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2 years ago

What is estimate + (-3.05) + (-9.8)

Mathematics

2 answers:

katovenus [111]2 years ago

8 0

-3.05 + -9.8 = -12.85

Hope this helps you! Happy Thanksgiving, here's a turkey!

serg [7]2 years ago

8 0

Since it is a estimate,

Round -3.05 to -3

Round -9.8 to -10

So, -3+-10=-13

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Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps

Firdavs [7]

ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the

x²y = -4 ... (I)

Condition 2: Real parts are the same

x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

x²y = -4 ... (I)
x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

y = -3 - x² ... (II)

Substituting into equation (I)

x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i

x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i

They result in conjugates

4 0

3 years ago

Read 2 more answers

Tyra's kitchen is 42 m wide and 6.3 m long. She is pasting a decorative border strip that costs $5.95 per meter around the top e

Setler [38]

Answer:

$124.95

Step-by-step explanation:

The length of the strip is equal to perimeter of the kitchen.

P = 2(4.2 + 6.3) = 21 m

Cost of the strip is:

21*$5.95 = $124.95

8 0

2 years ago

Harry church borrowed 17,500.00 at 6.5% exact interest. He had to pay back a maturity value of 17,873.97 to pay off the loan. Wh

kirill [66]

Answer:the term of the loan is approximately 4 months

Step-by-step explanation:

The term of the loan means the period for which the loan was given.

We would apply the formula for simple interest which is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

P = 17500

R = 6.5%

I = total amount paid - principal

I = 17,873.97 - 17,500.00 = 373.97

Therefore

373.97 = (17500 × 6.5 × T)/100

373.97 = 1137.5T

T = 373.97/1137.5

T = 0.32 years

Converting to months, it becomes

0.32 × 12 = 3.84

Approximately 4 months.

3 0

2 years ago

olchik [2.2K]

The correct answer is: [B]: " 25 a²⁵ b²⁵ " .
_________________________________________________________
Explanation:
_________________________________________________________
Given the expression:
_________________________________________________________
→ " (−5a⁵b⁵)² (a³b³)⁵ " ; Simplify.
_________________________________________________________
Let us being by examining:
______________________________________
→ "(−5a⁵b⁵)² " .

→ "(−5a⁵b⁵)² = (-5)² * (a⁵)² * (b⁵)² = (-5)(-5) * a⁽⁵ˣ²⁾ * b⁽⁵ˣ²⁾ = 25a⁽¹⁰⁾b⁽¹⁰⁾ ;

{Note the following properties of exponents:
(xy)ⁿ = xⁿ * yⁿ ;

(xᵃ)ᵇ = x⁽ᵃ * ᵇ) ;

(xᵃ) * (xᵇ) = x⁽ᵃ ⁺ ᵇ⁾ .}.
______________________________________

Then, we examine:
______________________________________
→ "(a³b³)⁵ " .

→ "(a³b³)⁵ = a⁽³ˣ⁵⁾b⁽³ˣ⁵⁾ = a⁽¹⁵⁾b⁽¹⁵⁾ .
______________________________________

So: " (−5a⁵b⁵)² (a³b³)⁵ = (-5)a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ;
________________________________________
Now, we simplify:

→ " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ;

→ " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ ;

= 25a⁽¹⁰⁾ a⁽¹⁵⁾b⁽¹⁰⁾ b⁽¹⁵⁾ ;

= 25a⁽¹⁰ ⁺¹⁵⁾ b⁽¹⁰⁺¹⁵⁾ ;

= 25a⁽²⁵⁾ b⁽²⁵⁾ ;
_______________________________________________
→ which is: Answer choice: [B]: " 25 a²⁵ b²⁵ " .
______________________________________________

5 0

2 years ago

Can somebody please help answer this word problem using grass method? And showing how u get the answer thanks!!!

xxTIMURxx [149]

Answer:3/20

Step-by-step explanation:

Fraction of total area mowed = (3/5) + (1/4) = 17/20

Therefore fraction of total area left = 1 - (17/20) = (20/20) - (17/20) = 3/20

8 0

1 year ago