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sladkih [1.3K]
3 years ago
13

Simply the imaginary number square root -45

Mathematics
1 answer:
Paraphin [41]3 years ago
6 0

Answer:

3i\sqrt{5}

Step-by-step explanation:

Using the rule of radicals

\sqrt{a} × \sqrt{b} ⇔ \sqrt{ab}

and \sqrt{-1} = i

Given

\sqrt{-45}

= \sqrt{9(5)(-1)}

= \sqrt{9} × \sqrt{5} × \sqrt{-1}

= 3 × \sqrt{5} × i

= 3i\sqrt{5}

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Multiplying in any order results in the same product is called
STatiana [176]

Answer:

C) commutative

Step-by-step explanation:

Example: a x b = b x a

7 0
3 years ago
I’m not sure how to do this
Brums [2.3K]

Answer: lim as x → -5 of f(x) and g(x) = 300

               Domain of f(x) and g(x) is All Real Numbers

               f(-5) = 200

               g(-5) = 300

<u>Step-by-step explanation:</u>

The limit of f(x) as x approaches -5:

f(x) =\dfrac{4x^3+500}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+125)}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+5^3)}{x+5}\qquad \text{we can factor the cubic}\\\\\\.\qquad =\dfrac{4(x+5)(x^2-5x+25)}{x+5}\\\\\\.\qquad =4(x^2-5x+25)\\\\\\\text{as x approaches -5, f(x) = }4[(-5)^2-5(-5)+25]\\\\.\qquad \qquad \qquad \qquad \qquad =4(25 + 25 + 25)\\\\.\qquad \qquad \qquad \qquad \qquad =4(75)\\\\.\qquad \qquad \qquad \qquad \qquad =300

The limit of g(x) as x approaches -5:

g(x) = 4x² - 20x + 100

      = 4(-5)² - 20(-5) + 100

      = 100 + 100 + 100

      = 300

There is a restriction at x = -5 for f(x), however, that discontinuity has been filled with the 200 at x = -5. So the domain is ALL REAL NUMBERs.

There are no restrictions on x for g(x) so the domain is ALL REAL NUMBERs.

5 0
3 years ago
I don't know what to do with this one????!!!!!
TiliK225 [7]

Answer:

Step-by-step explanation:

height of post ÷ length of shadow = 2/10 = ⅕

height of tower is ⅕ the length of its shadow.

⅕×125 = 25

The tower is 25 feet tall

8 0
3 years ago
Which expression is equal to x + (y + z)?
arsen [322]
X+(y+z) is equal to saying (x+y)+z

This is called the cumulative property when order doesn’t matter or doesn’t change the equation. As in 1+2 is the same as 2+1. No matter which way we get the same answer. This only works with multiplication and addition though. Hope this helps. Any questions please just ask!! Thank you so much!!
5 0
4 years ago
Read 2 more answers
Josie took a road trip. She drove for 45 minutes at 70 miles per hour. Then she drove 15 minutes at 20 miles per hour. How far d
Hunter-Best [27]

Answer:

Therefore Josie drove  57.5 miles.

Step-by-step explanation:

Speed: The ratio of distance to time.

To find the distance we use the following formula

Distance= time \times speed

Given that Josie drove 45 minutes at 70 miles per hour.

45 \ minutes= \frac{45}{60}\ h=\frac34\ h

In 45 minutes, she traveled  = (70\times \frac34) \ miles

                                                =52.5 miles.

The she drove 15 minutes at 20 mile per hour.

15 \ minutes= \frac{15}{60}\ h=\frac14\ h

In 15 minutes, she traveled =(20\times \frac 14) \ miles

                                            =5 miles

Therefore Josie drove (52.5+5) miles= 57.5 miles.

3 0
3 years ago
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