Savvas Texas Algebra II
Topic 1 Performance Task
Topic 1 Performance Task
Filling Balloons
You are planning a surprise birthday party, and you would like to decorate with some
helium-filled balloons. You plan to use two different sizes of balloons. You will need to
purchase balloons and helium based on your party plans. The volume and cost of balloons
and helium tanks are listed below:
• The volume of each small balloon is 300 in."
3
• The volume of each large balloon is 1000 in.'.
• One package of 50 small balloons costs $2.59.
• One package of 24 large balloons costs $1.99.
• One small tank of pressurized helium can fill 20 ft of balloons. It costs $10.49.
You would like to fill at least 30 of each size of balloon for your party, but you would like to
use all of the helium you purchase. In addition, you would like to spend the least money
possible for balloons.
Task Description
Use functions to determine the number of balloons you need and how much your
supplies will cost.

It may seem random, but it's heavily biased toward those who participate in politics. It leaves out people who have not contacted the senator. A better method would be to look at voter registration data, and send out surveys to random people on the list.

Answer:

if the radius and diameter of two circles is same/equal then those two circles are similar

Step-by-step explanation:

Answer:

if the radius and diameter of two circles is same/equal then those two circles are similar

Step-by-step explanation:

Answer:

<1 and <2 value is 120°

hope it will help you

Answer:

(3x-2y)=-4(5x-3y)=-2

Answer:

44.73 mph

Step-by-step explanation:

Answer:

20 meters per second

Step-by-step explanation:

400m/20s = 20 m/s

Answer:

182

Step-by-step explanation:

182= 13.49

162= 12.73

204= 14.28

221=14.87

The irrational number represented by point D is 182. The correct option is A.

Irrational numbers are all real numbers that are not rational numbers in mathematics. Irrational numbers, on the other hand, cannot be stated as the ratio of two integers.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

The value on the number line 13.49 is equal to the square root of 182.

√182= 13.49

√162= 12.73

√204= 14.28

√221=14.87

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Answer:

80N

Step-by-step explanation:

F = ma (Newton's second law)

When F=48N, a = 6m/s2

--> m = F/a = 48/6 = 8 (kg)

When a = 10m/s2

--> F = ma = 8 . 10 = 80N

Answer:

Put in the question that you need help with

Step-by-step explanation:

I would probably be able to answer it for you.

Answer:

The answer to which expression is equivalent to 2(a+3b) is 2a+6b

Answer:Do you have a picture of the answers

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

[tex]z^{2}[/tex] + 3z - 3

36 + 18 - 3

51

Answer:

it is a function

Step-by-step explanation:

Answer:

Since there is one value of y for every value of x in ( − 4, 5 ), ( 1, − 1 ), ( 2, − 2), this relation is a function.

The relation is a function.

Hope this helps (●'◡'●)

Answer:32

Step-by-step explanation:

Answer:

just look it up it says 32 fluid ounces in one quart

Answer:

C. 6 rooms

Step-by-step explanation:

I think you means he uses 3/4 gallon for 1 room.

This is a division problem. Divide the amount of paint he has by the amount he uses to paint one room.

(4 1/2)/(3/4) = (9/2)/(3/4) = 9/2 * 4/3 = 36/6 = 6

Answer: 6 rooms

Answer:

end point ₂ of a segment  X₂ = - 22 ;  Y₂ = 29

Step-by-step explanation:

given;

midpoint = ( Mx = - 15 , My = 22 )

endpoint ₁  = ( X₁ = - 8 ,  Y₁ = 15 )

find the other endpoint ₂ ( X₂ , Y₂)

use the mid point formula to get the other endpoint:

Mx = ( X₁ + X₂ ) / 2              My = ( Y₁ + Y₂ ) / 2

- 15 = (-8 + X₂) / 2                 22 = (15 + Y₂) / 2

-30 = - 8 + X₂                         44 = 15 + Y₂

X₂ = -22                                    Y₂ = 29

Answer:

So, the formula for finding the midpoint of a segment given the coordinates of its endpoints is: ((x 1 + x2)/2, (y 1 + y 2 )/2 {Average of the x coordinates, average of the y coordinates}. For this problem we know the coordinates of the midpoint along with one of the endpoints.

Step-by-step explanation:

Use the midpoint formula

M = (  (x1 + x2) / 2  ,  (y1 + y2) / 2 )

(9, 0) = (  (x1 + 12) / 2  ,   (y1 + 3) / 2)

Break up this formula into two equations.

(x1 + 12) / 2 = 9   and (y1 + 3) / 2 = 0

 Solve for x1 and y1 from the equations.

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

Work Shown:

x = amount of money collected before tax is added

3% = 3/100 = 0.03

3% of x = 0.03x = amount of tax

x + 0.03x = adding on tax to original amount

1.03x = amount after tax is added

1.03x = 2766.58

x = 2766.58/1.03

x = 2686 is the amount of money before the 3% sales tax is added

0.03x = 0.03*2686 = 80.58 is the amount of sales tax collected

As a check,

2686+80.58 = 2766.58

which confirms our answer

Answer:

Tax collected= $80.58

Step-by-step explanation:

Let's say that the amount he got from services was "x", and to that he had to add a 3% of sales tax.

Recall that 3% in math form is written as: 3/100 = 0.03

then, he had to include 0.03 times x to the "x" amount in hotel services:

x + 0.03 x = 2766.58

1.03 x = 27688.58

x = 27688.58/1.03

x= $2686

Then, the amount for the taxes is 3% of this which is:

0.03 * 2686 = $80.58

Answer:

x = 5.5 units

Step-by-step explanation:

Since, B is the midpoint of AC.

[tex] \therefore \: AB = BC \\ 14 = 2x + 3 \\ 14 - 3 = 2x \\ 11 = 2x \\ x = \frac{11}{2} \\ x = 5.5 \: units \\ [/tex]

Answer:

Step-by-step explanation:

4x - y = 5..........… Equation 1

x + 2y = 8 ............. Equation 2

Make x the subject in equation 2 and substitute it into equation 1

That's

x = 8 - 2y

We have

4( 8 - 2y ) - y = 5

32 - 8y - y = 5

- 9y = - 27

Divide both sides by - 9

We have the final answer as

Substitute y = 3 into x = 8 - 2y

That's

x = 8 - 2(3)

= 8 - 6

Hope this helps you

Step-by-step explanation:

4x-y=5-----×1.

x+2y=8----×4.

which will be....

4x-y=5

- 4x+8y=32.

____________

-9y=-27

----- ----

-9. -9.

y=3.

then substitute into any equation...

equation one.

4x-3=5.

4x=5+3.

4x=8.

x=8/4.

x=2.

therefore y=3 and x=2.

The sum of the expressions (7x – 6y) and (3x – 5y) will be 10x – 11y.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The expressions are given below.

(7x – 6y) and (3x – 5y)

Then the sum of the expressions will be

⇒ (7x – 6y) + (3x – 5y)

⇒ 7x – 6y + 3x – 5y

⇒ 10x – 11y

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Answer:

C, Yes; for any given number of hours,there is only one possible cost.

Step-by-step explanation:

Simple Function question, if there’s an X with the same number, it’s not a function. It wasn’t D since it’s justifying the range being the same number

Answer:

20 m

Step-by-step explanation:

2) t = -b/2a (FROM QUAD. FORMULA)

   t =  -20/2(-5)

   t = 4/2 = 2/1 = 2

t = 2, insert

h(2) = -5(2)² + 20(2)

h(2) = -20 + 40

h(2) = 20 m

VERTEX: (2,20)

Answer:

20m

Step-by-step explanation:

Answer:

The interval over  which the cost is constant is from >0 to 15,000 gallons

The interval for which the the cost is increasing is from above 15,000 gallons

Step-by-step explanation:

For 15,000 gal or less the cost of the monthly water bill = $15.50

For over 15,000 gal, the cost of the monthly water bill = $15.50 plus $1 for each 1000 gal over 15,000 with any fraction of $1,000 charged at a fraction of $1

The interval for which the cost is constant is from 0 ≤ x ≤ 15,000 gal

The interval over which the const is increasing per 1000 gal over 15,000 gallons is from x > 15,000 gal.

Answer:

The interval in which the cost is constant is

[0,15000]

Step-by-step explanation:

The interval is increasing by [1500,∞]

Answer:

−10x2+−18x+26

Step-by-step explanation:

Let's simplify step-by-step.

−5x2−9x+8−5x2−9x+8−−6x2+5−6x2+5

=−5x2+−9x+8+−5x2+−9x+8+6x2+5+−6x2+5

Combine Like Terms:

=−5x2+−9x+8+−5x2+−9x+8+6x2+5+−6x2+5

=(−5x2+−5x2+6x2+−6x2)+(−9x+−9x)+(8+8+5+5)

Answer:

(1,2) (3,2) ( 5,2)

Step-by-step explanation:

Each input value can only go to one output value

The only one that has each input only going to one output is (1,2) (3,2) ( 5,2)

Answer:

The diagram for the question is missing, but I found an appropriate diagram fo the question:

Proof:

since OC = CD = 297mm Therefore, Δ OCD is an isoscless triangle

∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

∠DOP = 22.5°

∠PDO = 67.5°

∠ADO = 22.5°

∠AOD = 67.5°

Step-by-step explanation:

Given:

AB = CD = 297 mm

AD = BC = 210 mm

BCPO is a square

∴ BC = OP = CP = OB = 210mm

Solving for OC

OCB is a right anlgled triangle

using Pythagoras theorem

(Hypotenuse)² = Sum of square of the other two sides

(OC)² = (OB)² + (BC)²

(OC)² = 210² + 210²

(OC)² = 44100 + 44100

OC = √(88200

OC = 296.98 = 297

OC = 297mm

An isosceless tringle is a triangle that has two equal sides

Therefore for △OCD

CD = OC = 297mm; Hence, △OCD is an isosceless triangle.

The marked angles are not given in the diagram, but I am assuming it is all the angles other than the 90° angles

Since BC = OB = 210mm

∠BCO = ∠BOC

since sum of angles in a triangle = 180°

∠BCO + ∠BOC + 90 = 180

(∠BCO + ∠BOC) = 180 - 90

(∠BCO + ∠BOC) = 90°

since ∠BCO = ∠BOC

∴  ∠BCO = ∠BOC = 90/2 = 45

∴ ∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

For ΔOPD

[tex]Tan\ \theta = \frac{opposite}{adjacent}\\ Tan\ (\angle DOP) = \frac{87}{210} \\(\angle DOP) = Tan^-1(0.414)\\(\angle DOP) = 22.5 ^{\circ}[/tex]

Note that DP = 297 - 210 = 87mm

∠PDO + ∠DOP + 90 = 180

∠PDO + 22.5 + 90 = 180

∠PDO = 180 - 90 - 22.5

∠PDO = 67.5°

∠ADO = 22.5° (alternate to ∠DOP)

∠AOD = 67.5° (Alternate to ∠PDO)

Answer:

I prefer leaving the answer as √5 since it is a shorter form and exact form of the answer.

Here are reasons for leaving it as a radical form or a decimal approximation.

If you are looking for an exact answer, then you should leave it as √5. For example, if you are told a square has area 5 square units, then the exact length of the side is √5 units.

If √5 is the length of something that has to be made to that length, then you need an approximation. For example, if you are asked to make a square out of cardboard whose area is 5 square feet, then you need an approximation of √5 ft, such as 2.24 ft, so you can make each side of the cardboard square in the length of 2.24 ft.

We shall prefer to keep √5 in radical form, as it is an irrational number and will never give an exact value when converted to decimal form.

A rational number is any number that can be represented in the form p/q, where p and q are integers, q ≠ 0, and p, q are co-prime to each other, that is, they do not have any common factor except 1.

All terminating and non-terminating recurring decimals are rational numbers.

An irrational number is a real number that cannot be represented in the above form of a rational number.

All non-terminating non-recurring decimals are irrational numbers.

We are asked, what would we prefer to do. Leave √5 in radical form or convert it into decimal form.

∵ √5 is an irrational number, we will never get a perfect value of it in decimal form, as irrational numbers are non-terminating non-recurring decimals. So, we shall prefer to keep √5 in the radical form.

Use of √5 in radical form: Gives the exact value in our calculations for equations.

Use of √5 = 2.236067977499........... in the decimal form: Used in trigonometry where we need to find the trigonometric ratio.

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Answer:

2 sqrt(5) =x

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2 + b^2 = c^2

2^2 +4^2 = x^2

4+16 = x^2

20 = x^2

Take the square root of each side

sqrt(20) = sqrt(x^2)

sqrt(4*5) = x

sqrt(4) sqrt(5) =x

2 sqrt(5) =x

If a submarine at -650 feet defends 400 more feet then integer that represents its new position will be; -1050 feet

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

Given that ;

The submarine is underwater. It’s position is 650 feet below sea level.

It rises in the water 400 feet and then descends 400 feet.

Since the submarine again came back to original position by covering the distance.

The integer will be;

-650+(-400)=-1050

Hence the integer representing the change in the Submarine’s position is -1050

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Hey there! I'm happy to help!

Let's call these numbers x and y and model the information we have.

x=1/5y

y-x=228 (we see that x is smaller than y in the first equation, so we put it second )

We see that x is equal to 1/5y. We can switch the x in the second equation with 1/5y and solve for y.

y-1/5y=228

4/5y=228

We divide both sides by 4/5.

y=285

We know that x is 1/5 of y, so we divide by 5.

285/5=57

x=57

So, our numbers are 57 and 285.

Have a wonderful day! :D

The 2 positive numbers are 285 and 57 and they have a difference of 228.

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the bigger positive number and y the smaller number. Hence:

Also:

Solving equation 1 and 2 simultaneously gives:

x = 285, y = 57

The 2 positive numbers are 285 and 57 and they have a difference of 228.

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The answer to the question is 9,700.

Collinear points are points that lie on the same straight line.

In the figure, we can see that points E, B, and F are all on the same straight line, meaning that they are three collinear points.

Hope this helps.

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