{35 POINTS} A factory produces t-shirts. The production cost, C(x), for x t-shirts can be modeled by a quadratic function.

Each of the following functions is a different form of the quadratic model for the situation given above. Which form would be the most helpful if attempting to determine the number of t-shirts that would minimize cost?
A.
C(x) = 0.02(x2 - 720x + 144,600)

B.
C(x) = 0.02(x - 360)2 + 300

C.
C(x) = 0.02x2 - 14.4x + 2,892

D.
C(x) = 0.02x(x - 720) + 2,892

Answer:

The area of the parallelogram is 108 inches² OR 0.75 foot²

Step-by-step explanation:

* Lets revise the properties of the parallelogram

- Each two opposite bases are are parallel

- Each two opposite bases are equal in length

- Each two opposite angles are equal in measure

- Each two adjacent angles are supplementary (their sum = 180°)

- Its two diagonals bisect each other

- Each base has an altitude (height) drawn from the opposite

 base to it

* Look to the attached figure to more understand

- The area of the parallelogram is the product of the length of one

 of its base and the corresponding altitude (height)

∵ Area = B1 × H1 ⇒ OR ⇒ Area = B2 × H2

∵ B1 = 1 1/2 feet

∵ H1 = 6 inches

- The base and the height have different units, so we must

 change the unit of one of them to the other

∵ 1 foot = 12 inches

∵ B1 = 1 1/2 = 1.5 feet

∴ B1 = 1.5 × 12 = 18 inches

∴ A = 18 × 6 = 108 inches²

* The area of the parallelogram is 108 inches²

OR

∵ B1 = 1 1/2 = 1.5 feet

∵ H1 = 6 inches

∴ H1 = 6 ÷ 12 = 1/2 = 0.5 foot

∴ A = 1.5 × 0.5 = 0.75 foot²

* The area of the parallelogram is 0.75 foot²

Answer:

108 square inches

Step-by-step explanation:

We know that the formula of area of a parallelogram is given by:

A = base × altitude

Since here we have different units for base and altitude, so either we will change the base to inches or the altitude to feet.

Base = [tex]1\frac{1}{2} ft = 1.5 ft[/tex]

[tex]\frac{1}{1.5ft} =\frac{12inches}{x}[/tex]

Base (x) = 18 inches

Substituting the values in the above formula to get:

Area of parallelogram = 18 × 6 = 108 square inches

Answer:

  (x, y) = (-6, -7)

Step-by-step explanation:

Substitute for y:

  2x +5 = 3x +11 . . . . . use the first expression for y in the second equation

  0 = x +6 . . . . . . . . . . subtract 2x+5

  -6 = x . . . . . . . . . . . . add -6

  y = 2(-6) +5 = -7 . . . .substitute for x

The solution is x = -6, y = -7.

Answer:

• n(t) = 150·2^t . . . . . . . . . . . . number of cells after t minutes

• a(t) = π(0.25 +0.50t)^2 . . . . area in cm^2 after t minutes

• d(t) = n(t)/a(t) = (2400·2^t)/(π(1+2t)^2)

Step-by-step explanation:

The number of cells (n(t)) is described by an exponential function of time (t) with an initial value of 150 and a growth factor of 2 each minute:

n(t) = 150·2^t . . . . . . n in cells; t in minutes

___

The area of the culture is given by ...

a(t) = π·(r(t))^2 . . . . where r(t) is the radius as a function of time.

The radius is linearly increasing with a rate of increase of 0.50 cm/min, so can be described by ...

r(t) = 0.25 +0.50t

Then the area is ...

a(t) = π·(0.25 +0.50t)^2

A factor of 0.25 can be removed from inside parentheses to make this be ...

a(t) = (π/16)(1 +2t)^2 . . . . . a in cm^2; t in minutes

___

The density is the number of cells divided by the area:

d(t) = n(t) / a(t) = 150·2^t/((π/16)(1 +2t)^2)

Simplifying a bit, this is ...

d(t) = (2400/π)(2^t)/(1 +2t)^2 . . . . . d in cells/cm^2; t in minutes

[tex]\bf \begin{cases} 5x-4y=16\\ \cline{1-1} x-2y=6\\ \boxed{x}=6+2y \end{cases}~\hspace{7em}\stackrel{\textit{substituting \underline{x} in the first equation}}{5\left( \boxed{6+2y} \right)-4y=16} \\\\\\ 30+10y-4y=16\implies 30+6y=16\implies 6y=-14 \\\\\\ y=-\cfrac{14}{6}\implies y=-\cfrac{7}{3}\implies \blacktriangleright y=-2\frac{1}{3} \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{since we know that}}{x=6+2y}\implies x=6+2\left( -\cfrac{7}{3} \right)\implies x=6+\left(-\cfrac{14}{3} \right) \\\\\\ x=6-\cfrac{14}{3}\implies x=\cfrac{18-14}{3}\implies x=\cfrac{4}{3}\implies \blacktriangleright x=1\frac{1}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 1\frac{1}{3} ~,~-2\frac{1}{3}\right)~\hfill[/tex]

The answers are:

[tex]x=15\\y=-10[/tex]

Solving systems of equations using elimination means multiplying/dividing the factors of the given equations in order to reduce variables and make the isolating process simpler, so, solving we have:

We are given the equations:

[tex]\left \{ {{-9x-2y=-115} \atop {-6x+2y=-110}} \right.[/tex]

We have that the terms that contains the variable "y" are equal with opposite signs, so, we can eliminate both directly, and then, isolate the variable "x", so, solving we have:

[tex]\left \{ {{-9x-2y=-115} \atop {-6x+2y=-110}} \right\\\\\left \{ {{-9x=-115} \atop {-6x=-110}} \right\\\\-9x-6x=-115-110\\\\-15x=-225\\\\x=\frac{-225}{-15}=25[/tex]

Now, that we know "x" we need to substitute it into any of the given equations in order to find "y", so, substituting we have:

[tex]-9x-2y=-115\\\\-9*(15)-2y=-115\\\\-135+115=2y\\\\2y=-20\\\\y=\frac{-20}{2}=-10[/tex]

Hence, we have that:

[tex]x=15\\y=-10[/tex]

Have a nice day!

ANSWER

(15,-10)

EXPLANATION

The given equations are:

–9x – 2y = –115 ...(1)

–6x + 2y = –110...(2)

Add equation (1) from equation (2) to eliminate y.

-9x+-6x=-110+-115

This implies that,

-15x=-225

Divide both sides by -15

[tex]x = 15[/tex]

Put the value of x into equation (2) to find y.

[tex] - 6(15 ) + 2y = - 110[/tex]

[tex] - 90+ 2y = - 110[/tex]

[tex]2y = - 110 + 90[/tex]

[tex]2y = - 20[/tex]

[tex]y = - 10[/tex]

The solution is (15,-10)

Answer:

See image and explanation

Step-by-step explanation:

Point (-7,-2) is the center of dilation. The scale factor is 2.

If point A has coordinates (-3,-2), then its image point H has coordinates (1,-2).

If point B has coordinates (-6,2), then its image point E has coordinates (-5,6).

If point C has coordinates (-4,3), then its image point F has coordinates (-1,8).

If point D has coordinates (-1,1), then its image point G has coordinates (5,4).

Answer:

hope this helps :)

Step-by-step explanation:

Answer:

im not sure but he is grading assignments at a faster rate

Step-by-step explanation:

25/20=1.25 so 1.25 mins per hw assignment

36/30=1.20 so 1.20 mins per hw assignment

it takes him 5 more seconds to grade 36 hw assignments so he's going at a faster rate

hope this helps :)

I think it’s C sorry if I’m wrong

For this case we have a system of sos equations with two unknowns:

[tex]x-5y = -3\\-7x + 8y = -33[/tex]

We clear "x" from the first equation:

[tex]x = -3 + 5y[/tex]

We substitute in the second equation:

[tex]-7 (-3 + 5y) + 8y = -33\\21-35y + 8y = -33\\-27y = -33-21\\-27y = -54\\y = \frac {-54} {- 27}\\y = 2[/tex]

We find the value of "x":

[tex]x = -3 + 5 (2)\\x = -3 + 10\\x = 7[/tex]

ANswer:

(7,2)

Option C

Answer:

  338 in

Step-by-step explanation:

If each of the measures shown is the measure from the vertex to the point of tangency, then that measure contributes twice to the perimeter (once for each leg from the vertex to a point of tangency).

  2(22 in + 27 in + 22 in + 98 in) = 2(169 in) = 338 in

Answer:

  (x, y) ⇒ (-y, x)

Step-by-step explanation:

You can see that the points (1, 2) and (3, 5) get mapped to (-2, 1) and (-5, 3), respectively. That is, the old value y, when negated, is the new value of x; and the old value of x is the new value of y.

___

I find it easier to think of a 270° CW rotation as being the same as a 90° CCW rotation.

Answer:

25

Step-by-step explanation:

Answer:

v(w) = 7w³

Step-by-step explanation:

The formula for the volume of a cuboid (rectangular prism, or box) is ...

V = LWH . . . . . . where L represent length, W represents width, and H represents height

The problem statement tells you that for a box of width w (in inches), the length is 2w, and the height is 3.5w. Using these values in the formula, we have ...

V = (2w)(w)(3.5w)

V = 7w³

Written as a function v(w), volume as a function of width, this is ...

v(w) = 7w³

Answer: P=8s

Perimeter of octagon=8sides(unit value of side)

Answer:

P=8s

Step-by-step explanation:

we know that

The perimeter of a regular figure is equal to multiply the number of sides by the length of one side

In this problem

A regular octagon has 8 sides

Let

s-----> the length of one side

The perimeter is equal to

P=8s

Answer:

D

Step-by-step explanation:

You need to get the x out of the position in which is currently sitting, which is exponential.  The only way to get an exponent out from that position is to take the log of both sides.  The power rule of logs allows us to move the exponent down in front of the log.  Like this:

7x - 2 log (125)=log(150)

Now you want to divide both sides by log(125) to get the 7x - 2 all by itself:

[tex]7x-2=\frac{log(150)}{log(125)}[/tex]

Do that on your calculator and you'll get this:

7x - 2 = 1.037760918

Add 2 to both sides to get

7x = 3.037760918

then divide both sides by 7:

x = .4339 which rounds to .4340

Answer:

D.) -0.1375

Step-by-step explanation:

Answer:

$27

Step-by-step explanation:

If the table was marked up 125%, you can find the retail price of it this way:

20 + 1.25(20) = retail price

$45 = retail price.

To find 40% off of that, use

$45 - .4($45) = sale price

$27 = sale price (aka discount price)

Answer:

66

6 x 10=60

6 x 1=6

60+6=66

Have a good day!!! <3 Hope this helped ma dude :)

Answer:

12 ft-lbs is your answer

12ft-lbs that she has done

Answer:

(0,170)  and (60,-70) and (5, 150)

Step-by-step explanation:

To see if a given point is on the line or not, you just have to enter the x value (first value in the parenthesis) and see if the function returns the correct y value (second number in the parenthesis).

f(x) = -4x + 170

(170,0)  => -4 (170) + 170 = -680 + 170 = 510.  NO, not equal to 0.

(0,170) =>  -4 (0) + 170 = 0 + 170 = 170. YES

(12, 126)  => -4 (12) + 170= -48 + 170= 122. No, not equal to 126.

(50,30)  => -4(50) + 170 = -200 + 170 = 130. No, not equal to 30.

(5, 150)  => -4(5) + 170 = -20 + 170 = 150. YES

(60,-70) => -4(60) + 170 = -240 + 170 = -70.  YES

Answer:

(0,170)  and (60,-70) and (5, 150)

Step-by-step explanation:

Answer: First option and Third option

Step-by-step explanation:

You can observe in the figure that the angle 1 and the angle 2 have a common vertex and a common side. These kind of angles are known as "adjacent angles".

You can observe that the intersection of the lines forms four equal anles wich are right angles (Angles of 90 degrees). Thererefore, the angles 1 and 2 and also "complementary angles", because the sum of them is 90 degrees.

Then, the answers are the first option and the third option.

ANSWER

x=5

EXPLANATION

The given quadratic function has x intercepts of (0,0) and (10,0) .

The x-value of the minimum point lies on the axis of symmetry of this graph.

The axis of symmetry is the midline of the x-intercepts

[tex]x = \frac{0 + 10}{2} [/tex]

The x-value of the minimum point is

[tex]x = 5[/tex]

Answer:

C) The y-intercept is the same for both

D) The graph and the equation expression an equivalent function.

Step-by-step explanation:

We are given graph a linear function and a equation of line y = -4x - 4

From the given graph, let's find the equation.

From the graph, we know the slope = rise/run

Here rise = 4 and run  -1

Slope = 4/-1 = -4

and

y-intercept is -4 (where the line cuts  the y-axis)

The equation of graph of the line y = -4x - 4

So, the graph and the given equation are also the same.

Therefore, the answers are

C) The y-intercept is the same for both

D) The graph and the equation expression an equivalent function.

Answer:

(3) The y-intercept is the same for both.

(4) The graph and the equation express an equivalent

function.

Step-by-step explanation:

The slope of both functions is negative since in the graph the line is going down, then the Y intercept is the same for both because when X is 0, in the graph the line is located at Y=-4 and in the function you can set x to 0 and the function would be -4, then you can see that the function and the graph have the same slope and the same Y intercept that means that they express an equivalent function.

Answer:

  $5.82

Step-by-step explanation:

A markup or markdown of p% on a price causes that price to be multiplied by ...

  (1 + p/100)

The price after the markup 115% is ...

  $7.74(1 + 115/100)

And the price after that has been marked down 65% is ...

  $7.74(1 +115/100)(1 -65/100) = $7.74×2.15×0.35 ≈ $5.82

The discount price was $5.82.

Answer:

C. 4(x – 3)

Step-by-step explanation:

(6 x - 4) - (2 x + 8)

6 x - 4 - 2 x - 8

4 x - 12

Factor

4 ( x - 3 )

Explanation:

First we need to find the amount of the diet that is fruit. (It is what is not biscuits or bamboo.) The quantity is given per day, so we need to multiply that by the number of days in 3 weeks.

  (1 - 23% -73%)·(1100 g/day)·(7 day/week)·(3 week) = (44 g/day)·(21 day)

  = 924 g . . . . of fruit

Trish ate her yummy breakfast at 7:30 :)

Answer:

7:30 am

Step-by-step explanation:

Subtract 90 minutes from 9:00 am to determine what time Trish ate breakfast.

Answer:

The height of the next door building is 41.7 feet

Step-by-step explanation:

* Lets study the situation in the problem

- The man standing on the roof of a building 64.0 feet high

- The angle of depression to roof of the next door building is 34.7°

- The angle of depression to the bottom of the next door building

  is 63.3°

- We need to find the height of the next door building

* Lets consider the height of the man building and the horizontal

 distance between the two building formed a right triangle and the

 angle of depression is opposite to the side which represented the

 height of the building

- Let the horizontal distance between the two buildings called x

# In the triangle

∵ The length of the side opposite to the angle of depression (63.3°)

  is 64.0

∵ The length of the horizontal distance is x which is adjacent to the

  angle of depression (63.3°)

- Use the trigonometry function tanФ = opposite/adjacent

∴ tan 63.3° = 64.0/x ⇒ use cross multiplication

∴ x (tan 63.3°) = 64 ⇒ divide both sides by (tan 63.3°)

∴ x = 64.0/(tan 63.3°)

∴ x = 32.1886 feet

- Lets use this horizontal distance to find the vertical distance between

  the roofs of the two buildings

* Lets consider the height of the vertical distance between the roofs

 of the two buildings  and the horizontal distance between the two

 building formed a right triangle and the

 angle of depression is opposite to the side which represented the

 vertical distance between the roofs of the two buildings

- Let the vertical distance between the roofs of the two buildings

 called y

# In the triangle

∵ The vertical distance between the roofs of the two buildings is y

   and opposite to the angle of depression (34.7°)

∵ The horizontal distance x is adjacent to the angle of

   depression (34.7°)

∴ tan (34.7°) = y/x

∵ x = 32.1886

∴ tan 34.7° = y/32.1886 ⇒ use the cross multiplication

∴ y = 32.1886 (tan 34.7°)

∴ y = 22.2884 ≅ 22.3 feet

∴ The vertical distance between the roofs of the two

   buildings is 22.3 feet

- The height of the next door building is the difference between the

  height of the man building and the vertical distance between the

  roofs of the two buildings

∴ The height of the next door building = 64.0 - 22.3 = 41.7 feet

Final answer:

This answer explains how to calculate the height of a building using trigonometry based on given angles of depression.

Explanation:

To determine the height of the building next door, we need to use trigonometric functions. Specifically, the tangent of an angle in a right triangle relates the angle to the ratio of the opposite side to the adjacent side.

The total height of the building next door will be H + D.

From the top of the 64.0 feet building, looking down with an angle of depression of 34.7° to the roof of the building next door gives us:

Tan(34.7°) = D/Distance

Similarly, looking down with an angle of depression of 63.3° to the bottom of the building next door gives us:

Tan(63.3°) = (H + D)/Distance

By creating a right triangle for each angle, we can establish the relationships to find the height, which turns out to be around 52.0 feet.

Answer:

f(x) = q • 1.025x + 5

Step-by-step explanation:

Mrs. Varner deposited q dollars in a bank account that has been earning annual interest.

The total value of the account is based on the function f(x) = q • 1.025x

where x represents the number of years the money has been in the account.

If no deposits or withdrawals are made after the initial deposit, the equation that represents the total value of the account 5 years from now is :

f(x) = q • 1.025x + 5

Answer:

b

Step-by-step explanation:

For this case we have a mixed number given by:

[tex]6 \frac {3} {4} = \frac {6 * 4 + 3 * 1} {4} = \frac {27} {4}[/tex]

We make a rule of three to get the miles that the car can travel.

36 ---------> 1

x ------------> [tex]\frac {27} {4}[/tex]

Where "x" represents the variable that gives the number of miles that the car can travel with [tex]\frac{27}{4}[/tex]gallons of gasoline

[tex]x = \frac {\frac {27} {4} * 36} {1}\\x = 243[/tex]

So, the car can travel 243 miles

ANswer:

243 miles

Answer:

I want to say its b

Answer:

the answer is C

Step-by-step explanation:

Answer:

1. MN≅QP

  MQ≅NP

2. MP≅MP

3. SSS congruence postulate

4. ∠N≅∠Q

5. CPCTC

Step-by-step explanation:

1. As per the property of parallelogram that opposite sides are congruent, in given case of parallelogram MNPQ the opposite sides

                    MN≅QP  and   MQ≅NP.

2. The reflexive property of congruence states that a line or a geometrical figure is reflection of itself and is congruent to itself. Hence in given case of parallelogram MNPQ

                                         MP≅MP

3. SSS congruence postulate stands for Side-Side-Side congruence postulate, it states that when three adjacent sides of two triangle are congruent then the two triangles are congruent. In given case of parallelogram MNPQ, as the sides MN≅Q, MQ≅NP and MP≅MP hence

                               ΔMQP≅ΔPNM

5. As proven in part 4 that ΔMQP is congruent to ΔPNM, so as per the property of CPCTC (congruent parts of congruent triangles are congruent)

                                 ∠N≅∠Q

5. CPCTC stands for congruent parts of congruent triangles are congruent.

!