a specialty food store carries four popcorn flavors. the presentage of each type of flavor carried by the store is shown below All the boxes of cinnamon and cheese popcorn are displayed at the front entrance is the display has 60 boxes how many boxes of popcorn does the store have in all

kettle corn 60%
caramel popcorn 10%
cinnamon popcorn 15%
cheese popcorn 15%

(answers)

A 400
B 200
C 100
D 30

Answer:  overspending $50 per month

Step-by-step explanation:

Income (Money In):           Expenses (Money out):

              $800                   Rent = $400

                                          Food = $200

                                          Gas   = $100

                                  Insurance = $ 50

                                      Phone = $100  

TOTAL = $800             TOTAL = $850

Jessie has more money out than money in so she is overspending

by $850 - $800 =  $ 50

Answer:

Part a) [tex]\$17,622.72[/tex]

Part b) [tex]\$20,442.36[/tex]

Part c) [tex]\$23,713.13[/tex]

Part d) [tex]\$27,507.23[/tex]

Step-by-step explanation:

we know that  

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

Part a) How much would you have at the end of 1 year?

in this problem we have

[tex]t=1\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*1}=\$17,622.72[/tex]

Part b) How much would you have at the end of 2 year?

in this problem we have

[tex]t=2\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*2}=\$20,442.36[/tex]

Part c) How much would you have at the end of 3 year?

in this problem we have

[tex]t=3\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*3}=\$23,713.13[/tex]

Part d) How much would you have at the end of 4 year?

in this problem we have

[tex]t=4\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*4}=\$27,507.23[/tex]

Answer:

28.8 ft

Step-by-step explanation:

SOH CAH TOA reminds you that ...

Tan = Opposite/Adjacent

The height to the top of the antenna is opposite the angle of elevation, and the distance to the building is adjacent. So, we have ...

tan(58°) = (160 ft +antenna height)/(118 ft)

(118 ft)·tan(58°) = 160 ft + antenna height . . . . . . . multiply by 118 ft

188.8 ft - 160 ft = antenna height = 28.8 ft . . . . . . subtract 160 ft, evaluate

The height of the antenna is 28.8 ft above the top of the building. (The total height of building + antenna is 188.8 ft.)

The problem can be solved using trigonometry. The tangent of the angle of elevation equals the total height (building plus antenna) divided by the distance from the point to the base of the building. Subtract the building's height from the total height to get the antenna's height.

To find the height of the antenna, we need to solve a right triangle problem using trigonometry. We know that the building is 160 Ft tall, and the angle of elevation to the top of the antenna is 58 degrees from a point 118 Ft from the base of the building. This forms a right triangle, with the building's height as one side, the horizontal distance of 118 Ft as another, and the antenna height as the hypotenuse. We can use the tangent of the angle to calculate the height of the antenna:

tangent(58) = opposite/adjacent

Here, 'opposite' represents the antenna's total height above the ground and 'adjacent' the distance from the point to the base of the building. So:

tangent(58) = total height / 118

To find the total height, we rearrange the formula:

total height = tangent(58) * 118

But remember the total height includes the building's height, so we subtract that to get the antenna's height:

antenna's height = total height - height of the building

Which, after substituting the known values, gives us the antenna's height.

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Answer:

C.  Each additional t-shirt being printed will increase the total cost by $11.

Step-by-step explanation:

We know that the total cost of custom t-shirts, y, in dollars, for x t-shirts is given by:

[tex]y = 11x + 25[/tex]

Here 11 is the price of the shirt, x is the number of shirts that are printed and 25 might be some additional charges.

For each additional shirt that is printed, the total price, y, will increase by $11 so the correct answer option is C.

Answer:

5 seconds

Step-by-step explanation:

The relationship between "d" and "the ground" is not described. If we assume that "d" is distance above the ground, then the rock will hit the ground when d=0. This gives rise to the quadratic equation ...

-t^2 +4t +5 = 0

-(t -5)(t +1) = 0

t = 5 or t = -1 are solutions. Only the positive solution is useful.

The rock will hit the ground after 5 seconds.

Answer:

  18 minutes 34.8 seconds

Step-by-step explanation:

We assume the minutes of commercials are proportional to the minutes of television, so we have ...

  (6 minutes of commercials)/(6 + 25 minutes of television) = x/(96 minutes of television)

Multiplying by 96, we get ...

  x = 96·6/31 = 576/31 = 18 18/31 . . . . minutes of commercials

That's about 18 minutes, 34.8 seconds of commercials in 1 hour 36 minutes of television.

let's firstly convert the mixed fractions to improper fractions and then add them up.

[tex]\bf \stackrel{mixed}{9\frac{3}{4}}\implies \cfrac{9\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{39}{4}}~\hfill \stackrel{mixed}{1\frac{1}{8}}\implies \cfrac{1\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{9}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{39}{4}+\cfrac{9}{8}\implies \stackrel{\textit{using and LCD of 8}}{\cfrac{(2)39~~+~~(1)9}{8}}\implies \cfrac{78+9}{8}\implies \cfrac{87}{8}\implies 10\frac{7}{8}[/tex]

Answer:

The vale of 6 is 'Thousands'

Answer:

Place value of 6 is thousand and tens.

Step-by-step explanation:

6560   is the number where 6 has 2 place value

(1) at thousands

(2) at tens .

6,560 = 6000+500+60

          = 6x1000 +5x100+6x10

              Here we can see that 6 is at two places

              thousand and tens

Answer:

73.19

Step-by-step explanation:

4 * (1/2)* (6.5) * (5.63)

Answer:4

Step-by-step explanation:4/5 / 1/10= 4/5*10/1=20/5=4

4/5 divided by1/10 equals 4/5 times 10/1 which is 40/5=8

Answer: 14 gallons

Step-by-step explanation:

Let's call the total gallons Abdul's tank can hold x.

Then, based on the information given in the problem, you can write the following expression:

[tex]\frac{1}{5}x+7=\frac{7}{10}x[/tex]

Therefore, when you solve for x, you obtain the following result:

[tex]\frac{1}{5}x+7=\frac{7}{10}x\\\\\frac{1}{5}x-\frac{7}{10}x=-7\\\\-\frac{1}{2}x=-7\\\\-x=(-7)(2)\\x=14[/tex]

Abdul's tank can hold 14 gallons of gas. This is determined by establishing that 7 gallons brought the tank level from 1/5 to 7/10 full and calculating that 7 gallons is equivalent to half the tank's total capacity.

When solving for how many gallons Abdul's tank can hold, we need to create an equation based on what we know from the problem.

Originally, the gas tank is 1/5 full. After adding 7 gallons of gas, it is 7/10 full. The difference between 7/10 and 1/5 (which is the same as 2/10) gives us the amount of gas that was added to reach 7/10 full from 1/5 full. Therefore, 7/10 - 2/10 equals 5/10 or 1/2. This means the 7 gallons added filled up half of the tank's capacity.

If 7 gallons represent 1/2 of the tank's capacity, then the full capacity (C) can be found by doubling the 7 gallons:

Therefore, Abdul's tank can hold 14 gallons.

Answer:

Step-by-step explanation:

f and g will be inverses if f(g(x)) = x.

A — f(g(x)) = 5(0.2x -2) +10 = x -10 +10 = x . . . . . inverses

B — f(g(x)) = (±√x+3)^2 +3 = x ±6√x +9 +3 ≠ x . . . . . not inverses

  (even if it is g(x) = ±√(x+3), the functions are still not inverses)

C — 1/2(2x -7) +7 = x -7/2 +7 = x +7/2 ≠ x . . . . . not inverses

D — 1/4(4x +4) -1 = x +1 -1 = x . . . . . inverses

Answer:

ΔXOY ≅ ΔZOW ⇒ proved down

Step-by-step explanation:

* Lets study some facts on the circle

- If two chords equidistant from the center of the circles,

 then they are equal in length

* the meaning of equidistant is the perpendicular distances

 from the center of the circle to the chords are equal in length

* Lets check this fact in our problem

∵ XY and WZ are two chords in circle O

∵ OT ⊥ XY

- OT is the perpendicular distance from the center to the chord XY

∵ OU ⊥ WZ

- OU is the perpendicular distance from the center to the chord WZ

∵ OT ≅ OU

- The two chords equidistant from the center of the circle

∴ The two chords are equal in length

∴ XY ≅ WZ

* Now in the two triangles XOY and ZOW , to prove that

 they are congruent we must find one of these cases:

1- SSS ⇒ the 3 sides of the 1st triangle equal the corresponding

               sides in the 2nd triangle

2- SAS ⇒ the two sides and the including angle between them

                in the 1st triangle equal to the corresponding sides and

                including angle in the 2nd triangle

3- AAS ⇒ the two angles and one side in the 1st triangle equal the

                corresponding angles and side in the 2nd triangle

* Lets check we will use which case

- In the two triangles XOY and ZOW

∵ XY = ZW ⇒ proved

∵ OX = OZ ⇒ radii

∵ OY = OW ⇒ radii

* This is the first case SSS

∴ ΔXOY ≅ ΔZOW

Give each month a number:

January = 0

February = 1

March = 2

April = 3

Now set X to 3 in the equation ad solve for t.

t = -30cos(x/6) +60

t = -30cos(3/6) +60

t = 33.672 degrees. ( Round as necessary)

You would need to change the +60 to a new starting point based on what the rise in temperature is due to global warming.

The model predicts a maximum afternoon temperature of around 33.67°C in April. To adjust for the impact of global warming, one can increase the constant term in the equation based on observed data. For instance, if there's a 2°C increase, the modified equation would be: t = -30cos(x/6) + (60 + 2).

Find the maximum temperature in April and how the model would change due to global warming:

Finding the maximum temperature in April:

Plug in x = 3: Since April is the fourth month (x = 0 for January), we need to substitute x with 3 in the equation:

t = -30cos(3/6) + 60

Calculate the temperature:

t = -30cos(0.5) + 60 ≈ 33.67°C

Therefore, the model predicts a maximum afternoon temperature of approximately 33.67°C in April.

Impact of global warming:

If the maximum temperature in April starts rising due to global warming, the model needs to be adjusted to account for the increase. Here's how:

Increase the constant term: The constant term in the equation (currently 60) represents the average temperature across all months. To account for a general rise in temperatures, we can increase this value.

Adjust the increase based on the observed data: The amount of increase should be based on observed data on how much the temperature has risen in April compared to the historical average.

For example, if observations show that the average April temperature has increased by 2°C due to global warming, we can modify the equation as follows:

t = - 30cos(x/6) + (60 + 2)  // Increase the constant term by 2

This new equation would then account for the simulated effect of global warming on the maximum afternoon temperature in April.

Answer: [tex](x+10)^2+(y+6)^2=121[/tex]

Step-by-step explanation:

The equation of a circle in the general form is:

 [tex]ax^{2}+by^2+cx+dy+e=0[/tex]

The equaton of  a circle in standard form is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where the center is at (h, k) and r is the radius

To write the equation of a circle from general form to standard form, you must complete the squaare, as you can see below:

1- Given the equation in general form:

[tex]x^{2}+y^2+20x+12y+15=0[/tex]

2- Complete the square:

-Group the like terms and move the constant to the other side.

- Complete the square on the left side of the equation.

- Add the same value to the other side.

Then you obtain:

[tex](x^{2}+20x)+(y^2+12y)=-15\\(x^2+20x+(\frac{20}{2})^2)+(y^2+12y+(\frac{12}{2})^2)=-15+(\frac{20}{2})^2+(\frac{12}{2})^2\\\\(x+10)^2+(y+6)^2=-15+100+36\\(x+10)^2+(y+6)^2=121[/tex]

Answer:

49.1 cm^2

Step-by-step explanation:

The appropriate area formula is ...

area = (1/2)(side 1)(side 2)(sin(angle between))

= (1/2)(10 cm)(12 cm)·sin(55°) = 60·sin(55°) cm^2

area ≈ 49.1 cm^2

Answer:

  B

Step-by-step explanation:

The question asks why you can use the argument that two angles are congruent. Hence, you want to have a statement that involves two angles in the two triangles. Only statement B is such a statement.

_____

Multiple choice questions often answer themselves, if you understand what you're reading.

Answer:

158

Step-by-step explanation:

Hey there!

503 - 345 = 158

Therefore, the answer is 158

Hope this helps you!

God bless ❤️

xXxGolferGirlxXx

Answer:

  buying in packets of 100

Step-by-step explanation:

Adding the given numbers results in a total that is twice the total number of cards the girls have. That total is 1256, so the total of the girls card collections is 628 cards.

  Mai has 628 -371 = 257 cards, so will need ceiling(257/9) = 29 pages

  Ellen has 628 -481 = 147 cards, so will need ceiling(147/9) = 17 pages

  Lora has 628 -404 = 224 cards, so will need ceiling(224/9) = 25 pages

Together, the girls need 29 +17 +25 = 71 pages.

If they were to buy packets of 10, they would need 8 packets, or 80 pages at 0.20 per page, for a cost of $16.00.

If they were to buy packets of 100, they would need 1 packet, or 100 pages at 0.15 per page, for a cost of $15.00.

Buying their pages in packets of 100 will cost the girls less.

First, we figure out how many cards each girl has, then determine how many pages they need in total. Comparing the costs, it is clear that it would cost less for the girls to buy the packets of 100 pages.

To answer this question, the first step is to find out how many cards each girl has. From the question, we understand that Ellen and Lora together have 371 cards and Lora and Mai together have 481 cards. The sum of Ellen's and Mai's cards totals to 404. By using these equations, we can determine that Lora has 227 cards, Ellen has 144 cards, and Mai has 254 cards.

Next, we need to find out how many pages each girl needs. Since each page has 9 pockets, Lora needs 26 pages (227 divided by 9, rounded up), Ellen requires 16 pages and Mai requires 29 pages. Altogether, they need 71 pages.

Now, let's get to the cost. At .20 cents per page, packets of 10 would cost $2, and they need 8 packets, which totals to $16. Alternatively, a packet of 100 costs .15 cents per page, which equals to $15.

Therefore, buying pages in packets of 100 will save the girls money as compared to buying in smaller packs of 10.

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We know that, usually,

[tex] c^2 = a^2+b^2 [/tex]

In this case, we also know that

[tex] c^2 = 2ab [/tex]

We deduce that

[tex] a^2+b^2 = 2ab [/tex]

If we subtract 2ab from both sides, we get

[tex] a^2-2ab+b^2 = 0 \iff (a-b)^2 = 0 \iff a=b [/tex]

So, the triangle is an isosceles right triangle, and so the angles are 90-45-45

Answer:

C) 7 ft 4 in

Step-by-step explanation:

Shadows are assumed to be proportional to the height of the object casting them. Hence the brother's shadow will satisfy ...

shadow/(6 ft) = (5.5 ft)/(4.5 ft) = 11/9 . . . . . reduce the fraction

shadow = (6 ft) · (11/9) . . . . . . . . . . . . . . . . . multiply by 6 ft

shadow = 7 1/3 ft = 7 ft 4 in

Answer:

y-5=3x+2

Step-by-step explanation:

1) to make up the equation through the given two points:

[tex]\frac{x+8}{-6+8}= \frac{y+1}{5+1}; \ => \ y=3x+24[/tex]

2) to change that equation according to the condition:

y-5=3x+24-5; ⇔ y-5=3x+19.

P.S. the way suggested above is not the shortest one.

Answer:

Step-by-step explanation:

We have alternative external corners.

The lines m and n are parallel. That is why the alternative external angles are congruent (they have the same measure).

In the triangle RTS we have angles:

[tex]4x^o,\ 54^o,\ 2x^o[/tex]

We know: The sum of the angles of the triangle is equal to 180 °.

Therefore we have the equation:

[tex]4x+54+2x=180[/tex]            subtract 54 from both sides

[tex]6x=126[/tex]           divide both sides by 6

[tex]x=21[/tex]

Answer:  [tex]sin\ 2x=-\dfrac{240}{289}\qquad cos\ 2x=\dfrac{161}{289}\qquad tan\ 2x=-\dfrac{240}{161}[/tex]

Step-by-step explanation:

[tex]cos\ x=\dfrac{15}{17}\quad and\quad csc\ x<0\implies sin\ x=-\dfrac{8}{17}\ and\ tan\ 2x=-\dfrac{8}{15}\\\\sin\ 2x=2(sin\ x\cdot cos\ x)\\\\.\qquad =2\bigg(\dfrac{-8}{17}\cdot \dfrac{15}{17}\bigg)\\\\\\.\qquad =2\bigg(\dfrac{-120}{289}\bigg)\\\\\\.\qquad=\large\boxed{-\dfrac{240}{289}}[/tex]

[tex]cos\ 2x=cos^2\ x-sin^2\ x\\\\.\qquad=\bigg(\dfrac{15}{17}\bigg)^2-\bigg(\dfrac{-8}{17}\bigg)^2\\\\\\.\qquad=\dfrac{225}{289}-\dfrac{64}{289}\\\\\\.\qquad=\large\boxed{\dfrac{161}{289}}[/tex]

[tex]tan\ 2x=\dfrac{sin\ 2x}{cos\ 2x}\\\\\\.\qquad=\large\boxed{-\dfrac{240}{161}}[/tex]

The trigonometry values are:[tex]\mathbf{sin(2x) = -\frac{240}{289}}[/tex], [tex]\mathbf{cos(2x) =\frac{161}{289}}[/tex] and [tex]\mathbf{tan(2x)= -\frac{240}{161}}\\[/tex]

The given parameter is:

[tex]\mathbf{cos(x) = \frac{15}{17}}[/tex]

If csc(x) is less than 0, then sin(x) is less than 0.

Using the following trigonometry ratio,

[tex]\mathbf{sin^2(x) +cos^2(x) = 1}[/tex]

Substitute [tex]\mathbf{cos(x) = \frac{15}{17}}[/tex]

[tex]\mathbf{sin^2(x) +(\frac{15}{17})^2 = 1}[/tex]

Expand

[tex]\mathbf{sin^2(x) +\frac{225}{289} = 1}[/tex]

Collect like terms

[tex]\mathbf{sin^2(x) = 1 -\frac{225}{289}}[/tex]

Take LCM

[tex]\mathbf{sin^2(x) = \frac{289-225}{289}}[/tex]

[tex]\mathbf{sin^2(x) = \frac{64}{289}}[/tex]

Take square roots

[tex]\mathbf{sin(x) = \pm\frac{8}{17}}[/tex]

Recall that, the sine of the angles is negative.

So, we have:

[tex]\mathbf{sin(x) = -\frac{8}{17}}[/tex]

sin(2x) is then calculated as:

[tex]\mathbf{sin(2x) = 2sin(x)cos(x)}[/tex]

This gives

[tex]\mathbf{sin(2x) = 2 \times \frac{-8}{17} \times \frac{15}{17}}[/tex]

[tex]\mathbf{sin(2x) = -\frac{240}{289}}[/tex]

cos(2x) is then calculated as:

[tex]\mathbf{cos(2x) =cos^2(x) - sin^2(x)}[/tex]

This gives

[tex]\mathbf{cos(2x) =(\frac{15}{17})^2 - \frac{64}{289}}[/tex]

[tex]\mathbf{cos(2x) =\frac{225}{289} - \frac{64}{289}}[/tex]

Take LCM

[tex]\mathbf{cos(2x) =\frac{225 - 64}{289}}[/tex]

[tex]\mathbf{cos(2x) =\frac{161}{289}}[/tex]

Lastly, tan(2x) is calculated using:

[tex]\mathbf{tan(2x)= \frac{sin(2x)}{cos(2x)}}[/tex]

So, we have:

[tex]\mathbf{tan(2x)= \frac{-240/289}{161/289}}[/tex]

[tex]\mathbf{tan(2x)= -\frac{240}{161}}\\[/tex]

Read more about trigonometry ratios at:

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Answer:

The answer is ⇒ No, because Deon starts with less bacteria,

but it grows at a faster rat than Cameron's bacteria

Step-by-step explanation:

* Lets study the graph and the equation

- At t = 0

# Cameron's population = 200

# Deon population = 100

- At t = 5

# From the equation b(5) = 200(1 + 0.08)^5 ≅ 294

# From the graph b(5) ≅ 200

∴ Cameron's population > Deon's population

- The increase of the Cameron's population ≅ 94

  (294 - 200 = 94)

- The increase of the Deon's population ≅ 100

  (200 - 100 = 100)

∴ The rat of increase of Deon > The rat of increase of Cameron

- At t = 8

# From the equation b(8) = 200(1 + 0.08)^8 ≅ 370

# From the graph b(8) ≅ 300

∴ Cameron's population > Deon's population

- The increase of the Cameron's population ≅ 76

  (370 - 294 = 76)

- The increase of the Deon's population ≅ 100

  (300 - 200 = 100)

∴ The rat of increase of Deon > The rat of increase of Cameron

- At t = 11

# From the equation b(11) = 200(1 + 0.08)^11 ≅ 466

# From the graph b(11) ≅ 500

∴ Cameron's population < Deon's population

- The increase of the Cameron's population ≅ 96

  (466 - 370 = 96)

- The increase of the Deon's population ≅ 200

  (500 - 300 = 200)

∴ The rat of increase of Deon > The rat of increase of Cameron

- At t = 14

# From the equation b(14) = 200(1 + 0.08)^14 ≅ 587

# From the graph b(14) ≅ 700

∴ Cameron's population < Deon's population

- The increase of the Cameron's population ≅ 121

  (587 - 466 = 121)

- The increase of the Deon's population ≅ 200

  (700 - 500 = 200)

∴ The rat of increase of Deon > The rat of increase of Cameron

* From all these calculations the rate of increase of

 Cameron's population is less than the rate of increase

 of Deon's population

∴ Cameron is not right because Deon starts with less bacteria,

   but it grows at a faster rat than Cameron's bacteria

Answer:

The answer is C

Step-by-step explanation:

Answer:

1/2 inch

Step-by-step explanation:

The area of a rectangle is the product of its length and width. So, the length and width of the photo will give a product of 24 when they are multiplied together.

One set of factors of 24 is 4 and 6, each of which is 1 unit less than the 5 and 7 dimensions of the paper on which the photo is printed. Hence a 1/2-inch border all around will result in a printed photo that is 4x6 on a 5x7 piece of paper.

___

If you want to write and solve equations, you can let b represent the border width. Then the photo area is ...

(5 -2b)(7 -2b) = 24

35 -24b +4b^2 = 24

4b^2 -24b +11 = 0

(2b -1)(2b -11) = 0

Solutions to this quadratic are b = 1/2, b = 11/2. The only viable solution is b = 1/2.

The border is 1/2 inch wide.

The answer is c)

Here’s why:

Answer: D. [tex] 7t^2+3+6[/tex]

Step-by-step explanation:

Given: The function 'a' represents the cost of manufacturing product A, in hundreds of dollars, and the function 'b' represents the cost of manufacturing product B, in hundreds of dollars.

[tex]a(t)=5t+2\\\\b(t)=7t^2-2t+4[/tex]

The expression that describes the total cost of manufacturing both products will be ,

[tex] a(t) + b(t)=5t+2+7t^2-2t+4[/tex]

Combining like terms, we  get

[tex] a(t) + b(t)=7t^2+5t-2t+4+2\\\\\Rightarrow\ a(t) + b(t)=7t^2+3+6[/tex]

Answer:

[tex]f^{-1}(x)=(+/-)\sqrt{4-x}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=4-x^{2}[/tex]

Let

y=f(x)

[tex]y=4-x^{2}[/tex]

Exchange the variables x for y and y for x

[tex]x=4-y^{2}[/tex]

Isolate the variable y

[tex]y^{2}=4-x[/tex]

square root both sides

[tex]y=(+/-)\sqrt{4-x}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=(+/-)\sqrt{4-x}[/tex] -----> inverse function

Answer:

f⁻¹(x) = ±√x-4

Step-by-step explanation:

We have given  a function.

f(x) = 4-x²

We have to find the inverse of given function.

Putting y = f(x) in given equation, we have

y  = 4-x²

Adding -4 to both sides of equation, we have

y-4 = 4-x²-4

y-4 = -x²

x² = 4-y

Taking square root to both sides of above equation, we have

x = ±√4-y

Putting x = f⁻¹(y) , we have

f⁻¹(y) = ±√4-y

Replacing y by x, we have

f⁻¹(x) = ±√x-4 which is the answer.

Answer:

 1) Methods:

-  Quadratic formula.

- Factorization.

- Completing the square.

2) If the determinant is less than zero ([tex]D<0[/tex]) then there are two roots that are complex conjugates.

Step-by-step explanation:

 Methods:

-  Quadratic formula

Given the quadratic equation in Standard form [tex]ax^2+bx+c=0[/tex], you can solve it with the quadratic formula:

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

- Factorization

You must find two expression that when you multply them, you get the original quadratic equation. For example:

[tex]x^2+6x+8=0[/tex]

Find two number whose sum is 6 and whose product is 8. These are 2 and 4. Then:

[tex](x+2)(x+4)=0[/tex]

When you make the multiplication indicated in [tex](x+2)(x+4)=0[/tex], you obtain [tex]x^2+6x+8=0[/tex]

- Completing the square

Given the quadratic equation in Standard form [tex]ax^2+bx+c=0[/tex],, you must turn it into:

[tex]a(x+d)^2+e=0[/tex]

Where:

[tex]d=\frac{b}{2a}\\\\e=c-\frac{b^2}{4a}[/tex]

Once you get that form, you must solve for x.

You can predict if the quadratic function will have a complex solution with the determinant:

[tex]D=b^2-4ac[/tex]

If [tex]D<0[/tex] then there are two roots that are complex conjugates.

Quadratic equations can be solved by several methods including the quadratic formula. The concept of a discriminant, calculated by b² - 4ac, can indicate if a function has a complex solution. A negative discriminant means the equation will have complex solutions.

Quadratic equations, or second-order polynomials, take on the form ax²+bx+c = 0. There are several methods to solve these equations, for instance, factoring, completing the square, using the quadratic formula or graphically.

The most general method is the quadratic formula: -b ± √b² - 4ac / 2a.

Indicator for a complex solution is called the discriminant(b² - 4ac). If the discriminant is negative, the equation will have complex solutions rather than real ones. This is because you'd be attempting to find the square root of a negative number, which is not possible within the set of real numbers, and hence the answer is in the form of a complex number.

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Answer:

B.) (x+3, y-7)

Step-by-step explanation:

x-coordinates increase farther to the right of the y-axis. Increasing the x-coordinate of a point by 3 will move the point 3 units to the right.

y-coordinates increase farther above the x-axis. Decreasing the y-coordinate of a point by 7 will move the point 7 units down.

To translate a point (x, y) 3 units right and 7 units down, the new coordinates need to be ....

(x +3, y-7) . . . . . . . . matches selection B