What are the coordinates for the function of the vertex for the quadratic function below

Answer:

For Kaisorn: [tex]y=50-2.50x[/tex]

For Thom: [tex]y=40-2x[/tex]

Step-by-step explanation:

Each month, Kaisorn deposits $50.00 onto her public transportation card.

It costs her $2.50 per trip to ride the subway. Means 2.50x

Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. Means 2x

Let x represents the number of trips

Let y represents the amount remaining in each account.

Then the system of equations represents their transportation costs are :

For Kaisorn: [tex]y=50-2.50x[/tex]

For Thom: [tex]y=40-2x[/tex]

[tex]\bf cot(x)cos(x)-cot(x)=0\implies cot(x)[cos(x)-1]=0 \\\\[-0.35em] ~\dotfill\\\\ cot(x)=0\implies \cfrac{cos(x)}{sin(x)}=0\implies cos(x)=0\\\\\\ x=cos^{-1}(0)\implies \boxed{x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ cos(x)-1=0\implies cos(x)=1\implies x=cos^{-1}(1)\implies \boxed{x=0}[/tex]

Answer:

x = π/2, 3π/2  

Step-by-step explanation:

cot(x)cos(x) - cot(x) = 0

Factor out cot(x)

cot(x)[cos(x) -1] = 0

Solve each part separately

cot(x) = 0                cos(x) - 1 = 0

x = π/2, 3π/2           cos(x) = 1

                                x = 0

There are three possible solutions:

x = 0, π/2, 3π/2

However, the function is undefined for x = 0.

∴ x = π/2, 3π/2

First, to simplify the expression 5 + 8(3 + x), distribute the 8 to everything inside the parentheses to get 5 + 24 + 8x. Then, combine the numerical terms to get the answer 29 + 8x.

The expression you are asked to simplify is 5 + 8(3 + x). To do this, you'll need to use the distributive property, which allows you to multiply a number outside a set of parentheses by every term inside the parentheses.

Start with the expression: 5 + 8(3 + x)

Before adding, you'll need to multiply eight by every term inside the parentheses, three, and x:

5 + 8*3 + 8*x

That changes your expression to:

5 + 24 + 8x

Now, you need to combine like terms (add together the numbers that are not attached to variable x):

5 + 24 = 29

So, the simplified version of the expression is:

29 + 8x

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A) multiples of 12 up to 72 ( 72 total cards)

12, 24, 36, 48, 60, 72 = 6 cards.

36 are gold.

Total gold cards and multiple of 12 = 36 + 6 =42

Probability of getting one of them is 42/72, which reduces to 7/12

B) 36 silver cards

Multiples of 9:  9, 18, 27, 36, 45, 54,63 = 7 cards

Silver cards are even and there is 3 even cards that are also multiples of 9, so subtract 3 from 7 to get 4.

Total silver cards and multiples of 9 = 36 + 4 = 40

Probability = 40/72 which reduces to 5/9

Answer:

Step-by-step explanation:

A.

Because there is no overlap between good card and card with a multiple of 12,

P(gold card or a card with a multiple of 12)

= P(gold card) + P(a card with a multiple of 12)

P(gold card)

= no. of gold cards / total no. of cards

= 36 / (36 + 36)

= 36 / 72

= 1/2

P(a card with a multiple of 12)

= no. of cards with multiples of 12 / total no. of cards

= (12, 24, 36, 48, 60, 72) / 72

= 6/72

= 1/12

P(gold card or a card with a multiple of 12)

= 1/2 + 1/12

= 7/12

B. There ARE overlaps between a silver card and a card with a multiple of 9,

P(silver card or a card with a multiple of 9)

= P(silver card) + P(a card with a multiple of 9) - P(silver card AND a multiple of 9)

P(silver card)

= no. of silver cards / total no. of cards

= 36 / (36 + 36)

= 36 / 72

= 1/2

P(a card with a multiple of 9)

= no. of cards with multiples of 9 / total no. of cards

= (9, 18, 27, 36, 45, 54, 63, 72) / 72

= 8/72

= 1/9

P(silver card AND a multiple of 9)

= no. of silver cards AND a multiple of 9 / total no. of cards

= (18, 36, 54, 72) / 72

= 4/72

= 1/18

P(silver card or a card with a multiple of 9)

= 1/2 + 1/9 - 1/18

= 10/18

= 5/9

Final answer:

The area of decorative paper needed, given the dimensions of length and width, is calculated as 50 square centimeters.

Explanation:

To answer the question about the area of decorative paper required, we need to use the formula for the area of a rectangle which is length times width. However, the given dimensions of a = 5 centimeters, w = 10 centimeters, and h = 6 centimeters seem to describe a box or a prism rather than a flat piece of paper. If the decorative paper is meant to cover the side of the box, then the relevant dimensions are likely length and width, not including the height. Assuming the decorative paper is to cover a flat surface, the formula for the area is A = length × width. Therefore, the required area of decorative paper is A = 5 cm × 10 cm = 50 square centimeters.

Answer:

0.78

Step-by-step explanation:

There are 500 students in total. Thus,

The probability that one of the students on the trip is an athlete or a band memeber is

[tex]Pr=\dfrac{325+40+25}{500}=\dfrac{390}{500}=0.78.[/tex]

Answer:

A

Step-by-step explanation:

Edge 2021

The inverse function of f(x) = 7x^9 is found to be f^{-1}(x) = (x/7)^{1/9}. By substituting f(x) into its inverse, we can verify that f^{-1}(f(x)) = x, which shows that the composition is indeed a function. Therefore, the correct answer is option a.

The student has asked to find the inverse function of f(x) = 7x^9 and determine if the composition of the original function and its inverse is a function. The inverse function, denoted as f^{-1}(x), undoes the action of the original function. To find the inverse, we replace f(x) with y, switch the roles of x and y, and then solve for y:

This gives us option a: y = (x/7)^{1/9}. To check if f^{-1}(f(x)) is a function, we substitute f(x) into the inverse, resulting in f^{-1}(7x^9) = (7x^9/7)^{1/9} = x, which is indeed a function. Therefore, f^{-1}(x) is a function, and option a is correct.

The ratio of muffins to donuts in the bakery is 4:7, calculated by dividing the number of muffins (36) by the number of donuts (63).

To find the ratio of muffins to donuts, we divide the number of muffins by the number of donuts.

Given:

- Number of donuts: 63

- Number of muffins: 36

Ratio of muffins to donuts:

[tex]\[ \text{Ratio} = \frac{\text{Number of muffins}}{\text{Number of donuts}} \][/tex]

[tex]\[ \text{Ratio} = \frac{36}{63} \][/tex]

We can simplify this ratio by finding the greatest common divisor (GCD) of 36 and 63, which is 9.

[tex]\[ \text{Ratio} = \frac{\frac{36}{9}}{\frac{63}{9}} \][/tex]

[tex]\[ \text{Ratio} = \frac{4}{7} \][/tex]

So, the ratio of muffins to donuts is  4:7 .

The ratio of muffins to donuts is [tex]\( \frac{4}{7} \)[/tex].

To find the ratio of muffins to donuts, we divide the number of muffins by the number of donuts:

[tex]\[ \text{Ratio of muffins to donuts} = \frac{\text{Number of muffins}}{\text{Number of donuts}} \][/tex]

Given that the bakery has 63 donuts and 36 muffins, we can substitute these values into the formula:

[tex]\[ \text{Ratio of muffins to donuts} = \frac{36}{63} \][/tex]

Now, we can simplify this fraction:

[tex]\[ \frac{36}{63} = \frac{4 \times 9}{7 \times 9} = \frac{4}{7} \][/tex]

So, the ratio of muffins to donuts is [tex]\( \frac{4}{7} \)[/tex].

Answer:

15

Step-by-step explanation:

10 + 25= 35 and 35-20 = 15

please give branlest

Answer:

Step-by-step explanation: She Needs To Deposit $35 Dollars To Return To The Orginal Ammount She Started With On Monday.

Answer:

Option b

Step-by-step explanation:

We know that, by definition:

[tex]secx = \frac{1}{cosx}[/tex]

We also know that:

[tex]tanx = \frac{sinx}{cosx}[/tex]

Applying these identities we can simplify the given expression

[tex]\frac{secx}{tanx} = \frac{\frac{1}{cosx}}{\frac{sinx}{cosx}}\\\\\frac{secx}{tanx} = \frac{cosx}{sinxcosx}\\\\\frac{secx}{tanx} = \frac{1}{sinx}[/tex]

We know that, by definition:

[tex]\frac{1}{sinx} = cscx[/tex]

Final answer:

To simplify sec x/tan x, we use trigonometric identities to show that sec x/tan x equals csc x, which is the cosecant of x.

Explanation:

To simplify the expression sec x/tan x, we need to recall the trigonometric identities for secant (sec) and tangent (tan). We know that sec x is equal to 1/cos x and tan x is equal to sin x/cos x. When we divide sec x by tan x, we are essentially dividing 1/cos x by sin x/cos x. This simplifies to:

To summarize, the simplified form of the expression sec x/tan x is csc x.

Answer:

Step-by-step explanation:

Part A

If it is compounded quarterly, the interest of 1.5 must be cut into a quarter of its present size. 1.5 //4 = 0.375 % per quarter.

In addition, the number of times that payment will be received is

4 quarters * 5 years = 20 quarters.

i = principle (1 + 0.375/100) ^20

i = principle (1 + 0.00375)^20

The principle = 4000 dollars.

i = 4000 * (1.00375)^20

i = 4000 * 1.07773

i = 4310.93

So she's tied up 4000 dollars to make 300 dollars.

Part B

I can't really give you an answer to this because I don't know if the 7% is compounded and over what period of time if it is, or if they mean 7% annually. There's a lot of variation in this question. Most people don't take money out of the market, so if it compounded, the formula would be

New Principle = starting amount (1.07)^4

New Principle = 4000 * 1.07^4

New Principle = 5243.18 so she would make about 4 times as much as the 300 she makes if she puts the money in a bond.

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

If the interest is simple interest

Gain would be 0.07 * 4000 = 280 dollars.

Over four years = 4*280 = 1120 dollars.

You are going to have to ask your teacher what is intended by this question.

Answer:

The distance between Bert and Ernie's apartments from Big Bird's nest

is 21 miles

Step-by-step explanation:

* Lets change the story problem to an equation to solve the problem

- The information i the story problem is

# The Big Bird's nest is halfway from there apartments

# The distance between Bert's apartment and Big Bird's nest is (5x + 4)

# The distance between Ernie's apartment and Big Bird's nest is (15x - 30)

* Now lets solve

∵ The Big Bird's nest is halfway from there apartments

∴ The distance between Bert's apartment and Big Bird's nest = The

   distance between Ernie's apartment and Big Bird's nest

∴ 5x + 4 = 15x - 30

- Collect the variable terms in one side and the numerical terms

 in th other side

∴ 15x - 5x = 30 + 4 ⇒ add

∴ 10x = 34

∴ x = 34 ÷ 10 = 3.4

* Now lets find the distance between Bert and Ernie's apartments

from the Big Bird's nest

- We can use any relation to find the distance

∵ The distance = 5x + 4

∵ x = 3.4

∴ The distance = 5(3.4) + 4 = 17 + 4 = 21 miles

You can check the answer by using second equation

∵ The distance = 15x - 30

∵ x = 3.4

∴ The distance = 15(3.4) - 30 = 51 - 30 = 21 miles

Answer:

The distance between Bert and Ernie's apartments from Big Bird's nest

is 21 miles

Step-by-step explanation:

* Lets change the story problem to an equation to solve the problem

- The information i the story problem is

# The Big Bird's nest is halfway from there apartments

# The distance between Bert's apartment and Big Bird's nest is (5x + 4)

# The distance between Ernie's apartment and Big Bird's nest is (15x - 30)

* Now lets solve

∵ The Big Bird's nest is halfway from there apartments

∴ The distance between Bert's apartment and Big Bird's nest = The

  distance between Ernie's apartment and Big Bird's nest

∴ 5x + 4 = 15x - 30

- Collect the variable terms in one side and the numerical terms

in th other side

∴ 15x - 5x = 30 + 4 ⇒ add

∴ 10x = 34

∴ x = 34 ÷ 10 = 3.4

* Now lets find the distance between Bert and Ernie's apartments

from the Big Bird's nest

- We can use any relation to find the distance

∵ The distance = 5x + 4

∵ x = 3.4

∴ The distance = 5(3.4) + 4 = 17 + 4 = 21 miles

You can check the answer by using second equation

∵ The distance = 15x - 30

∵ x = 3.4

∴ The distance = 15(3.4) - 30 = 51 - 30 = 21 miles

Answer:

x = 5

Step-by-step explanation:

For the parallelogram to be a square we use the property

The diagonals of a square are congruent, hence

12x - 23 = 4x + 17 ( subtract 4x from both sides )

8x - 23 = 17 ( add 23 to both sides )

8x = 40 ( divide both sides by 8 )

x = 5

Answer:

the answer is 0

Step-by-step explanation:

Bryant's score is 55 (given)

Jack's score is twice the score of Bryant, so it's

[tex]55\cdot 2 = 110[/tex]

Brenda's score is 13 less than Jack, so it's

[tex]110-13 = 97[/tex]

Answer:

[tex]8\ games[/tex]

Step-by-step explanation:

Let

x----->number of games won by the football team

we know that

[tex]25\%=25/100=0.25[/tex]

so

[tex]x=0.25(32)=8\ games[/tex]

Answer:  (2, 6.5)

Step-by-step explanation:

[tex]Midpoint_{x,y}=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{-3+7}{2},\dfrac{4+9}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{4}{2},\dfrac{13}{2}\bigg)\\\\\\.\qquad \qquad \quad=\large\boxed{(2,6.5)}[/tex]

There are 64 pieces that each child receive.

It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Here, Joelle's parents have combined all the candy = 256 candy

          Total number of Children = 4

         Equal division of candy in 4 children = Total Candy/No. of children

                                                                        = 256 / 4

                                                                       = 64

Thus, there are 64 pieces that each child receive.

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Final answer:

Each of the four children, including Joelle, will receive 64 pieces of candy after dividing the total of 256 pieces evenly among them.

Explanation:

To find out how many pieces of candy each child receives, we need to divide the total number of pieces by the number of children. Joelle and her three siblings make a group of four children in total. They have accumulated 256 pieces of candy. To divide this evenly, we do the following calculation:

Divide the total number of candies (256) by the number of children (4).

The division gives us the result 64 pieces of candy for each child.

Therefore, each child, including Joelle, will receive 64 pieces of candy.

➷ Find the difference from one peak ( highest point) to the next

In this case, it is 2 pi

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Answer:

2 pi

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

[tex]y=\frac{1}{4}x+2[/tex]

Step-by-step explanation:

The point-slope form of the equation of a line that passes that through points (8, 4) and (0, 2) is given as;

[tex]y-4=\frac{1}{4}(x-8)[/tex]

To find the slope-intercept form of this line, we need to expand the point-slope form.

[tex]y-4=\frac{1}{4}x-2[/tex]

We now solve for y to obtain;

[tex]y=\frac{1}{4}x-2+4[/tex]

We simplify to obtain:

[tex]y=\frac{1}{4}x+2[/tex]

This equation is now in the form;

[tex]y=mx+c[/tex]

This is what we refer to as the slope-intercept form.

Answer:

The value of x = 0.41

Step-by-step explanation:

∵ [tex]6e^{2x}-5e^{x}=6[/tex]

Let [tex]e^{x}=y[/tex]

∴ [tex]e^{2x}=y^{2}[/tex]

∴ 6y² - 5y = 6

∴ 6y² - 5y - 6 = 0 ⇒ factorize

∴ (3y + 2)(2y - 3) = 0

∴ 3y + 2 = 0 ⇒ 3y = -2 ⇒ y = -2/3

∴ 2y - 3 = 0 ⇒ 2y = 3 ⇒ y = 3/2

∵ [tex]y=e^{x}[/tex]

∴ [tex]e^{x}=\frac{-2}{3}[/tex] ⇒ refused

  ([tex]e^{ax}[/tex] never gives -ve values)

∵ [tex]e^{x}=3/2[/tex] ⇒ insert ln in both sides

∵ [tex]lne^{ax}=axlne=ax[/tex] ⇒ ln(e) = 1

∴ [tex]xlne=ln(3/2)[/tex]

∴ x = ln(3/2) = 0.41

Answer:

2

Step-by-step explanation:

Let's disect the problem. Three times a particular number plus fourteen equals 20. Let's make an equation, and replace the number with x.

We'll first minus 14 from each side to balance the equation, but with the intention of isolating the variable, x.

We have almost successfully isolated the variable. To isolate the variable, we can divide by three on each side.

Answer:

Reflection across x-axis, horizontal stretch by a factor of 10

and vertical translation up 4 units ⇒ answer (c)

Step-by-step explanation:

* The basic function of tanФ is

# y = tanФ

1- If y = -tanФ ⇒ reflect y over the x-axis

2- If y = tan(-Ф) ⇒ reflect y over the y-axis

3- If y = tan(Ф - k) ⇒ shift y right k units

4- If y = tan(Ф + k) ⇒ shift y left k units

5- If y = tanФ + k ⇒ shift y up k units

6- If y = tanФ - k ⇒ shift y down k units

7- If y = k tanФ ⇒ multiply y-values by k

 (k > 1 stretch, 0 < k < 1 compressed vertical)

 The scale factor is k

8- If y = tan(kФ) ⇒ divide x-values by k

 (k > 1 compressed, 0 < k < 1 stretch horizontal)

 The scale factor is 1/k

* Lets solve the problem

∵ y = -tan(1/10)x + 4

* We will use rules number 1 , 5 and 8

∴ Reflect y over the x-axis, shift y up k units and stretch

   horizontal by scale factor is 1/k (0 < k < 1)

∴ Reflection across x-axis, horizontal stretch by a factor of 10

  and vertical translation up 4 units

The vertex, would be the tip of the pyramid. If it was sliced at the vertex, the shape would be a triangle. Since the slice doesn't intersect the vertex, the point of the pyramid would net be included, it would be as if the tip was cut off.

You would then have a trapezoid, because the top would be a straight horizontal line parallel with the bottom line.

D

generally,

[tex] \sin( \alpha ) = \cos(90 - \alpha )[/tex]

you can visualize this by drawing a right triangle with acute angles a and 90-a

Answer:

D.  Both a and c are true.

Step-by-step explanation:

a . sin 18 = cos (90 - 18) = cos 72 so a is True.

b. this is not true.

c. sin 72 = cos(90 - 72) = cos 18, so c is true.

Answer:

Step-by-step explanation:

We have a rectangle measuring 25 feet × 9 feet. Remove from the rectangle two regular hexagons with a side length equal to 2 feet.

The formula of an area of a rectangle:

[tex]A_r=lw[/tex]

l - length, w - width.

Substitute l = 25 ft and w = 9 ft:

[tex]A_r=(25)(9)=225\ ft^2[/tex]

The formula of an area of a regular hexagon:

[tex]A_h=6\cdot\dfrac{a^2\sqrt3}{4}[/tex]

a - side

Substitute a = 2 ft:

[tex]A_h=6\cdot\dfrac{2^2\sqrt6}{4}=6\sqrt3\ ft^2[/tex]

The area of the wall:

[tex]A=A_r-2A_h[/tex]

Substitute:

[tex]A=225-2(6\sqrt3)=225-12\sqrt3\approx225-20.785=204.215\ ft^2[/tex]

Paiting the wall costs $1.75 per ft². Calculate:

[tex](\$1.75)(204.215)\approx\$357[/tex]

Answer:

Angles UWV and UWZ are complementary

Step-by-step explanation:

we know that

If the sum of the measures of two angles is equal to 90 degrees, then, the angles are complementary

so

In this problem

[tex]m<UWZ+m<UWV=90\°[/tex]

therefore

Angles UWV and UWZ are complementary