If the quadratic formula is used to solve 2x^2 - 3x - 1 = 0, what are the solutions?

Sunland Mining Company purchased land on February 1, 2020, at a cost of $975,900. It estimated that a total of 57,600 tons of mineral was available for mining. After it has removed all the natural resources, the company will be required to restore the property to its previous state because of strict environmental protection laws. It estimates the fair value of this restoration obligation at $110,700. It believes it will be able to sell the property afterwards for $123,000. It incurred developmental costs of $246,000 before it was able to do any mining. In 2020, resources removed totaled 28,800 tons. The company sold 21,120 tons.

Calculate :

a. Per unit mineral cost.

b. Total material cost of December 31, 2020, inventory

c.  Total materials cost in cost of goods sold at December 31, 2014.

Answer:

a. Per unit mineral cost  is $21

b. Total material Cost of ending inventory is $161280

c. Total materials cost in cost of goods sold is  $443520

Step-by-step explanation:

The Per unit mineral cost can be computed as follows:

Details                                           Amount ($)

Cost of land                                  975900

Add: Restoration obligation         110700

Add: Development cost              246000  

                                                     1332600

Less: Resale value of property    123000

Total cost of land                         1209600  

Divide:Total estimated cost            57600  

of minerals    

Per unit mineral cost                               21

b. The ending inventory cost on December 31, 2020 can be calculated as follows:

Ending inventory = Total mined tons - sold tons

Ending inventory = 28800 - 21120

Ending inventory = 7680

Cost per ton= $21

Cost of ending inventory = 7680 × $21

Cost of ending inventory = $161280

c.To calculate the cost of goods sold in December 2020; we have:

Cost per ton = $21

Total units sold = 21120

Cost of goods sold = 21120 × $21

Cost of goods sold = $443520

====================================================

Work Shown:

y = x^2 + 8x + 3 is the same as y = 1x^2 + 8x + 3

It is in the form y = ax^2 + bx + c

a = 1

b = 8

c = 3

Plug the values of a and b into the formula below to get the x coordinate of the vertex (h,k)

h = -b/(2a)

h = -8/(2*1)

h = -8/2

h = -4

Plug this into the original equation to get its paired y value. This will get us the value of k

y = x^2 + 8x + 3

y = (-4)^2 + 8(-4) + 3

y = 16 - 32 + 3

y = -13

This is the smallest y output possible. Therefore it is the minimum. The minimum occurs at the vertex (h,k) = (-4, -13)

We know we are dealing with a minimum because a = 1 is positive forming a parabola that opens upward. If a < 0, then the parabola would open downward to yield a maximum.

Answer:

Step-by-step explanation:

Its d

Answer :Answer: Did you get helped on this one?          

Step-by-step explanation: okay yup yup have a good day OKAY

Step-by-step explanation: HAVE A GOOD ONE OKAY

Answer:

a. 43,200 drips

b. 4 gallons (approximately, actual value is 3.8)

c. 61 cups(approximately, actual value is 60.8, using 3.8 gallons and not 4 gallons)

Step-by-step explanation:

Here, we have a faucet wasting water at a rate of 15 drips per 30 seconds, now we want to calculate the number of drips wasted in a day

To find this, what we need to do is fund the number of seconds in a day first

There are 24 hours with 60 minutes, with each minute having 60 seconds

So the number of seconds in a day = 24 * 60 * 60 = 86,400 seconds

Now 15 drips is wasted in 30 seconds

x will be wasted in 86,400 seconds

x = (15 * 86400)/30 = 43,200 drips are wasted in a day

b. Mathematically , there are about 3,000 drips in a liter of water

So;

3,000 drips = 1 liter

43,200 drips = x liter

x = 43200/3000 = 14.4 liters of water

Mathematically,

1 liter = 0.264 gallons

So 14.4 liters = 14.4 * 0.264 = 3.8 gallon

which is equal to 4 gallons of water approximately

c. Mathematically;

1 gallon = 16 cups of water

So 3.8 gallons of water will measure 3.8 * 16 = 60.8 which is approximately 61 gallons of water

Answer:

C = 1/4

Step-by-step explanation:

When solving a quadratic equation, there are steps to follow and I'll highlight them here.

Assuming we have an equation

ax² + bx + c = 0

Step 1

If a is not equal to 1, divide all through by a

x² + bx + c = 0

Take c to the other side of the equation

x² + bx = c

Step 2

Add (b/2)² to both sides of the equation

x² + bx + (b/2)² = c + (b/2)²

In our original question,

We had x² + x = 3

a = 1 , b = 1 c = 3

Using step two, we would have

(b / 2)² = (½)² = ¼ (which is the answer)

Now back to the steps

Step 3

We factor our left side of the equation so as to have a perfect square

[x + (b/2)]² = c + (b/2)²

Step 4

Take the square root of both sides of the equation and solve for x

x + b/2 = ±√[c + (b/2)²]

The answer to the question is ¼

Answer:

1/4

Step-by-step explanation:

Answer:

Are you asking what the value of x is if [tex]n^{x} * n^2 = 343[/tex] ?

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

With this one, you can just plug in 3 into each of the equations until the answer is 1.

When u plug 3 into x for solution A.

(1/3)×3=1

1^2=1

Answer:

[tex]\boxed{ \mathrm{A} }[/tex]

Step-by-step explanation:

The point is given (3, 1)

x = 3

y = 1

y = (1/3x)²

Plug x as 3 and y as 1.

The equation should be equal.

1 = (1/3(3))²

1 = 1²

1 = 1 True

Answer:

Step-by-step explanation:

Given figure : Trapezoid

Base sides,

a = 2.5

b = 7.5

Height ( h ) = 2.5

Now, finding the area:

[tex] \frac{1}{2} (a + b) \times h[/tex]

Plug the values

[tex] = \frac{1}{2 } \times (2.5 + 7.5) \times 2.5[/tex]

Calculate the sum

[tex] = \frac{1}{2} \times 10 \times 2.5[/tex]

Reduce the numbers with G.C.F 2

[tex] = 5 \times 2.5[/tex]

Calculate the product

[tex]12.5 \: \: {units}^{2} [/tex]

Hope this helps...

Best regards!

Answer:

27π Sq in.

Step-by-step explanation:

Circle A is equal to 9π sq inches. (Radius squared times Pi), Segment BC is a radii of Circle B and the diameter of Circle A. Meaning Circle B's radius is 6 inches. The area of circle B would be 36π sq inches. Now we subtract Circle A's area from Circle B's area(36π sq in. - 9π sq in.), the area of the shaded region is 27π sq in.

Answer:

[tex] f = 10.7 [/tex]

Step-by-step explanation:

Given ∆DEF,

<F = 36°

DF = e = 15

EF = d = 6

DE = f = ?

f can be found using the Law of Cosine as shown below:

[tex] f^2 = d^2 + e^2 - 2(d)(e)*cos(F) [/tex]

Plug in your values:

[tex] f^2 = 6^2 + 15^2 - 2(6)(15)*cos(36) [/tex]

Evaluate:

[tex] f^2 = 36 + 225 - 180*0.809 [/tex]

[tex] f^2 = 261 - 145.62 [/tex]

[tex] f^2 = 115.38 [/tex]

[tex] f = 10.74 [/tex]

[tex] f = 10.7 [/tex] (to nearest tenth)

Answer:

the height that represents the 99th percentile is 69.324  inches

Step-by-step explanation:

Given that :

the mean height =  62.8 inches

standard deviation = 2.8  inches

For 99th percentile;

Let X be the random variable;

SO, P(Z≤ z)  = 0.99

From the standard normal z tables

P(Z )= 2.33

The standard z score formula is :

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]2.33 = \dfrac{X- 62.8}{2.8}[/tex]

2.33 × 2.8 = X - 62.8

6.524 = X - 62.8

6.524 +62.8 =  X

69.324  = X

X = 69.324

Therefore; the height that represents the 99th percentile is 69.324  inches

Answer:

C. 120

Step-by-step explanation:

The figure shows that angles BEC and KEC are congruent. Their measures are equal.

m<KEC = m<BEC

10x = 6x + 24

4x = 24

x = 6

m<BEK = 2m<KEC

m<BEK = 2 * 10x

m<BEK = 2 * (10)(6)

m<BEK = 2 * 60

m<BEK = 120

====================================================

Explanation:

Each cube has a side length of 4. Placed together like this, the total horizontal side combines to 4+8 = 8. This is the segment HP as shown in the diagram below. I've also added point Q to form triangle HPQ. This is a right triangle so we can find the hypotenuse QH

Use the pythagorean theorem to find QH

a^2 + b^2 = c^2

(HP)^2 + (PQ)^2 = (QH)^2

8^2 + 4^2 = (QH)^2

(QH)^2 = 64 + 16

(QH)^2 = 80

QH = sqrt(80)

Now we use segment QH to find the length of segment EH. Focus on triangle HQE, which is also a right triangle (right angle at point Q). Use the pythagorean theorem again

a^2 + b^2 = c^2

(QH)^2 + (QE)^2 = (EH)^2

(EH)^2 = (QH)^2 + (QE)^2

(EH)^2 = (sqrt(80))^2 + (4)^2

(EH)^2 = 80 + 16

(EH)^2 = 96

EH = sqrt(96)

EH = sqrt(16*6)

EH = sqrt(16)*sqrt(6)

EH = 4*sqrt(6), showing the answer is choice C

-------------------------

A shortcut is to use the space diagonal formula. As the name suggests, a space diagonal is one that goes through the solid space (rather than stay entirely on a single face; which you could possibly refer to as a planar diagonal or face diagonal).

The space diagonal formula is

d = sqrt(a^2+b^2+c^2)

which is effectively the 3D version of the pythagorean theorem, or a variant of such.

We have a = HP = 8, b = PQ = 4, and c = QE = 4 which leads to...

d = sqrt(a^2+b^2+c^2)

d = sqrt(8^2+4^2+4^2)

d = sqrt(96)

d = sqrt(16*6)

d = sqrt(16)*sqrt(6)

d = 4*sqrt(6), we get the same answer as before

The space diagonal formula being "pythagorean" in nature isn't a coincidence. Repeated uses of the pythagorean theorem is exactly why this is.

Answer:

see explanation

Step-by-step explanation:

I will begin with part two, first.

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius.

Given

x² - 18x + y² - 10y = - 6

Using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is

(x - 9)² + (y - 5)² = 100 ← in standard form

with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10

Answer:

890 m^3 to the nearest whole number.

Step-by-step explanation:

Volume = volume of the cylinder + volume of the hemisphere:

= π r^2 h + 1/2 * 4/3 π r^3

= π*5^2 * 8 + 1/2 * 4/3  π 5^3

= 890.12

Answer:

-2

Step-by-step explanation:

Hello,

First of all, let's check the denominator.

[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]

Now, let's see the numerator.

[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]

So we cannot factorise the numerator with (x+2) or (x-3)

Then, -2 and 3 are the the discontinuities of the expression.

There is only -2 in the list, this is the correct answer.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

AC denotes the length of the hypotenuse and AB and BC denote the lengths of the other two sides, so:

[tex]\cos(\angle A)=\dfrac{AB}{AC}=\sin(\angle C)=x[/tex]

Answer:

It took 31 days for the patch to cover half the lake

Step-by-step explanation:

The patch grows to double its size everyday

the patch completely covers the lake in 32 days

Since the patch doubles itself everyday, this means that the previous day before the 32nd day, the lake was just half covered.

Therefore, the the patch covered half the lake on the 31st day, i.e it took 31 days for the patch to cover half the lake

Answer:

18

Step-by-step explanation:

Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.

Sidenote: I hope this answer helps!

The properties of a pentagon and the given right triangle formed by

segments EF and FD give the measure of ∠FDE.

Response:

The given parameters are;

A, E, F are points on the same line.

ABCDE is a regular pentagon

∠EFD = 90°

Required:

The measure of ∠FDE

Solution:

The points A and E are adjacent points in the pentagon, ABCDE

Therefore;

line AEF is an extension of line side AE to F

Which gives;

∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;

The sum of the acute angles of a right triangle = 90°

Therefore;

∠DEF + ∠FDE = 90°

Which gives;

72° + ∠FDE = 90°

∠FDE = 90° - 72° = 18°

Learn more about the properties of a pentagon here:

https://brainly.com/question/15392368

Answer:

Rhombus.

Step-by-step explanation:

A rhombus is a  quadrilateral, meaning that it has four lateral sides. A Rhombus is a 2-dimensional shape, and has two lines of symmetry.  A Rhombus has a rotational symmetry of order two, and the opposite sides are parallel. Also, the opposite angles in Rhombus are equal. Th diagonals of a Rhombus bisect each other at a right angle.

Other quadrilateral shapes includes the Rectangle, Parallelogram, and the Kite.

Answer:

2x -5

Step-by-step explanation:

-3 + 2(x - 1)

Distribute

-3 +2x -2

Combine like terms

2x -5

Answer:

5x -2

Step-by-step explanation:

Answer:

Your ans is. a12 = 47/12

Step-by-step explanation:

First, you need to find if the series has a common ratio or a common difference between each term. Based from observation, there is a common difference of 1/3 so the series is an arithmetic series.

The solution for this problem goes like this

an=a1+(n-1)d

a12=1/n+(12-1)(1/3)

a12=47/12

Hope it helped you.. Please mark BRAINLIEST

Tysm

Answer:

[15, ∞).

Step-by-step explanation:

–3(6 – 2x) ≥ 4x + 12

-18 + 6x ≥ 4x + 12

6x - 4x ≥ 12 + 18

2x ≥ 30

x ≥ 15

This means that the minimum of x is 15, and the most is infinity, which is the same thing as [15, ∞).

Hope this helps!

Answer: x Less-than-or-equal-to 2.25

Step-by-step explanation:

The given inequality: 47.75 + x Less-than-or-equal-to 50.

To determine: How much more weight can be added to Li’s suitcase without going over the 50-pound limit.

i.e. inequality for x.

[tex]47.75+x\leq50[/tex]

Subtract 47.75 from both the sides, we get

[tex]x\leq50-47.75\\\\\Rightarrow\ x\leq2.25[/tex]

So, the solution set is "x Less-than-or-equal-to 2.25"

Hence, the correct answer is "x Less-than-or-equal-to 2.25."

Answer

A x <_ 2.25

Step-by-step explanation:

There are 18 rectangles inside the playing field.  And if you include the fence around the field, that makes 19.

Answer:

a) BOC and AOD

b) BOA and AOE

c) BOE and EOD

d) BOA and AOD

e) AOE and EOD

Step-by-step explanation:

An obtuse angle is an angle that has more than 90° and vertically opposite angles are angle formed by two lines crossed. So, Obtuse vertically opposite angles are BOC and AOD

Adjacent angles are angles in which one angle is beside the other and complementary angles are angles whose sum is equal to 90°, so,  a pair of adjacent complementary angles are BOA and AOE.

Supplementary angles are angles whose sum is equal to 180°, so BOE and EOD are equal suplementary angles and BOA and AOD are unequal supplementary angles

Finally, AOE and EOD are adjacent angles that don’t form a linear pair.

Answer:

[tex]-(3x+2)(x+1)[/tex]

Step-by-step explanation:

So we have the polynomial:

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

(I moved the negative to the outside. This is optional, but it makes things cleaner and you will have to do it eventually.)

This is a quadratic. To factor this, we need to find two numbers p and q such that:

[tex]p\cdot q=ac\\p+q=b[/tex]

From there, we can substitute these numbers in for b.

From the quadratic, a=3, b=5, and c=2. We ignore the negative sign.

In other words, ac=6 and b=5.

After guessing and checking, two numbers that work are 3 and 2 since 3(2)=6 ad 3+2=5. We substitute these values in for b. So:

[tex]-(3x^2+5x+2)\\-(3x^2+3x+2x+2)\\=-(3x(x+1)+2(x+1))\\=-(3x+2)(x+1)[/tex]

Answer: 90,000

Step-by-step explanation:

From the question, we are informed that in a local town, 54,000 families have incomes less than $25,000 per year. We are further told that this number of families is 60% of the families that had this income level 12 years ago.

To calculate the number of families who had incomes less than 25,000 per year 12 years ago goes thus:

Let the the number of families who had incomes less than 25,000 per year 12 years ago be represented by x.

Since we are told that this number of families is 60% of the families that had this income level 12 years ago. This means that:

60% of x = 54,000

60/100 × x = 54,000

0.6 × x = 54,000

0.6x = 54,000

Divide by 0.6

0.6x/0.6 = 54000/0.6

x = 90,000

The number of families who had incomes less than 25,000 per year 12 years ago was 90,000.