ALGEBRA 2 FINALS
1. SPORTS Last year the volleyball team paid $5 per pair for socks and $17 per pair for shorts on a total purchase of $315. This year they spent $342 to buy the same number of pairs of socks and shorts because the socks now cost $6 a pair and the shorts cost $18.
a. Write a system of two equations that represents the number of pairs of socks and shorts bought each year. b. How many pairs of socks and shorts did the team buy each year?
Indicate the answer choice that best completes the statement or answers the question.
Determine whether each function has a maximum or minimum value, and find that value. Then state the domain and range of the function.
2. v(x) = –x2 + 14x – 57
a. minimum; –8; all real numbers; {f(x) | f(x) –8}
b. maximum; –57; all real numbers; {f(x) | f(x) –57} c. maximum; 14; all real numbers; {f(x) | f(x) 14}
d. maximum; –8; all real numbers; {f(x) | f(x) –8}

Answer:

Option (D)

Step-by-step explanation:

Given equation is,

[tex]8e^{2x+1}=4[/tex]

Taking natural log on both the sides of the equation,

[tex]\text{ln}(8e^{2x+1})=\text{ln}(4)[/tex]

[tex]\text{ln}(2^3)+\text{ln}(e^{2x+1})=\text{ln}(2^2)[/tex]

3ln(2) + (2x + 1)[ln(e)] = 2ln(2)

2n(2) - 3ln(2) = (2x + 1)

2x = -ln(2) - 1

[tex]2x=\text{ln}(\frac{1}{2})-1[/tex]  [Since, -ln(2) = ln(1) - ln(2) = [tex]\text{ln}(\frac{1}{2})[/tex]]

[tex]2x=\text{ln(0.5)}-1[/tex]

[tex]x=\frac{\text{ln(0.5)-1}}{2}[/tex]

Therefore, Option (D) will be the correct option.

Answer:

341 in sq

Step-by-step explanation:

When you are finding the area of trapezoids you have to do b1+b2/2 times height because there are two bases you have to include them both so adding 40 and 22 gives 62 and you have to divide that by 2 because the numbers will be too big and way off so 62/2 = 31 and you multiply that by the height to get 341 in sq. Hope it helps :P

Answer:

The length of the arc is 6.28 inches

Step-by-step explanation:

Given

[tex]\theta = 60[/tex]

Required

Length of the arc

This is calculated as:

[tex]L = \frac{\theta}{360} * 2\pi r[/tex]

So, we have:

[tex]L = \frac{60}{360} * 2 * \frac{22}{7} * 6[/tex]

[tex]L = \frac{15840}{2520}[/tex]

[tex]L = 6.28in[/tex]

Answer:

B

Step-by-step explanation:

you are comparing percent to percent and total boys to total class.

Answer:

P/100=6/9

Step-by-step explanation:

P represent percentage and percentage is 100. so

The height is 8.4.

Calculated with H = V / πr^2, with H for height, V for volume, and r for radius (the diameter divided by 2).

Answer:

answer is the first one

Step-by-step explanation:

i dont know how to explain it

9514 1404 393

Answer:

  40 cm²

Step-by-step explanation:

The area is given by the formula ...

  A = bh

  A = (8 cm)(5 cm) = 40 cm²

__

The length of the slanted side is irrelevant. The height is measured perpendicular to the base.

Answer:

1. y=5    x=8

2. x=9     y=5

3. x=12    z=4

Step-by-step explanation:

1.    4(5)+5(8)=60

2.   5(9)+3(5)=60

3.   4(12)+3(4)=60

Answer:

Number 2 is 3:4.

Number 1 is d.

Step-by-step explanation:

Boxers and collies added together gives you 12:16. Divide them both by 4 and you get 3:4.

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The number of student in class 4 (6) divided by the total number of kids in the entire class (18) gives you 0.33333333333. Multiply that by 100 and it gives you 33.3333333333. As a percentage it is 33 1/2 %

Answer:

1536 boys.

Step-by-step explanation:

Quite simple! 51.2% is 0.512, which we can use to calculate the number.

[tex]3000 * 0.512 = 1536[/tex] boys.

Alternative notation: 3000 * 51.2% = 1536

A = p(1+r)^t

1600 = p(1+0.08)¹⁰

P = 1600/2.1589

P= 741.12

741.12 dollar money did you originally deposit into your savings account!

Answer:

Simple interest:  Principal = $2000

Annual compound interest:  Principal = $1380.59

Step-by-step explanation:

As the question does not stipulate which type of interest was applied, please find below calculations for both simple interest and annual compound interest.

Simple Interest Formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for P:

[tex]\implies \sf 1600=P(0.08)(10)[/tex]

[tex]\implies \sf 1600=0.8P[/tex]

[tex]\implies \sf P=\dfrac{1600}{0.8}[/tex]

[tex]\implies \sf P=2000[/tex]

Therefore, the initial deposit (principal) was $2000.

.....................................................................................................

Annual Compound Interest Formula

[tex]\large \text{$ \sf I=P\left[\left(1+r\right)^{t} -1\right]$}[/tex]

where:

Given:

Substitute the given values into the formula and solve for P:

[tex]\implies \sf 1600=P\left[\left(1+0.08)^{10}-1\right][/tex]

[tex]\implies \sf 1600=P\left[\left(1.08)^{10}-1\right][/tex]

[tex]\implies \sf 1600=P\left[2.15892...-1\right][/tex]

[tex]\implies \sf 1600=P\left[1.15892...\right][/tex]

[tex]\implies \sf P=\dfrac{1600}{1.15892...}[/tex]

[tex]\implies \sf P=1380.5897...[/tex]

Therefore, the initial deposit (principal) was $1380.59 (nearest cent).

Learn more about simple interest here:

https://brainly.com/question/27743947

Learn more about compound interest here:

https://brainly.com/question/27747709

Answer: Crissy is correct

Step-by-step explanation:

Given

The volume of the rectangular prism is [tex]360\ units^3[/tex]

The height of the prism is [tex]h=10\ units[/tex]

Suppose A is the area of the base

So, the volume is given by

[tex]\Rightarrow V=A\times h[/tex]

Insert the values

[tex]\Rightarrow 360=A\times 10\\\Rightarrow A=36\ \text{or}\ 6\times 6\ units^2[/tex]

As 36 is the perfect square of 6, therefore, the base is a square with the dimension of [tex]6\times 6\ units^2[/tex]

Crissy's claim is correct.  

Answer:

i)  Speed and travel time

ii) Coffee and car

Step-by-step explanation:

i) Example of a pair of variable that have a negative Linear correlation

A negative correlated pair of variables simply means that the variables are inversely proportional to each other .and an example of such pair of variables is

Speed and Travel Time

Increase in speed causes a decrease in travel time. ( because the faster a car travels the shorter the travel time spent by the car while the slower a car travels the longer the travel time spent by the car )

ii) Example of a pair of variable with no linear correlation ( almost zero )

A close to zero linear correlation shows that there i no actual relationship between the variables.

Coffee and car

Increase or decrease in the cost of coffee will have no significant effect ( either negative or positive ) on the price of cars in the open market.

Answer:

B.

Step-by-step explanation:

$2.25 is the cost of each video that is rented, so $2.25 times v (or 2.25v) represents the cost of 'v' videos.

$20 is the constant, as it costs $20 to join the club. Since this doesn't change, it is the constant.

So, we would have the equation:

f(v) = 2.25v + 20

f(v) is the total cost.

B is your answer because it is the only one with the correct equation.

Hope this helps!

Answer:

i think its A

Step-by-step explanation:

if its not I'm sorry- um i think this cuz in the first figure where it says 8 its the same height side to side same thing with the 12. the second shape is also doing the same thing. really only thing that differes is the size. the second image is like a smaller version of the first one.

Answer:

Step-by-step explanation:

f'(x)=-sin x

[tex]f'(x)=\frac{cos \frac{\pi }{3} -cos (\frac{-\pi }{3}) }{\frac{\pi }{3} -(\frac{-\pi }{3}) } \\-sin x=\frac{\frac{1}{2} -\frac{1}{2} }{\frac{\pi }{3} +\frac{\pi }{3} } \\sin x=0\\at x=c ,sin c=0,c=0[/tex]

c=0∈(-π/3,π/3)

Answer:

I think the answer is 75.

Step-by-step explanation:

because 35 + 70 is equal to 105. So now we will just subtract 105 by 180. which will give us 75.

Answer:

24

Step-by-step explanation:

Total number of students and adult per class = 28 + 7 = 35

Van capacity = 9

Number of classes = 6

Total number of students including adults = (35 * 6) = 210

Number of vans needed = total / van capacity

= 210 / 9

= 23.333

Atleast 24 vans

ANSWER:

A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches.

A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.

A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches.

A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.

Step-by-step explanation:

HOPE IT HELPS

#CARRYONLEARNING

Answer:

1, 3, 5. *please report my answer if it is incorrect.*

Step-by-step explanation:

A cross-section parallel to the base is a rectangle measuring 15 inches by 8 inches.

A cross-section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.

A cross-section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.

Answer:

y = 0.5 (2)^x

Step-by-step explanation:

3rd option

you can plug in a coordinate point like (2, 2) to check this.

Answer:

Use Cross product Or Multiply both sides by 6 to get x alone

x/6 = 4/5

Multiplying 6 on both sides

we have

x=4/5 x 6

x=24/5 = 4.8

Answer:

Radius, r = 2.50 inches

Step-by-step explanation:

Given the following data;

Slant height of cone = 6 inches

Lateral surface area (LSA) of cone = 47.1 sq inches

To find the radius of the cone;

Mathematically, the lateral surface area of a cone is given by the formula;

LSA = πrl

47.1 = 3.142 * r * 6

47.1 = 18.852r

Radius, r = 47.1/18.852

Radius, r = 2.50 inches

Answer:

3 can

Step-by-step explanation:

there

peeeeeeeeeeeeeeeeeeeeeeeeeenas

Answer: what method? GCF or LCM

Step-by-step explanation: