 48

Step-by-step explanation:

Let the number of hours = t

The total amount Miguel earns =

C

To edit a manuscript, Miguel charges 12 dollars per hour for the first 4 hours and 15 dollars per hour after the first 4 hours.

C = 12 + 15(x - 4)

Expand the t

C = 12 + 15x - 60

C = 15x - 48

Therefore, an expression for the amount, in dollars, Miguel charges if it takes him t hours to edit a manuscript, where t>4 is given as:

C = 15x - 48

Answer:

3 * 10^4

Step-by-step explanation:

Here, we want to make a division

We want to divide 9 * 10^2 by 3 * 10^-2

That would be;

(9 * 10^2)/(3 * 10^-2)

= 9/3 * 10^2-(-2)

= 3 * 10^4

Answer:

4/6 of a book in an hour

Step-by-step explanation:

1/6 = 1/4

1/4 x 4/1 = 1

1/6 x 4/1 = 4/6

Bam! UwU

Lol Hope This Helps !