1 Calculator What is the area of this figure? Enter your answer in the box. units²

[tex](1-3i)(1-i)(1+i)(1+3i)=\\(1^2-(3i)^2)(1^2-i^2)=\\(1+9)(1+1)=\\10\cdot2=20[/tex]

Answer:

[tex]\huge\boxed{(1-3i)(1-i)(1+i)(1+3i)=20}[/tex]

Step-by-step explanation:

[tex](1-3i)(1-i)(1+i)(1+3i)\\\\\text{use the commutative property}\\\\=(1-3i)(1+3i)(1-i)(1+i)\\\\\text{use the associative property}\\\\=\bigg[(1-3i)(1+3i)\bigg]\bigg[(1-i)(1+i)\bigg]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\bigg[1^2-(3i)^2\bigg]\bigg[1^2-i^2\bigg]\\\\=\bigg(1-9i^2\bigg)\bigg(1-i^2\bigg)\\\\\text{use}\ i=\sqrt{-1}\to i^2=-1\\\\=\bigg(1-9(-1)\bigg)\bigg(1-(-1)\bigg)\\\\=\bigg(1+9\bigg)\bigg(1+1\bigg)\\\\=(10)(2)\\\\=20[/tex]

Answer:

7.1%

The percentage increase is 7.1%

Step-by-step explanation:

Percentage increase %∆P is the percentage change in the price.

Percentage increase %∆P = ∆P/Pr × 100%

Where;

∆P = change in sales price = $241,500-$225,400

Pr = regular price = $225,400

Substituting the given values;

%∆P = (241,500-225,400)/225,400 × 100%

%∆P = 7.142857142857% = 7.1%

The percentage increase is 7.1%

Answer:

[tex]3 -\sqrt[2]3[/tex]

Step-by-step explanation:

Given

[tex]\frac{2\sqrt[3]{9}}{1 + \sqrt[3]{3} + \sqrt[3]{9}}[/tex]

Required

Simplify

Rewrite the given expression in index form

[tex]\frac{2 * 9 ^\frac{1}{3}}{1 + 3^{\frac{1}{3}} + 9^{\frac{1}{3}}}[/tex]

Express 9 as 3²

[tex]\frac{2 * 3^2^*^\frac{1}{3}}{1 + 3^{\frac{1}{3}} + 3^2^*^{\frac{1}{3}}}[/tex]

[tex]\frac{2 * 3^\frac{2}{3}}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}}[/tex]

Multiply the numerator and denominator by [tex]1 - 3^{\frac{1}{3}}[/tex]

[tex]\frac{2 * 3^\frac{2}{3}}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}} * \frac{1 - 3^{\frac{1}{3}}}{1 - 3^{\frac{1}{3}}}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) (1 - 3^{\frac{1}{3}})}{(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})(1 - 3^{\frac{1}{3}})}[/tex]

Open the bracket

[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{2}{3})(3^{\frac{1}{3}})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

Simplify the Numerator using Laws of Indices

[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{2+1}{3})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

Further Simplify

[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{3}{3})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3^1)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

Simplify the denominator

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - (3^{\frac{1}{3}})(3^{\frac{1}{3}}) - (3^{\frac{1}{3}})(3^{\frac{2}{3}})}[/tex]

Further Simplify Using Laws of Indices

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - (3^{\frac{1+1}{3}}) - (3^{\frac{1+2}{3}})}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3^{\frac{3}{3}}}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3^1}}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3}}[/tex]

Collect Like Terms

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 - 3+ 3^{\frac{1}{3}} - 3^{\frac{1}{3}}+ 3^{\frac{2}{3}} - 3^{\frac{2}{3}} }}[/tex]

Group Like Terms for Clarity

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{(1 - 3) + (3^{\frac{1}{3}} - 3^{\frac{1}{3}}) + (3^{\frac{2}{3}} - 3^{\frac{2}{3}} )}}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{(- 2)+ (0) + (0)}}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{-2}}[/tex]

Divide the fraction

[tex]-(3^\frac{2}{3}) + (3)[/tex]

Reorder the above expression

[tex]3 -3^\frac{2}{3}[/tex]

The expression can be represented as

[tex]3 -\sqrt[2]3[/tex]

Hence;

[tex]\frac{2\sqrt[3]{9}}{1 + \sqrt[3]{3} + \sqrt[3]{9}}[/tex] when simplified is equivalent to [tex]3 -\sqrt[2]3[/tex]

Answer:

[tex]\boxed{44}[/tex]

Step-by-step explanation:

[tex][-5+(-7)]^2-(7+3)^2[/tex]

Resolving Parenthesis

[tex](-5-7)^2-(10)^2\\(-12)^2-100\\144-100[/tex]

=> 44

Answer:

[tex]\boxed{44}[/tex]

Step-by-step explanation:

[tex][-5+(-7)]^2-(7+3)^2[/tex]

Solve for brackets first.

[tex][-12]^2-(10)^2[/tex]

Solve the exponent or power.

[tex]144-100[/tex]

Subtract the numbers.

[tex]=44[/tex]

Answer:

706.86 cm

Step-by-step explanation:

=4pi(r^2)

=12.56(r^2)

=12.56(7.5^2)

=12.56(56.25)

=706.86

Answer:

0.60

Step-by-step explanation:

find the probability it is a 2:

0.40 / 1 = 0.4 or 40%

find the probability it isn't a 2:

1 - 0.4 = 0.6

Answer:

A. 0.60

Step-by-step explanation:

I did geometry last year. My teacher assigned it to us.

Hope this helps :)

Answer:

4x-2

Step-by-step explanation:

4x(3x+5)-2(3x+5)

(4x-2)(3x+5)

you can see that 4x-2 is a factor

The pyramid consists of 4 congruent triangular faces, and 1 square base.

Area of 1 triangular face:

1/2 * (5 in)/2 * (5.6 in) = 7 in^2

Area of base:

(5 in)^2 = 25 in^2

Then the total surface area is

4 * (7 in^2) + 25 in^2 = (28 + 25) in^2 = 53 in^2

Answer:

(B) 3/5

Step-by-step explanation:

In the figure above, both circles have their centers at point O. Point A lies on segment OB. If OA = 3 and AB = 2, what is the ratio of the circumference of the smaller circle to the circumference of the larger circle?

(A) 2/3

(B) 3/5

(C) 9/16

(D) 1/2

(E) 4/9

Answer: The circumference of a circle is the perimeter of the circle, that is it is the arc length of the circle. The circumference of a circle is given as:

Circumference = 2 π r.   Where r is the radius of the circle.

The radius of the bigger circle = length of OB = OA + AB = 3 + 2 = 5

Circumference of the bigger circle = 2 π (5) = 10π

The radius of the smaller circle = length of OA = 3

Circumference of the smaller circle = 2 π (3) = 6π

The ratio of the circumference of the smaller circle to the circumference of the larger circle = circumference of the smaller circle / circumference of the larger circle = 6π / 10π = 3/5

Answer:

1.475

Step-by-step explanation:

Answer:

$10.5 dollars

Step-by-step explanation:

Keep your brains.

Using the data given:

(18+4+12+8)÷4=

42÷4=

$10.5 dollars

Answer:

720 seating arrangments

Step-by-step explanation:

There are eight people but driver is always the same so we only have to deal with combinations of the other 7 seats.

the combination of the five seats has 5! times 2 combinations for each of the 3 passengers willing to ride in the two boat seats thus the total number of different seating arrangements is 5! times 3! or 720

hope this helps :)

Using the Fundamental Counting Theorem, it is found that there are 5760 possible seating arrangements.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

Hence:

[tex]N = 8 \times 6 \times 5! = 5760[/tex]

There are 5760 possible seating arrangements.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

Answer:

If you wish to find any term (also known as the {n^{th}}n  

th

 term) in the arithmetic sequence, the arithmetic sequence formula should help you to do so. The critical step is to be able to identify or extract known values from the problem that will eventually be substituted into the formula itself.

Step-by-step explanation:

Answer:

Line y = −x + 4 intersects the line y = 3x + 3.

Step-by-step explanation:

Please Help! Which description best describes the solution to the following system of equations?

y = −x + 4

y = 3x + 3

Line y = −x + 4 intersects the line y = 3x + 3.

This is the response because the solution to a system of two equations is represented by the intersection of the equations of the two lines/curves.

Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.

Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.

Line y = −x + 4 intersects the origin.

Answer:

C. Rectangle

Step-by-step explanation:

A parallelogram can not have a single 90° angle. This is because the opposite angles of a parallelogram are equal.

Therefore, the two opposite sides are equal.

In a parallelogram, neighboring angles add up to 180°. This therefore implies that all the angles are 90°.

This describes a rectangle.

Answer:

Step-by-step explanation:

Any time you have compounding more than once a year (which is annually), unless we are talking about compounding continuously, you will use the formula

[tex]A(t)=P(1+\frac{r}{n})^{(n)(t)}[/tex]

Here's what we have:

The amount after a certain time that she has in the bank is 4672.12; that's A(t).

The interest rate in decimal form is .18; that's r.

The number of times the interest compounds is 12; that's n

and the time that the money is invested is 3.5 years; that's t.

Filling all that into the formula:

[tex]4672.12=P(1+\frac{.18}{12})^{(12)(3.5)}[/tex] Simplifying it down a bit:

[tex]4672.12=P(1.015)^{42}[/tex] Raise 1.015 to the 42nd power to get

4672.12 = P(1.868847115) and divide to get P alone:

P = 2500.00

She invested $2500.00 initially.

Answer:

x = - 1, x = 1

Step-by-step explanation:

Given

f(x) = [tex]\frac{2x^2+3x+6}{x^2-1}[/tex]

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

x² - 1 = 0 ← difference of squares

(x - 1)(x + 1) = 0

x - 1 = 0 ⇒ x = 1

x + 1 = 0 ⇒ x = - 1

x = - 1 and x = 1 are vertical asymptotes

Answer:

29%

Step-by-step explanation:

48-34 = 14 dollar saving

14/48 = 29.17 % = 29% saving

Answer:

29%

Step-by-step explanation:

48-34= 14 dollar saving

14/48 = 29.17% = 29% saving

Answer:

Increasing if X is positive decreasnig if X is negative

Step-by-step explanation:

Answer:

increasing

Step-by-step explanation:

positive slope of 75 so line goes up to the right

Answer:

Toa

48/55

Step-by-step explanation:

O/A

48/55

Answer:

{ 1,2}

Step-by-step explanation:

The ∩ means intersection, or what is in common for the two sets

The intersection of A and B is what is in the overlapping circles

The intersection of A and B is { 1,2}

Answer:

15 ml

Step-by-step explanation:

We are told

Solution A = 15% of water

Solution B = 20% of water

Let's assume, the entire solution = 100ml

We are told that in the beaker we have 10 ml of Solution A already

Mathematically,

100 ml = 15%

10 ml = X

100ml × X = 15 × 10

X = 150/ 100

X = 1.5%

Hence in the beaker, we have 1.5% of water from Solution A

We are asked to find how many ml of solution B must be added to make the solution have 18% of water

Let y = number of ml of solution B

Hence

10 ml × 15%(0.15) = 1.5 ml of water - Equation 1

y ml × 20%( 0.20) = 0.20y ml of water ...... Equation 2

Add up the above equation

10ml + y ml ×18% (0.18) = 1.5 + 0.20y

(10 + y)(0.18) = 1.5 + 0.20y

1.8 + 0.18y = 1.5 + 0.20y

Collect like terms

1.8 - 1.5  = 0.20y - 0.18y

0.3 = 0.02y

y = 0.3/0.02

y = 15ml                              

Therefore,15mL of solution B must be added to the beaker in order to create a mixture that is 18% water

Answer:

(0-5)=-5

-5-5 = 0

x=0

Step-by-step explanation:

Answer: 69

Step-by-step explanation:

Answer:

option three!!!!!

Step-by-step explanation:

its closed circle

on 6

and pointing  left

Answer: A. 82

Step-by-step explanation:

The measure of <BAD can be found by simply adding 25(<BAC)+57(<CAD) = 82.

[tex]\mathrm{BAD}=\mathrm{BAC}+\mathrm{CAD}=25^{\circ}+57^{\circ}=82^{\circ}[/tex].

Hope this helps.

Answer:

2 possible values

Step-by-step explanation:

The given expression is:

[tex]\sqrt[3]{\frac{144}{y} }[/tex]

In order for this to result in a whole number, 144/y must be a perfect cube, the possible perfect cubes (under 144) are:

1, 8, 27, 64, 125

The values of y that would result in those numbers are:

[tex]y=\frac{144}{1}=144 \\y=\frac{144}{8}=18 \\y=\frac{144}{27}=5.333\\y=\frac{144}{64}=2.25\\y=\frac{144}{125}=1.152[/tex]

Only two values of y are integers, therefore, there are only two possible values of y for which the given expression results in a whole number.

Answer:it’s b

Step-by-step explanation:

Just took quiz on edge 2020

Answer -3(2m-3n+4)

Step-by-step explanation:

Answer:

46°

Step-by-step explanation:

We can tell that this triangle is an isosceles triangle because 2 of it's sides are the same, therefore, two of it's angles are the same.

Looking at it, we can assume that the two angles not defined (x and the other one) are the two angles that are the same because they look similar.

Now, the angles of all triangles add up to 180°. So, we can subtract 88° from 180 to see what the two angles add up to.

[tex]180-88=92[/tex]

So both of these angles add up to 92 degrees. Since there are two, we divide 92 by 2.

[tex]92 \div 2 = 46[/tex]

Hope this helped!