Alex purchased 1 adult ticket and 2 student tickets for a total of $22. Jen purchased
1 adult ticket and 3 student tickets for a total of $28.
Let a = cost of adult ticket
Let s = cost of student ticket
Write the two equations which could be used to solve this problem using
elimination.

Answer:

[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]

Step-by-step explanation:

The standard form for a polynomial equation in its factored form is:

[tex]f(x)=a(x-p)(x-q)...[/tex]

Where p and q are the zeros and a is the leading coefficient.

We know that the degree of the polynomial is 5.

We are also given roots at x=3 and x=-2. Hence, our factors are (x-3) and (x+2).

These have a multiplicity of two, so we will square them.

We also know that there is a root at x=4. Hence, the factor is (x-4). This has a multiplicity of 1.

Therefore, our polynomial is now:

[tex]f(x)=a(x-3)^2(x+2)^2(x-4)[/tex]

We know that the y-intercept is 12. Therefore, if we substitute in 0 for x, we should get 12 for y. Here, we are solving for our a. Therefore:

[tex]12=a(0-3)^2(0+2)^2(0-4)[/tex]

Evaluate:

[tex]12=a(9)(4)(-4)[/tex]

Evaluate:

[tex]-144a=12[/tex]

Divide both sides by -144:

[tex]a=-1/12[/tex]

Hence, our entire polynomial is:

[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]

Answer: 3.082185x^2

Step-by-step explanation: Find the exact value using trigonometric identities

Answer:

A

Step-by-step explanation:

To find the change, we do final-beggining

since his first rating is -7 and his final rating is -2

-2-(-7)

Answer:

to get a green and pink it would be 24

i cant find find the special edit sorry

Step-by-step explanation:

Answer:

g^2 + 4 > -5

Step-by-step explanation:

sum implies addition so add it with 4

i can’t put the equal to thing on here but there is supposed to be a line under the greater than symbol

Answer:

[tex]g\geq +/- 3i[/tex]

Step-by-step explanation:

Using clues given in the problem, we can set up a solvable inequality.

A number g squared: [tex]g^{2}[/tex]

The sum of a number g squared and 4: [tex]g^{2}+4[/tex]

Is greater than or equal to: [tex]g^{2}+4\geq[/tex]

Greater than or equal to -5: [tex]g^{2}+4\geq-5[/tex]

Isolate [tex]g[/tex]:

[tex]g^{2}\geq -9[/tex]

Solve for [tex]g[/tex]:

[tex]\sqrt{g^{2}}\geq \sqrt{-9}[/tex]

This^ looks bad because of the negative, but as I'll show you in the next step it can be split up and you will use the value [tex]i[/tex], or [tex]\sqrt{-1}[/tex].

[tex]g\geq \sqrt{9} \sqrt{-1}[/tex]

[tex]g\geq +/-3i[/tex]

I hope this helps!

Answer:

$25.2

Step-by-step explanation:

Because 20% of $125.99 is 25.198 and if you round that number to the nearest cent you get 25.2.

Have a fantastic day!!!!!!!!!!!!!!

Answer:9

Step-by-step explanation: im not really sure I kinda just guess and check, so like, 2/3 times 3 is 6/3 which is 2. so 6/2 is 3. 3 times 3 is nine.

Answer:

we kinda need to see the prism

Answer:

what is the prisim

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

correct on edge

The answer is, sin (2x)=4√21/25

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here, given that,

sin(x)=2/5

and tan(x)>0

Then, cos(x)=√21/25

tan(x)=2/√21

Now, sin (2x)=2tan(x)/1+tan²(x)

                    =0.873/1.19

                    =0.733

                    =4√21/25

To learn more trigonometry click:

https://brainly.com/question/26719838

#SPJ2

Answer:

I don't know but do you know how to answer this:

Two similar right triangles have areas of 6 square inches and

150 square inches. The length of the hypotenuse of the smaller

triangle is 5 inches. What is the sum of the lengths of the legs

of the larger triangle?  

Answer:

:>

Step-by-step explanation:

Answer: It is 10

Step-by-step explanation:

Answer:

2 bonus stars

Step-by-step explanation:

0.04 million= 40,000

40000/1701= 23.5

23.5(3)= 70.5

70.5/33= 2 stars

Answer:

54

Step-by-step explanation:

Answer:

The radius of the circle is: 4.09 cm

Step-by-step explanation:

Assuming the shape to be a circle.

The perimeter of a circle is called circumference and is given by the formula.

[tex]C = 2\pi r[/tex]

For the time being, we know

[tex]\pi = 3.142\\C = 25.71cm[/tex]

Putting the values in the formula we get: as x is the radius

[tex]25.71 = 2 * 3.142 * x\\25.71 = 6.284x\\x = \frac{25.71}{6.284}\\x = 4.09\ cm[/tex]

Hence,

The radius of the circle is: 4.09 cm

Answer:

(A) the subtraction property of equality

Step-by-step explanation:

Given

The steps in the question

Require

Justify step 2 to 3

Write out step 2:

[tex]-4x+9 = 2x+10[/tex]

Apply subtraction property by subtracting 2x from both sides

[tex]-4x-2x+9 = 2x-2x+10[/tex]

[tex]-6x+9 = 10[/tex]

Notice that the above equation is represented in step 3.

Hence, option A answers the question.

A. the subtraction property of equality

Given :

A new car depreciates as soon as you drive it out of the parking lot. A certain car depreciates to  half its original value in 4 years. If you bought a car 8 years ago and it is now worth $5,000.

To Find :

How  much did you pay for the car originally.

Solution :

Let, original price is x.

It is given that price gets half after 4 years.

So, price after 8 year is, P = x/4 .

x/4 = 5,000

x = $20,000

Therefore, price of new of car is $20,000.

Hence, this is the required solution.

Answer:

- 5/6

- 1/3

Step-by-step explanation:

Answer:

A and F

Step-by-step explanation:

5/6 and 1/3

Answer:

The weights of ice cream cartons produced by a manufacturer are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.5 oun

Answer:

Fraction of composite numbers = 6/10

Fraction of prime numbers = 4/10

Step-by-step explanation:

A composite number can be defined as a positive integer that will be formed when we multiply two smaller positive integers. It can also be said to be a positive integer that has at least one divisor of which 1 and itself are not included.

Thus, it means that the set of numbers given to us which is;

(11, 12, 13, 14, 15, 16, 17, 18, 19, 20), the composite numbers are;

12, 14, 15, 16, 18, 20

This is because each of them have at least one divisor that is neither itself or 1.

Thus, we have 6 out of the 10 numbers as composite.

Fraction of composite numbers = 6/10

Now, a prime number is a number that are only divisible by itself and 1.

Thus,from the given set, the prime numbers are; 11, 13, 17 & 19

We have 4 out of 10 numbers as prime numbers.

Thus, fraction of prime numbers = 4/10

Answer:

x

x

are

Step-by-step explanation:

For x ≥ 0, the value of f(g(x)) is x,For x ≥ 0, the value of g(f(x)) will be x and functions f and g are inverse functions.Option a from all the choices is corect.

A connection between independent variables and the dependent variable.is defined by the function.

Functions help to represent graphs and equations. A function is represented by two variables one is dependent and another one is an independent function.

The relation between them is shown as y if dependent and x is the independent variable;

Given function;

f(x) = 16x²

g(x)=(1/4)√x

For x ≥ 0, the value of f(g(x)) is found as;

f(x) = 16x²

[tex]\rm f(g(x)) = 16 (\frac{1}{4} \sqrt x) ^2\\\\ f(g(x)) =\frac{16}{16} x\\\\ f(g(x)) = x[/tex]

For x ≥ 0, the value of g(f(x)) is

g(x)=(1/4)√x

[tex]\rm g(x)=\frac{1}{4}\sqrt x \\\\ g(x ) = \frac{1}{4} \times \sqrt{16 \ x^2}\\\\ g(x) = \frac{4}{4} x \\\\ g(x) = x[/tex]

For x ≥ 0, functions f and g are  inverse functions

Let,

y=F(X)

If,

y= 16x²

x=16y²

y² = x/16

y=(1/4)√x

Hence,For x ≥ 0, the value of f(g(x)),For x ≥ 0, the value of g(f(x)) will be x and x respectively.and For x ≥ 0, functions f and g are inverse functions.

Hence, option a from all the choices is corect.

To learn more about the function refer to the link https://brainly.com/question/12431044.

#SPJ2

It's closer to 2, so it would be rounded from 1.682 in to 2 in.

Answer:

No, its most likely 2

Step-by-step explanation:

6 is closer to 10

hope this helps :) btw if ya like rap follow my brother on yt his rap his name is Ghxstboiireaper

Answer:

1,087.59014, 23.7, 0.6868

Step-by-step explanation:

Any decimal that ends.

Answer:

125 boys, 90 girls and 20 adults

Step-by-step explanation:

Let the number of boys be x

Let the number of girls be y

Let the number of adults be z

If there are 235 people at the summer camp, then;

x + y+ z = 235 ..... 1

If there are 35 more boys than girls, then;

x = y + 35 .... 2

If there are 70 fewer adults than girls then;

y = z - 70

z = y - 70....3

Substitute 2 and 3 into 1;

x + y+ z = 235 ..

(y+35)+y+(y-70) =235

3y -35 = 235

3y = 270

3y/3 = 270/3

y = 90

Since x = y + 35

x = 90 + 35

x = 125

Also z = y - 70

z = 90+70

z = 20

There are 125 boys, 90 girls and 20 adults

Answer:

There are 90 girls, 125 boys, and 20 adults.

Step-by-step explanation:

Let x be the number of girls. How many boys were there?

x + 35

How many adults were there?

x - 70

We know that 235 people are at RSM summer camp. Use this to make an equation.

x + (x + 35) + (x - 70) = 235

x + x + 35 + x - 70 = 235

3x - 35 = 235

3x - 35 + 35 = 235 + 35

3x = 270

3x ÷ 3 = 270 ÷ 3

x = 90

x, x + 35, x - 70

90, 125, 20

Answer:

160

Step-by-step explanation:

120/3 = 40

40 x 4 = 160

May I have brainliest please? :)

Answer:

the answer is 81.402 in expanded form using the powers of ten = (8 x 10^1) + (1 x 10^0) + (4/10^1) + (0/10^2) + (2/10^3)

Step-by-step explanation:

Answer:

48/10

Step-by-step explanation:

Answer:

The expected game value is -1 cent

Step-by-step explanation:

Here, we want to calculate the expected value of the game

We have 4 aces and 4 kings, including 26 red cards

The number of aces is 4

Probability of drawing an ace is 4/52 = 1/13

Probability of drawing a king is also 4/52 = 1/13

There are 26 red cards

The number of red cards that are neither ace nor king

There are 2 red aces and 2 red kings

So the number of cards that are red but are not

aces nor kings are 26-2-2 = 22

The probability of selecting this is 22/52 = 11/26

So the expected value is simply the probability multiplied by the amount

Thus, we have;

(60 * 1/13) + (30 * 1/13) + (5 * 11/26)

= 60/13 + 30/13 + 55/26

= (120 + 60 + 55)/26 = 9.038 cents which is approximately 9 cents

we subtract this from the 10 cents we are playing with, thus we are left with 9-10 = -1 cent

Answer:

If 3 letters are picked from the word 'PROBABILITY', the chances of it being P is 33.33%.

Hope this helps and if you could mark me as brainliest. Thanks!