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Nat2105 [25]
1 year ago
14

Find all zeros.

Mathematics
1 answer:
Jet001 [13]1 year ago
5 0

Answer:

{ 0, 3, - 3 }

Step-by-step explanation:

f(x) = x(2x - 3)(x + 3)

to find the zeros let f(x) = 0 , that is

x(2x - 3)(x + 3) = 0

equate each factor to zero and solve for x

x = 0

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = \frac{3}{2}

x + 3 = 0 ⇒ x = - 3

zeros are { 0, \frac{3}{2} , - 3 }

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If (2i/2+i)-(3i/3+i)=a+bi, then a=<br>A. 1/10<br>B. -10<br>C. 1/50<br>D. -1/10​
Verizon [17]

Answer:

Option A is correct.

Step-by-step explanation:

We are given:

\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi

We need to find the value of a.

The LCM of (2+i) and (3+i)  is (2+i)(3+i)

=\frac{2i(3+i)}{(2+i)(3+i)}-\frac{3i(2+i)}{(2+i)(3+i)}\\=\frac{6i+2i^2}{(2+i)(3+i)}-\frac{6i+3i^2}{(2+i)(3+i)}\\=\frac{6i+2i^2-(6i+3i^2)}{(2+i)(3+i)}\\=\frac{6i+2i^2-6i-3i^2)}{5+5i}\\=\frac{-i^2}{5+5i}\\i^2=-1\\=\frac{-(-1)}{5+5i}\\=\frac{1}{5+5i}

Now rationalize the denominator by multiplying by 5-5i/5-5i

=\frac{1}{5+5i}*\frac{5-5i}{5-5i} \\=\frac{5-5i}{(5+5i)(5-5i)}\\=\frac{5-5i}{(5+5i)(5-5i)}\\(a+b)(a-b)= a^2-b^2\\=\frac{5(1-i)}{(5)^2-(5i)^2}\\=\frac{5(1-i)}{25+25}\\=\frac{5(1-i)}{50}\\=\frac{1-i}{10}\\=\frac{1}{10}-\frac{i}{10}

We are given

\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi

Now after solving we have:

\frac{1}{10}-\frac{i}{10}=a+bi

So value of a = 1/10 and value of b = -1/10

So, Option A is correct.

8 0
3 years ago
Write the word sentence as an equation.
irinina [24]

Answer:

b - 9 = 2 I believe would be it

4 0
3 years ago
Read 2 more answers
Solve the following equation. 14 + (2x + 7) = 9x x=​
Dvinal [7]

Answer:

x=1

Step-by-step explanation:

14+2x+7=9x

2x-9x=7-14

-7x= -7

x= -7/-7

x=1

3 0
2 years ago
Tisha orders a carpet for a room that measures 270 square feet. The salesman says the carpet costs $12.00 per square yard. He ex
Tomtit [17]

Answer:

What error did the salesman make?

The salesman made an error when convert 270 square feet to yards.

What should be the actual cost of the carpet?

The actual cost of the carpet is $360

Step-by-step explanation:

From the question, we are told that:Tisha orders a carpet for a room that measures 270 square feet.

This means the room needs 270 square feet of carpet

But from the question, we know that the carpet is sold in square yards

We convert square feet to square yards

For our conversion rates

3 ft = 1 yard

9 ft² = 1 square yards(yd²)

270 ft² = x

Cross Multiply

9 ft² × x = 270ft² × 1 yd²

x yd²= 270ft² × 1 yd²/9 ft²

x = 30 yd²

Hence, 270ft² = 30yd²

Cost of carpet =

1 yd² = $12.00

30 yd² =

Cross Multiply

= 30 × $12.00

= $360.00

The actual cost of the carpet is $360

What error did the salesman make?

The salesman made an error when convert 270 square feet to square yards.

He said 270 square feet = 90 square yards

But he was wrong.

270 square feet = 30 square yards.

What should be the actual cost of the carpet?

The actual cost of the carpet is $360

3 0
3 years ago
Determine the constant of variation for the direct variation given. Type a numerical answer in the space provided.
Andreyy89

Answer:

B. 4

Step-by-step explanation:

Determine the constant of variation for the direct variation given.

(0, 0), (3, 12), (9, 36)

A. 3

B. 4

C.12

Direct variation is given by:

y = kx

Where,

k = constant of variation

(3, 12)

x = 3; y = 12

y = kx

12 = k*3

12 = 3k

k = 12 / 3

k = 4

(9, 36)

x = 9; y = 36

y = kx

36 = k * 9

36 = 9k

k = 36 / 9

= 4

k = 4

Constant of the variation = 4

5 0
3 years ago
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