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evablogger [386]
3 years ago
10

A builder uses squares to lay out various projects. Write two equations. The first equation should express the area of the squar

e (a) as a function of the length (l) of a side. The second should express the volume of a cube (v) as a function of the length (s) of a side.
Mathematics
1 answer:
Gnoma [55]3 years ago
3 0
Area as a function of length can be written as

f(l) = l^2

And volume of cube can be expressed as a function of side s as,

f(s) = s^3
You might be interested in
15 points pls brainliest show your work no calculator
FinnZ [79.3K]

Based on the calculations on the given expressions, the correct answers are as follows:

  1. Expression = 25/2 or 12.5.
  2. Difference = 5.
  3. n = 6.
  4. Expression = 31/15.
  5. Prime factorization of 96 = 2⁵ × 3¹.
  6. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, and 48.
  7. Inequality = 2³ < 3².
  8. Total amount = $255.
  9. Expression = 5.

<h3>How to evaluate this expression?</h3>

In order to evaluate this expression, we would substitute the value of x into upper and lower part respectively and then simplify as follows:

Expression = (6x + 8)/(4x - 24)

Expression = (6(7) + 8)/(4(7) - 24)

Expression = (42 + 8)/(28 - 24)

Expression = 50/4

Expression = 25/2 or 12.5.

Next, we would translate the given word problem into an algebraic expression:

Difference = 10 - 5

Difference = 5.

To solve for the value of n in the given expression:

-15 + n = -9

n = -9 + 15

n = 15 - 9

n = 6.

Expression = 2/3 + 1 2/5

Expression = 2/3 + 7/5

Expression = (10 + 21)/15

Expression = 31/15.

Next, we would write the prime factorization of 96:

Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

96 = 2 × 2 × 2 × 2 × 2 × 3

96 = 2⁵ × 3¹.

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, and 48.

<h3>How to determine the inequality symbol?</h3>

2³ __  3²  ≡  8 __ 9

Since 8 is less than 9, the inequality symbol which would complete the number sentence is < and it would be written as follows:

Inequality = 2³ < 3².

Next, we would calculate the total amount of money that KeeKee will spend:

Initial cost = 3 × $60 = $180

Total amount = initial cost + final cost

Total amount = $180 + $75

Total amount = $255.

Finally, we would simplify the given expression:

Expression = 3² + 2(12 ÷ 4 - 2 + 3)

Applying BODMAS, we have:

Expression = 3² + 2(3 - 2 + 3)

Expression = 3² + 2(3 - 5)

Expression = 3² + 2(-2)

Expression = 9 - 4

Expression = 5.

<h3>What is an expression?</h3>

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Read more on expressions here: brainly.com/question/28260012

#SPJ1

7 0
1 year ago
Choose two values, a and b, each between 8 and 15. Show how to use the identity a^3+b^3=(a+b)(a^2-ab+b^2) to calculate the sum o
qaws [65]

Answer:

Step-by-step explanation:

a = 8

b  = 10

a^3 =8^3 = 512

b^3= 10^3 =1000

a^3 + b^3 = 1512

a^2 = 64

-ab = - 80

b^2 = 100

a + b=18

(a + b) (64 -  80+ 100)

18 * (84)

1512'

5 0
3 years ago
Emma also wonders how long it will take her balance of $300 to reach $450, assuming she doesn't make any payments
Mama L [17]

Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.

An increasing exponential function is modeled by:

A(t) = A(0)(1+r)^t

In which:

A(0) is the initial value.

r is the growth rate, as a decimal.

In this problem:

Her initial balance is of $300, hence . A(0)=300

The growth rate is of 15%, hence R =0.15

Then,

A(t) = A(0)(1+r)^t

A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\

It will reach $450 after t years, for which A(t) = 450, hence:

A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9

It will take about 2.9 years for Emma's balance to reach $450

Learn more about logarithm here

brainly.com/question/247340

#SPJ4 .

3 0
1 year ago
Wynn is 24 years old and has decided to reduce the number of cups of coffee he buys by 2 cups per day. One cup of coffee typical
Usimov [2.4K]

The total amount he would have at 69 is $343,347.81.

<h3>What is the total amount saved?</h3>

The formula that can be used to determine the future value of the deferred annuity is:

Future value = annuity factor x monthly deposit

Annuity factor = {[(1+r)^n] - 1} / r

Where:

  • r = interest rate = 5.5 /2 = 2.75%
  • n = number of payments = 2 x (69 - 24) = 90

Amount he would save every 6 months:

  • amount saved per day = $2.50 x 2 = $5
  • Amount saved per month : $5 x 30 = $150
  • Amount saved every 6 months = $150 x 6 = $900

Future value : 900 x {[(1.0275^90) - 1] / 0.275}= $343,347.81

To learn more about annuities, please check: brainly.com/question/24108530

#SPJ1

5 0
1 year ago
Josiah owns a food truck that sells tacos and burritos. He only has
bogdanovich [222]

Answer:

Therefore Josiah must sell 68 or 69 or 70 tacos in order to meet the requirement.

Step-by-step explanation:

Given , Josiah owns a food truck that sells tacos and burritos.

He sells each burritos for $7.50. If 79 burritos were sold.

Then the price of 79 burritos is $(7.50×79) =$592.50

Let x tacos were sold.

He sells each tacos for $5.

Then the price of x tacos is = $(x × 5)=$5x

Also given that Josiah must sell a minimum of $930 worth of tacos and burritos.

Therefore,

5x+592.50≥ 930

⇔5x≥930-592.50

⇔5x≥337.5

⇔x≥67.5

But he only has enough supplies to make 149 tacos or burrito.

He already sold 79 burrito.

So, remain space for tacos is = (149-79) = 70

So,67.5≤x≤70

∴x = 68 or 69 or 70

Therefore Josiah must sell 68 or 69 or 70 tacos in order to meet the requirement.

8 0
3 years ago
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