What is the vertex of the parabola defined by the equation
(x − 2)2 = -12(y − 2)?
A.
(-12, 2)
B.
(2, 2)
C.
(6, 2)
D.
(2, -2)

Answer:

Step-by-step explanation:

Let [tex]u^2=x^4\\u = x^2[/tex]

Subbing in:

[tex]9u^2-2u-7=0[/tex]

a = 9, b = -2, c = -7

The product of a and c is the aboslute value of -63, so a*c = 63.  We need 2 factors of 63 that will add to give us -2.  The factors of 63 are {1, 63}, (3, 21}, {7, 9}.  It looks like the combination of -9 and +7 will work because -9 + 7 = -2.  Plug in accordingly:

[tex]9u^2-9u+7u-7=0[/tex]

Group together in groups of 2:

[tex](9u^2-9u)+(7u-7)=0[/tex]

Now factor out what's common within each set of parenthesis:

[tex]9u(u-1)+7(u-1)=0[/tex]

We know this combination "works" because the terms inside the parenthesis are identical.  We can now factor those out and what's left goes together in another set of parenthesis:

[tex](u-1)(9u+7)=0[/tex]

Remember that [tex]u=x^2[/tex]

so we sub back in and continue to factor.  This was originally a fourth degree polynomial; that means we have 4 solutions.

[tex](x^2-1)(9x^2+7)=0[/tex]

The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis.  Factoring [tex](x^2-1)[/tex] gives us that x = 1 and -1.  The other set is a bit more tricky.  If

[tex]9x^2+7=0[/tex] then

[tex]9x^2=-7[/tex] and

[tex]x^2=-\frac{7}{9}[/tex]

You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:

[tex]x=[/tex]±[tex]\sqrt{-\frac{7}{9} }[/tex]

which will simplify down to

[tex]x=[/tex]±[tex]\frac{\sqrt{7} }{3}i[/tex]

Those are the 4 solutions to the quartic equation.

We're given pairs (A,B) and asked if we have

enough calcium,

5A + 4B >= 24

enough iron

4A + 6B >= 15

and enough vitamins

7A + 4B >= 15

We check each constraint on each pair; if we find any false we can stop for that pair.

(A,B)=(1,4)

5(1)+4(4)=21   under 24, NO CHECK

(A,B)=(1,5)

5(1) + 4(5) = 25, bigger than 24, good

4(1) + 6(5) = 34, bigger than 15, good

7(1) + 4(5) = 27, bigger than 15, good   CHECK

(A,B)=(2,3)

5(2)+4(3)=22, NO CHECK

(A,B)=(3,2)

5(3)+4(2)=23, NO CHECK

(A,B)=(4,1)

5(4) + 4(1) = 24, ok

4(4) + 6(1) = 22, ok

7(4) + 4(1) = 32, ok, CHECK

Answer:

(1,5),  (4,1)

Step-by-step explanation:

Let's check the possible answers and see if they will Steve to meet his requirements:

We'll start by looking if each answer (dose) will provide enough calcium first.  If it does, we'll get iron and vitamins if needed.

a) (1,4)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (1) + 4 (4)

24 ≤ 5 + 16

24 ≤ 21

NO!

b) (1,5)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (1) + 4 (5)

24 ≤ 25   YES!

Iron, at least 15 mg

15 ≤ 4x + 6y

15 ≤ 4(1) + 6(5)

15 ≤ 34 YES!

Vitamins, at least 16 mg

16 ≤ 7x + 4y

16 ≤ 7 (1) + 4 (5)

16 ≤ 27  YES

YES, YES, YES...

c) (2,3)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (2) + 4 (3)

24 ≤ 22 NO!

d) (3,2)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (3) + 4 (2)

24 ≤ 23 NO!

e) (4,1)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (4) + 4 (1)

24 ≤ 24   YES!

Iron, at least 15 mg

15 ≤ 4x + 6y

15 ≤ 4(4) + 6(1)

15 ≤ 22 YES!

Vitamins, at least 16 mg

16 ≤ 7x + 4y

16 ≤ 7 (4) + 4 (1)

16 ≤ 32 YES

YES, YES, YES...

Answer:

(C)

10

Step-by-step explanation:

Let y = cost of items

Let x = number of items

Total cost  = fixed charge + (cost per item x number of items)

Given:

company A fixed charge = $50 , cost per item = $7

company B fixed charge = $30 , cost per item = $9

For company A,

Total Cost = $50 + ($7 x number of items),

          or

     y = 50 + 7x

Similarly for company B,

Total Cost = $30 + ($9 x number of items),

          or

     y = 30 + 9x

Hence (C) is the correct answer.

For the cost to be the same, Total cost for A = total cost for B

i.e 50 + 7x = 30 + 9x

x = 10 items  (Answer)

The correct system to solve the problem is y=50+7x and y=30+9x. The cost will be the same at both companies when there are 10 items.

The correct system that could be used to solve the problem is (C) y=50+7x and y=30+9x.

To find the number of items where the cost will be the same at both companies, we need to set the two equations equal to each other and solve for x.

50+7x = 30+9x

20 = 2x

x = 10

Therefore, the cost will be the same at both companies when there are 10 items.

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Answer:

Option C) [tex]0 \leq x \leq 9[/tex]

Step-by-step explanation:

We are given the following information in the question:

The number of users of a cell tower  increased by a factor of 1.5 every year from 2010 to 2019.

[tex]f(x) = 5000(1.5)^x[/tex]

where f(x) is the number of cell tower users and x is the years from the year 2010.

We have to find the domain for the given function.

Domain of a function is defined as the possible values of x the function can take, so that the function is defined.

Since this function gives the number of cell users from 2010 to 2019, thus, it is applicable from year 2010 to 2019.

x takes the value of years after 2010.

Thus  for year 2010, x = 0 and for year 2019, x = 9

Thus, the domain of the given function is given by:

[tex]0 \leq x \leq 9[/tex]

Answer:

29; 30

Step-by-step explanation:

1. To the nearest whole number.

Whole numbers are numbers like 27, 28, 29, and 30.

A is between 28 and 29, but it is closer to 29.

To the nearest whole number, A = 29.

2. To the nearest 10

The tens are numbers like 10, 20, 30, and 40.

A is between 20 and 30, but it is closer to 30.

To the nearest ten, A = 30.

Answer:

1. 7

2. 25

3. 2/3

4. 132/425

Step-by-step explanation:

Probability is the likelihood of an event occurring and it can be computed by:

[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}[/tex]

1. So when you are given a probability of 7/9:

[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{7}{9}[/tex]

So the answer is 7.

2. Given the probability is 14/25:

[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{25}[/tex]

The number of possible outcomes is 25.

3. You have 14 favorable outcomes out of 21 possible outcomes.

[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{21}\div \dfrac{7}{7}=\dfrac{2}{3}[/tex]

The answer is 2/3.

The least likely even would be the smallest fraction. If you want to do this the easy way, just change them all to decimal and find the value with the least.

17/35 = 0.49

5/13 = 0.38

132/425 = 0.31

1/2 = 0.5

Since 132/425 = 0.31 is the smallest, then it is the least likely probability.

Answer:

the functions f(x) and g(x) are equivalent

Step-by-step explanation:

Your full question is attached below

The equations of your problem are

f(x) = √(16^x)

f(x) = √(4^(2x))

f(x) = √(4^(2x)) = √(4^x.4^x)

f(x) = 4^(x)

and

g(x) = ∛64^x

g(x) = ∛4^(3x)

g(x) = ∛4^(3x)  =  ∛4^(x) .4^(x) .4^(x)

g(x) = 4^(x)

Thus, the functions f(x) and g(x) are equivalent

Answer:

h = 32.25.

Step-by-step explanation:

h^2 = 28^2 + 16^2 (Pythagoras theorem).

h = √1040

h = 32.25.

Using the Pythagorean theorem, the length of the hypotenuse in a right triangle with legs of lengths 28 and 16, rounded to the nearest hundredth, is 32.25.

The question asks for the length of the hypotenuse in a right triangle with legs of lengths 28 and 16. To find this, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). Thus, according to the equation a² + b² = c², we substitute the given values to find the hypotenuse length.

Using the given lengths:

a = 28

b = 16

We calculate:

c = √(28² + 16²)

c = √(784 + 256)

c = √(1040)

c = 32.249

Rounded to the nearest hundredth, the length of the hypotenuse is therefore 32.25.

Answer:

[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]

Step-by-step explanation:

The given quadratic equation is

[tex]-3x^2-2x+6=0[/tex]            .... (1)

If a quadratic equation is defined as

[tex]ax^2+bx+c=0[/tex]            .... (2)

then the quadratic formula is

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

On comparing (1) and (2), we get

[tex]a=-3,b=-2,c=6[/tex]

Substitute [tex]a=-3,b=-2,c=6[/tex] in the above formula.

[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]

Therefore, the correct substitution of the values a, b, and c in the quadratic formula is [tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex].

Step-by-step explanation:

The ratio of the perimeters = the scale

P₂ / P₁ = 6 / 4 = 3 / 2

The ratio of the areas = the square of the scale

A₂ / A₁ = (6 / 4)² = (3 / 2)² = 9 / 4

Same for the triangles:

P₂ / P₁ = 6 / 3 = 2

A₂ / A₁ = (6 / 3)² = (2)² = 4

Answer:its a. 5,000,000

Step-by-step explanation:

Final answer:

Option a, 5,000,000 nanometers, is the correct choice as it does not equate to 50 millimeters; it equates to 5 millimeters instead, making it not equal to the other options listed.

Explanation:

The question asks which of the provided options is not equal to 50 millimeters. We can convert each option to see which one does not equal 50 mm:

a. 5,000,000 nanometers (nm) - This equates to 5,000,000 nm × 1 m / 1,000,000,000 nm = 0.005 m or 5 mm, which is not equal to 50 mm.

b. 0.05 meters (m) - This is equal to 0.05 m × 1000 mm / 1 m = 50 mm, which is equal to 50 mm.

c. 5 centimeters (cm) - This is equal to 5 cm × 10 mm / 1 cm = 50 mm, which is equal to 50 mm.

d. 50,000 micrometers (µm) - As 1 µm is 1/1000 mm, this is equal to 50,000 µm × 1 mm / 1000 µm = 50 mm, which is equal to 50 mm.

Therefore, the correct answer is a. 5,000,000 nanometers, as it is the only option that does not equate to 50 mm.

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

      = [tex]253x-2x^2[/tex]

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

                      = 3*x

                      = 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

      = [tex]253x-2x^2 - (3x+6972)\\253x-2x^2-3x-6972\\253x-3x-2x^2-6972\\250x-2x^2-6972\\-2x^2+250x-6972\\[/tex]

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

[tex]-2x^2+250x-6972[/tex]=0

now we have to solve the above equation for x

[tex]-2x^2+250x-6972 = 0[/tex]

Dividing both sides by -2 we get

[tex]x^2-125x+3486 = 0\\[/tex]

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

[tex]x^2-42x-83x+3486 = 0\\x(x-42)-83(x-43)=0\\(x-42)(x-83)=0\\[/tex]

Hence

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

Final answer:

The cost function is C(x) = $6972 + ($3 × x). The revenue function is R(x) = 253x - 2x². The profit function is P(x) = (253x - 2x²) - ($6972 + $3x). The smallest break-even point is where P(x) = 0.

Explanation:

To answer the student's series of questions involving cost, revenue, and profit functions, as well as the break-even quantity, we need to derive these functions from the given information and perform the necessary calculations. The unit cost to produce bins of cat food is $3, and the fixed cost is $6972. Meanwhile, the price-demand function is given by p(x) = 253 - 2x.

The cost function, C(x), which represents the total cost of producing x units, can be expressed as:

C(x) = Fixed Costs + (Variable Cost per Unit × x)
Thus, C(x) = $6972 + ($3 × x).

The revenue function, R(x), is the total income from selling x units, defined by:

R(x) = Price per Unit × x
So, using the price-demand function, R(x) = (253 - 2x)x = 253x - 2x².

The profit function, P(x), is found by subtracting the cost function from the revenue function:

P(x) = R(x) - C(x)
Therefore, P(x) = (253x - 2x²) - ($6972 + $3x).

To calculate the break-even point, where profit is zero, you need to solve the equation P(x) = 0 for x.

Answer:

4 wrong

Step-by-step explanation:

Just do .84 times 25.

.84(25)=21

That means you got 21 questions right.

Answer:

You missed 4 questions.

Step-by-step explanation:

If you have a 100 questions test with 1 point each and you get and 84% that means you missed 16 questions. Since there was 25 questions on this test that is 1 quarter of 100. Divide the number of questions missed on a 100 questions test by the fraction of the actual test. So by 4. 16 divided by 4 = 4

Answer:

n = -174

Step-by-step explanation:

What I did was 696 divided by -4 and got B) n = -174.

Please mark brainliest and have a great day!

Answer:1 out of 13

Step-by-step explanation:

because you take both of them and add them together and if one gets a banana and the other one gets an orange that will be one out of thirteen

Answer:

93%

Step-by-step explanation:

1 + 3 + 21 + 35 = 60 = 100%

21 + 35 = 56 = x%

60 = 100%

56 = x%

60x = 56 * 100

x = 56* 100 / 60

x = 2*23*2*2*5*5 / 2*2*3*5

x = 23*2*5/3

x = 93%

To find the percent of soldiers in the new army unit, you divide the number of soldiers in the unit by the total number of soldiers in the army and multiply by 100. However, the question doesn't provide the total number of soldiers in the army, making it impossible to calculate this percentage.

The question is asking what percent of the soldiers in the newly formed army unit consists of the total personnels. The total number of soldiers in the unit is the sum of staff sergeants, sergeants, PFCs, and PVTs which is 1 + 3 + 21 + 35 = 60 soldiers. The percent of soldiers in the army is the number of soldiers in the unit divided by the total number of soldiers in the army multiplied by 100. However, without the context of the total number of soldiers in the army, it is impossible to calculate this percentage. For example, if the total army size is 600, then the percent of soldiers in this unit would be (60/600)*100 = 10%. The keywords here are

percent

,

total soldiers

, and

army unit

.

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Answer:

D. not congruent

Step-by-step explanation:

Only two pairs of congruent sides are given to us, when we need either 3 pairs of congruent sides (SSS) or two pairs of congruent sides & 1 pair of congruent angles (SAS), or two pairs of congruent angles & one pair of congruent sides (ASA).

~

Answer:

  40 ft by 70 ft

Step-by-step explanation:

The 50 ft side of the house can add to the total perimeter of the play area, allowing it to be 170+50 = 220 feet. Then the sum of length and width will be half that, or 110 feet.

Factors of 2800 that have a sum of 110 are 40 and 70.

The play area fence can extend 10 ft either side of the house, out 40 ft, then 70 ft across the back, for a total length of 170 ft. Dimensions of the play area are 40 ft by 70 ft.

Answer:

None.

Step-by-step explanation:

5/a - 2 / (1 - a) = 2 (a - 1)

Multiply each term by  a(1 - a)(a - 1):

5 (1 - a)(a - 1) - 2a(a - 1)  = 2a(1 - a)

5( a - 1 - a^2 + a)  - 2a^2 + 2a = 2a - 2a^2

5(-a^2 +  2a  - 1) - 2a^2 + 2a = 2a - 2a^2

-5a^2 + 10a - 5 - 2a^2 + 2a - 2a + 2a^2 = 0

-5a^2 + 10a - 5 = 0

-5(a^2 - 2a + 1) = 0

= -5(a - 1)^2 = 0

So a = 1.

But a = 1 cannot be a root because 2/ 1 - a would be 2/0 which is undefined.

Also 2 / (a - 1) is undefined.

Answer:

  $28

Step-by-step explanation:

Put the given value into the formula and do the arithmetic.

  p(15) = -2(15 -9)^2 +100

  = -2(6^2) +100

  = -72 +100

  = 28

The profit on T-shirts selling for $15 would be $28.

Answer:

B -$28

Step-by-step explanation:

Answer:

√3 + 12 = x

Step-by-step explanation:

Simplify both sides of the equation, isolating the variable.

Answer:

139 ft

Step-by-step explanation:

So the zip line forms a right triangle.  The height of the triangle is 150 ft, and the opposite angle is 40°.  The horizontal distance covered by the zip liner can be found with trigonometry, specifically with tangent.

tan 40° = 150 / x

x = 150 / tan 40°

x ≈ 179 feet

But this includes the 40 ft long body of water, so the amount of ground covered is:

179 ft - 40 ft = 139 ft

1. This kite has a 90 degree angle, which is equivalent to angle B.

2. Distance RB is 2.

3. Distance SB is 1.

4. The kite forms a right triangle.

5. Distance RS is the hypotenuse which has not been given. We can call RS by any variable of choice.

Answer:

if a line has a slope equal to zero, then it is horizontal

Step-by-step explanation:

Answer:

If a line does not have zero slope, then it is not a horizontal line.

Step-by-step explanation:

edg

x^2+10x+21

(x+3)(x+7)= 0

x^2+7x+3x+21= x^2+10x+21

x+3-3= 0-3

x+7-7= 0-7

Answers are :

x= -3 , x= -7

Answer:

x=-7,-3

Step-by-step explanation:

Final answer:

To find the total number of votes polled in the election with three candidates and invalid votes, the sum of votes received by each candidate and the invalid votes is calculated. The total number of votes polled is 1,027,601.

Explanation:

The question pertains to vote totals and calculating the overall number of votes polled in an election with three candidates. To solve this, we will perform simple addition of the votes received by each candidate and also include votes that were declared invalid.

Candidate A received 345,983 votes. Candidate B won the election by a margin of 15,967 votes more than Candidate A, which means Candidate B received 345,983 + 15,967 = 361,950 votes. Candidate C received 279,845 votes, and there were 39,823 invalid votes.

To find the total number of votes polled, add together all the votes:

Votes for Candidate A: 345,983

Votes for Candidate B: 361,950 (since Candidate B won by 15,967 votes more than Candidate A)

Votes for Candidate C: 279,845

Invalid votes: 39,823

Adding these together:

345,983 + 361,950 + 279,845 + 39,823 = 1,027,601

Therefore, the total number of votes polled in the election is 1,027,601.

Answer:

[tex]14\ miles[/tex]

Step-by-step explanation:

Let

[tex]A(-2, 2), B(1, 2), C(1, -2),D(-2, -2)[/tex]

Plot the coordinates

see the attached figure

we know that

The perimeter is equal to

[tex]P=2(AB+AD)[/tex]

we have

[tex]AB=(1-(-2))=3\ units[/tex]

[tex]AD=(2-(-2))=4\ units[/tex]

substitute

[tex]P=2(3+4)=14\ units[/tex]

Convert to miles

If each unit represents 1 mile

then

[tex]14\ units=14\ miles[/tex]

Answer:

15 units sq

Step-by-step explanation:

Good job

Answer:

[tex]330\ kg[/tex]

Step-by-step explanation:

Remember that

1 kg=1,000 g

1 m= 100 cm

The volume of the granite countertop in cubic centimeters is equal to

[tex]V=(100)(300)(4)\ cm^{3}[/tex]

The density in kg per cubic centimeter is equal to

[tex]D=2.75(\frac{1}{1,000}) \frac{kg}{cm^{3}}[/tex]

Multiply the density by the volume

[tex]2.75(\frac{1}{1,000})(100)(300)(4)[/tex]

[tex]2.75(120)=330\ kg[/tex]

[tex]{_{15}C_{11}}\cdot {_{11}C_2}=\dfrac{15!}{11!4!}\cdot\dfrac{11!}{2!9!}=\dfrac{12\cdot13\cdot14\cdot15}{2\cdot3\cdot4}\cdot\dfrac{10\cdot11}{2}=75,075[/tex]

Answer: There are 715 ways to choose his starting lineup which includes designating the two captions.

Step-by-step explanation:

Since we have given that

Number of members = 15

Number of players = 11

Number of captions must be included = 2

So, Number of remaining members = 15-2 = 13

Number of remaining players = 11 - 2 = 9

So, Number of ways to choose starting line up is given by

[tex]^{13}C_9\\\\=715[/tex]

Hence, there are 715 ways to choose his starting lineup which includes designating the two captions.

Answer:

[tex](f + g) (x)=x^2 +x +3[/tex]

[tex](f - g) (x)=-x^2 +5x +1[/tex]

Step-by-step explanation:

We have the following functions:

[tex]f(x)=3x +2\\[/tex] and [tex]g(x) = x^2 -2x +1[/tex]

First we find [tex](f + g) (x)[/tex]

To find [tex](f + g) (x)[/tex] we must add the function f(x) with the function g(x)

[tex](f + g) (x)=3x +2 + x^2 -2x +1[/tex]

[tex](f + g) (x)=x^2 +x +3[/tex]

Now we find [tex](f - g) (x)[/tex]

To find [tex](f - g) (x)[/tex] we must subtract the function f(x) with the function g(x)

[tex](f - g) (x)=3x +2 - (x^2 -2x +1)[/tex]

[tex](f - g) (x)=3x +2 - x^2 +2x -1[/tex]

[tex](f - g) (x)=-x^2 +5x +1[/tex]