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3 years ago

Challenge An arts academy requires there to be 4 teachers for every 76 students and 3 tutors for

Mathematics

1 answer:

klio [65]3 years ago

3 0

Answer:

12. 5

11.

15. 7

14. 11

18. 3

loo

Step-by-step explanation:

12. 5

11.

15. 7

14. 11

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Need help to do this step by step please <br> 3x2 - 2x=-1

sdas [7]

Answer:

Solving the expression $3x^2-2x=-1$ we get: $\mathbf{x=\frac{1+\sqrt{2}i }{3}\:or\:x=\frac{1-\sqrt{2}i }{3}}$

Step-by-step explanation:

We need to solve the expression: $3x^2-2x=-1$

This is a quadratic expression and it can be solved using quadratic formula

Solving:

$3x^2-2x=-1\\$

we can write it as:

$3x^2-2x+1=0$

The quadratic formula is: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where a = 3, b = -2 and c= 1

Putting values and solving:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(1)}}{2(3)}\\x=\frac{2\pm\sqrt{4-12}}{2(3)}\\x=\frac{2\pm\sqrt{-8}}{6}\\We\:know\:that\:\sqrt{-1}=i\\x=\frac{2\pm\sqrt{8}\sqrt{-1} }{6} \\We\:know\:\sqrt{8}=\sqrt{2\times 2 \times 2}=\sqrt{2^2 \times 2}=2\sqrt{2} \\x=\frac{2\pm2\sqrt{2}i }{6}\\Now,\\x=\frac{2+2\sqrt{2}i }{6}\:or\:x=\frac{2-2\sqrt{2}i }{6}\\x=\frac{2(1+\sqrt{2}i) }{6}\:or\:x=\frac{2(1-\sqrt{2}i) }{6}\\x=\frac{1+\sqrt{2}i }{3}\:or\:x=\frac{1-\sqrt{2}i }{3}$

So, solving the expression $3x^2-2x=-1$ we get: $\mathbf{x=\frac{1+\sqrt{2}i }{3}\:or\:x=\frac{1-\sqrt{2}i }{3}}$

8 0

3 years ago

Logan is getting a second dog and wants to increase the length of the play space by 3 feet and the width by 3 feet. What will be

alexgriva [62]

Answer:

$(3x+3y+9)\ ft^{2}$

Step-by-step explanation:

Let

x------> the length of the original play space

y-----> the width of the original play space

we know that

The area of the original play space is equal to

$A=xy$

The area of the new play space is equal to

$An=(x+3)(y+3)\\An=xy+3x+3y+9$

Find the difference

$An-A=(xy+3x+3y+9)-(xy)\\An-A= (3x+3y+9)\ ft^{2}$

4 0

3 years ago

Michael puts 3 beads next to each other on a pice of string to make a bracelet. Each bead has a width of 5/6 inch. Which express

pentagon [3]

Answer:

3 (5/6)

5/2

Step-by-step explanation:

Hi, to answer this question we have to write an expression with the information given.

The total width of the three beads must be equal to the number of beads (3) multiplied by the length of each bead (5/6)

Mathematically speaking:

3 (5/6)

Solving:

5/2

Feel free to ask for more if needed or if you did not understand something.

8 0

3 years ago

Ace Cars says they will pay Jim a 10% commission on the sale price of each car. Budget Cars says they will pay him $500 per week

Arisa [49]

Answer:

$20,000

Step-by-step explanation:

You can quickly figure this by recognizing that the difference in commission must be the same as the base salary:

2.5%(car price) = $500

car price = $500/0.025 = $20,000

If you prefer, you can get there with equations.

At Job 1, the pay is ...

y = 10%×(car price)

At Job 2, the pay is ...

y = 7.5%×(car price)

Setting the equal (the two opportunities pay the same), we have ...

0.10(car price) = 500 +0.075(car price)

0.025(car price) = 500 . . . . . . . . subtract 0.075(car price)

car price = 500/0.025 = 20,000 . . . . divide by 0.025

Jim would have to sell a $20,000 car each week for the jobs to pay the same.

8 0

3 years ago

1854times845 could someone help me

vivado [14]

Answer:

1,566,630

Step-by-step explanation:

1854*845=1,566,630

8 0

3 years ago