Henry steps onto an elevator at the first floor. He goes up to the 9th floor and then comes down 2 floors. He then goes up 4 floors and down 6 floors. What floor is Henry on?

Since you have the answers, I'll just show the steps on how to get there.

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Problem 19

[tex](1+4i)^2\\\\(1+4i)(1+4i)\\\\1*1 + 1*4i + 4i*1 + 4i*4i\\\\1 + 4i + 4i + 16i^2\\\\1 + 4i + 4i + 16(-1)\\\\1 + 4i + 4i-16\\\\(1-16) + (4i+4i)\\\\(1-16) + (4+4)i\\\\-15 + 8i\\\\[/tex]

Keep in mind that [tex]i = \sqrt{-1}[/tex] by definition. Squaring both sides leads to [tex]i^2 = -1[/tex]

In the second step, I used the idea that x^2 = x*x. Right after that, I used the FOIL rule to expand everything out.

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Problem 21

We could follow the same idea as problem 19, but I'll use a different approach.

[tex](A+B)^2 = A^2+2AB+B^2\\\\(3+i)^2 = 3^2 + 2*3*i + i^2\\\\(3+i)^2 = 9 + 6i - 1\\\\(3+i)^2 = 8 + 6i\\\\[/tex]

The formula on the first line is the perfect square binomial formula.

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Problem 23

The FOIL rule can be used if you want, but I'll use the difference of squares rule instead.

[tex](m+n)(m-n) = m^2 - n^2\\\\(3+5i)(3-5i) = (3)^2 - (5i)^2\\\\(3+5i)(3-5i) = 9 - 25i^2\\\\(3+5i)(3-5i) = 9 - 25(-1)\\\\(3+5i)(3-5i) = 9 + 25\\\\(3+5i)(3-5i) = 34\\\\[/tex]

It turns out that multiplying any complex number of the form a+bi with its conjugate a-bi will result in a purely real number (that has no imaginary part). More specifically: [tex](a+bi)(a-bi) = a^2+b^2[/tex]

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Problem 25

We could use the difference of squares rule again, but I'll show a different approach. This time using the distribution rule. The FOIL rule could also be used if you wanted.

[tex](6+7i)(6-7i)\\\\x(6-7i)\\\\6x-7xi\\\\6(x)-7i(x)\\\\6(6+7i)-7i(6+7i)\\\\6(6)+6(7i)-7i(6)-7i(7i)\\\\36+42i-42i-49i^2\\\\36-49(-1)\\\\36+49\\\\85\\\\[/tex]

I used x = 6+7i and the substitution property to help distribute. Lines 3 and 6 are where distribution is applied.

Answer:

5

Step-by-step explanation:

The answer is 60/12 becuase we can simfly both of theese mixed numbers into an improper fraction, wich will be 4/3*15/4. We do the multiplication, and we get 60/12. 60/12 can be simplifed to 5 becuase 60 divided by 12 is 5

Answer:

Can you provide how long it took to print per copy

Step-by-step explanation:

Answer:

it will take him 50 min because their are 730 and that is lot so it will take him 50min

Step-by-step explanation:

It is represented by ,

=> y ≥ 1/4x -1

make two pair of line segment of PQ andQP and construct use of a scale and the parallel line give the point name

Answer:

42x-42

Step-by-step explanation:

(7x)(6x)+(6)(-7)=42x°-42°

Answer:

$154.96

Step-by-step explanation:

difference means to subtract so 879.95-724.99=154.96

The left pic :

[tex]x = 46 \times \cos(70°) [/tex]

[tex]x = 46 \times 0.342[/tex]

[tex]x = 15.732[/tex]

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The right pic :

[tex] \tan(18°) = \frac{15}{x} \\ [/tex]

[tex]0.325 = \frac{15}{x} \\ [/tex]

Thus :

[tex]x = \frac{15}{0.325} \\ [/tex]

[tex]x = 46.1538[/tex]

There u go ...

Have a great day ❤

Answer:

w = win

Step-by-step explanation:

w=13

Answer:

w = 13

Step-by-step explanation:

16w - w = 15w

15w - 12w = 3w

3w - 2w = w

w = 13

Answer:

After reviewing the question you posted I have deduced that the correct answers are:

11) Max has $10.00. He earns $25.75 per lawn that he mows.

12) No. She is wrong. She did not group like terms correctly.

Step-by-step explanation:

11)

For 11) I first identified the independent variable of the equation, being "10".

And then the dependent variable of the equation, being "25.75". (The dependent variable of an equation will always be affected by the x)

I then looked at all the possible answers to see which one shared a independent variable of "10" and a dependent variable of "25.75".

The only possible answer that matches is Max has $10.00. He earns $25.75 per lawn that he mows.

This is because the only two possible answers that have "10" being a variable that does not change (independent variable) are:

--- "Max has $10.00. He earns $25.75 per lawn that he mows.

--- "Jon buys 10 toycars for $25.75 each"

However!

"Jon buys 10 toycars for $25.75 each" is an incorrect answer because it uses "10", although independent, as the x variable that affects the independent variable of "25.75".

12)

To find the correct answer for this question I simplified the equation from:

8t-15+3t   =   11m-15

Into:

8t+3t-15   =   11m-15

Which further simplifies into:

11t-15   =   11m-15

Which then you can notice that the two equations are similiar indeed, however they do not share like terms. One equation has "t" as their term, and the other as "m" as their term. Thus they do not share any like terms and are not equivalent.

Answer:

9a + 3b + 6c

Step-by-step explanation:

4a-6b+9c + 5a+9b-3c

4a + (-6b) + 9c + 5a + 9b + (-3c)

(4a + 5a) + (-6b+9b) + (9c-3c)

9a + 3b + 6c

Answer:

the person below is correct I believe

Step-by-step explanation:

hope this helped have a good rest of your night :)❤

Recall the half-angle identity for cosine:

cos²(x) = 1/2 (1 + cos(2x))

Then we can rewrite the integrand as

cos³(4x) = cos(4x) cos²(4x) = 1/2 cos(4x) (1 + cos(8x))

So we have

[tex]\displaystyle \int \cos^3(4x) \, dx = \frac12 \int (\cos(4x) + \cos(4x)\cos(8x)) \, dx[/tex]

Next, recall the cosine product identity,

cos(a) cos(b) = 1/2 (cos(a - b) + cos(a + b))

so that the integral is equivalent to

[tex]\displaystyle \int \cos^3(4x) \, dx = \frac12 \int \cos(4x) \, dx + \frac14 \int (\cos(4x - 8x) + \cos(4x + 8x)) \, dx[/tex]

[tex]\displaystyle \int \cos^3(4x) \, dx = \frac34 \int \cos(4x) \, dx + \frac14 \int \cos(12x) \, dx[/tex]

Computing the rest is trivial:

[tex]\displaystyle \int \cos^3(4x) \, dx = \boxed{\frac3{16} \sin(4x) + \frac1{48} \sin(4x) + C}[/tex]

Answer:

$425000

Step-by-step explanation:

561000*100/132=425000

Answer:

15227707.5

More info

Step-by-step explanation:

45x676787 the divide it by 2

Answer:

b = 24 ft

h = 10 ft

Step-by-step explanation:

120 = ½hb

120 = ½h(3h - 6)

240 = h(3h - 6)

240 = 3h² - 6h

 80 = h² - 2h

    0 = h² - 2h - 80

    0 = (h - 10)(h + 8)

    h = 10 ft or -8 ft

 we ignore -8 as it makes no sense for a triangle side length.

b = 3(10) - 6 = 24 ft

Answer:

Answer is A

Step-by-step explanation:

Subtract 47 from both sides to get 0

3x² - 18x - 42 = 0

Use Quadratic formula to get

[tex]3+\sqrt{23} \\3-\sqrt{23}[/tex]

Answer:

Step-by-step explanation:

9 1/2 is the same as a number decreased by 15

I guess that's the right answer maybe i'm wrong if I am oh well

Answer:

the ansewer is 56

Step-by-step explanation:

Answer:

a b d e

Step-by-step explanation:

i just took the test and got a hundred

Equations A, B, and E are true, i.e 66: 10 = 6.6, 660: 10° = 66, 6: 100 = 0.06​.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

Make sure your equation is correct by comparing the values on either side of the equals sign to create a true equation. A true equation must have the same numerical values on both sides of the "=" sign. One real equation is, for instance, 9 = 9. A valid equation is 5 + 4 = 9.

As a result, the true equations are,

66: 10 = 6.6

660: 10° = 66

6: 100 = 0.06​

Thus, equations A, B, and E are true, i.e 66: 10 = 6.6, 660: 10° = 66, 6: 100 = 0.06​.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ2

Step-by-step explanation:

Proportional = time/cars washed

= 1/3

no. of hours= 90hours

cars washed = 30 cars washed

Answer:

it would take 100 days for it to get better that just makes sense I think and for number two it would be 365% better

Step-by-step explanation:

Answer:

y = 10

Step-by-step explanation:

y = (-2)(x) + 4

y = (-2)(-3) + 4

y = 6 + 4

y = 10

Answer:

16

Step-by-step explanation:

8x8 is 64, so half of 8 is 4 so 4x4 is 16

Answer:

c

Step-by-step explanation:

In Line 4, she forgot to take the negative square root, because squaring both 8 and −8 equals 64.

Answer:

The ribbon costs 1.25 per meter

Step-by-step explanation:

5/4=1.25

Answer:

Sometimes it's better to leave them as roots because it's easier sometimes to solve problems with them still as roots

Answer:

We choose to leave radicals as roots without calculating them because calculating the square roots of a non perfect squares result in an irrational, non terminating decimal.

Step-by-step explanation:

Why do we do Radicals in the first place?

Radicals are used to write the square root or the nth root of a number. We sometimes leave specific numbers (non-perfect squares) as a radical because the output would be infinity

Example:

[tex]\sqrt45[/tex] is not a perfect square, it lies between [tex]\sqrt36[/tex]  and [tex]\sqrt49[/tex]

This means the number lies in between 6 and 7

The true root of 45 is irrational. Recall that irrational numbers are numbers of non-perfect squares. [tex]\sqrt45[/tex] = 6.7082039.......

Simplify:

[tex]\sqrt 45 = \sqrt 9 * \sqrt 5\\[/tex]

[tex]= \sqrt3^2 * \sqrt 5\\\\ \\= 3\sqrt5[/tex]

We choose not to pursue simplifying this because  [tex]\sqrt5[/tex]  is irrational (square root of a non-perfect square)

Summary:

We choose to leave radicals as roots without calculating them because calculating the square roots of a non perfect squares result in an irrational, non terminating decimal.

-Chetan K

Answer:

the answer is 12.2

[tex] \frac{b}{0.52} \\ we \: know \: b = 6.344 \\ then \\ \frac{6.344}{0.52} \\ = 12.2[/tex]

60

Step-by-step explanation:

(-47)-(-107)

(-47)-1(-107)

-47+107

=60